Recent Advances in our Understanding of GRB emission mechanism

Pawan Kumar

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Outline†

Constraints on radiation mechanisms♪

High energy emission from GRBs and High energy emission from GRBs and our understanding of Fermi data.our understanding of Fermi data.

♪My goal is to generate a good discussion of this topic

Moscow, October 9, 2013

central engine

relativistic outflow

Jet energy dissipation

and γ-ray generation

External shock

radiation

central engine jet -rays

A good fraction of >102MeV photons appear to be generated in external shock; (photo-pion & other hadronic processes might also contribute for ~30s or so)

Understanding the radiation mechanism for ~10keV – 10 MeV band is one of the most challenging problems in GRBs.

Emission in this band lasts for <102s, however it carries a good fraction of the total energy release in GRBs.

And it offers the best link to the GRB central engine.

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Internal/external shocks, magnetic reconnection etc.Internal/external shocks, magnetic reconnection etc.

Conversion of jet energy to thermal energy Conversion of jet energy to thermal energy

Radiation mechanism (sub-MeV photons)Radiation mechanism (sub-MeV photons)

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•1. Synchrotron 2. SSC (or IC of external photons) 1. Synchrotron 2. SSC (or IC of external photons) 3. 3. photospheric mechanismphotospheric mechanism……

Piran et al. ; Rees & Meszaros; Dermer;Thompson; Lyubarsky; Blandford, Lyutikov;Spruit…

Papathanassiou & Meszaros, 1996; Sari, Narayan & Piran, 1996; Liang et al. 1996; Ghisellini et al. 2000; Thompson (1994); Lazzati et al. (2000); Medvedev (2000); Meszaros & Rees 1992-2007; Totani 1998; Paczynski & Xu 1994; Zhang & Meszaros 2000; Meszaros & Rees 1994; Pilla & Loeb 1996; Dermer et al. 2000; Wang et al. 2001 & 06; Zhang & Meszaros 2001; Sari & Esin 01’; Granot & Guetta 2003; Piran et al. 2004; Fan et al. 2005 & 08; Beloborodov 2005; Fan & Piran 2006; Galli & Guetta 2008; Pe’er et al. 06; Granot et al. 08; Bošnjak, Daigne & Dubus 09; Katz 1994; Derishev et al. 1999; Bahcall & Meszaros 2000; Dermer & Atoyan 2004; Razzaque & Meszaros 2006; Fan & Piran 2008; Gupta & Zhang 2008; Granot et al. 08; Daigne, Bošnjak & Dubus 2011 …

Energy dissipation: internal shocks (current paradigm)

Gehrels et al. (2002); Scientific American

(Prof. Bosnjak will talk about this model in detail)

Distance (Rs) of γ-ray source from the center of explosion

1.1. Steep decline of flux at end of GRB prompt phaseSteep decline of flux at end of GRB prompt phase suggests: Rsuggests: Rs s ≈ 2c≈ 2c22δδt ~ 10t ~ 101616cmcm (Lyutikov; Lazzati & Begelman; Kumar et al.)(Lyutikov; Lazzati & Begelman; Kumar et al.) ((RRss can be smaller if the steep decline is due to central can be smaller if the steep decline is due to central engine activityengine activity))

2. Prompt bright optical flash from GRBs: Rs 1016cm (GRB 080319B – Zou, Piran & Sari 2009(GRB 080319B – Zou, Piran & Sari 2009))~>

tt-5-5 (Too steep to be RS) (Too steep to be RS)

(RS)

Kumar & Kumar & Panaitescu, 09Panaitescu, 09

GR

B 0

8031

9B:

x-ra

y &

op

tica

l LC

s

Prompt Prompt -ray emission from-ray emission fromGRB 080319B also suggestsGRB 080319B also suggests Rs 1016cm; Kumar & Narayan;; Racusin et al. 2008

~>

Shen & Zhang (2009) provide alimit on Rs from prompt opticalfor a number of GRBs.

