27
Draft version February 26, 2019 Typeset using L A T E X twocolumn style in AASTeX62 AstroSat-CZTI detection of variable prompt emission polarization in GRB 171010A Vikas Chand , 1 Tanmoy Chattopadhyay , 2 Gor Oganesyan * , 3, 4 A. R. Rao, 1 Santosh V. Vadawale, 5 Dipankar Bhattacharya, 6 V. B. Bhalerao, 7 and Kuntal Misra 8, 9 1 Tata Institute of Fundamental Research, Mumbai, India 2 Pennsylvania State University, State College, PA, USA 3 Gran Sasso Science Institute, Viale F. Crispi 7, I-67100, LAquila, Italy 4 INFN - Laboratori Nazionali del Gran Sasso, I-67100 LAquila, Italy 5 Physical Research Laboratory, Ahmedabad, Gujarat, India 6 The Inter-University Centre for Astronomy and Astrophysics, Pune, India 7 Indian Institute of Technology, Bombay, India 8 Aryabhatta Research Institute of observational sciecES (ARIES), Manora Peak, Nainital, India 9 Department of Physics, University of California, 1 Shields Ave, Davis, CA 95616-5270, USA ABSTRACT We present spectro-polarimetric analysis of GRB 171010A using data from AstroSat, Fermi, and Swift, to provide insights into the physical mechanisms of the prompt radiation and the jet geometry. Prompt emission from GRB 171010A was very bright (fluence > 10 -4 ergs cm -2 ) and had a complex structure composed of the superimposition of several pulses. The energy spectra deviate from the typical Band function to show a low energy peak 15 keV — which we interpret as a power-law with two breaks, with a synchrotron origin. Alternately, the prompt spectra can also be interpreted as Comptonized emission, or a blackbody combined with a Band function. Time-resolved analysis confirms the presence of the low energy component, while the peak energy is found to be confined in the range of 100–200 keV. Afterglow emission detected by Fermi-LAT is typical of an external shock model, and we constrain the initial Lorentz factor using the peak time of the emission. Swift-XRT measurements of the afterglow show an indication for a jet break, allowing us to constrain the jet opening angle to > 6 . Detection of a large number of Compton scattered events by AstroSat-CZTI provides an opportunity to study hard X-ray polarization of the prompt emission. We find that the burst has high, time-variable polarization, with the emission have higher polarization at energies above the peak energy. We discuss all observations in the context of GRB models and polarization arising due to due to physical or geometric effects: synchrotron emission from multiple shocks with ordered or random magnetic fields, Poynting flux dominated jet undergoing abrupt magnetic dissipation, sub-photospheric dissipation, a jet consisting of fragmented fireballs, and the Comptonization model. Keywords: gamma-ray burst: general – gamma-ray burst: individual (GRB 171010A) – polarization – radiation mechanisms: non-thermal 1. INTRODUCTION The emission mechanisms of gamma ray bursts (GRBs) and the radiation processes involved in pro- ducing the complex structure during the prompt phase have eluded a complete understanding in spite of the fact [email protected] [email protected] * [email protected] that these energetic cosmological events have been stud- ied for more than five decades. Based on the duration of the observed prompt emission, GRBs are broadly clas- sified into two families named as long and short GRBs with a demarcation at 2 s. The long GRBs are found to be associated with with type Ic supernovae pointing at their massive star origin. To extract energy efficiently to power a GRB such a collapse results in a black hole or a rapidly spinning and highly magnetized neutron star (Woosley & Bloom 2006; Cano et al. 2017). The recent arXiv:1807.01737v2 [astro-ph.HE] 24 Feb 2019

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Page 1: Draft version February 26, 2019 A twocolumn style in

Draft version February 26 2019Typeset using LATEX twocolumn style in AASTeX62

AstroSat-CZTI detection of variable prompt emission polarization in GRB 171010A

Vikas Chanddagger1 Tanmoy ChattopadhyayDagger2 Gor Oganesyanlowast3 4 A R Rao1 Santosh V Vadawale5

Dipankar Bhattacharya6 V B Bhalerao7 and Kuntal Misra8 9

1Tata Institute of Fundamental Research Mumbai India2Pennsylvania State University State College PA USA

3Gran Sasso Science Institute Viale F Crispi 7 I-67100 LAquila Italy4 INFN - Laboratori Nazionali del Gran Sasso I-67100 LAquila Italy

5Physical Research Laboratory Ahmedabad Gujarat India6The Inter-University Centre for Astronomy and Astrophysics Pune India

7Indian Institute of Technology Bombay India8Aryabhatta Research Institute of observational sciecES (ARIES) Manora Peak Nainital India9Department of Physics University of California 1 Shields Ave Davis CA 95616-5270 USA

ABSTRACT

We present spectro-polarimetric analysis of GRB 171010A using data from AstroSat Fermi and

Swift to provide insights into the physical mechanisms of the prompt radiation and the jet geometry

Prompt emission from GRB 171010A was very bright (fluence gt 10minus4 ergs cmminus2) and had a complex

structure composed of the superimposition of several pulses The energy spectra deviate from the

typical Band function to show a low energy peak sim 15 keV mdash which we interpret as a power-law

with two breaks with a synchrotron origin Alternately the prompt spectra can also be interpreted

as Comptonized emission or a blackbody combined with a Band function Time-resolved analysis

confirms the presence of the low energy component while the peak energy is found to be confined in

the range of 100ndash200 keV

Afterglow emission detected by Fermi-LAT is typical of an external shock model and we constrain

the initial Lorentz factor using the peak time of the emission Swift-XRT measurements of the afterglow

show an indication for a jet break allowing us to constrain the jet opening angle to gt 6

Detection of a large number of Compton scattered events by AstroSat-CZTI provides an opportunity

to study hard X-ray polarization of the prompt emission We find that the burst has high time-variable

polarization with the emission have higher polarization at energies above the peak energy

We discuss all observations in the context of GRB models and polarization arising due to due to

physical or geometric effects synchrotron emission from multiple shocks with ordered or randommagnetic fields Poynting flux dominated jet undergoing abrupt magnetic dissipation sub-photospheric

dissipation a jet consisting of fragmented fireballs and the Comptonization model

Keywords gamma-ray burst general ndash gamma-ray burst individual (GRB 171010A) ndash polarization

ndash radiation mechanisms non-thermal

1 INTRODUCTION

The emission mechanisms of gamma ray bursts

(GRBs) and the radiation processes involved in pro-

ducing the complex structure during the prompt phase

have eluded a complete understanding in spite of the fact

daggervikaschandphysicsgmailcom

Daggertxc344psuedu

lowastgoroganesyangssiit

that these energetic cosmological events have been stud-

ied for more than five decades Based on the duration of

the observed prompt emission GRBs are broadly clas-

sified into two families named as long and short GRBs

with a demarcation at 2 s The long GRBs are found to

be associated with with type Ic supernovae pointing at

their massive star origin To extract energy efficiently to

power a GRB such a collapse results in a black hole or

a rapidly spinning and highly magnetized neutron star

(Woosley amp Bloom 2006 Cano et al 2017) The recent

arX

iv1

807

0173

7v2

[as

tro-

phH

E]

24

Feb

2019

2 Chand et al

groundbreaking discovery of gravitational waves and its

electromagnetic counterpart object (a short GRB) re-

solved the problem of identifying progenitors of short

GRBs at least for the case of one joint GWGRB de-

tection (Abbott et al 2016) The commonly accepted

scenario for the production of the emerging radiation is

based on the premise of relativistic jets being launched

from the central engine When the jet pierces through

an ambient medium which is either a constant den-

sity interstellar medium (ISM) or a wind-like medium

whose density varies with distance external shocks are

formed and the generated radiation has contributions

from both the forward and the reverse shocks The

resultant emission constitutes the widely observed af-

terglows in GRBs (Rees amp Meszaros 1992 Meszaros amp

Rees 1993 Meszaros amp Rees 1997 Akerlof et al 1999

Meszaros amp Rees 1999) A plateau phase in the X-ray

emission is however thought to be associated with a

long term central engine activity or the stratification

in Lorentz factor of the ejecta could also give extended

energy injection (Dai amp Lu 1998 Zhang et al 2006)

The prompt emission can arise due to various mech-

anisms the leading candidates among them are (i) in-

crease of the jet Lorentz factor with time leading to

the collision of inner layers with the outer ones gener-

ating internal shocks which produce non-thermal syn-

chrotron emission as the electrons gyrate in the existing

magnetic field (Narayan et al 1992 Rees amp Meszaros

1994) A variant of internal shock model is the Internal-

Collision-induced MAgnetic Reconnection and Turbu-

lence (ICMART) model where abrupt dissipaton occurs

through magnetic reconnections in a Poynting flux domi-

nated jet (Zhang amp Yan 2011) (iii) dissipation occurring

within a fuzzy photosphere the photosphere is specially

invoked to explain the quasi-thermal shape of the spec-

trum The process manifests itself in such a way that

it can produce a non-thermal shape of the spectrum as

well (Beloborodov 2017) (iii) gradual magnetic dissipa-

tion that occurs within the photosphere of a Poynting

flux dominated jet (Beniamini amp Giannios 2017) and (iv)

Comptonization of soft corona photons off the electrons

present in the outgoing relativistic ejecta (Titarchuk

et al 2012 Frontera et al 2013) These models are de-

signed to explain the spectral properties of the prompt

emission of GRBs and are successful to a certain extent

Some prominent features like the evolution of the spec-

tral parameters and the presence of correlations among

GRB observables are not well understood and most of

them remain unexplained within the framework of a sin-

gle model

Another crucial information that can be added to the

existing plethora of observations of the prompt emission

like the spectral and timing properties presence of af-

terglows presence of associated supernovae etc is the

polarization of the prompt emission Detection of po-

larization therefore provides an additional tool to test

the theoretical models of the mechanism of GRB prompt

emission This however has remained a scarcely ex-

plored avenue due to the unavailability of dedicated po-

larimeters and reliable polarization measurements The

Cadmium Zinc Telluride Imager (CZTI) on board As-

troSat offers a new opportunity to reliably measure po-

larization of bright GRBs in the hard X-rays (Chat-

topadhyay et al 2014 Vadawale et al 2015 Chattopad-

hyay et al 2017) The polarization expected from dif-

ferent models of prompt emission is not only different

in magnitude but also in the expected pattern of tem-

poral variability depending on the emission mechanism

jet morphology and view geometry (see eg Covino amp

Gotz 2016) A study of the time variability characteris-

tics is very important because bright GRBs whose spec-

tra have been studied in great detail often found to have

spectra deviating significantly from the standard Band

function conventionally used to model the GRB spectra

(Abdo et al 2009 Izzo et al 2012 Ackermann et al

2010 Vianello et al 2017 Wang et al 2017)

GRB 171010A is a bright GRB and it presents an op-

portunity for a multi-pronged approach to understand

the GRB prompt emission It has been observed by

both Fermi and AstroSat-CZTI Afterglows in gamma-

rays (FermiLAT) X-rays (Swift-XRT) and optical have

been detected and an associated supernova SN 2017htp

has been found on the tenth day of the prompt emission

A redshift z = 033 has been measured spectroscopi-

cally by the extended Public ESO Spectroscopic Survey

for Transient Objects (ePESSTO) optical observations

(Kankare et al 2017) We present here a comprehen-

sive analysis of this GRB using the Fermi observation

for spectral properties and attempt to relate the prompt

spectral properties to the detection of variable high po-

larization using AstroSat-CZTI We present a summary

of the observations in Section 2 The Fermi light curves

and spectra are constructed in various energy bands and

time bins respectively and they are presented in Sections

2 3 and 4 The polarization measurements in different

time intervals and energies are presented in Section 6

We discuss our results and derive conclusions in Section

7 The cosmological parameters chosen were Ωλ = 073

Ωm = 027 and H0 = 70 km Mpcminus1 secminus1 (Komatsu

et al 2009)

2 GRB 171010A

GRB 171010A triggered the Fermi-LAT and Fermi-

GBM at 19005058 UT (T0) on 2017 October 10

Variable prompt emission polarization in GRB 171010A 3

(Omodei et al 2017 Poolakkil amp Meegan 2017) The

observed high peak flux generated an autonomous

re-point request (ARR) in the GBM flight software

and the Fermi telescope slewed to the GBM in-flight

location A target of opportunity observation was

carried out by the Niel Gehrels Swift Observatory

(Evans 2017) and the Swift-XRT localized the burst

to RA(J2000) 6658092 and Dec minus 1046325

(DrsquoAi et al 2017) Swift-XRT followed the burst for

sim 2 times 106 s1 The prompt emission was also observed

by Konus-Wind (Frederiks et al 2017) The fluence

observed in the Fermi-GBM 10 - 1000 keV band from

T0 + 512 sec to T0 + 15155 s is (642 plusmn 005) times 10minus4

erg cmminus2 (Poolakkil amp Meegan 2017) Here T0 is the

trigger time in the Fermi-GBM The first photon in

LAT (gt 100 MeV ) with a probability 09 of its associ-

ation with the source is received at sim T0 + 374 s and

has an energy sim 194 MeV and a photon with energy

close to 1 GeV (930 MeV) is detected at sim 404 s The

highest energy photon (sim 19 GeV ) in the Fermi-LAT

is detected at sim 2890 s The rest frame energy of this

photon is sim 25 GeV

3 LIGHT CURVES

We examined the light curves of the GRB as obtained

from all 12 NaI detectors and found that detectors n7

n8 and nb (using the usual naming conventions) have

significant detections (source angles are n7 69 n8

31 and nb 40) We have used data from all three

detectors to examine the broad emission features of the

GRB For wide band temporal and spectral analysis

however we chose n8 and nb which have higher count

rates than the other detectors and the angles made with

the source direction for these two detectors are less than

50 degrees The time scale used throughout this paper

is relative to the Fermi-GBM trigger time ie t = T minusT0 Of the two BGO scintillation detectors the detector

BGO 1 (b1) which is positioned on the same side on

the satellite as the selected NaI detectors is chosen for

further analysis

The light curve is shown in Figure 1 and it shows

two episodes of emission (a) beginning at sim minus5s of the

main burst and lasts up to sim 205 s followed by a quies-

cent state when the emission level meets the background

level and (b) the emission becomes active again after a

short period at sim 246 s and radiation from the burst is

detected till sim 278 s We name these emission phases

as Episode 1 amp 2 In Figure 1 we also show the light

curve in the 100 - 400 keV region (the energy range of

AstroSat-CZTI observations) and we use this light curve

1 httpwwwswiftacukxrt curves00020778

0 50 100 150 200 250 300

104

n7 + n8 + nb8 - 900 keV

0 50 100 150 200 250 300Time since GBM trigger (s)

2000

4000

6000

8000

n7 + n8 + nb100 - 400 keV

Coun

tss

ec

Figure 1 Fermi-GBM light curve of GRB 171010A ob-tained from three NaI detectors n7 n8 and nbUpper Panel Log-scale light curve in the full energy range(8 ndash 900 keV) binned in 1 s intervals The two emissionepisodes used for time-integrated spectral analysis (minus5 s to205 s 246 s to 278 s) are shaded and demarcated with verti-cal dotted lines The red envelope shows the Bayesian blocksrepresentation of the light curveLower panel Linear-scale light curve and Bayesian blocksrepresentation for the 100 ndash 400 keV energy range used intime-resolved spectral analysis

to divide the data for time resolved spectral analysis

The blocks of constant rate (Bayesian blocks) are con-

structed from the light curves and over-plotted on the

count rate light curves to show statistically significant

changes in them (Scargle et al 2013)

The light curves summed over the chosen GBM detec-

tors (n8 and nb) in six different energy ranges are shown

in Figure 2 The GRB has complex structure with mul-

tiple peaks and the high energy emission (above 1 MeV)

is predominant till about 50 s as seen in the light curve

for gt 1 MeV Bayesian blocks are constructed from the

light curves and over-plotted on the count rate

4 SPECTRAL ANALYSIS

The burst is very bright and even with a signal to

noise ratio of 50 we are able to construct more than

150 time bins We created time bins therefore from

the Bayesian blocks constructed from the light curve in

the energy range 100 keV to 400 keV where CZTI is sen-

sitive for polarization measurements These bins (large

number of Bayesian blocks) track significantly varying

features in the lightcurve and will also be sufficient to

give a substantial idea about the energetics of the burst

The spectra are reduced using Fermi Science tools soft-

4 Chand et al

1200

1400

1600 b1 1 - 30 MeV

1000

2000

3000

b1 03 - 1 MeV

500

1000n8 + nb200 - 300 keV

2000

4000n8 + nb100 - 200 keV

250050007500

n8 + nb30 - 100 keV

0 50 100 150 200Time since GBM trigger (s)

250050007500

n8 + nb 8 - 30 keV

Coun

tss

ec

Figure 2 Fermi-GBM light curve of GRB 171010A in six different energy ranges with Bayesian blocks over-plotted in redAt the highest energies (1 ndash 30 MeV top panel) the emission is low after sim 50 s

ware rmfit2 by standard methodology described in the

tutorial3

GRB prompt emission spectra generally show a typi-

cal shape described by the Band function (Band et al

1993) however for a number of bursts additional com-

ponents are observed in the spectra such as quasi-

thermal components modeled by blackbody function

(Ryde 2005 Page et al 2011 Guiriec et al 2011 Basak

amp Rao 2015) or they show additional non-thermal com-

ponents modeled by a power-law or a power-law with an

exponential cut-off (Abdo et al 2009 Ackermann et al

2013) Additionally for a few cases spectra with a top-

hat shape are also observed and modeled by a Band-

function with an exponential roll-off at higher energies

(Wang et al 2017 Vianello et al 2017)

2 Fermi Science Tools rmfit httpsfermigsfcnasagovsscdataanalysisrmfit

3 Fermi tutorial httpsfermigsfcnasagovsscdataanalysisscitoolsrmfit tutorialhtml

The above models are driven by data and phe-

nomenology The physical models devised to explain

the GRB prompt emission radiation have the syn-

chrotron emission or the Compton scattering as the

core processes The synchrotron spectrum for a pow-

erlaw distribution of electrons consists of power-laws

joined at energies which depend upon cooling frequency

(νc) minimum-injection frequency (νm) and absorption

frequency (νa) The Comptonization models include

inverse Compton scattering as a primary mechanism

(Lazzati et al 2000 Titarchuk et al 2012) Comp-

tonization signatures (XSPEC grbcomp model) have

been detected for a set of GRBs observed by Burst

and Transient Source Experiment (BATSE) on board

Compton Gamma Ray Observatory (Frontera et al

2013) The grbcomp model differs from the other Comp-

tonization model the Compton drag model In the

Compton drag model the single inverse Compton scat-

terings of thermal photons shape the spectrum while

in the grbcomp multiple Compton scatterings are as-

sumed Another major difference is that the scattering

Variable prompt emission polarization in GRB 171010A 5

is off the outflow which is sub-relativistic in case of

grbcomp model while relativistic in the Compton drag

model

We apply this prior knowledge of spectral shapes

from the previous observations of GRBs to study

GRB 171010A The spectra are modeled by various

spectroscopic models available in XSPEC (Arnaud

1996) The statistics pgstat is used for optimization

and testing the various models4 We start with the

Band function and use the other models based upon

the residuals of the data and model fit The functional

form of the Band model used to fit the photon spectrum

is given in Equation 1 (Band et al 1993)