(This would help determine if radiation mechanism is photospheric or not)

3. Detection of high energy 3. Detection of high energy -ray photons by Fermi/LAT-ray photons by Fermi/LAT

(GRB 080916C…) 103 Rs = 2cΓ2δt 1016cm~~>>~~>>

However, Zou, Fan & Piran (2011), Hascoet et al. (2012) suggest Γ~300 However, Zou, Fan & Piran (2011), Hascoet et al. (2012) suggest Γ~300

This implies Rs~1015 cm, and that is still much larger than photospheric radius (~1012 cm) – this is for MeV photon emission and δt ~ 0.1 s.

So the photospheric radiation is not the correct mechanism for MeV γ-rays at least for some GRBs

GRB 080916C, a very bright Fermi burst, had a very stringent upper limit on thermal component (Zhang & Pe’er, 2009).

Incidentally, Γ>103 would rule out baryonic and leptopic thermal fireball model for GRBs since Γmax ~ 850 L52

1/4 R0,7-1/4;

where R0 the jet launching radius.

MeV γ-ray radiation mechanismMeV γ-ray radiation mechanism

1. SynchrotronSynchrotron

Synchrotron peak at ~102 kev Bi2 ~ 2x1013

Electron cooling

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ttcool cool = ~ (7x10= ~ (7x10−7−7 s) s) i3i333 2 2 « « t ~ 0.1st ~ 0.1s

66mmeec(1+z)c(1+z)——————————TTBB22i i

ff −1/2−1/2 (or (or αα = −1.5) = −1.5) which holds for only a small fraction of GRBswhich holds for only a small fraction of GRBs

This is basically Ghisellini et al. (2000) argument; Sari & Piran 1997This is basically Ghisellini et al. (2000) argument; Sari & Piran 1997

Note: 1. Synchrotron solutions with α = −2/3 is possible provided that Rs>1016cm, and Γ> 300 –– Kumar & McMahon (2008), Beniamini & Piran (2013) ––

but in this case the variability time can’t be smaller than a few sec.

2. IC cooling in KN regime (Nakar, Ando & Sari, 2009; Bosnjak et al.; Barniol Duran et al.) helps but not enough..

3. Continuous acceleration of electrons can fix the low energy spectral index problem.

2. 2. Synchrotron-self-Compton solutionsSynchrotron-self-Compton solutions

It can be shown that for SSC solutions Ee α R3 and EB α R−4

emission must be produced within a narrow range of R (factor ~2)emission must be produced within a narrow range of R (factor ~2) and that seems unlikely -- especially for the IS model. and that seems unlikely -- especially for the IS model.

There is another problem with the SSC solution:There is another problem with the SSC solution:

A lack of an excess in the Fermi/LAT band (100 MeV to A lack of an excess in the Fermi/LAT band (100 MeV to 100 GeV), and absence of a bright optical flash severely 100 GeV), and absence of a bright optical flash severely constrains the SSC model (e.g. Piran, Sari and Zou, 2009). constrains the SSC model (e.g. Piran, Sari and Zou, 2009).

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The spectral peak (EThe spectral peak (Epp) ) for SSC: α γfor SSC: α γii

4 4 so one so one would expect a broad would expect a broad distribution for Edistribution for Epp but but that is not what GRB that is not what GRB observations find observations find

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Bos

nja

k e

t al

. (20

13)INTEGRAL: black

BATSE: violet Fermi/GBM: red

3. 3. Thermal radiation + ICThermal radiation + IC Thompson (1994 & 06); Liang et al. 1997; Thompson (1994 & 06); Liang et al. 1997; Ghisellini & Celloti 1999; Meszaros & Rees (2001); Ghisellini & Celloti 1999; Meszaros & Rees (2001); Daigne & Mochkovitch (2002); Pe’er et al. (2006), Daigne & Mochkovitch (2002); Pe’er et al. (2006), Beloborodov (2009)…Beloborodov (2009)…

(for prompt (for prompt -rays)-rays)

Low energy spectrum should be fν ν—ν2 which is rarely seen.