NBand(E) =

KB(E100)

αexp (minusE (2 + α) Ep) E lt Eb

KB(αminus β)Ep [100 (2 + α)](αminusβ) exp (β minus α) (E100)β E ge Eb

(1)

Other models include blackbody5 (BB) and a power

law with two breaks (bkn2pow)6 to model the broad

band spectrum

Nbkn2pow(E) =

KEminusα1 E le E1

KE1α2minusα1Eminusα2 E1 le E le E2

KE1α2minusα1E2

α3minusα2Eminusα3 E ge E3

(2)

For the Comptonization model proposed by Titarchuk

et al 2012 XSPEC local model grbcomp is fit to the pho-

ton spectrum7 The pivotal parameters of this model

are temperature of the seed blackbody spectrum (kTs)

the bulk outflow velocity of the thermal electrons (β)

the electron temperature of the sub-relativistic outflow

(kTe) and the energy index of the Greenrsquos function with

which the formerly Comptonized spectrum is convolved

(αb) Using the normalization of the grbcomp model

the apparent blackbody radius can be obtained To

avoid degeneracy in the parameters or the case when

parameters are difficult to constrain we froze some of

the parameters

To fit the spectra with synchroton radiation model we

implemented a table model for XSPEC We assumed a

population of electrons with a power-law energy distri-

bution (as a result of acceleration) dNdγ prop γminusp for

γ gt γm where γm is the minimum Lorentz factor of

electrons The cooling of electrons by synchrotron ra-

diation is considered in slow and fast cooling regimes

4 httpsheasarcgsfcnasagovxanaduxspecmanualnode293html

5 blackbody model httpsheasarcgsfcnasagovxanaduxspecmanualnode136html

6 bkn2pow model httpsheasarcgsfcnasagovxanaduxspecmanualnode141html

7 grbcomp model httpsheasarcnasagovdocsxanaduxspecmodelsgrbcomphtml

depending on ratio between γm and the cooling Lorentz

factor γc (Sari et al 1998) We computed the resulting

photon spectrum of population of electrons assuming

that the average electron distribution at a given time is

dNdγ prop γminus2 for γc lt γ lt γm and dNdγ prop γminuspminus1

for γ gt γm in fast cooling regime while dNdγ prop γminusp

for γm lt γ lt γc and dNdγ prop γminuspminus1 for γ gt γc in

slow cooling regime The synchrotron model is made of

four free parameters the ratio between characteristic

Lorentz factors γmγc the peak energy of Fν spectrum

Ec which is simply the energy which corresponds to the

cooling frequency the power-law index of electrons dis-

tribution p and the normalization We built the table

model for the range of 01 le γmγc le 100 and 2 le p le 5

To fit the time integrated spectrum of Episode 1 we

use the four models described above (i) Band (ii) Band

+ blackbody (BB) (iii) broken power law (bkn2pow)

and (iv) the Comptonization model (grbcomp) The

best fit parameters of the tested models are reported

in Table 1 The νFν plots along with the residuals

are shown in Figure 3 for the four models used The

Band fit shows deviations at lower energies signifying

deviations from the power law that is used to model the

spectra from the low energy threshold of 8 keV to the

peak energy of the Band function (sim150 keV) We have

examined these residuals in detail by progressively rais-

ing the low energy threshold to 40 keV (greater than

the energy in which the deviations are seen) and ex-

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

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Poolakkil S amp Meegan C 2017 GRB Coordinates

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 2: Draft version February 26, 2019 A twocolumn style in

2 Chand et al

groundbreaking discovery of gravitational waves and its

electromagnetic counterpart object (a short GRB) re-

solved the problem of identifying progenitors of short

GRBs at least for the case of one joint GWGRB de-

tection (Abbott et al 2016) The commonly accepted

scenario for the production of the emerging radiation is

based on the premise of relativistic jets being launched

from the central engine When the jet pierces through

an ambient medium which is either a constant den-

sity interstellar medium (ISM) or a wind-like medium

whose density varies with distance external shocks are

formed and the generated radiation has contributions

from both the forward and the reverse shocks The

resultant emission constitutes the widely observed af-

terglows in GRBs (Rees amp Meszaros 1992 Meszaros amp

Rees 1993 Meszaros amp Rees 1997 Akerlof et al 1999

Meszaros amp Rees 1999) A plateau phase in the X-ray

emission is however thought to be associated with a

long term central engine activity or the stratification

in Lorentz factor of the ejecta could also give extended

energy injection (Dai amp Lu 1998 Zhang et al 2006)

The prompt emission can arise due to various mech-

anisms the leading candidates among them are (i) in-

crease of the jet Lorentz factor with time leading to

the collision of inner layers with the outer ones gener-

ating internal shocks which produce non-thermal syn-

chrotron emission as the electrons gyrate in the existing

magnetic field (Narayan et al 1992 Rees amp Meszaros

1994) A variant of internal shock model is the Internal-

Collision-induced MAgnetic Reconnection and Turbu-

lence (ICMART) model where abrupt dissipaton occurs

through magnetic reconnections in a Poynting flux domi-

nated jet (Zhang amp Yan 2011) (iii) dissipation occurring

within a fuzzy photosphere the photosphere is specially

invoked to explain the quasi-thermal shape of the spec-

trum The process manifests itself in such a way that

it can produce a non-thermal shape of the spectrum as

well (Beloborodov 2017) (iii) gradual magnetic dissipa-

tion that occurs within the photosphere of a Poynting

flux dominated jet (Beniamini amp Giannios 2017) and (iv)

Comptonization of soft corona photons off the electrons

present in the outgoing relativistic ejecta (Titarchuk

et al 2012 Frontera et al 2013) These models are de-

signed to explain the spectral properties of the prompt

emission of GRBs and are successful to a certain extent

Some prominent features like the evolution of the spec-

tral parameters and the presence of correlations among

GRB observables are not well understood and most of

them remain unexplained within the framework of a sin-

gle model

Another crucial information that can be added to the

existing plethora of observations of the prompt emission

like the spectral and timing properties presence of af-

terglows presence of associated supernovae etc is the

polarization of the prompt emission Detection of po-

larization therefore provides an additional tool to test

the theoretical models of the mechanism of GRB prompt

emission This however has remained a scarcely ex-

plored avenue due to the unavailability of dedicated po-

larimeters and reliable polarization measurements The

Cadmium Zinc Telluride Imager (CZTI) on board As-

troSat offers a new opportunity to reliably measure po-

larization of bright GRBs in the hard X-rays (Chat-

topadhyay et al 2014 Vadawale et al 2015 Chattopad-

hyay et al 2017) The polarization expected from dif-

ferent models of prompt emission is not only different

in magnitude but also in the expected pattern of tem-

poral variability depending on the emission mechanism

jet morphology and view geometry (see eg Covino amp

Gotz 2016) A study of the time variability characteris-

tics is very important because bright GRBs whose spec-

tra have been studied in great detail often found to have

spectra deviating significantly from the standard Band

function conventionally used to model the GRB spectra

(Abdo et al 2009 Izzo et al 2012 Ackermann et al

2010 Vianello et al 2017 Wang et al 2017)

GRB 171010A is a bright GRB and it presents an op-

portunity for a multi-pronged approach to understand

the GRB prompt emission It has been observed by

both Fermi and AstroSat-CZTI Afterglows in gamma-

rays (FermiLAT) X-rays (Swift-XRT) and optical have

been detected and an associated supernova SN 2017htp

has been found on the tenth day of the prompt emission

A redshift z = 033 has been measured spectroscopi-

cally by the extended Public ESO Spectroscopic Survey

for Transient Objects (ePESSTO) optical observations

(Kankare et al 2017) We present here a comprehen-

sive analysis of this GRB using the Fermi observation

for spectral properties and attempt to relate the prompt

spectral properties to the detection of variable high po-

larization using AstroSat-CZTI We present a summary

of the observations in Section 2 The Fermi light curves

and spectra are constructed in various energy bands and

time bins respectively and they are presented in Sections

2 3 and 4 The polarization measurements in different

time intervals and energies are presented in Section 6

We discuss our results and derive conclusions in Section

7 The cosmological parameters chosen were Ωλ = 073

Ωm = 027 and H0 = 70 km Mpcminus1 secminus1 (Komatsu

et al 2009)

2 GRB 171010A

GRB 171010A triggered the Fermi-LAT and Fermi-

GBM at 19005058 UT (T0) on 2017 October 10

Variable prompt emission polarization in GRB 171010A 3

(Omodei et al 2017 Poolakkil amp Meegan 2017) The

observed high peak flux generated an autonomous

re-point request (ARR) in the GBM flight software

and the Fermi telescope slewed to the GBM in-flight

location A target of opportunity observation was

carried out by the Niel Gehrels Swift Observatory

(Evans 2017) and the Swift-XRT localized the burst

to RA(J2000) 6658092 and Dec minus 1046325

(DrsquoAi et al 2017) Swift-XRT followed the burst for

sim 2 times 106 s1 The prompt emission was also observed

by Konus-Wind (Frederiks et al 2017) The fluence

observed in the Fermi-GBM 10 - 1000 keV band from

T0 + 512 sec to T0 + 15155 s is (642 plusmn 005) times 10minus4

erg cmminus2 (Poolakkil amp Meegan 2017) Here T0 is the

trigger time in the Fermi-GBM The first photon in

LAT (gt 100 MeV ) with a probability 09 of its associ-

ation with the source is received at sim T0 + 374 s and

has an energy sim 194 MeV and a photon with energy

close to 1 GeV (930 MeV) is detected at sim 404 s The

highest energy photon (sim 19 GeV ) in the Fermi-LAT

is detected at sim 2890 s The rest frame energy of this

photon is sim 25 GeV

3 LIGHT CURVES

We examined the light curves of the GRB as obtained

from all 12 NaI detectors and found that detectors n7

n8 and nb (using the usual naming conventions) have

significant detections (source angles are n7 69 n8

31 and nb 40) We have used data from all three

detectors to examine the broad emission features of the

GRB For wide band temporal and spectral analysis

however we chose n8 and nb which have higher count

rates than the other detectors and the angles made with

the source direction for these two detectors are less than

50 degrees The time scale used throughout this paper

is relative to the Fermi-GBM trigger time ie t = T minusT0 Of the two BGO scintillation detectors the detector

BGO 1 (b1) which is positioned on the same side on

the satellite as the selected NaI detectors is chosen for

further analysis

The light curve is shown in Figure 1 and it shows

two episodes of emission (a) beginning at sim minus5s of the

main burst and lasts up to sim 205 s followed by a quies-

cent state when the emission level meets the background

level and (b) the emission becomes active again after a

short period at sim 246 s and radiation from the burst is

detected till sim 278 s We name these emission phases

as Episode 1 amp 2 In Figure 1 we also show the light

curve in the 100 - 400 keV region (the energy range of

AstroSat-CZTI observations) and we use this light curve

1 httpwwwswiftacukxrt curves00020778

0 50 100 150 200 250 300

104

n7 + n8 + nb8 - 900 keV

0 50 100 150 200 250 300Time since GBM trigger (s)

2000

4000

6000

8000

n7 + n8 + nb100 - 400 keV

Coun

tss

ec

Figure 1 Fermi-GBM light curve of GRB 171010A ob-tained from three NaI detectors n7 n8 and nbUpper Panel Log-scale light curve in the full energy range(8 ndash 900 keV) binned in 1 s intervals The two emissionepisodes used for time-integrated spectral analysis (minus5 s to205 s 246 s to 278 s) are shaded and demarcated with verti-cal dotted lines The red envelope shows the Bayesian blocksrepresentation of the light curveLower panel Linear-scale light curve and Bayesian blocksrepresentation for the 100 ndash 400 keV energy range used intime-resolved spectral analysis

to divide the data for time resolved spectral analysis

The blocks of constant rate (Bayesian blocks) are con-

structed from the light curves and over-plotted on the

count rate light curves to show statistically significant

changes in them (Scargle et al 2013)

The light curves summed over the chosen GBM detec-

tors (n8 and nb) in six different energy ranges are shown

in Figure 2 The GRB has complex structure with mul-

tiple peaks and the high energy emission (above 1 MeV)

is predominant till about 50 s as seen in the light curve

for gt 1 MeV Bayesian blocks are constructed from the

light curves and over-plotted on the count rate

4 SPECTRAL ANALYSIS

The burst is very bright and even with a signal to

noise ratio of 50 we are able to construct more than

150 time bins We created time bins therefore from

the Bayesian blocks constructed from the light curve in

the energy range 100 keV to 400 keV where CZTI is sen-

sitive for polarization measurements These bins (large

number of Bayesian blocks) track significantly varying

features in the lightcurve and will also be sufficient to

give a substantial idea about the energetics of the burst

The spectra are reduced using Fermi Science tools soft-

4 Chand et al

1200

1400

1600 b1 1 - 30 MeV

1000

2000

3000

b1 03 - 1 MeV

500

1000n8 + nb200 - 300 keV

2000

4000n8 + nb100 - 200 keV

250050007500

n8 + nb30 - 100 keV

0 50 100 150 200Time since GBM trigger (s)

250050007500

n8 + nb 8 - 30 keV

Coun

tss

ec

Figure 2 Fermi-GBM light curve of GRB 171010A in six different energy ranges with Bayesian blocks over-plotted in redAt the highest energies (1 ndash 30 MeV top panel) the emission is low after sim 50 s

ware rmfit2 by standard methodology described in the

tutorial3

GRB prompt emission spectra generally show a typi-

cal shape described by the Band function (Band et al

1993) however for a number of bursts additional com-

ponents are observed in the spectra such as quasi-

thermal components modeled by blackbody function

(Ryde 2005 Page et al 2011 Guiriec et al 2011 Basak

amp Rao 2015) or they show additional non-thermal com-

ponents modeled by a power-law or a power-law with an

exponential cut-off (Abdo et al 2009 Ackermann et al

2013) Additionally for a few cases spectra with a top-

hat shape are also observed and modeled by a Band-

function with an exponential roll-off at higher energies

(Wang et al 2017 Vianello et al 2017)

2 Fermi Science Tools rmfit httpsfermigsfcnasagovsscdataanalysisrmfit

3 Fermi tutorial httpsfermigsfcnasagovsscdataanalysisscitoolsrmfit tutorialhtml

The above models are driven by data and phe-

nomenology The physical models devised to explain

the GRB prompt emission radiation have the syn-

chrotron emission or the Compton scattering as the

core processes The synchrotron spectrum for a pow-

erlaw distribution of electrons consists of power-laws

joined at energies which depend upon cooling frequency

(νc) minimum-injection frequency (νm) and absorption

frequency (νa) The Comptonization models include

inverse Compton scattering as a primary mechanism

(Lazzati et al 2000 Titarchuk et al 2012) Comp-

tonization signatures (XSPEC grbcomp model) have

been detected for a set of GRBs observed by Burst

and Transient Source Experiment (BATSE) on board

Compton Gamma Ray Observatory (Frontera et al

2013) The grbcomp model differs from the other Comp-

tonization model the Compton drag model In the

Compton drag model the single inverse Compton scat-

terings of thermal photons shape the spectrum while

in the grbcomp multiple Compton scatterings are as-

sumed Another major difference is that the scattering

Variable prompt emission polarization in GRB 171010A 5

is off the outflow which is sub-relativistic in case of

grbcomp model while relativistic in the Compton drag

model

We apply this prior knowledge of spectral shapes

from the previous observations of GRBs to study

GRB 171010A The spectra are modeled by various

spectroscopic models available in XSPEC (Arnaud

1996) The statistics pgstat is used for optimization

and testing the various models4 We start with the

Band function and use the other models based upon

the residuals of the data and model fit The functional

form of the Band model used to fit the photon spectrum

is given in Equation 1 (Band et al 1993)

NBand(E) =

KB(E100)

αexp (minusE (2 + α) Ep) E lt Eb

KB(αminus β)Ep [100 (2 + α)](αminusβ) exp (β minus α) (E100)β E ge Eb

(1)

Other models include blackbody5 (BB) and a power

law with two breaks (bkn2pow)6 to model the broad

band spectrum

Nbkn2pow(E) =

KEminusα1 E le E1

KE1α2minusα1Eminusα2 E1 le E le E2

KE1α2minusα1E2

α3minusα2Eminusα3 E ge E3

(2)

For the Comptonization model proposed by Titarchuk

et al 2012 XSPEC local model grbcomp is fit to the pho-

ton spectrum7 The pivotal parameters of this model

are temperature of the seed blackbody spectrum (kTs)

the bulk outflow velocity of the thermal electrons (β)

the electron temperature of the sub-relativistic outflow

(kTe) and the energy index of the Greenrsquos function with

which the formerly Comptonized spectrum is convolved

(αb) Using the normalization of the grbcomp model

the apparent blackbody radius can be obtained To

avoid degeneracy in the parameters or the case when

parameters are difficult to constrain we froze some of

the parameters

To fit the spectra with synchroton radiation model we

implemented a table model for XSPEC We assumed a

population of electrons with a power-law energy distri-

bution (as a result of acceleration) dNdγ prop γminusp for

γ gt γm where γm is the minimum Lorentz factor of

electrons The cooling of electrons by synchrotron ra-

diation is considered in slow and fast cooling regimes

4 httpsheasarcgsfcnasagovxanaduxspecmanualnode293html

5 blackbody model httpsheasarcgsfcnasagovxanaduxspecmanualnode136html

6 bkn2pow model httpsheasarcgsfcnasagovxanaduxspecmanualnode141html

7 grbcomp model httpsheasarcnasagovdocsxanaduxspecmodelsgrbcomphtml

depending on ratio between γm and the cooling Lorentz

factor γc (Sari et al 1998) We computed the resulting

photon spectrum of population of electrons assuming

that the average electron distribution at a given time is

dNdγ prop γminus2 for γc lt γ lt γm and dNdγ prop γminuspminus1

for γ gt γm in fast cooling regime while dNdγ prop γminusp

for γm lt γ lt γc and dNdγ prop γminuspminus1 for γ gt γc in

slow cooling regime The synchrotron model is made of

four free parameters the ratio between characteristic

Lorentz factors γmγc the peak energy of Fν spectrum

Ec which is simply the energy which corresponds to the

cooling frequency the power-law index of electrons dis-

tribution p and the normalization We built the table

model for the range of 01 le γmγc le 100 and 2 le p le 5

To fit the time integrated spectrum of Episode 1 we

use the four models described above (i) Band (ii) Band

+ blackbody (BB) (iii) broken power law (bkn2pow)

and (iv) the Comptonization model (grbcomp) The

best fit parameters of the tested models are reported

in Table 1 The νFν plots along with the residuals

are shown in Figure 3 for the four models used The

Band fit shows deviations at lower energies signifying

deviations from the power law that is used to model the

spectra from the low energy threshold of 8 keV to the

peak energy of the Band function (sim150 keV) We have

examined these residuals in detail by progressively rais-

ing the low energy threshold to 40 keV (greater than

the energy in which the deviations are seen) and ex-

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Narayan R Paczynski B amp Piran T 1992 ApJL 395

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

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Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 3: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 3

(Omodei et al 2017 Poolakkil amp Meegan 2017) The

observed high peak flux generated an autonomous

re-point request (ARR) in the GBM flight software

and the Fermi telescope slewed to the GBM in-flight

location A target of opportunity observation was

carried out by the Niel Gehrels Swift Observatory

(Evans 2017) and the Swift-XRT localized the burst

to RA(J2000) 6658092 and Dec minus 1046325

(DrsquoAi et al 2017) Swift-XRT followed the burst for

sim 2 times 106 s1 The prompt emission was also observed

by Konus-Wind (Frederiks et al 2017) The fluence

observed in the Fermi-GBM 10 - 1000 keV band from

T0 + 512 sec to T0 + 15155 s is (642 plusmn 005) times 10minus4

erg cmminus2 (Poolakkil amp Meegan 2017) Here T0 is the

trigger time in the Fermi-GBM The first photon in

LAT (gt 100 MeV ) with a probability 09 of its associ-

ation with the source is received at sim T0 + 374 s and

has an energy sim 194 MeV and a photon with energy

close to 1 GeV (930 MeV) is detected at sim 404 s The

highest energy photon (sim 19 GeV ) in the Fermi-LAT

is detected at sim 2890 s The rest frame energy of this

photon is sim 25 GeV

3 LIGHT CURVES

We examined the light curves of the GRB as obtained

from all 12 NaI detectors and found that detectors n7

n8 and nb (using the usual naming conventions) have

significant detections (source angles are n7 69 n8

31 and nb 40) We have used data from all three

detectors to examine the broad emission features of the

GRB For wide band temporal and spectral analysis

however we chose n8 and nb which have higher count

rates than the other detectors and the angles made with

the source direction for these two detectors are less than

50 degrees The time scale used throughout this paper

is relative to the Fermi-GBM trigger time ie t = T minusT0 Of the two BGO scintillation detectors the detector

BGO 1 (b1) which is positioned on the same side on

the satellite as the selected NaI detectors is chosen for

further analysis

The light curve is shown in Figure 1 and it shows

two episodes of emission (a) beginning at sim minus5s of the

main burst and lasts up to sim 205 s followed by a quies-

cent state when the emission level meets the background

level and (b) the emission becomes active again after a

short period at sim 246 s and radiation from the burst is

detected till sim 278 s We name these emission phases

as Episode 1 amp 2 In Figure 1 we also show the light

curve in the 100 - 400 keV region (the energy range of

AstroSat-CZTI observations) and we use this light curve

1 httpwwwswiftacukxrt curves00020778

0 50 100 150 200 250 300

104

n7 + n8 + nb8 - 900 keV

0 50 100 150 200 250 300Time since GBM trigger (s)

2000

4000

6000

8000

n7 + n8 + nb100 - 400 keV

Coun

tss

ec

Figure 1 Fermi-GBM light curve of GRB 171010A ob-tained from three NaI detectors n7 n8 and nbUpper Panel Log-scale light curve in the full energy range(8 ndash 900 keV) binned in 1 s intervals The two emissionepisodes used for time-integrated spectral analysis (minus5 s to205 s 246 s to 278 s) are shaded and demarcated with verti-cal dotted lines The red envelope shows the Bayesian blocksrepresentation of the light curveLower panel Linear-scale light curve and Bayesian blocksrepresentation for the 100 ndash 400 keV energy range used intime-resolved spectral analysis

to divide the data for time resolved spectral analysis

The blocks of constant rate (Bayesian blocks) are con-

structed from the light curves and over-plotted on the

count rate light curves to show statistically significant

changes in them (Scargle et al 2013)

The light curves summed over the chosen GBM detec-

tors (n8 and nb) in six different energy ranges are shown

in Figure 2 The GRB has complex structure with mul-

tiple peaks and the high energy emission (above 1 MeV)

is predominant till about 50 s as seen in the light curve

for gt 1 MeV Bayesian blocks are constructed from the

light curves and over-plotted on the count rate

4 SPECTRAL ANALYSIS

The burst is very bright and even with a signal to

noise ratio of 50 we are able to construct more than

150 time bins We created time bins therefore from

the Bayesian blocks constructed from the light curve in

the energy range 100 keV to 400 keV where CZTI is sen-

sitive for polarization measurements These bins (large

number of Bayesian blocks) track significantly varying

features in the lightcurve and will also be sufficient to

give a substantial idea about the energetics of the burst

The spectra are reduced using Fermi Science tools soft-

4 Chand et al

1200

1400

1600 b1 1 - 30 MeV

1000

2000

3000

b1 03 - 1 MeV

500

1000n8 + nb200 - 300 keV

2000

4000n8 + nb100 - 200 keV

250050007500

n8 + nb30 - 100 keV

0 50 100 150 200Time since GBM trigger (s)

250050007500

n8 + nb 8 - 30 keV

Coun

tss

ec

Figure 2 Fermi-GBM light curve of GRB 171010A in six different energy ranges with Bayesian blocks over-plotted in redAt the highest energies (1 ndash 30 MeV top panel) the emission is low after sim 50 s

ware rmfit2 by standard methodology described in the

tutorial3

GRB prompt emission spectra generally show a typi-

cal shape described by the Band function (Band et al

1993) however for a number of bursts additional com-

ponents are observed in the spectra such as quasi-

thermal components modeled by blackbody function

(Ryde 2005 Page et al 2011 Guiriec et al 2011 Basak

amp Rao 2015) or they show additional non-thermal com-

ponents modeled by a power-law or a power-law with an

exponential cut-off (Abdo et al 2009 Ackermann et al

2013) Additionally for a few cases spectra with a top-

hat shape are also observed and modeled by a Band-

function with an exponential roll-off at higher energies

(Wang et al 2017 Vianello et al 2017)

2 Fermi Science Tools rmfit httpsfermigsfcnasagovsscdataanalysisrmfit

3 Fermi tutorial httpsfermigsfcnasagovsscdataanalysisscitoolsrmfit tutorialhtml

The above models are driven by data and phe-

nomenology The physical models devised to explain

the GRB prompt emission radiation have the syn-

chrotron emission or the Compton scattering as the

core processes The synchrotron spectrum for a pow-

erlaw distribution of electrons consists of power-laws

joined at energies which depend upon cooling frequency

(νc) minimum-injection frequency (νm) and absorption

frequency (νa) The Comptonization models include

inverse Compton scattering as a primary mechanism

(Lazzati et al 2000 Titarchuk et al 2012) Comp-

tonization signatures (XSPEC grbcomp model) have

been detected for a set of GRBs observed by Burst

and Transient Source Experiment (BATSE) on board

Compton Gamma Ray Observatory (Frontera et al

2013) The grbcomp model differs from the other Comp-

tonization model the Compton drag model In the

Compton drag model the single inverse Compton scat-

terings of thermal photons shape the spectrum while

in the grbcomp multiple Compton scatterings are as-

sumed Another major difference is that the scattering

Variable prompt emission polarization in GRB 171010A 5

is off the outflow which is sub-relativistic in case of

grbcomp model while relativistic in the Compton drag

model

We apply this prior knowledge of spectral shapes

from the previous observations of GRBs to study

GRB 171010A The spectra are modeled by various

spectroscopic models available in XSPEC (Arnaud

1996) The statistics pgstat is used for optimization

and testing the various models4 We start with the

Band function and use the other models based upon

the residuals of the data and model fit The functional

form of the Band model used to fit the photon spectrum

is given in Equation 1 (Band et al 1993)

NBand(E) =

KB(E100)

αexp (minusE (2 + α) Ep) E lt Eb

KB(αminus β)Ep [100 (2 + α)](αminusβ) exp (β minus α) (E100)β E ge Eb

(1)

Other models include blackbody5 (BB) and a power

law with two breaks (bkn2pow)6 to model the broad

band spectrum

Nbkn2pow(E) =

KEminusα1 E le E1

KE1α2minusα1Eminusα2 E1 le E le E2

KE1α2minusα1E2

α3minusα2Eminusα3 E ge E3

(2)

For the Comptonization model proposed by Titarchuk

et al 2012 XSPEC local model grbcomp is fit to the pho-

ton spectrum7 The pivotal parameters of this model

are temperature of the seed blackbody spectrum (kTs)

the bulk outflow velocity of the thermal electrons (β)

the electron temperature of the sub-relativistic outflow

(kTe) and the energy index of the Greenrsquos function with

which the formerly Comptonized spectrum is convolved

(αb) Using the normalization of the grbcomp model

the apparent blackbody radius can be obtained To

avoid degeneracy in the parameters or the case when

parameters are difficult to constrain we froze some of

the parameters

To fit the spectra with synchroton radiation model we

implemented a table model for XSPEC We assumed a

population of electrons with a power-law energy distri-

bution (as a result of acceleration) dNdγ prop γminusp for

γ gt γm where γm is the minimum Lorentz factor of

electrons The cooling of electrons by synchrotron ra-

diation is considered in slow and fast cooling regimes

4 httpsheasarcgsfcnasagovxanaduxspecmanualnode293html

5 blackbody model httpsheasarcgsfcnasagovxanaduxspecmanualnode136html

6 bkn2pow model httpsheasarcgsfcnasagovxanaduxspecmanualnode141html

7 grbcomp model httpsheasarcnasagovdocsxanaduxspecmodelsgrbcomphtml

depending on ratio between γm and the cooling Lorentz

factor γc (Sari et al 1998) We computed the resulting

photon spectrum of population of electrons assuming

that the average electron distribution at a given time is

dNdγ prop γminus2 for γc lt γ lt γm and dNdγ prop γminuspminus1

for γ gt γm in fast cooling regime while dNdγ prop γminusp

for γm lt γ lt γc and dNdγ prop γminuspminus1 for γ gt γc in

slow cooling regime The synchrotron model is made of

four free parameters the ratio between characteristic

Lorentz factors γmγc the peak energy of Fν spectrum

Ec which is simply the energy which corresponds to the

cooling frequency the power-law index of electrons dis-

tribution p and the normalization We built the table

model for the range of 01 le γmγc le 100 and 2 le p le 5

To fit the time integrated spectrum of Episode 1 we

use the four models described above (i) Band (ii) Band

+ blackbody (BB) (iii) broken power law (bkn2pow)

and (iv) the Comptonization model (grbcomp) The

best fit parameters of the tested models are reported

in Table 1 The νFν plots along with the residuals

are shown in Figure 3 for the four models used The

Band fit shows deviations at lower energies signifying

deviations from the power law that is used to model the

spectra from the low energy threshold of 8 keV to the

peak energy of the Band function (sim150 keV) We have

examined these residuals in detail by progressively rais-

ing the low energy threshold to 40 keV (greater than

the energy in which the deviations are seen) and ex-

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

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Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

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mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

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Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 4: Draft version February 26, 2019 A twocolumn style in

4 Chand et al

1200

1400

1600 b1 1 - 30 MeV

1000

2000

3000

b1 03 - 1 MeV

500

1000n8 + nb200 - 300 keV

2000

4000n8 + nb100 - 200 keV

250050007500

n8 + nb30 - 100 keV

0 50 100 150 200Time since GBM trigger (s)

250050007500

n8 + nb 8 - 30 keV

Coun

tss

ec

Figure 2 Fermi-GBM light curve of GRB 171010A in six different energy ranges with Bayesian blocks over-plotted in redAt the highest energies (1 ndash 30 MeV top panel) the emission is low after sim 50 s

ware rmfit2 by standard methodology described in the

tutorial3

GRB prompt emission spectra generally show a typi-

cal shape described by the Band function (Band et al

1993) however for a number of bursts additional com-

ponents are observed in the spectra such as quasi-

thermal components modeled by blackbody function

(Ryde 2005 Page et al 2011 Guiriec et al 2011 Basak

amp Rao 2015) or they show additional non-thermal com-

ponents modeled by a power-law or a power-law with an

exponential cut-off (Abdo et al 2009 Ackermann et al

2013) Additionally for a few cases spectra with a top-

hat shape are also observed and modeled by a Band-

function with an exponential roll-off at higher energies

(Wang et al 2017 Vianello et al 2017)

2 Fermi Science Tools rmfit httpsfermigsfcnasagovsscdataanalysisrmfit

3 Fermi tutorial httpsfermigsfcnasagovsscdataanalysisscitoolsrmfit tutorialhtml

The above models are driven by data and phe-

nomenology The physical models devised to explain

the GRB prompt emission radiation have the syn-

chrotron emission or the Compton scattering as the

core processes The synchrotron spectrum for a pow-

erlaw distribution of electrons consists of power-laws

joined at energies which depend upon cooling frequency

(νc) minimum-injection frequency (νm) and absorption

frequency (νa) The Comptonization models include

inverse Compton scattering as a primary mechanism

(Lazzati et al 2000 Titarchuk et al 2012) Comp-

tonization signatures (XSPEC grbcomp model) have

been detected for a set of GRBs observed by Burst

and Transient Source Experiment (BATSE) on board

Compton Gamma Ray Observatory (Frontera et al

2013) The grbcomp model differs from the other Comp-

tonization model the Compton drag model In the

Compton drag model the single inverse Compton scat-

terings of thermal photons shape the spectrum while

in the grbcomp multiple Compton scatterings are as-

sumed Another major difference is that the scattering

Variable prompt emission polarization in GRB 171010A 5

is off the outflow which is sub-relativistic in case of

grbcomp model while relativistic in the Compton drag

model

We apply this prior knowledge of spectral shapes

from the previous observations of GRBs to study

GRB 171010A The spectra are modeled by various

spectroscopic models available in XSPEC (Arnaud

1996) The statistics pgstat is used for optimization

and testing the various models4 We start with the

Band function and use the other models based upon

the residuals of the data and model fit The functional

form of the Band model used to fit the photon spectrum

is given in Equation 1 (Band et al 1993)

NBand(E) =

KB(E100)

αexp (minusE (2 + α) Ep) E lt Eb

KB(αminus β)Ep [100 (2 + α)](αminusβ) exp (β minus α) (E100)β E ge Eb

(1)

Other models include blackbody5 (BB) and a power

law with two breaks (bkn2pow)6 to model the broad

band spectrum

Nbkn2pow(E) =

KEminusα1 E le E1

KE1α2minusα1Eminusα2 E1 le E le E2

KE1α2minusα1E2

α3minusα2Eminusα3 E ge E3

(2)

For the Comptonization model proposed by Titarchuk

et al 2012 XSPEC local model grbcomp is fit to the pho-

ton spectrum7 The pivotal parameters of this model

are temperature of the seed blackbody spectrum (kTs)

the bulk outflow velocity of the thermal electrons (β)

the electron temperature of the sub-relativistic outflow

(kTe) and the energy index of the Greenrsquos function with

which the formerly Comptonized spectrum is convolved

(αb) Using the normalization of the grbcomp model

the apparent blackbody radius can be obtained To

avoid degeneracy in the parameters or the case when

parameters are difficult to constrain we froze some of

the parameters

To fit the spectra with synchroton radiation model we

implemented a table model for XSPEC We assumed a

population of electrons with a power-law energy distri-

bution (as a result of acceleration) dNdγ prop γminusp for

γ gt γm where γm is the minimum Lorentz factor of

electrons The cooling of electrons by synchrotron ra-

diation is considered in slow and fast cooling regimes

4 httpsheasarcgsfcnasagovxanaduxspecmanualnode293html

5 blackbody model httpsheasarcgsfcnasagovxanaduxspecmanualnode136html

6 bkn2pow model httpsheasarcgsfcnasagovxanaduxspecmanualnode141html

7 grbcomp model httpsheasarcnasagovdocsxanaduxspecmodelsgrbcomphtml

depending on ratio between γm and the cooling Lorentz

factor γc (Sari et al 1998) We computed the resulting

photon spectrum of population of electrons assuming

that the average electron distribution at a given time is

dNdγ prop γminus2 for γc lt γ lt γm and dNdγ prop γminuspminus1

for γ gt γm in fast cooling regime while dNdγ prop γminusp

for γm lt γ lt γc and dNdγ prop γminuspminus1 for γ gt γc in

slow cooling regime The synchrotron model is made of

four free parameters the ratio between characteristic

Lorentz factors γmγc the peak energy of Fν spectrum

Ec which is simply the energy which corresponds to the

cooling frequency the power-law index of electrons dis-

tribution p and the normalization We built the table

model for the range of 01 le γmγc le 100 and 2 le p le 5

To fit the time integrated spectrum of Episode 1 we

use the four models described above (i) Band (ii) Band

+ blackbody (BB) (iii) broken power law (bkn2pow)

and (iv) the Comptonization model (grbcomp) The

best fit parameters of the tested models are reported

in Table 1 The νFν plots along with the residuals

are shown in Figure 3 for the four models used The

Band fit shows deviations at lower energies signifying

deviations from the power law that is used to model the

spectra from the low energy threshold of 8 keV to the

peak energy of the Band function (sim150 keV) We have

examined these residuals in detail by progressively rais-

ing the low energy threshold to 40 keV (greater than

the energy in which the deviations are seen) and ex-

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Burgess J M Preece R D Connaughton V et al

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Cano Z Wang S-Q Dai Z-G amp Wu X-F 2017

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Chattopadhyay T Vadawale S V Rao A R

Sreekumar S amp Bhattacharya D 2014 Experimental

Astronomy 37 555

Chattopadhyay T Vadawale S V Aarthy E et al

2017 ArXiv e-prints arXiv170706595

Covino S amp Gotz D 2016 Astronomical and

Astrophysical Transactions 29 205

DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

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1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