Photospheric radius ~ 10Photospheric radius ~ 101212cm cm 33−3−3 L Lj53j53; ; so the IC of thermal radiation is

expected to take place at a much smaller radius than Rs ~ 1016cm we are finding.

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Observational constraintsObservational constraints

However, recent work of Burgess et al. (arXiv:1304.4628) claims to see a thermal component for 5 out of 8 Fermi GRBs they analyzed.

Vrum et al. (2013) & Asano & Meszaros (2013) provide general constraints on photospheric models for MeV emission (Vrum’s talk on Monday)

They find that a large fraction of jet energy should be dissipated at a radius of 1010–1011 cm –– optical depth ~10 –– and jet LF at this radius should be order a few 10s, i.e. the dissipation should take place at a high but not too large optical depth, i.e. some fine tuning needed.

Theoretical constraintsTheoretical constraints

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Consider a baryonic jet consisting of np+. Neutrons accelerate with the fireball expansion as long as they collide frequently with protons.

Eventually at some radius (Rnp) n & p+ decouple & hereafter nare no longer accelerated whereas p+ Lorentz factor could continue to increase with R as long as Γ(Rnp) < η.

The resulting differential velocity between n & p+ result in theircollision and conversion of a fraction of jet KE to thermal energy below the photosphere.

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Since GRB spectra are largely non-thermal, there are many different proposals as to how to modify the photospheric radiation so that the emergent spectrum is non-thermal.

Let us consider one particular photosphere model – n-p collision

n–p decoupling radius is given by –

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η > 0L

4πmpc3R0

⎡

⎣ ⎢

⎤

⎦ ⎥

14

= 485 L511/ 4R0,7

−1/ 4

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tnp' =RcΓ ⇒

4πRnp2 mpc

2ηΓ

σ 0L=RnpcΓ

€

Rnp =σ 0L

4πmpc3ηΓ2or

For n – p to develop differential velocity: Rnp < Rs = R0 η

Thus, GRB jets consisting of n& p& terminal Lorentz factor > 400 will undergo n– pcollisions below the Thomson photosphere & convert a fraction of jet kinetic energy to radiation & e± thermal energy (Beloborodov 2010; Vurm et al. 2011 & Meszaros & Rees 2011)

n– pdifferential motion can also arise in internal shocks

Bel

obor

odov

, 201

0

Radius where internal collisions occur: Rcol = c Γc Γ22 δδt t

And the radius where the probability of n-p collisions drop below 0.5 is: Rnp α Γ-3

Rcol/Rnp α Γ5

For an efficient conversion of outflow kinetic energy to thermal energy via n–p collisions these radii should be approximately equal, and that requires:

50 < Γ < 102

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Which does not appear to be consistent with GRB data.

Origin of high energy photons (>100 MeV)

Prompt phase: high energy photons during this phase might have a separate origin than photons that come afterwards if rapid

fluctuations and correlation with MeV lightcurve is established. Observers need to quantify the statistical significance of this!

Hadronic processes: proton synchrotron, photo-meson …

Inefficient process – typically requires several order more energy than we see in the MeV band (unless Γ were to be small, of order a few hundred, which few people believe is the case for Fermi/LAT bursts), e.g. Razzaque et al. 2010, Crumley & Kumar 2013.

Bottcher and Dermer, 1998; Totani, 1998; Aharonian, 2000; Mucke et al., 2003; Reimer et al., 2004; Gupta and Zhang, 2007b; Asano et al., 2009; Fan and Piran, 2008; Razzaque et al. 2010; Asano and Meszaros, 2012; Crumley and Kumar, 2013….