L12

Evans P A 2017 GRB Coordinates Network Circular

Service No 21986 1-2018 (2017) 21986

Frail D A Kulkarni S R Sari R et al 2001 ApJL

562 L55

Frederiks D Golenetskii S Aptekar R et al 2017 GRB

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1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

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1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

Lundman C Vurm I amp Beloborodov A M 2016 ArXiv

e-prints arXiv161101451

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Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

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1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

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Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

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Vadawale S V Chattopadhyay T Rao A R et al

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751 90

Page 5: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 5

is off the outflow which is sub-relativistic in case of

grbcomp model while relativistic in the Compton drag

model

We apply this prior knowledge of spectral shapes

from the previous observations of GRBs to study

GRB 171010A The spectra are modeled by various

spectroscopic models available in XSPEC (Arnaud

1996) The statistics pgstat is used for optimization

and testing the various models4 We start with the

Band function and use the other models based upon

the residuals of the data and model fit The functional

form of the Band model used to fit the photon spectrum

is given in Equation 1 (Band et al 1993)

NBand(E) =

KB(E100)

αexp (minusE (2 + α) Ep) E lt Eb

KB(αminus β)Ep [100 (2 + α)](αminusβ) exp (β minus α) (E100)β E ge Eb

(1)

Other models include blackbody5 (BB) and a power

law with two breaks (bkn2pow)6 to model the broad

band spectrum

Nbkn2pow(E) =

KEminusα1 E le E1

KE1α2minusα1Eminusα2 E1 le E le E2

KE1α2minusα1E2

α3minusα2Eminusα3 E ge E3

(2)

For the Comptonization model proposed by Titarchuk

et al 2012 XSPEC local model grbcomp is fit to the pho-

ton spectrum7 The pivotal parameters of this model

are temperature of the seed blackbody spectrum (kTs)

the bulk outflow velocity of the thermal electrons (β)

the electron temperature of the sub-relativistic outflow

(kTe) and the energy index of the Greenrsquos function with

which the formerly Comptonized spectrum is convolved

(αb) Using the normalization of the grbcomp model

the apparent blackbody radius can be obtained To

avoid degeneracy in the parameters or the case when

parameters are difficult to constrain we froze some of

the parameters

To fit the spectra with synchroton radiation model we

implemented a table model for XSPEC We assumed a

population of electrons with a power-law energy distri-

bution (as a result of acceleration) dNdγ prop γminusp for

γ gt γm where γm is the minimum Lorentz factor of

electrons The cooling of electrons by synchrotron ra-

diation is considered in slow and fast cooling regimes

4 httpsheasarcgsfcnasagovxanaduxspecmanualnode293html

5 blackbody model httpsheasarcgsfcnasagovxanaduxspecmanualnode136html

6 bkn2pow model httpsheasarcgsfcnasagovxanaduxspecmanualnode141html

7 grbcomp model httpsheasarcnasagovdocsxanaduxspecmodelsgrbcomphtml

depending on ratio between γm and the cooling Lorentz

factor γc (Sari et al 1998) We computed the resulting

photon spectrum of population of electrons assuming

that the average electron distribution at a given time is

dNdγ prop γminus2 for γc lt γ lt γm and dNdγ prop γminuspminus1

for γ gt γm in fast cooling regime while dNdγ prop γminusp

for γm lt γ lt γc and dNdγ prop γminuspminus1 for γ gt γc in

slow cooling regime The synchrotron model is made of

four free parameters the ratio between characteristic

Lorentz factors γmγc the peak energy of Fν spectrum

Ec which is simply the energy which corresponds to the

cooling frequency the power-law index of electrons dis-

tribution p and the normalization We built the table

model for the range of 01 le γmγc le 100 and 2 le p le 5

To fit the time integrated spectrum of Episode 1 we

use the four models described above (i) Band (ii) Band

+ blackbody (BB) (iii) broken power law (bkn2pow)

and (iv) the Comptonization model (grbcomp) The

best fit parameters of the tested models are reported

in Table 1 The νFν plots along with the residuals

are shown in Figure 3 for the four models used The

Band fit shows deviations at lower energies signifying

deviations from the power law that is used to model the

spectra from the low energy threshold of 8 keV to the

peak energy of the Band function (sim150 keV) We have

examined these residuals in detail by progressively rais-

ing the low energy threshold to 40 keV (greater than

the energy in which the deviations are seen) and ex-

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Narayan R Paczynski B amp Piran T 1992 ApJL 395

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

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Poolakkil S amp Meegan C 2017 GRB Coordinates

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

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Page 6: Draft version February 26, 2019 A twocolumn style in

6 Chand et al

trapolating the model to the low energies The low en-

ergy features could still be seen The presence of such

an anomaly is found in previous studies (Tierney et al

2013) and we conclude that a separate low energy fea-

ture in the spectra can exist We included a blackbody

(BB) along with the Band model for higher energies but

the residuals still show a systematic hump We also tried

another model for this feature of the spectrum a pow-

erlaw with two breaks (bkn2pow model) The bkn2pow

model is preferable as the pgstat is much less for the

same number of parameters (∆pgstat = 41) The pres-

ence of a narrow residual hump also necessitate the need

of a sharper break than a smooth blackbody curvature

This also hints that the break does not evolve much in

time and thus is not smeared out The Comptonization

model (grbcomp) however gives the best fit for the time

integrated spectrum of Episode 1 All the parameters of

this model other than β fbflag and log(A) were left

free The parameter β was frozen to the value 02 to

ignore terms O(sim β2) and fbflag was set to zero to in-

clude only the first order bulk Comptonization term A

value of 39 for γ shows deviation for the seed photons

from the seed blackbody spectrum However during the

time resolved spectral analysis as reported in the next

subsection we kept it fixed to 3 to consider a blackbody

spectrum for the seed photons

The isotropic energy (Eγiso) is calculated in the cos-

mological frame of the GRB by integrating the observed

energy spectrum over 1 keV(1 + z) to 10MeV(1 + z)

The tested models differ significantly only at low en-

ergies and yield similar Eγiso We have Eγiso =

22 times 1053 erg for the best fit model grbcomp The

Γ0 minus Eγ iso correlation between the initial Lorentz fac-

tor and the isotropic energy can be used to estimate Γ0

of the fireball ejecta (Liang et al 2010) The estimated

Γ0 is 392+38minus34 The errors are propagated from the nor-

malization and slope of the correlation The episode 2

could be spectrally well described by a simple power-law

and the best fit power-law index is 190+007minus006 for pgstat

274 for 229 degrees of freedom

41 Parameters evolution

We performed time resolved analysis to capture the

variations in the spectral properties by dividing the data

into time segments based on the Bayesian blocks made

from the 100 - 400 keV light curve We test the models

that were used for the time-integrated analysis The de-

viation from Band spectrum at low energies observed in

the time-integrated spectrum is also present in the time-

resolved bins thus justifying the need to use more com-

plex models than the simple Band function We how-

ever find that the three additional models (Band+BB

bknpwl and grbcomp) represent the time resolved spec-

tral data equally well The evolution of the model pa-

rameters is shown in Figure 4 In Fermi-GBM energy

range 8-20 keV is divided into 12 energy channels and

thus it provided sufficient data points to constrain the

power-law or BB temperature whenever BB peak or low

energy break falls well within these energy channels In

case of bkn2pow the low energy index is very steep

(sim minus3) when the break energy E1 found to be close

to the lower edge of the detection band For such cases

we froze the index to minus3 to obtain constraints on the

other parameters of the model When we fit with the

Band function the peak energy Ep shows three pulse

like structures in their temporal evolution and these can

be identified as showing a hard to soft (HTS) evolution

for peaks in the photon flux The first structure in Ep(at sim10 s) can be associated with the enhancement seen

in the gt1 MeV flux (Figure 2 top panel) When the low

energy feature is modeled using bkn2pow almost all the

peak energies fall below 200 keV The variation in the

low energy break (E1) remains concentrated in a very

narrow band (10 minus 20 keV) The best fit parameters

for all the models are presented in Table 5

The evolution of the derived parameters of grbcomp

model such as photospheric radius (Rph) and bulk pa-

rameter (δ) is shown in Figure 6

411 Distribution of parameters

Despite the fact that the best fit to the time integrated

spectrum is the Comptonization model (grbcomp) we

have tested the models (i) Band (ii) bkn2pow (iii)

BB+Band and (iv) grbcomp for the time resolved spec-

tra The distribution of the parameters is presented in

Figure 7 and are summarized here

For the Band function the low energy index α is dis-

tributed with a mean value minus1 (σ = 013) The maxi-

mum value observed is minus025 for a few time bins and in

the other cases α remains mostly belowminus08 The values

of low energy index agree with what is typically observed

for long GRBs (lt α gt= minus1) which is however known

to be harder than the synchrotron radiation in the fast

cooling regime The high energy index follows a bimodal

distribution with a mean value of minus27 (σ = 03) for the

major chunk concentrated around minus3 lt β lt minus2 and can

be interpreted as values normally observed for GRBs

The peak energy Ep is between 32 keV and 365 keV

with a median sim 140 (σ = 83) keV Its distribution also

shows a bimodal nature which reflects the evolution of

Ep

In the case of bkn2pow we observed that when the

lower break energy E1 is near the lower edge of the

detection band the power-law index below E1 is very

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Chattopadhyay T Vadawale S V Aarthy E et al

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Dai Z G amp Lu T 1998 AampA 333 L87

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Evans P A 2017 GRB Coordinates Network Circular

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Frail D A Kulkarni S R Sari R et al 2001 ApJL

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Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

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Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

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1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

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Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

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1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

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Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

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751 90

Page 7: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 7

Table 1 The best fit parameters for the time integrated spectrum of GRB 171010A Episode 1

Model

Band α β Ep (keV) pgstatdof

minus115+001minus001 minus240+003

minus003 163+3minus3 2786335

BB+Band α β Ep (keV) kTBB (keV) pgstatdof

minus075+004minus003 minus240+004

minus003 1500+25minus26 58+01

minus01 1465333

bkn2pow α1 α2 α3 E1 (keV) E2 (keV) pgstatdof

048+006minus007 1464+0006

minus0005 233+002minus002 172+04

minus04 1327+23minus23 1421333

grbcomp kTs (keV) kTe (keV) τ αb Rph (1010 cm) pgstatdof

48+05minus04 55+3

minus3 415+018minus015 152+004

minus004 80+22minus20 1281332

Synchrotron model γmγc Ec (keV) p pgstatdof

406+003minus008 216+02

minus04 gt 482 2520335

steep This is expected because there are only a few

channels here and the fit probably gives an unphysical

result We thus fixed the values to minus3 as they are diffi-

cult to constrain by the fits and also hamper the over-

all fitting process Note that bkn2pow model is defined

with an a-priori negative sign with it and we have to

be cautious while comparing it with the Band function

where the indices are defined without a negative sign

For the purpose of comparison we will explicitly reverse

the signs of the bkn2pow indices The mean value of minusα1

is sim 03(σ = 065) Here we have ignored values gt 15

as they form another part of the bimodal distribution

with low E1 during the time when E1 is near the lower

edge of the GBM energy band The mean value of minusα2

is sim minus14 (σ = 022) This forms the second power law

from E1 to E2 The third segment of the emission has

power law index minusα3 with a mean of sim minus26 (σ = 023)

The low energy break E1 has a mean sim 16 (σ = 23) keV

and it falls in a narrow range of 11 to 20 keV The mean

E2 is sim 140 (σ = 32) keV comparable to the mean of

Band function peak energy with a uni-modal distribu-

tion The E2 values are concentrated in the range 93 to

350 keV

When a blackbody is added the fits have an improved

statistics compared to the Band function throughout

the burst (see Figure 5) The blackbody temperature

vary between 4 minus 10 keV with a median of sim 63(σ =

112) keV The α distribution has harder values while

Ep and β are similar to the distributions of their counter-

parts in the Band function The presence of blackbody

does not seem to move the peak energies significantly

albeit an upward shift is noticeable In the grbcomp

model the average temperature of the seed photons was

68 (σ = 08) keV The electron temperature kTe was

found to be 55 (σ = 21) keV We derived the photo-

spheric radius from the normalization of the model We

found the photospheric radius sim 1011 cm The grbcomp

model parameters are reasonable and a photospheric ra-

dius of 1011 cm is consistent with its predictions (Fron-

tera et al 2013)

412 Correlations of parameters

We explore two parameter correlations and present

the graphs in Figure 8

(i) kTBB vs Ep Thermal components observed in a

set of bright Fermi single pulse GRBs are correlated to

the peak of non-thermal emission (Burgess et al 2014a)

The exponent of the power-law relation (Ep prop T q) indi-

cates the position of the photosphere if it is in the coast-

ing phase or acceleration phase The jet is dominated by

magnetic fields when q is 2 and baryonic if q is nearly 1

However these results were found on GRBs with single

pulses and for GRBs made up of overlapping pulses such

criteria may not be valid For GRB 171010A a positive

correlation (Ep prop T 22) between Ep and kTBB is found

with a log linear Pearson correlation coefficient of 081

p-value sim 10minus15 The index points out therefore a

magnetically dominated jet with photosphere below the

saturation radius We will discuss this result coupled

with the polarization results in Section 7 The peak en-

ergy from Band function and BB + Band function are

also found to be correlated Ep Band prop E12p BB+Band

(ii) Correlations among grbcomp parameters Corre-

lations between grbcomp model parameters and other

model parameters are reported in Frontera et al (2013)

We found a strong correlation between peak energy of

the Band function and the bulk parameter (δ) with

log linear Pearson coefficient and p-value r(p) of -068

(sim 10minus9) The seed photon temperature kTBB and

photospheric radius Rph are uncorrelated contrary to a

strong anti-correlation reported in Frontera et al 2013

The seed blackbody temperature and the electron tem-

perature are not correlated consistent with the pre-

dictions of grbcomp model The parameter kTe and

peak energy of BB + Band model are correlated with

kTe prop E1p BB+Band

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Chattopadhyay T Vadawale S V Aarthy E et al

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Covino S amp Gotz D 2016 Astronomical and

Astrophysical Transactions 29 205

DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

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1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

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Evans P A 2017 GRB Coordinates Network Circular

Service No 21986 1-2018 (2017) 21986

Frail D A Kulkarni S R Sari R et al 2001 ApJL

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Frederiks D Golenetskii S Aptekar R et al 2017 GRB

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1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

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1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

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e-prints arXiv161101451

Meszaros P amp Rees M J 1993 ApJ 405 278

Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

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1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 8: Draft version February 26, 2019 A twocolumn style in

8 Chand et al

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

01

1

10

100

1000

νF

ν (

keV

cm

minus2 s

minus1)

n8

nb

b1

10 100 1000 104

minus10

0

10

Resid

uals

Energy (keV)

Figure 3 The time integrated νFν plot of Episode 1 of GRB 171010A (-5 s to 246 s) along with the best fit models Residualsto the fit are shown in the bottom panels The Band model (top left) shows a low energy feature and can be either modeled by ablackbody (top right) or by adding another powerlaw at the low energy (middle left) The best fit model is the Comptonizationmodel grbcomp (middle right) The synchrotron model is shown in bottom panel

5 AFTERGLOWS

We have analyzed the afterglow data of GRB 171010A

in gamma-rays (Fermi-LAT) and X-rays (Swift-XRT)

and the results are shown in Figure 9 and 10

51 γ-ray afterglows

A 12 region of interest (ROI) was selected around the

refined Swift-XRT coordinates and an angle of 100 be-

tween the GRB direction and Fermi zenith was selected

based on the navigation plots The zenith cut is ap-

plied to reduce the contamination from γ-rays of Earth

albedo Transient event class and its instrument re-

sponse function P8R2 TRANSIENT020E V 6 is used

as it is appropriate for GRB durations Details about

LAT analysis methods and procedures can be found in

the Fermi-LAT GRB catalog (Ackermann et al 2013)

A simple power-law temporal decay is observed for the

LAT light curve with a hint of momentary increase or

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Chattopadhyay T Vadawale S V Aarthy E et al

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Covino S amp Gotz D 2016 Astronomical and

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Dai Z G amp Lu T 1998 AampA 333 L87

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Evans P A 2017 GRB Coordinates Network Circular

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Frail D A Kulkarni S R Sari R et al 2001 ApJL

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1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

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Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

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543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

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Komatsu E Dunkley J Nolta M R et al 2009 ApJS

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Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

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Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

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Lloyd N M amp Petrosian V 2000 ApJ 543 722

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Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

Coordinates Network Circular Service No 21985

1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

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Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 9: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 9

Figure 4 Upper Left The evolution of peak energy and the low energy spectral index of the Band model fit to time resolvedspectra The low energy spectral indices lie between fast and slow cooling limits of synchrotron radiation (indicated by dottedline and dot-dashed line respectively) Intervals used for polarization measurement are segregated by vertical dottedlines to guide the eye The photon flux is shown as a grey histogram (right hand side scale) Upper Right The evolution ofpeak energy blackbody temperature and low energy index when the low energy anomaly seen in the Band function fit is modeledby an additional blackbody Low energy indices are now above the slow cooling limit but below the limit of jitter radiation(black solid line) Lower Left The Evolution of two break energies and indices for a broken power law fit The index minusα2 inthis case shifts closer to the fast cooling line or even softer than this limit The energy index α1 below the low energy breakis harder with a median value 13 The break energy is also low and falls in the range between 15 - 25 keV Bottom Right Evolution of electron temperature seed photon temperature and high energy index αbf of the Comptonization model grbcomp

0 20 40 60 80 100 120 140 160t

06

08

10

12

14

16

18

20

pgst

atD

OF

bkn2powBandGRBCOMPBB + BandSynchrotron

Figure 5 The variation of the statistic pgstat with time A low energy break is preferable in almost all the bins All threemodels BB+Band bkn2pow synchrotron and grbcomp have comparable pgstat values and provide acceptable fits to the data inthe time-resolved analysis However in time-averaged analysis the grbcomp model provides the best fit

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

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21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

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Rees M J amp Meszaros P 1992 MNRAS 258 41P

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Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 10: Draft version February 26, 2019 A twocolumn style in

10 Chand et al

0 25 50 75 100 125 150t (s)

10

15

20

25

30

35

40R p

h(1

011 c

m)

0 25 50 75 100 125 150t (s)