Internal shock and SSC: e.g. Bosnjak et al. 2009, Daigne et al. 2011

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Afterglow: external shock synchrotron, IC in forward or reverse shock of prompt radiation or afterglow photons; IC of CMB photons by e± in

IGM; pair enrichment of external medium and IC…

Dermer et al., 2000; Zhang and Meszaros, 2001; Wang et al. 2001; Granot and Guetta, 2003; Gupta and Zhang, 2007b; Fan and Piran, 2008; Zou et al., 2009; Meszaros and Rees 1994; Beloborodov 2005; Fan et al., 200; Dai and Lu 2002; Dai et al. 2002; Wang et al. 2004; Murase et al. 2009; Beloborodov 2013….

GRB 130427A (Perley et al. arXiv:1307.4401)MeV duration (T90) = 138s, LAT duration (TGeV) > 4.3x103s; TGeV/T90 > 31

Highest energy photon (95 GeV) detected 242s after T0; z=0.34; Eγ,iso= 7.8x1053erg

GRB 110731A (Ackermann et al. 2013)

Kumar & Barniol Duran (2009) and Ghisellini, Ghirlanda & Nava (2010) showed that high energy γ-ray radiation from GRBs, after the prompt phase, are produced in the external-forward shock via the synchrotron process. The reasoning for this will be described in the next several slides.

Gehrels, Piro & Leonard: Scientific American, Dec 2002

Flux above νc is independent of density and almost independent of εB

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ρ ∝ r−sConsider GRB circumstellar medium density profile:

Blast wave dynamics follows from energy conservation:

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∝ r−(3−s) / 2

Observer frame elapsed time:

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tobs ≈ r2cΓ 2 ∝ r4 −s

Comoving magnetic field in shocked fluid:

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B'2∝ εBρΓ2

Synchrotron characteristic frequency:

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m ∝ B'γ m2 Γ∝ ε B

1/ 2tobs−3 / 2

Observed flux at νm:

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fν m ∝ εB1/ 2r−s / 2

Synchrotron cooling frequency:

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c ∝ εB−3 / 2r(3s−4 )/ 2

Observed flux at ν:

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fν = fν mν mν c( )

(p−1)/ 2 ν cν( )

p / 2

∝ εB(p−2)/ 4 tobs

−(3p−2)/ 4

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.. .

The flux from the external shock above the cooling frequency is given by:

Note that the flux does not depend on the external medium density or stratification, and has a very weak dependence on εB.

0.2 0.2 mJymJy E E5555(p+2)/4 (p+2)/4 ε εee

p-1p-1 ε εBB(p-2)/4(p-2)/4(1+z)(1+z)(p+2)/4(p+2)/4

fν =ddL28L28

22(t/10s)(t/10s)(3p-2)/4(3p-2)/4 ν ν88p/2 p/2 (1+Y) (1+Y)

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Y << 1 due to Klein-Nishina effect for electrons radiating 102MeV photons.

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Temporal decay index in Fermi/LAT band; Ackermann et al. 2013

The expected decline of the >100 MeV lightcurve according to the external shock model is t-(3p-2)/4. For p=2.2 the expected decline is t-1.1 which is in agreement with Fermi/LAT observations.

Table of expected and observed 100 MeV flux

080916C

090510

090902B

110731A

130427A

50

9

300

8

48

67

14

220

~5

~40

Expected flux♪ from ES in nJy

Observed flux (nJy)

Time (observer frame in s)

150

100

50

100

600

4.3

0.9

1.8

2.83

0.34

z

8.8

0.11

3.6

0.6

0.78

Eγ,54_____________________________________________________________

♪We have taken energy in blast wave = 3Eγ, εe=0.2, p=2.4, εB=10-5

Nav

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al.

2013

--

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iv:1

308.