1

2

3

4

5

6

7

Figure 6 The evolution of the photospheric radius (upperpanel) and the bulk parameter (lower panel) obtained fromthe grbcomp model

steady emission in both energy and photon fluxes during

the first and second time bins 346minus 514 s amp 514minus 635

s The LAT photon flux varies with time as a power law

with an index minus156 plusmn 040 and the energy flux variesas a power law with an index minus137plusmn 045 The photon

index of LAT-HE is ΓL = minus20 plusmn 01 from a spectral

fit obtained by fitting the first 105 sec data This gives

spectral index βL = ΓL + 1 to be minus10plusmn 01 The time

resolved spectra do not show variation in the photon

index in the first four bins

In the external shock model for ν gt maxνm νcwhich is generally true for reasonable shock parame-

ters we can derive the power law index of the shocked

electrons by fν prop νminusp2 We have synchrotron energy

flux fL prop νminusβLtminusαL (see the LAT lightcurve in Figure

9) We found αL = 137 plusmn 045 and βL = 10 plusmn 01

The value of βL gives us p = 20 plusmn 02 Thus the

power-law index for the energy flux decay can be pre-

dicted by using fL prop t(2minus3p)4 The calculated value of

αL is minus10 plusmn 02 which agrees well with the observed

value of minus137 plusmn 045 Hence we can conclude that

for GRB 171010A the LAT high energy afterglows are

formed in an external forward shock

For the thin shell case in a homogeneous medium and

assuming that the peak of the LAT afterglow (tp) occurs

either before or in the second time bin gives tp lt 530 s

and we can constrain the initial Lorentz factor (Γ0) of

the GRB jet (see eg Sari amp Piran 1999 Molinari et al

2007) using

Γ0 gt 193(nη)minus18 times

(Eγ52t3pz2

)18

(3)

where mp is the mass of proton η is the radiation

efficiency tp is the time when afterglow peaks Eγ52is the k corrected rest frame energy of the GRB in

the 1 minus 10 000 keV band For a typical density

n = 01 cmminus3 of homogeneous ambient medium and

η = 05 we can constrain the initial Lorentz factor

Γ0 gt 330 This limit is consistent with Γ0 found in

Section 4 from Γ0 minus Eγ iso correlation

The photon index hardens in the 2150 minus 6650 s time

bin and the flux also seems to deviate from the power

law fit This hints at a contribution from an inverse

Compton component The highest energy photon with

a rest frame energy of sim 25 GeV is also observed during

this interval

52 X-ray afterglows

The primary goal of the Swift satellite is to detect

GRBs and observe the afterglows in X-ray and optical

wavelengths If a GRB is not detected by Swift but is de-

tected by some other mission (like Fermi etc) target of

opportunity (ToO) mode observations can be initiated in

Swift for very bright bursts For such bursts the prompt

phase is missed by Swift and afterglow observations arealso inevitably delayed However the detection of X-ray

afterglows with Swift-XRT not only allows us to study

the delayed afterglow emissions but also to precisely lo-

calize the GRB for further ground and space based ob-

servations at longer wavelengths The X-ray afterglow of

GRB 171010A was observed by Swift sim 24300 s (sim 03

days) after the burst We have used the XRT prod-

ucts and lightcurves from the XRT online repository8 to

study the light curve and spectral characteristics The

statistically preferred fit to the count rate light curve in

the 03 minus 10 keV band has three power-law segments

with two breaks The temporal power-law indices and

the break times in the light curve as given in the GRB

online repository are listed in Table 3 The data are also

8 httpwwwswiftacukxrt productsindexphp

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Abdo A A Ackermann M Ajello M et al 2009 ApJL

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Burgess J M Preece R D Connaughton V et al

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Cano Z Wang S-Q Dai Z-G amp Wu X-F 2017

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Chattopadhyay T Vadawale S V Rao A R

Sreekumar S amp Bhattacharya D 2014 Experimental

Astronomy 37 555

Chattopadhyay T Vadawale S V Aarthy E et al

2017 ArXiv e-prints arXiv170706595

Covino S amp Gotz D 2016 Astronomical and

Astrophysical Transactions 29 205

DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

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1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

L12

Evans P A 2017 GRB Coordinates Network Circular

Service No 21986 1-2018 (2017) 21986

Frail D A Kulkarni S R Sari R et al 2001 ApJL

562 L55

Frederiks D Golenetskii S Aptekar R et al 2017 GRB

Coordinates Network Circular Service No 22003

1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

Coordinates Network Circular Service No 22002

1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

Lundman C Vurm I amp Beloborodov A M 2016 ArXiv

e-prints arXiv161101451

Meszaros P amp Rees M J 1993 ApJ 405 278

Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

Coordinates Network Circular Service No 21985

1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 11: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 11

1 0Band

0

10

20

Num

ber -102

100 200 300 400Ep Band

14125

75 50 25Band

-277

1 0BB + Band

0

5

10

15

Num

ber -046

100 200 300 400Ep BB + Band

14169

75 50 25 00BB + Band

-265

20 403kTBB + Band

1826

1 02 bkn2pow

00

25

50

75

100

Num

ber -14

100 200 300 400E2 bkn2pow

13446

75 50 25 003 bkn2pow

-255

20 40E1 bkn2pow

156

100 200 300 4003kTe grbcomp

00

25

50

75

100

Num

ber 16567

20 403kTs grbcomp

0

5

10

15

20

Num

ber 2077

Figure 7 The distributions of best-fit parameters for Band bkn2pow and grbcomp models Each histogram consists of ten binsbetween minimum and maximum values Thick vertical dot-dashed lines represent the median of the observed distribution ofthe parameters

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Chattopadhyay T Vadawale S V Aarthy E et al

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Komatsu E Dunkley J Nolta M R et al 2009 ApJS

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Lloyd N M amp Petrosian V 2000 ApJ 543 722

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

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1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 12: Draft version February 26, 2019 A twocolumn style in

12 Chand et al

1026 times 101 2 times 102 3 times 102

Ep BB + Band (keV)

102

103

E pB

and (

keV)

1014 times 100 6 times 100

kTBB BB + Band (keV)

102

103

E pB

B+

Ban

d (

keV)

102

Ep BB + Band (keV)

101

102

grbc

omp

kTe

(keV

)

101 2 times 101

E1 (keV)

102

103

E 2 (

keV)

102

2 times 100

3 times 100

4 times 100

6 times 100

E pB

and (

keV)

1014 times 100 6 times 100

kTs (keV)

101

102

kTe

(keV

)

1014 times 100 6 times 100

kTs (keV)

1011

2 times 1011

3 times 1011

4 times 1011

R ph

(cm

)

Figure 8 Correlations obtained for various model parameters and derived parameters

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Narayan R Paczynski B amp Piran T 1992 ApJL 395

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

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Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 13: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 13

consistent with 3 breaks (Table 3) The light curve with

three breaks resembles the canonical GRB light curves

observed in XRT (Zhang et al 2006 Nousek et al 2006)

We have analysed the XRT spectral data and generated

the energy flux light curve shown in Figure 10 The flux

light curve in the 03 - 10 keV energy band is fit with

a single powerlaw and a broken powerlaw with a single

break at time tb The best fit single powerlaw shows

a decay index of fX prop tminus144plusmn003 while in the bro-

ken powerlaw the pre- and post-break decay indices are

129 plusmn 005 and 197 plusmn 024 respectively with the break

at tb = (337 plusmn 103) times 105 s These values are consis-

tent with the fits for the count rate light curves given in

Table 3

We name the two segments of the light curve with

three breaks as phase 1 (see Table 3) before tb2 and

phase 2 after tb2 The phase 1 is subjectively divided

into 3 time bins to track the evolution of spectral pa-

rameters during this phase The phase 2 is also divided

at the tb3 for inspecting the spectral change with the

apparent rise in the light curve after this point

We froze the equivalent hydrogen column density (nH)

to its Galactic value (Willingale et al 2013) Another

absorption model tbabs in XSPEC is used to model

intrinsic absorption and nH corresponding to it is frozen

to the value obtained from the time integrated fit A

simple power law fits the spectrum for both the phases

The photon index in the XRT band is found to be

ΓX = minus19 plusmn 01 for phase 1 and ΓX = minus17+03minus06 for

phase 2 The evolution of energy flux in 03 minus 10 keV

and the photon index are shown in Figure 10 Similar

to LAT it also predicts p sim 2 when both νm and νcevolve to energies that lie below the XRT band If we

consider p sim 22 (See eg Zhang et al 2006 Nousek

et al 2006) which will be nearly consistent with the

p inferred from LAT afterglow and also near to XRT-

afterglow value Thus for the late time decay we have

αX sim minus115 When the light curve is modeled by a bro-

ken power-law we get fX prop tminus129plusmn005 before the break

and fX prop tminus197plusmn024 thereafter Therefore predicted

αX sim minus115 is nearly consistent with αX sim 129plusmn 005

(three times the error bar) The αX before and after

the break are consistent with the late time decay in the

external shock model And the break observed can be

identified as a jet break (tbreak = 34times 105 s) and used

for finding the opening angle (θj) of the jet as given by

Eq 4 (Frail et al 2001) However an achormatic break

at all wavelengths in the lightcurves is required to claim

it as a jet break The absence of a break till the last

data point observed in XRT can also be utilized to put

a lower limit on the jet break (see for example Wang

et al 2018) So any break before corresponding to last

data point in XRT will also respect that limit because

for a given initial Lorentz factor (Γ0) the jet break will

occur later for a wider jet

θj asymp 0057

(tj

86 400 s

)38(1 + z

2

)minus38(Eiso

1053 erg

)minus18 ( η

02

)18 ( n

01 cmminus3

)18(4)

We get θj = 011 rad (= 63) by using eq 4 The

beaming angle can be estimated by using Lorentz fac-

tor Γ0 using θbeam = 1Γ0 For Γ0 = 330 we have

θbeam = 0003 rad (= 017) Thus we have a wide

bright jet with a narrow beaming angle The Lorentz

factor estimated above is for the final merged shells

propagating to the circum-burst medium (CBM) and

forming an external shock The Lorentz factor for indi-

vidual shells can even be higher than our estimate The

jet energy corrected for collimation is 137times 1051 erg

6 POLARIZATION MEASUREMENTS

GRB 171010A is one of the brightest GRBs detected

in CZTI with an observed fluence gt 10minus4 ergcm2 This

makes the GRB one of potential candidates for polariza-

tion measurement CZTI works as a Compton polarime-

ter where polarization is estimated from the azimuthal

angle distribution of the Compton scattering events be-

tween the CZTI pixels at energies beyond 100 keV

Polarization measurement capability of CZTI has been

demonstrated experimentally during its ground calibra-

tion (Chattopadhyay et al 2014 Vadawale et al 2015)

First on board verification of its X-ray polarimetry mea-

surement capability came with the detection of high po-

larization in Crab in 100 mdash 380 keV (Vadawale et al

2017) Crab was observed for sim 800 ks in two years

after its launch and this was statistically the most sig-

nificant polarization measurement till date in hard X-

rays Polarimetric sensitivity of CZTI for off-axis GRBs

is expected to be less than that for ON-axis sources

(eg Crab) but the high signal to background ratio

for GRBs and availability of pre-GRB and post-GRB

background makes CZTI equally sensitive to polariza-

tion measurements of GRBs Recently we reported sys-

tematic polarization measurement for 11 GRBs with

sim3σ detection for 5 GRBs andsim2σ detection for 1 GRB

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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2017 ArXiv e-prints arXiv170706595

Covino S amp Gotz D 2016 Astronomical and

Astrophysical Transactions 29 205

DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

Coordinates Network Circular Service No 21989

1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

L12

Evans P A 2017 GRB Coordinates Network Circular

Service No 21986 1-2018 (2017) 21986

Frail D A Kulkarni S R Sari R et al 2001 ApJL

562 L55

Frederiks D Golenetskii S Aptekar R et al 2017 GRB

Coordinates Network Circular Service No 22003

1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

Coordinates Network Circular Service No 22002

1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

Lundman C Vurm I amp Beloborodov A M 2016 ArXiv

e-prints arXiv161101451

Meszaros P amp Rees M J 1993 ApJ 405 278

Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

Coordinates Network Circular Service No 21985

1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

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Nature Astronomy 2 69

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751 90

Page 14: Draft version February 26, 2019 A twocolumn style in

14 Chand et al

103 104 105

Time(s)

102

103

104

Ener

gy(M

eV) pgt09

09gtpgt0808gtpgt0707gtpgt0606gtpgt0505gtp

103 104 105

10 10

10 9

10 8

10 7

10 6

10 5

Flux

LAT energy flux (01-10 GeV erg cm 2 s 1)LAT photon flux (01-10 GeV ph cm 2 s 1)

103 104 105

Time since GBM trigger (s)

252015

L

Figure 9 Top panel Energies of individual Fermi-LAT photons (gt 100 MeV) detected more than 345 s after the triggerThe color and transparency of circles depend on the probability (p) of their association with source Middle panel Fermi-LATphoton and energy fluxes in 01 mdash 10 GeV range The photon index in the first time bin was fixed to minus2 to get an upper limiton the fluxes The dashed curve in the background shows the evolution of the LAT photon flux assuming a constant photonindex minus2 The photon flux rises fast initially peaks at sim 530 s and then declines This flux peak was used to obtain a lowerlimit on the Lorentz factor of the ejecta (sect4) Bottom panel Photon indices for FermiLAT in the 01 mdash 10 GeV range

and upper limit estimation for the remaining 5 GRBs

GRB 171010A is a bright GRB registering around sim2000 Compton events in CZTI It is the second bright-

est GRB in terms of number of Compton events after

GRB 160821A and therefore is a potential candidate

for polarization analysis

The details of the method of polarization measure-

ment of GRBs with CZTI can be found in Chattopad-

hyay et al (2017) Here we briefly describe the different

steps involved in the analysis procedure

bull The first step is to identify and select the valid

Compton events We select the double pixel events

during the prompt emission by identifying events

happening within a 40 micros time window The dou-

ble pixel events are then filtered against various

Compton kinematics criteria to finally obtain the

Compton scattered events

bull The selection of Compton events is confined within

the 3times3 pixel block of CZTI modules which re-sults in an 8 bin azimuthal scattering angle dis-

tribution We compute the azimuthal scattering

angles for events during both the GRB prompt

emission and the background before and after

the prompt emission The combined pre and

post-GRB azimuthal distribution is used for back-

ground subtraction to finally obtain the azimuthal

distribution for the GRB

bull The background corrected prompt emission az-

imuthal distribution shows some modulation due

to (a) asymmetry in the solid angles subtended

by the edge and the corner pixels to the central

scattering pixel and (b) the off-axis viewing angle

of the burst These two factors are corrected by

normalizing the azimuthal angle distribution with

a simulated distribution for the same GRB spec-

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Chattopadhyay T Vadawale S V Aarthy E et al

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DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

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1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

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Evans P A 2017 GRB Coordinates Network Circular

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Frail D A Kulkarni S R Sari R et al 2001 ApJL

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Frederiks D Golenetskii S Aptekar R et al 2017 GRB

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1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

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1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

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e-prints arXiv161101451

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Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

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1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 15: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 15

105 106

10 13

10 12

10 11

Flux

(er

g cm

2 s

1 )

105 106

Time since GBM trigger (s)

2

1

X

Figure 10 Swift-XRT energy flux in the range 03 - 10 keV(upper panel) A single power law fit (red dotted line) tothe flux gives fX prop tminus144plusmn003 When a break is introducedat tb (red solid line) the powerlaw indices are 129 plusmn 005and 197plusmn024 before and after the break respectively Thebreak observed is at (337plusmn103)times105 s The photon indicesfor the Swift-XRT spectra are shown in the bottom panel

tra at the same off-axis angle assuming the GRB

is completely unpolarized The simulation is per-

formed in Geant4 with a full mass model of CZTI

and AstroSat

bull We fit background and geometry corrected az-

imuthal angle distribution using MCMC simula-

tion to estimate the modulation factor and polar-

ization angle (in CZTI plane) This is followed up

by detailed statistical tests to determine whether

the GRB is truly polarized or not This is an im-

portant step particularly because there can be

systematic effects which can produce significant

modulation in the azimuthal angle distribution

even for completely unpolarized photons These

effects are even more prominent in cases where the

GRB is not very bright

bull If the statistical tests suggest that the GRB is

truly polarized we estimate the polarization frac-

tion by normalizing the fitted modulation fac-

tor with micro100 which is the modulation factor for

100 polarized photons obtained by simulating

the GRB simulated in Geant4 with the AstroSat

mass model If the GRB is found to be unpolar-

ized we estimate the upper limit of polarization

(see Chattopadhyay et al (2017))

275 300 325 350 375 400 425Time + 245357750 sec

20

40

60

80

Coun

tsb

in (

Com

pton

)

Figure 11 Observed Compton event light curve forGRB 171010A in 100 mdash 300 keV band with 1 second binningThe events in the time interval between 300mdash370 seconds inthe light curve are used for polarization analysis

Figure 12 The background subtracted and geometry cor-rected modulation curve for GRB 171010A in 100 mdash 300 keVThe blue solid line is the sinusoidal fit to the modulationcurve We find no clear sinusoidal variation in the azimuthalangle distribution

Figure 11 shows the light curve of GRB 171010A in

Compton events in 100 mdash 300 keV The burst is clearly

seen in Compton events We used a total of 747 sec-

onds of background before and after the burst for the

final background estimation After background subtrac-

tion the number of Compton events during the prompt

emission is found to be sim 2000 Figure 12 shows the

modulation curve in the 100 mdash 300 keV band follow-

ing background subtraction and geometry correction as

discussed in the last section We do not see any clear

sinusoidal modulation in the azimuthal angle distribu-

tion Figure 13 shows the corresponding contour plot

for GRB 171010A Both polarization fraction and an-

gle are poorly constrained signifying that the burst is

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Covino S amp Gotz D 2016 Astronomical and