5442

According to the external shock model the LAT flux should be proportional to E(p+2)/4 εe

p-1 or ~ (Eεe)

(E is proportional to Eγ,iso and PIC simulations suggest εe~0.1-0.2)

tt-(3p-2)/4-(3p-2)/4 ≈ t ≈ t-1.1-1.1

(independent of n, ε )(independent of n, ε )BB

Abdo et al. 2009

(GRB 080916C)(GRB 080916C)

Long lived lightcurve for >102MeV (Abdo et al. 2009)

ffνν α ν α ν -1.2

-1.2 t t -1.2-1.2

α = 1.5β – 0.5 (FS)

α = 1.5β – 0.5 (FS)

>10>1022MeV data MeV data expected ES flux in the X-ray and optical band expected ES flux in the X-ray and optical band (GRB 080916C) (GRB 080916C)

We can then compare it with the available X-ray and optical data.We can then compare it with the available X-ray and optical data.

Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009

Long lived lightcurve for >102MeV (Abdo et al. 2009)

Ku

mar

& B

arn

iol D

uran

(20

09)

Or we can go in the reverse direction…

Assuming that the late (>1day) X-ray and optical flux are from ES, calculate the expected flux at 100 MeV at early times

And that compares well with the available Fermi data.And that compares well with the available Fermi data.

X-ray

Optical

> 100MeV

50 - 300keV

Abdo et al. 2009, Greiner et al. 2009, Evans et al. 2009

Ku

mar

& B

arn

iol D

ura

n (

2009

)

The expected flux between 100 MeV and ~10 GeV due to synchrotron emission in external shock is within a factor 2 of the observed flux (as long as electrons are accelerated as per Fermi mechanism).

The predicted flux is independent of ISM density and εB. And hence the flux predictions are robust.

An alternate mechanism to explain the >100 MeV flux observed by Fermi/LAT would have to make a more compelling case than the external shock model.

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A Brief Summary

Let us look at one recent proposal…

According to the recent proposal of Beloborodov et al. (2013) – IC scattering of MeV photons by e± produced in the external medium – when R(1+z)/2cΓ2 (observer frame time for arrival of IC photons) exceeds a few time T90 the GeV flux should decline sharply.

080916C

090510

090902B

110731A

130427A

>7

360

23

75

>30

60

0.3

30

7.3

138

>400

120

700

550

>4300

T90,MeV

(s)TLAT (Power-lawdecline part) in s

TLAT/T90,MeV

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In other words this model suggests TLAT < 3 T90,MeV ~

There is little evidence for high density CBM required for this model to work (A* ~ 0.5). Moreover, the high density is likely to over produce 100 keV flux at tobs< T90,MeV

The large optical flux according to this model (~1 Jy) could have escaped detection. However, its IC scattering off of e± produces ~10 keV photons with flux ~ τ± fopt ~ a few mJy that is harder to hide.

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What about 10 GeV – 95 GeV photons detected from GRB 130427A?

Highest energy photon (95 GeV) was detected 242s after the trigger (z=0.34, Eγ,iso= 7.8x1053erg) when Γ~ 102.

Highest possible energy for synchrotron photons is when

Could these be produced by the synchrotron process?

electrons lose half their energy in one Larmor time

(Because electrons gain energy by a factor ~2 in shock acceleration in ~ a few Larmor time)

me γe cqB

Larmor time = Synchrotron loss rate = σT B2 γe

2c6π

Larmor time x Synchrotro loss rate < meγe c2

νmax = q γe

2 ΓB

2π mec<

9mec3 Γ

16π q2= 50 Γ MeV

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< 10GeV~

>10GeV photons might be due to IC in external shock, however, perhaps the above limit could be violated by inhomogeneous B.

Summary

High energy photons (>100 MeV), after the prompt phase, are produced by the simplest possible mechanism one could imagine, i.e. synchrotron in external shock. However, it is unclear how >10 GeV photons are produced.

The mechanism for generation of photons of energy between ~10 keV and 10 MeV remains elusive.

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