Astrophysical Transactions 29 205

DrsquoAi A Melandri A Sbarufatti B et al 2017 GRB

Coordinates Network Circular Service No 21989

1-2018 (2017) 21989

Dai Z G amp Lu T 1998 AampA 333 L87

Deng W Zhang H Zhang B amp Li H 2016 ApJL 821

L12

Evans P A 2017 GRB Coordinates Network Circular

Service No 21986 1-2018 (2017) 21986

Frail D A Kulkarni S R Sari R et al 2001 ApJL

562 L55

Frederiks D Golenetskii S Aptekar R et al 2017 GRB

Coordinates Network Circular Service No 22003

1-2018 (2017) 22003

Frontera F Amati L Farinelli R et al 2013 ApJ 779

175

Gao H amp Zhang B 2015 ApJ 801 103

Guiriec S Connaughton V Briggs M S et al 2011

ApJL 727 L33

Izzo L Ruffini R Penacchioni A V et al 2012 AampA

543 A10

Kankare E OrsquoNeill D Izzo L et al 2017 GRB

Coordinates Network Circular Service No 22002

1-2018 (2017) 22002

Komatsu E Dunkley J Nolta M R et al 2009 ApJS

180 330

Lazzati D amp Begelman M C 2009 ApJL 700 L141

Lazzati D Ghisellini G Celotti A amp Rees M J 2000

ApJL 529 L17

Liang E-W Yi S-X Zhang J et al 2010 ApJ 725

2209

Lloyd N M amp Petrosian V 2000 ApJ 543 722

Lundman C Vurm I amp Beloborodov A M 2016 ArXiv

e-prints arXiv161101451

Meszaros P amp Rees M J 1993 ApJ 405 278

Meszaros P amp Rees M J 1997 ApJ 476 232

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

Coordinates Network Circular Service No 21985

1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

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Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

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751 90

Page 16: Draft version February 26, 2019 A twocolumn style in

16 Chand et al

Figure 13 Contour plot of polarization angle and fractionfor GRB 171010A in 100 mdash 300 keV as obtained from theMCMC method The red green and blue represent the 68 90 and 99 confidence levels respectively

either unpolarized or polarization fraction is below the

sensitivity level of CZTI

In order to verify this we measure Bayes factor for

sinusoidal (for polarized photons) and constant model

(unpolarized photons) by utilizing lsquoThermodynamic In-

tegrationrsquo method on the MCMC parameter space (for

details refer to Chattopadhyay et al (2017)) This yields

a value less than 2 which is assumed to be the threshold

value of Bayes factor for claiming detection of polariza-

tion We therefore estimate the upper limit of polar-

ization for GRB 171010A which is done in two steps

First step involves estimation of polarization detection

threshold (Pthr) by limiting the probability of false de-

tection (to 005 for sim2σ or 001 for sim3σ) The false po-

larization detection probability is estimated by simulat-

ing GRB 171010A for the observed number of Compton

and background events with 100 unpolarized photons

The second step involves measurement of the probabil-

ity of detection of polarization such that probability of

detection of a certain level of polarization (Pupper) being

greater than the polarization detection threshold (Pthr)

is ge 05 (see Chattopadhyay et al (2017) for more de-

tails) The 2σ upper limit (5 of false detection proba-

bility) for GRB 171010A is found to besim42 It is to be

noted that in the sample of bursts used for polarization

analysis in Chattopadhyay et al (2017) GRB 160821A

was found to possess maximum number of Compton

events (sim 2500) The next brightest burst was GRB

160623A with sim 1400 Compton events We estimated

sim 50 polarization at gt 3σ detection significance for

GRB 160821A In comparison GRB 171010A is found

to have sim 2000 Compton events The GRB is detected

at an off-axis angle of 55 We expect CZTI to have sig-

nificant polarmetric sensitivity at such off-axis angles

Therefore polarization for this GRB should be detected

at a significant detection level provided the GRB is at

least sim50 polarized This is consistent to our estima-

tion of 2σ polarization upper limit of sim42

This is an interesting result considering the fact that

the spectral analysis suggests the time integrated peak

energy for all the models is less than 200 keV which falls

within the energy range of polarization analysis There-

fore in order to see the variation of polarization below

and above the peak energy we estimate polarization in

two different energy ranges mdash 100 mdash 200 keV and 200

mdash 300 keV (see Figure 14) There is no clear modulation

at the lower energies whereas we see a sinusoidal varia-

tion in the modulation curve in 200 mdash 300 keV which

is beyond the peak energy of the GRB However it is

to be noted that the Bayes factors for both the energy

ranges are less than 2 signifying that there is no firm

detection of polarization The modulation at higher en-

ergies therefore is just a hint of polarization which is

still an interesting result

One major difference between GRB 160821A (or GRB

160802A GRB 160910A (Chattopadhyay et al 2017))

and GRB 171010A is that the later lasts longer and has

multiple pulses We also see significant variation of peak

energy with time (see Figure 4) These pulses might ex-

hibit different polarization signatures resulting in a net

zero or low polarization when integrated in time We

therefore divided the whole burst in 3 different time in-

tervals mdash 0 mdash 20 seconds 20 mdash 28 seconds and 28 mdash

70 seconds where lsquo0rsquo is the onset of the burst Since

we have already seen a hint of polarization signature in

200 mdash 300 keV we further divided the signals in 100 mdash

200 keV and 200 mdash 300 keV Figure 15 shows the vari-

ation of polarization fraction (middle panel) and po-

larization angle (bottom panel) in three time intervals

for 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

The errors in polarization angle in the first two inter-

vals in both the energy ranges are quite large with no

significant modulation in azimuthal angle distribution

consistent to being unpolarized This is independently

verified with the estimation of low values of Bayes fac-

tor The third interval on the other hand shows high

polarization fraction with a very clear sinusoidal mod-

ulation in the azimuthal angle distribution in 200 mdash

300 keV (see Figure 16) The polarization angle is also

constrained within 13 uncertainty The Bayes factor for

this interval in 200 mdash 300 keV is found to be sim2 with a

false polarization detection probability by chance lt 1

clearly signifying that the GRB is polarized at the later

part of the emission at higher energies

7 DISCUSSIONS AND CONCLUSIONS

We presented the spectral timing and polarization

analysis of GRB 171010A which has an observed flu-

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Oganesyan G Nava L Ghirlanda G amp Celotti A

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Page K L Starling R L C Fitzpatrick G et al 2011

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Poolakkil S amp Meegan C 2017 GRB Coordinates

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

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751 90

Page 17: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 17

Figure 14 Same as Figure 12 but for different energy ranges mdash 100 mdash 200 keV (left) and 200 mdash 300 keV (right) We see asinusoidal modulation in the 200 mdash 300 keV modulation curve

Figure 15 Compton light curve (top) polarization fraction (middle) and angle (bottom) for three different time intervalsduring the prompt emission of GRB 171010A in 100 mdash 200 keV (left) and 200 mdash 300 keV (right)

ence gt 10minus4 ergs cmminus2 We found that the spectrum

integrated over the duration of the burst is peculiar as it

shows a low energy break and can be modeled by either

a BB or another power law Some GRBs have shown

the presence of such a component which was modeled

by a BB with peaks ranging up to 40 keV (Guiriec et al

2011) In a comprehensive joint analysis of X-

rays and higher energies in the prompt emission

a break was found in the XRT-energy window

(Zheng et al 2012 Oganesyan et al 2018 2017)

and also in the GBM energy range (Ravasio et al

2018) To study the detailed evolution of the spectral

parameters we sliced the spectrum into multiple time

bins and found that Band Ep shows a bimodal distri-

bution Inclusion of a low energy component (modeled

as a BB or a separate power-law) shows that the distri-

bution of the peak energy remains gt 100 keV and also

falls in a concentrated region of between 100 minus 200 keV

The mean value of the break energy in the power-law

with two breaks model (E2) is sim 140 keV The power

law index above the break is softer than the index α

obtained from the Band function The mean value of

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

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Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 18: Draft version February 26, 2019 A twocolumn style in

18 Chand et al

Figure 16 Azimuthal angle distribution for the third time interval (28 mdash 70 seconds at 200 mdash 300 keV) We see a clear andhigh modulation signature in the azimuthal distribution The Bayes factor is found to be around 2 with a false polarizationdetection probability by chance less than 1

minusα2 is -145 and we are tempted to identify it with the

synchrotron fast cooling process E2 can therefore be

identified with the minimum energy injected to the elec-

trons and the corresponding frequency is νm On the

other hand minusα1 is 03 harder than the value of spectral

index minus23 allowed below the cooling frequency νc of

synchrotron radiation However absorption frequency

which can be near the GBM lower energy window has

expected index to be +1 thus it is possible that the

cooling frequency falls very near to the absorption fre-

quency In such a case E1 can be either identified as

νc or νa as the ratio νcνa or νaνc will be closer to

1 Now relating to the fast cooling scenario minusα3 can

be set equal to minusp2 minus 1 to get the index of power-

law distribution of electron energies We get p 32

and for the distribution shown by minusα3 allowed values

of p fall in the range 2 to 4 The component at the

low energy end can also be interpreted as being of pho-tospheric origin generated in a region that is optically

thick to the radiation and radiation escaping at a ra-

dius where it becomes transparent We have tested

also the synchrotron model since bkn2pow gives a

possibility that synchrotron model in marginally

fast cooling regime could in principle work The

direct fitting of the prompt emission spectra by

the synchrotron model have been performed in

number of studies (Tavani 1996 Lloyd amp Pet-

rosian 2000 Burgess et al 2014b Zhang et al

2016 2018 Burgess et al 2018) that give the

preference to the slow or moderataly fast cool-

ing regimes of radiation In our analysis the

synchrotron model returns small ratio between

γm and γc and the range of pgstatdof that is

similar to other models and it has same number

of parameters as Band function Our results show

that the spectral data can also be well described by a

Comptonization (grbcomp) model

From the afterglows observed in LAT (gt100 MeV) and

XRT (03 -10 keV) we concluded that the afterglows are

produced in an external shock propagating into the am-

bient medium By assuming the ambient medium to be

homogeneous we estimated the initial Lorentz factor of

the ejecta However the Lorentz factor thus obtained is

for the merged ejecta The sub-MeV emission possibly

arises from multiple internal shocks and a stratification

in the Lorentz factor can not be ruled out From the ob-

served break in the XRT light curve we obtained the jet

opening angle GRB 171010A consists of a jet with ini-

tial beaming angle much narrower than the jet opening

angle

The burst shows high polarization however significant

variation in the polarization fraction (PF) and angle

(PA) can be seen with energy and time Such variations

in PA can arise due to ordered magnetic field or random

magnetic fields produced in shocks and when within the

beaming angle the net magnetic field can be oriented in

any direction independent of the other shells For a high

polarization the coherence length of the magnetic field

(θB) should be larger than or comparable to the beam-

ing angle 1Γ ie θB amp 1Γ In case of a Poynting

flux dominated jet a pulse is produced in each

ICMART event The peak energy and polari-

sation decreases in each ICMART event The

polarisation degree and angle can vary (Zhang

amp Yan 2011 Deng et al 2016) The spectrum

can be a hybrid of blackbody and Band func-

tion We have observed a low energy feature

and the spectrum deviating from Band function

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 19: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 19

which was also modelled by a blackbody This

can be contribution from a photosphere (Gao amp

Zhang 2015) The lower polarisation at ener-

gies below 200 keV can be due to multiple events

superimposing and decreasing the net degree of

polarization The change is polarisation angle

with energy also supports this argument There-

fore the spectrum and polarization measurents

are consistent with ICMART model

In the Comptonization model multiple Compton scat-

terings are assumed producing higher energy photons

in the jet The photons below the peak energy in the

grbcomp model are produced by the Comptonization of

the seed blackbody photons during the sub-relativistic

phase This component is therefore expected to be

unpolarized The high energy photons above the peak

energy are mostly generated by further inverse Comp-

ton scattering off the non-thermal relativistic electrons

of the relativistic outflow This can give a polarization

up to 100 when the emission is observed at an an-

gle 1Γ with the beaming axis and unpolarized when

viewed on-axis (Rybicki amp Lightman 1979) As for po-

larization the highest value is expected for emission in

the jet because in this case a photon originating in the

Compton cloud illuminates the jet (or outflow) and un-

dergoes a single up-scattering Single scattering off jet

electrons can result in a degree of polarization up to

100 Change in the polarization fraction and angle can

be possible only if jet is fragmented and we are observ-

ing it at different viewing angles The measured high

polarization below the peak is in contradiction with the

predictions of this model

The photospheric component found in the spectra

suggests that the overall spectral shape may also be

explained by the sub-photospheric dissipation model

(Vurm amp Beloborodov 2016) The polarization expected

in the sub-photospheric dissipation model is low and

tends to decrease at higher energies because the higher

energy photons are produced deep within the photo-

sphere and are reprocessed through multiple Compton

scatterings before finally leaving the system at the pho-

tosphere (Lundman et al 2016) The observed increase

in the polarization with energy is in contradiction with

the predictions of this model

Another interpretation independent of the syn-

chrotron or inverse Compton origin is that the emis-

sion is from fragmented fireballs moving with different

velocity vectors (Lazzati amp Begelman 2009) The frag-

ments moving into the direction of the observer will

have the least polarization If the intrinsic brightness of

all the fragments are the same then this would also be

the brightest fragment The fragments making larger

angle with the line of sight on the other hand will have

higher polarization and lower intensity The polariza-

tion angle can sweep randomly between different pulses

in this setting Another prediction of this geometry is

that the PF and PA should not change within a single

pulse In time integrated analysis we also find a change

in polarization with energy One possible explanation

for this is that given the variability seen in the low en-

ergy light curve (100 - 200 keV) the contribution in

this energy range could be from more fragments than

that in the high energy light curve (200 - 300 keV)

The averaging effect thus results in a relatively lower

polarization fraction (maximum PF up to 100 can be

achieved for the fragments viewed at 1Γ where Γ is

the Lorentz factor of a fragment) and a different posi-

tion angle at lower energies in comparison to those in

the high energy band The change in polarization with

time can be explained by temporally separated internal

shocks produced in the different fragments Therefore

the change in polarization from high to low seen in the

100 - 200 keV energy can be explained by considering

the first pulse produced off-axis and the other brighter

pulses near the axis (line of sight) In the high energy

part an increase in polarization with time is observed as

well as the polarization angle are found to anti-correlate

with the low energy counterpart This suggests that the

high energy emission has increased contribution with

time from energetic off-axis fragments

In the fragmented fireball scenario the jet should be

fragmented into small scale (θfragment lt θbeam) The

Lorentz factor Γ0 was calculated from the LAT high

energy afterglows that were produced in the external

shocks If the internal shocks were produced before the

saturation in Lorentz factor was achieved then we can

have a lower value of Lorentz factor when the internal

shocks occur This will allow a little room to increase

θbeam If the internal shocks are produced at small radii

then the velocity vector within the θbeam for a radially

expanding ejecta will also have more divergence in their

direction

We conclude that the polarization results when used

with spectral and temporal information are highly con-

straining Although we cannot decisively select a single

model we find that models with a decrease in polar-

ization with energy are either less probable or contribu-

tions from multiple underlying shocks in different energy

ranges are needed to explain the apparent modulation

with energy Comptonization model has low polariza-

tion at low energies is contradiction with our observa-

tions However independent of emission mechanisms a

geometric model consisting of multiple fragments can

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 20: Draft version February 26, 2019 A twocolumn style in

20 Chand et al

explain the data but demands fragmentation at small

angular scale well within θbeam

ACKNOWLEDGEMENTS

This research has made use of data obtained through

the HEASARC Online Service provided by the NASA-

GSFC in support of NASA High Energy Astrophysics

Programs This publication also uses the data from the

AstroSat mission of the Indian Space Research Organ-

isation (ISRO) archived at the Indian Space Science

Data Centre (ISSDC) CZT-Imager is built by a con-

sortium of Institutes across India including Tata Insti-

tute of Fundamental Research Mumbai Vikram Sarab-

hai Space Centre Thiruvananthapuram ISRO Satellite

Centre Bengaluru Inter University Centre for Astron-

omy and Astrophysics Pune Physical Research Labo-

ratory Ahmedabad Space Application Centre Ahmed-

abad contributions from the vast technical team from

all these institutes are gratefully acknowledged The

polarimetric computations were performed on the HPC

resources at the Physical Research Laboratory (PRL)

We thank Lev Titarchuk for discussions on the grbcomp

model

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Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

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Molinari E Vergani S D Malesani D et al 2007

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Ravasio M E Oganesyan G Ghirlanda G et al 2018

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processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 21: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 21

Table 2 LAT emission (gt 100 MeV) in different time intervals for a fit with a power-law spectrum

Time Index Energy flux Photon flux Test Statistic

(s) ( 10minus9 ergs cmminus2 sminus1) (times10minus7 photons cmminus2 sminus1) (TS)

(0) 0 - 346 minus2 (fixed) lt 144 lt 193 0

(1) 346 - 514 minus235plusmn 033 843plusmn 333 170plusmn 48 39

(2) 514 - 635 minus197plusmn 025 1300plusmn 525 167plusmn 46 85

(3) 635 - 1200 minus195plusmn 025 346plusmn 180 44plusmn 13 62

(4) 1200 - 2150 minus243plusmn 036 123plusmn 048 27plusmn 8 33

(5) 2150 - 6650 minus150plusmn 023 143plusmn 055 90plusmn 14 58

(6) 6650 - 100000 minus2 (fixed) lt 0093 lt 22 9

Table 3 Best fit parameters for power law fits with multiple breaks for the low energy light curve from XRT Power law withtwo breaks is the best fit model

breaks α1 tb1 α2 tb2 α3 tb3 α4

(104 s) (105 s) (105 s)

1 130+007minus008 340+00

minus150 20+00minus00

2 237+032minus017 86+16

minus50 minus095+213minus055 158+157

minus014 185+014minus014

3 237+039minus016 70+00

+30 0+1minus2 18+00

minus04 20+60minus05 80+00

minus60 1+7minus3

Table 4 Spectral fit to the XRT spectra at different time intervals using the power law (PL) model

Time Model nHi αpo CSTATdof

(104 s) PL 1022

Phase 1

(243 - 175) 19+01minus01

Phase 2 027+005minus005

513566

(175 1322) 20+02minus02

Phase 1 PL αpo CSTATdof

(243 258) 145+032minus070

179222

(303 317) 17+01minus01

211246

(359 416) 171+015minus015

204205

(133 175) 19+02minus02

109135

Phase 2

(175 772) 18+02minus02

151188

(85 1322) 14+05minus04

4541

mdash 1999 MNRAS 306 L39

Molinari E Vergani S D Malesani D et al 2007

AampA 469 L13

Narayan R Paczynski B amp Piran T 1992 ApJL 395

L83

Nousek J A Kouveliotou C Grupe D et al 2006 ApJ

642 389

Oganesyan G Nava L Ghirlanda G amp Celotti A

2017 ApJ 846 137

mdash 2018 AampA 616 A138

Omodei N Vianello G amp Ahlgren B 2017 GRB

Coordinates Network Circular Service No 21985

1-2018 (2017) 21985

Page K L Starling R L C Fitzpatrick G et al 2011

MNRAS 416 2078

Poolakkil S amp Meegan C 2017 GRB Coordinates

Network Circular Service No 21992 1-2018 (2017)

21992

Ravasio M E Oganesyan G Ghirlanda G et al 2018

AampA 613 A16

Rees M J amp Meszaros P 1992 MNRAS 258 41P

mdash 1994 ApJL 430 L93

Rybicki G B amp Lightman A P 1979 Radiative

processes in astrophysics

Ryde F 2005 ApJL 625 L95

Sari R amp Piran T 1999 ApJ 520 641

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

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Wang X-G Zhang B Liang E-W et al 2018 ApJ

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Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

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Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 22: Draft version February 26, 2019 A twocolumn style in

22 Chand et al

Table 5 Time-resolved Spectral fitting for different models

Band

Sr no (t1t2) α β Ep (keV) KB pgstatdof

1 -1 7 minus12+01minus01

minus93+194minusinfin 141

+16minus19

0016+0004minus0003

420339

2 7 9 minus110+005minus005

minus88+188minusinfin 222

+28minus23

0029+0004minus0005

284339

3 9 10 minus108+01minus007

minus77+177minusinfin 274

+111minus74

0054+0011minus0009

212339

4 10 12 minus10+01minus01

minus22+02minus05

303+107minus51

0081+0011minus0011

310339

5 12 14 minus090+007minus006

minus23+02minus03

362+72minus52

010+001minus001

311339

6 14 17 minus090+007minus006

minus215+010minus017

329+63minus50

009+001minus001

400339

7 17 18 minus08+01minus01

minus24+02minus04

206+43minus31

018+004minus003

290339

8 18 19 minus08+01minus01

minus240+017minus025

217+27minus23

023+003minus003

210339

9 19 20 minus082+007minus007

minus25+02minus03

241+31minus27

026+003minus003

341339

10 20 24 minus080+003minus003

minus250+008minus001

230+11minus10

033+002minus001

620339

11 24 26 minus100+006minus006

minus26+02minus02

130+10minus9

030+004minus030

443339

12 26 29 minus110+004minus003

minus28+02minus04

196+14minus13

022+001minus001

519339

13 29 30 minus100+007minus006

minus28+03minus16

255+40minus30

022+003minus002

314339

14 30 31 minus100+004minus004

minus94+19494 316

+28minus26

024+002minus001

293339

15 31 32 minus083+005minus005

minus25+02minus03

284+32minus26

035+003minus003

418339

16 32 34 minus082+003minus003

minus25+01minus01

273+17minus15

043+002minus002

506339

17 34 35 minus080+005minus005

minus25+01minus02

264+23minus20

047+004minus003

314339

18 35 36 minus090+005minus005

minus27+02minus05

250+24minus21

040+003minus003

320339

19 36 38 minus080+004minus004

minus26+01minus01

134+7minus6

049+004minus004

480339

20 38 39 minus10+01minus01

minus27+02minus04

101+10minus9

035+007minus005

357339

21 39 41 minus03+03minus03

minus280+005minus006

42+5minus4

259+307minus121

494339

22 41 44 minus125+004minus004

minus3+03minus07

110+7minus6

023+002minus002

612339

23 44 45 minus11+01minus01

minus3+04minusinfin 131

+14minus16

027+005minus004

288339

24 45 46 minus105+005minus005

minus28+03minus11

191+18minus14

032+003minus003

366339

25 46 47 minus10+01minus01

minus25+02minus05

103+15minus12

033+009minus006

356339

26 47 48 minus120+007minus007

minus94+19minusinfin 98

+7minus6

021+003minus003

328339

27 48 50 minus12+02minus01

minus28+04minus12

65+7minus10

017+010minus004

341339

28 50 51 minus11+01minus01

minus29+04minus11

93+11minus11

021+006minus004

291339

29 51 53 minus11+01minus01

minus28+02minus03

99+8minus7

028+004minus003

397339

30 53 55 minus110+005minus004

minus33+06minusinfin 208

+17minus19

021+002minus001

434339

31 55 56 minus100+005minus004

minus41+12minusinfin 248

+22minus21

025+002minus002

329339

32 56 57 minus105+004minus004

minus9+19minusinfin 268

+23minus20

029+002minus002

339339

33 57 58 minus101+004minus004

minus9+19minusinfin 252

+19minus18

036+002minus002

378339

34 58 59 minus100+005minus004

minus29+03minus10

245+25minus21

037+003minus001

390339

35 59 60 minus105+005minus005

minus29+03minus11

233+26minus23

031+003minus002

383339

36 60 61 minus100+006minus006

minus26+02minus06

212+28minus22

037+004minus003

369339

37 61 63 minus100+005minus005

minus25+02minus02

165+13minus12

027+003minus002

421339

38 63 64 minus10+01minus01

minus27+03minus06

141+17minus16

025+005minus004

305339

39 64 65 minus10+01minus01

minus28+03minusinfin 154

+24minus16

029+004minus004

316339

40 65 67 minus100+004minus004

minus28+02minus03

165+11minus10

039+003minus003

551339

41 67 68 minus104+006minus006

minus3+03minus1

137+12minus11

039+005minus004

415339

42 68 69 minus103+005minus005

minus3+03minus07

153+12minus12

049+005minus004

382339

43 69 70 minus10+02minus01

minus230+013minus015

87+13minus16

043+023minus009

389339

44 70 71 minus108+006minus006

minus280+025minus064

140+15minus12

034+004minus004

379339

45 71 72 minus100+004minus002

minus9+19minusinfin 158

+8minus4

046+003minus003

363339

46 72 73 minus102+009minus008

minus28+03minus04

93+8minus8

039+008minus006

316339

47 73 74 minus09+08minus02

minus24+02minus02

56+12minus19

045+179minus018

315339

48 74 76 minus110+007minus006

minus28+02minus03

89+6minus6

0331+005minus004

506339

49 76 77 minus11+01minus01

minus29+04minus07

84+9minus8

027+007minus005

313339

50 77 78 minus03+05minus09

minus21+01minus08

47+57minus8

168+371minus168

318339

51 78 82 minus12+01minus01

minus26+02minus02

75+6minus7

015+003minus002

500339

52 82 84 minus11+01minus01

minus24+02minus02

139+15minus14

020+003minus002

441339

53 84 85 minus11+02minus01

minus270+035minusinfin 109

+28minus17

011+004minus003

252339

54 85 90 minus12+02minus01

minus26+03minus01

76+7minus14

013+008minus002

560339

55 90 101 minus12+01minus01

minus24+02minus03

83+9minus10

006+002minus001

529339

56 101 113 minus130+008minus007

minus30+04minus10

86+8minus8

004+001minus001

506339

57 113 136 minus13+01minus01

minus3+05minus08

66+4minus6

0036+0008minus0004

676339

58 136 137 minus13+01minus01

minus9+19minusinfin 83

+13minus10

008+003minus002

266339

59 137 150 minus13+01minus01

minus3+04minusinfin 66

+5minus5

004+001minus001

491339

60 150 171 minus11+14minus03

minus23+02minus02

33+8minus12

004+026minus002

382339

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β K pgstatdof

1 -1 7 [minus30] 123+02minus11

16+06minus06

256+47minus122

7+infinminus4

00001+0002minus000004

408337

2 7 9 [minus30] 127+18minus20

14+01minus01

142+59minus28

24+06minus03

00002+00002minus000007

275338

3 9 10 09+07minus05

17+infinminus17

13+01minus01

194+73minus51

25+07minus04

5+29minus5

215338

4 10 12 minus05+05minusinfin 170

+12minus15

125+005minus004

170+41minus23

21+01minus01

014+002minus001

287338

5 12 14 02+06minus07

18+5minus4

120+004minus005

212+52minus27

22+01minus01

09+26minus09

315337

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

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751 90

Page 23: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 23

Table 5 Time-resolved Spectral fitting (continued)

Broken power-law

Sr no (t1t2) α1 E1 (keV) α2 E2 (keV) β Kb pgstatdof

6 14 17 minus1+1minus1

16+3minus2

120+005minus004

185+50minus22

21+01minus01

0023+0296minus0023

373337

7 17 18 minus08+0808 15

+2minus2

110+007minus006

124+23minus13

22+01minus01

011+003minus002

288338

8 18 19 04+03minus04

19+infinminus19

100+006minus006

1380+223minus154

22+01minus01

298+478minus298

218338

9 19 20 minus02+08minus09

17+4minus4

110+005minus005

146+14minus12

23+01minus01

067+473minus067

337337

10 20 24 minus02+04minus07

17+2minus2

110+002minus002

158+8minus8

230+005minus005

080+143minus066

611337

11 24 26 minus08+12minus08

15+5minus2

140+006minus004

118+10minus9

25+01minus01

025+207minus025

386337

12 26 29 02+03minus05

18+2minus1

150+002minus002

352+24minus26

53+08minus06

0013+0001minus0001

571337

13 29 30 minus13+12minus08

155+25minus15

130+004minus004

205+30minus28

26+02minus02

0044+0490minus0044

283337

14 30 31 minus01+05minus06

15+infinminus15

120+003minus003

177+16minus14

24+01minus01

116+350minus116

298338

15 31 32 minus06+04minus05

167+infinminus167

110+003minus003

1860+204minus173

23+01minus01

035+070minus035

408338

16 32 34 minus02+04minus08

180+27minus23

110+003minus003

1750+13minus11

230+006minus005

109+217minus109

485337

17 34 35 006+040minus060

19+4minus4

110+004minus004

174+15minus13

23+01minus01

215+408minus215

317337

18 35 36 01+04minus07

18+3minus3

110+004minus003

159+14minus12

24+01minus01

231+452minus231

319337

19 36 38 minus03+04minus06

17+14minus15

130+003minus003

116+7minus6

250+007minus007

110+169minus110

386337

20 38 39 minus03+05minus10

17+2minus2

160+005minus005

114+16minus13

27+02minus02

094+266minus094

294337

21 39 41 03+03minus03

190+15minus14

180+004minus005

126+22minus22

3+03minus03

524+523minus310

391337

22 41 44 minus06+02minus03

15+infinminus15

160+002minus002

133+11minus10

280+014minus014

051+044minus029

443338

23 44 45 [minus25] 123+06minus07

140+004minus004

108+13minus11

25+02minus01

0005+0001minus0001

271338

24 45 46 [minus20] 144+06minus06

140+003minus003

169+16minus21

26+02minus02

0013+0002minus0001

292338

25 46 47 [minus30] 130+05minus05

150+004minus005

110+12minus17

25+02minus02

0001200002minus00002 313338

26 47 48 [minus30] 130+06minus06

160+004minus005

121+17minus14

30+03minus03

000128+00003minus00002

290338

27 48 50 [minus30] 126+04minus04

180+004minus005

104+13minus23

30+04minus04

000114+00002minus00002

288338

28 50 51 [minus30] 133+07minus07

160+006minus006

109+20minus17

28+04minus03

000085+00002minus00002

255338

29 51 53 minus08+08minus10

150+16minus14

160+004minus004

113+15minus13

27+02minus02

024+153minus024

335337

30 53 55 [minus30] 13+04minus04

140+003minus003

157+17minus14

25+01minus01

00011+00002minus00001

370338

31 55 56 minus02+06minus07

17+3minus3

130+004minus004

200+31minus24

26+02minus02

088+329minus088

309337

32 56 57 minus12+15minus09

14+4minus1

130+004minus003

177+19minus15

25+01minus01

009+096minus009

330337

33 57 58 minus06+1minus08

150+31minus23

130+003minus003

169+15minus13

250+014minus012

056+212minus056

359337

34 58 59 minus06+09minus05

150+30minus23

130+003minus003

168+14minus12

24+01minus01

057+299minus057

366337

35 59 60 04+03minus04

210+34minus28

140+004minus004

211+36minus25

26+02minus01

593+667minus402

364337

36 60 61 02+04minus05

190+30minus23

140+004minus003

166+14minus13

24+01minus01

340+585minus258

330337

37 61 63 [minus3] 130+05minus05

130+003minus003

120+9minus9

23+01minus01

00012+00002minus00002

375338

38 63 64 minus14+14minusinfin 14

+1minus1

130+005minus005

120+15minus13

250+016minus015

004+0007minus0005

283338

39 64 65 040+035minus040

21+5minus3

150+006minus005

164+23minus26

27+02minus02

451+711minus304

289337

40 65 67 minus08+07minus10

153+19minus16

100+003minus003

132+10minus9

250+008minus008

032+168minus032

461337

41 67 68 minus05+07minus1

160+21minus16

140+004minus004

130+14minus14

26+02minus02

081+382minus081

366337

42 68 69 02+04minus06

18+3minus4

14+005minus01

146+18minus30

26+02minus03

5+10minus5

340337

43 69 70 minus007+04minus05

170+18minus17

160+005minus005

109+18minus16

24+01minus01

215+462minus215

334337

44 70 71 005+030minus050

18+2minus2

15+004minus004

154+20minus18

27+02minus02

262+364minus2624

301337

45 71 72 minus02+05minus05

17+18minus16

140+003minus003

149+12minus10

28+02minus01

159+397minus159

307337

46 72 73 03+03minus05

182+22minus20

160+005minus005

105+10minus9

270+014minus020

557+805minus557

275337

47 73 74 04+03minus09

18+2minus5

18+01minus02

110+31minus44

27+03minus04

560812minus560 278337

48 74 76 minus01+04minus08

16+15minus17

16+004minus005

108+12minus15

27+02minus02

186362minus186 410337

49 76 77 04+04minus05

19+3minus2

170+006minus005

129+15minus17

30+04minus03

452+812minus452

285337

50 77 78 minus1+1minus1

150+33minus16

170+006minus006

136+21minus34

30+04minus03

018+352minus018

271337

51 78 82 03+03minus05

173+15minus17

180+004minus004

108+12minus10

27+02minus02

291+358minus215

381337

52 82 84 minus13+09minus09

150+15minus11

150+004minus004

128+20minus15

24+02minus01

006+057minus006

352337

53 84 85 03+06minus08

170+44minus53

16+01minus01

119+23minus24

26+04minus03

215+485minus215

238337

54 85 90 minus02+06minus08

16+2minus2

180+004minus005

118+15minus21

28+02minus02

071227minus071 462337

55 90 101 [minus2] 127+04minus04

160+003minus005

101+13minus23

25+02minus03

000456000054minus000046 470338

56 101 113 [minus3] 128+04minus04

170+003minus003

122+14minus12

29+03minus03

000027+000004minus000003

403338

57 113 136 [minus30] 1220+004minus030

18+003minus006

97+15minus15

29+04minus03

00003+0000005minus000003

556337

58 136 137 [minus30] 124+09minus10

180+007minus006

181+51minus68

51+infinminus22

00008+00003minus00002

256338

59 137 150 [minus30] 116+01minus04

170+004minus004

94+12minus10

29+04minus02

00004+000001minus000006

449337

60 150 171 04+08minus08

140+4minus15

20+01minus01

95+39minus62

29+08minus06

093+578minus093

372337

b photons keVminus1 cmminus2 sminus1 at 1 keV

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

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Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

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Zhang B-B Uhm Z L Connaughton V Briggs M S

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Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 24: Draft version February 26, 2019 A twocolumn style in

24 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

BB+Band

Sr no (t1t2) α β Ep (keV) KB kTBB (keV) KBB pgstatdof

1 -1 7 minus09+05minus03

minus94+19minusinfin 153

+34minus23

002+001minus001

65+24minus16

050+039minus034

414337

2 7 9 001+180minus090

minus24+03minusinfin 149

+68minus34

008+036minus005

55+13minus11

136+078minus081

276337

3 9 10 minus11+02minus02

minus9+19minusinfin 299

+191minus41

005+001minus001

13+infinminus8

073+200minus073

212337

4 10 12 minus04+04minus04

minus21+01minus02

215+81minus34

012+006minus004

70+15minus10

255+078minus103

296337

5 12 14 minus08+02minus03

minus22+01minusinfin 331

+383minus59

010+002minus004

72+infinminus31

079+105minus079

309337

6 14 17 minus05+04minus02

minus21+01minus01

260+66minus54

011+005minus002

80+15minus11

209+106minus088

383337

7 17 18 minus05+05minus02

minus23+02minus03

185+51minus34

022+017minus004

7+7minus2

213+220minus190

287337

8 18 19 minus07+03minus04

minus24+02minusinfin 219

+219minus34

023+008minus012

10+infinminus10

120+224minus120

209337

9 19 20 minus06+05minus02

minus24+02minus03

218+42minus41

031+017minus006

70+30minus15

316+299minus221

335337

10 20 24 minus05+01minus01

minus24+01minus01

212+14minus12

039+004minus004

73+08minus06

426+119minus114

579337

11 24 26 minus01+04minus03

minus25+01minus01

122+10minus9

063+041minus019

60+04minus04

779+214minus194

390337

12 26 29 minus08+01minus01

minus100+00minusinfin 196

+8minus7

025+002minus002

60+05minus05

455+099minus094

458337

13 29 30 minus05+01minus02

minus26+02minus03

213+33minus21

030+011minus006

70+09minus08

563+214minus208

293337

14 30 31 minus07+02minus02

minus30+02minus06

256+59minus31

029+006minus004

57+15minus12

274+203minus137

289337

15 31 32 minus06+02minus02

minus24+01minus02

254+38minus30

040+008minus006

74+23minus15

414+257minus236

409337

16 32 34 minus05+01minus01

minus24+01minus01

241+20minus18

052+007minus005

80+07minus06

767+213minus200

460337

17 34 35 minus05+02minus01

minus24+01minus01

241+27minus26

054+011minus007

77+16minus12

562+314minus278

302337

18 35 36 minus06+03minus02

minus26+02minus03

224+32minus30

046+013minus007

67+19minus12

425+303minus256

313337

19 36 38 01+04minus03

minus25+01minus01

122+8minus7

123+070minus036

60+03minus03

1135+250minus235

400337

20 38 39 03+1minus06

minus27+02minus02

1030+105minus95

121+303minus061

59+04minus04

1189+333minus313

305337

21 39 41 minus04+05minus03

minus28+02minus03

99+8minus9

050045minus016 60+04minus03

1120+222minus193

399337

22 41 44 minus04+03minus02

minus28+02minus02

116+7minus7

049+020minus011

55+02minus02

1036+160minus148

456337

23 44 45 minus05+05minus04

minus26+02minus03

116+17minus12

052+049minus019

50+08minus06

601+302minus289

276337

24 45 46 minus04+02minus01

minus25+01minus02

167+16minus9

053+006minus010

65+04minus05

1077+156minus148

317337

25 46 47 minus02+08minus05

minus25+02minus03

107+16minus13

070+117minus031

60+07minus05

929+336minus290

320337

26 47 48 minus03+07minus05

minus31+04minusinfin 108

+14minus10

045+051minus019

57+06minus05

826+263minus273

293337

27 48 50 minus03+11minus05

minus28+03minus06

81+8minus6

042+175minus021

495+040minus034

587+205minus180

303337

28 50 51 01+13minus07

minus28+03minus06

99+13minus12

067+282minus038

55+05minus05

690+259minus259

268337

29 51 53 minus04+03minus03

minus27+02minus02

100+8minus7

058+029minus017

50+infinminus01

653+143minus177

354337

30 53 55 minus07+02minus02

minus27+02minus04

177+21minus17

029+007minus005

60+06minus05

509+156minus155

402337

31 55 56 minus07+02minus01

minus4+1minusinfin 241

+23minus26

028+005minus003

7+1minus1

548+213minus198

307337

32 56 57 minus09+01minus01

minus9+19minusinfin 267

+23minus20

0305+0065minus0022

75+14minus12

487+221minus212

325337

33 57 58 minus08+02minus01

minus31+05minusinfin 234

+25minus25

041+007minus005

7+1minus1

684+257minus249

356337

34 58 59 minus07+02minus02

minus26+02minus04

219+29minus23

044+009minus006

7+1minus1

737+283minus267

367337

35 59 60 minus08+02minus01

minus28+03minus06

225+31minus26

034+006minus004

8+1minus1

639+238minus224

359337

36 60 61 minus06+03minus02

minus25+014minus03

190+35minus20

048+014minus010

70+10minus07

953+305minus275

330337

37 61 63 minus05+04minus03

minus240+012minus015

143+17minus15

046+024minus012

57+05minus04

583+204minus188

389337

38 63 64 minus04+06minus04

minus25+02minus02

130+22minus18

041+040minus014

60+13minus08

468+249minus228

293337

39 64 65 minus080+040minus015

minus34+0834 182

+25minus34

028+015minus005

84+14minus15

731+235minus224

285337

40 65 67 minus03+02minus02

minus26+01minus01

146+10minus9

069+019minus013

63+03minus02

1053+200minus198

464337

41 67 68 minus04+04minus03

minus27+02minus03

132+13minus11

066+034minus017

60+06minus05

1057+319minus293

373337

42 68 69 minus06+03minus02

minus27+02minus04

147+15minus13

069+024minus014

64+07minus05

1130+322minus300

336337

43 69 70 minus015+11minus05

minus24+01minus02

97+18minus15

096+277minus051

60+07minus04

1153+410minus346

345337

44 70 71 minus05+03minus02

minus27+02minus03

141+14minus13

053+023minus012

60+05minus05

1114+270minus253

318337

45 71 72 minus05+02minus02

minus32+03minus10

153+10minus10

065+017minus011

60+06minus05

1067+290minus284

317337

46 72 73 01+11minus06

minus27+02minus03

97+10minus8

125344minus067 60+04minus04

1190+422minus381

276337

47 73 74 01+infinminus06

minus26+02minus02

81+10minus9

104+029minus003

52+04minus03

973+128minus047

275337

48 74 76 01+08minus04

minus27+02minus02

95+7minus8

114+226minus049

55+03minus03

1156+280minus238

413337

49 76 77 minus05+05minus04

minus3+03minus07

98+11minus9

040+036minus015

60+09minus06

666+254minus230

290337

50 77 78 minus05+06minus04

minus28+03minus06

111+15minus13

038+042minus014

62+07minus05

902+262minus252

275337

51 78 82 00+07minus04

minus27+02minus02

91+6minus6

049+066minus021

50+02minus02

657+123minus120

386337

52 82 84 minus03+05minus03

minus2+01minus02

131+15minus15

038028minus011 60+05minus04

661+167minus155

380337

53 84 85 04+40minus10

minus26+03minus04

104+17minus19

054+6034minus036

55+08minus06

513+204minus206

235337

54 85 90 minus03+1minus04

minus26+02minus02

91+8minus11

031+043minus012

53+03minus03

464+139minus097

463337

55 90 101 minus02+45minus04

minus25+02minus02

88+101minus20

017+7502minus008

5+03minus03

202+119minus053

477337

56 101 113 minus03+05minus04

minus3+03minus05

100+10minus8

009+008minus003

5+03minus03

169+036minus036

441337

57 113 136 025minus025minus090

minus26+02minus06

72+11minus11

027+4062minus019

45+02minus02

165+056minus046

610337

58 136 137 minus08+06minus04

minus93+1993 103

+18minus15

011+0102minus004

50+08minus07

285+171minus170

257337

59 137 150 minus05+07minus04

minus3+03minus06

79+6minus6

010+015minus004

40+03minus03

140+049minus047

463337

60 150 171 minus11+11minus04

minus28+05minusinfin 63

+16minus24

002+036minus001

4+1minus1

057+084minus030

374337

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 25: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 25

Table 5 Time-resolved Spectral fitting (continued)

grbcomp

Sr no (t1t2) kTs (keV) kTe (keV) τ δ αb Rph (1010) cm pgstatdof

1 -1 7 [53] 90+4minus14

[32] 150 plusmn minus005 30+infinminus24

87+02minus03

412339

2 7 9 [41] 77+20minus32

40+15minus09

180 plusmn 007 26+infinminus13

17+1minus1

281338

3 9 10 [45] 78+40minus32

4+1minus1

170 plusmn 006 18+16minus07

20+1minus1

213338

4 10 12 77+15minus18

117+90minus62

30+21minus08

120 plusmn 003 14+06minus03

10+6minus2

287337

5 12 14 65+17minus26

86+30minus22

4+1minus1

160 plusmn 005 1302minus02 14+17minus4

305337

6 14 17 81+15minus17

91+45minus31

36+15minus08

150 plusmn 005 12+02minus01

9+4minus2

371337

7 17 18 [7] 57+32minus18

50+27minus14

240 plusmn 013 14+04minus02

147+03minus03

283338

8 18 19 [6] 58+16minus12

5+1minus1

236 plusmn 012 14+03minus02

216+04minus04

207338

9 19 20 74+17minus23

62+19minus16

45+20minus10

220 plusmn 010 15+03minus02

17+16minus4

329337

10 20 24 73+07minus08

63+7minus6

48+05minus04

22 plusmn 01 15+01minus01

19+4minus2

551337

11 24 26 76+07minus07

355+115minus93

7+15minus2

38 plusmn 03 16+03minus02

17+3minus2

386337

12 26 29 68+05minus05

530+98minus78

50+10minus07

26 plusmn 014 170+02minus015

20+3minus2

462337

13 29 30 77+11minus12

69+22minus17

45+15minus09

20 plusmn 01 17+04minus02

16+6minus3

286337

14 30 31 63+11minus15

672+137minus101

49+09minus07

20 plusmn 01 16+03minus02

23+16minus5

285337

15 31 32 71+13minus15

743+153minus126

45+08minus06

183 plusmn 007 15+02minus01

21+11minus4

397337

16 32 34 83+08minus09

71+10minus9

46+06minus05

19 plusmn 01 15+01minus01

19+4minus2

437337

17 34 35 76+13minus16

68+12minus11

48+10minus06

2 plusmn 01 15+02minus01

22+11minus4

291337

18 35 36 70+12minus15

64+12minus11

50+10minus07

2 plusmn 01 16+02minus02

24+14minus5

304337

19 36 38 80+05minus06

300+64minus52

126+infinminus53

45 plusmn 05 16+01minus01

18+2minus8

395337

20 38 39 75+05minus05

285+26minus25

[10] 47 plusmn 05 18+02minus02

18+2minus2

302338

21 39 41 70+05minus05

50+25minus20

38+25minus09

27 plusmn 02 24+17minus06

20+3minus2

388337

22 41 44 70+04minus04

40+10minus84

58+27minus12

34 plusmn 03 20+03minus03

21+2minus2

448337

23 44 45 60+09minus13

42+18minus15

50+51minus13

32 plusmn 02 18+06minus03

25+14minus5

271337

24 45 46 78+08minus08

54+16minus13

50+23minus11

25 plusmn 01 17+04minus02

19+4minus3

310337

25 46 47 7+1minus1

47+32minus23

44+116minus14

29 plusmn 02 19+11minus04

20+7minus3

314337

26 47 48 7+1minus1

47+25minus18

50+62minus14

29 plusmn 02 28+infinminus09

19+6minus3

290337

27 48 50 61+07minus08

33+24minus17

5+infinminus2

41 plusmn 04 22+21minus06

20+6minus3

302337

28 50 51 7+1minus1

27+24minus8

11+infinminus7

51 plusmn 06 20+13minus04

16+6minus2

267337

29 51 53 68+06minus07

43+16minus13

48+3minus11

31 plusmn 02 22+08minus04

20+5minus3

335337

30 53 55 64+06minus07

64+14minus12

43+09minus06

21 plusmn 01 19+04minus03

23+5minus3

387337

31 55 56 72+11minus15

85+20minus18

39+08minus05

160 plusmn 006 23+12minus05

19+8minus3

301337

32 56 57 67+11minus13

83+20minus17

38+07minus05

160 plusmn 006 20+06minus03

24+11minus4

317337

33 57 58 69+10minus13

78+16minus14

40+07minus05

175 plusmn 007 21+06minus04

25+11minus4

349337

34 58 59 70+10minus11

72+15minus13

42+08minus06

19 plusmn 01 18+03minus02

24+9minus4

359337

35 59 60 69+10minus12

86+20minus18

35+06minus05

160 plusmn 006 20+05minus03

23+101minus4

345337

36 60 61 75+10minus12

81+25minus21

35+10minus06

167 plusmn 006 18+05minus03

21+7minus3

315337

37 61 63 67+07minus07

44+12minus10

56+25minus11

31 plusmn 02 15+02minus02

21+5minus3

378337

38 63 64 66+11minus14

45+20minus16

5+5minus1

30 plusmn 02 17+06minus03

19+11minus4

288337

39 64 65 73+12minus18

827+30minus252

33+1minus06

160 plusmn 006 25+25minus07

19+7minus4

277337

40 65 67 75+05minus06

47+10minus9

55+18minus1

29 plusmn 02 17+02minus02

21+3minus2

447337

41 67 68 71+07minus08

49+16minus13

5+24minus11

28 plusmn 02 20+06minus03

23+6minus3

366337

42 68 69 70+07minus08

57+16minus14

43+13minus07

24 plusmn 01 20+06minus03

26+6minus3

323337

43 69 70 66+07minus1

75+42minus47

29+43minus07

18 plusmn 01 20+13minus06

24+8minus3

335337

44 70 71 74+07minus08

56+21minus16

42+20minus09

24 plusmn 01 20+07minus03

21+4minus3

308337

45 71 72 72+07minus07

56+10minus95

48+1minus07

24 plusmn 01 24+07minus04

24+5minus3

306337

46 72 73 74+07minus09

26+18minus62

118minus12minus7

52 plusmn 06 19+05minus02

20+5minus2

274337

47 73 74 70+05minus06

230+33minus32

[10] 60 plusmn 08 17+03minus02

20+3minus2

275338

48 74 76 72+05minus05

250+117minus64

128+infinminus72

55 plusmn 06 18+02minus02

minus20+3minus2

406337

49 76 77 67+09minus13

45+28minus21

43+64minus125

30 plusmn 02 24+37minus07

19+10minus3

284337

50 77 78 72+09minus1

52+34minus27

40+84minus12

26 plusmn 02 23+4minus07

18+5minus3

270337

51 78 82 [7] 24+82minus55

11+infinminus5

57 plusmn 07 2+02minus02

153+02minus02

384338

52 82 84 74+07minus07

384+171minus123

6+86minus19

35 plusmn 03 14+03minus02

16+3minus2

375337

53 84 85 7+1minus1

38+6minus6

[6] 36 plusmn 03 20+08minus05

14+4minus2

237338

54 85 90 66+05minus05

32+19minus15

58+infinminus2

42 plusmn 04 20+06minus03

15+2minus2

462337

55 90 101 61+04minus04

30+34minus34

[6] 45 plusmn 04 17+03minus02

12+2minus1

473338

56 101 113 65+06minus06

39+20minus15

50+83minus16

35 plusmn 03 22+15minus05

9+2minus1

437337

57 113 136 58+05minus05

25+17minus10

78+infinminus34

20 plusmn 01 19+10minus04

11+2minus1

603337

58 136 137 58+1minus2

67+26minus26

35+19minus08

20 plusmn 01 30+infinminus27

17+18minus4

256337

59 137 150 56+06minus07

28+16minus12

66+160minus23

48 plusmn 05 22+14minus05

12+4minus2

462337

60 150 171 45+09minus17

61+146minus50

30+21minus13

22 plusmn 01 34+infinminus20

13+19minus3

372337

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 26: Draft version February 26, 2019 A twocolumn style in

26 Chand et al

Table 5 Time-resolved Spectral fitting (continued)

Synchrotron model

Sr no (t1t2) γmγc Ec (keV) p pgstatdof

1 -1 7 36+05minus14

182+34minus57

gt 304 420339

2 7 9 37+35minus21

296+220minus121

gt 233 286339

3 9 10 35+08minus21

412+150minus132

gt 243 214339

4 10 12 50+14minus16

452+87minus65

gt 298 296339

5 12 14 41+07minus13

698+124minus89

gt 318 302339

6 14 17 48+13minus18

605+113minus74

gt 269 384339

7 17 18 26+09minus21

624+1258minus113

gt 286 285339

8 18 19 18+08minus08

819+1507minus192

393+089minus087

207339

9 19 20 19+08minus09

848+1463minus179

gt 341 334339

10 20 24 16+01minus01

895+1337minus105

388+054minus037

602339

11 24 26 23+03minus07

354+73minus23

gt 328 434339

12 26 29 33+01minus03

328+09minus26

gt 424 558339

13 29 30 31+06minus07

517+107minus69

gt 381 311339

14 30 31 23+05minus04

776+119minus121

gt 413 298339

15 31 32 23+04minus05

909+205minus64

gt 409 406339

16 32 34 18+03minus01

994+192minus104

gt 362 485339

17 34 35 15+06minus02

1137+2009minus199

gt 337 304339

18 35 36 21+02minus08

814+858minus53

gt 433 314339

19 36 38 17+00minus07

629+12minus126

360+034minus027

478339

20 38 39 23+05minus07

261+60minus43

gt 356 347339

21 39 41 27+01minus06

155+25minus14

gt 367 470339

22 41 44 35+02minus03

149+18minus09

gt 455 572339

23 44 45 24+01minus06

302+65minus33

gt 377 285339

24 45 46 29+01minus04

376+24minus52

gt 389 364339

25 46 47 28+05minus08

229+49minus34

gt 341 339339

26 47 48 25+01minus05

197+14minus34

gt 399 321339

27 48 50 27+01minus08

132+32minus17

gt 345 326339

28 50 51 20+02minus06

263+60minus65

gt 358 287339

29 51 53 25+01minus05

230+39minus12

gt 399 378339

30 53 55 35+04minus05

301+40minus28

gt 428 446339

31 55 56 26+01minus04

533+62minus85

gt 404 345339

32 56 57 30+05minus05

473+73minus53

gt 420 351339

33 57 58 28+04minus05

508+78minus54

gt 410 392339

34 58 59 28+04minus04

507+64minus57

gt 405 397339

35 59 60 33+06minus04

405+48minus48

gt 413 374339

36 60 61 32+04minus05

407+49minus41

gt 405 346339

37 61 63 29+01minus06

360+42minus11

gt 366 414339

38 63 64 22+03minus15

395+698minus66

gt 302 302339

39 64 65 27+05minus06

340+64minus47

gt 390 300339

40 65 67 25+05minus03

400+18minus31

gt 439 531339

41 67 68 25+01minus04

314+40minus43

gt 398 406339

42 68 69 27+03minus04

333+45minus34

gt 401 367339

43 69 70 29+01minus08

195+41minus22

gt 342 361339

44 70 71 31+04minus05

254+40minus30

gt 392 358339

45 71 72 20+01minus03

447+63minus56

gt 454 372339

46 72 73 22+04minus06

250+53minus37

gt 377 305339

47 73 74 25+07minus09

149+58minus33

gt 297 303339

48 74 76 25+01minus04

205+29minus16

gt 396 481339

49 76 77 23+05minus08

214+62minus41

gt 340 303339

50 77 78 28+01minus08

177+42minus23

gt 336 300339

51 78 82 29+06minus07

136+25minus17

gt 331 465339

52 82 84 32+10minus10

240+44minus34

gt 268 427339

53 84 85 31+04minus13

192+82minus38

gt 298 250339

54 85 90 28+01minus06

150+25minus13

gt 360 524339

55 90 101 32+02minus11

142+32minus13

gt 295 511339

56 101 113 33+02minus07

128+23minus12

gt 352 485339

57 113 136 29+01minus06

113+19minus17

gt 372 654339

58 136 137 30+12minus10

130+18minus46

gt 339 265339

59 137 150 30+08minus06

112+24minus12

gt 370 485339

60 150 171 21+16minus17

76+155minus33

gt 256 378339

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90

Page 27: Draft version February 26, 2019 A twocolumn style in

Variable prompt emission polarization in GRB 171010A 27

Sari R Piran T amp Narayan R 1998 ApJL 497 L17

Scargle J D Norris J P Jackson B amp Chiang J 2013

ApJ 764 167

Tavani M 1996 ApJ 466 768

Tierney D McBreen S Preece R D et al 2013 AampA

550 A102

Titarchuk L Farinelli R Frontera F amp Amati L 2012

ApJ 752 116

Vadawale S V Chattopadhyay T Rao A R et al

2015 Astronomy amp Astrophysics 578 73

Vadawale S V Chattopadhyay T Mithun N P S et al

2017 Nature Astronomy doi101038s41550-017-0293-z

Vianello G Gill R Granot J et al 2017 ArXiv

e-prints arXiv170601481

Vurm I amp Beloborodov A M 2016 ApJ 831 175

Wang X-G Zhang B Liang E-W et al 2018 ApJ

859 160

Wang Y-Z Wang H Zhang S et al 2017 ApJ 836 81

Willingale R Starling R L C Beardmore A P Tanvir

N R amp OrsquoBrien P T 2013 MNRAS 431 394

Woosley S E amp Bloom J S 2006 ARAampA 44 507

Zhang B Fan Y Z Dyks J et al 2006 ApJ 642 354

Zhang B amp Yan H 2011 ApJ 726 90

Zhang B-B Uhm Z L Connaughton V Briggs M S

amp Zhang B 2016 ApJ 816 72

Zhang B-B Zhang B Castro-Tirado A J et al 2018

Nature Astronomy 2 69

Zheng W Shen R F Sakamoto T et al 2012 ApJ

751 90