1

Analysis of GRBs KONUS/Wind Spectra from 2002 to 2004 :

The correlation R-H ?

Mourad FOUKA

CRAAG, Algiers Observatory, Algeria

Gamma Ray Bursts & Neutron Stars March 30 - April 4, 2009

Cairo & Alexandria, Egypt

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► Model of fit : PLE+PL

► Results and discussion:

● Distribution of spectral parameters

● Correlations:

□ Epeak -H

□ Ftotal - H

□ Correlation R – H ? how to interpret it ?

► SSC model and the high energy range ?

► Unified model for Konus spectra: SSC (internal)+IC (external)

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101 102 103 104

10-4

10-3

10-2

GRB20040324 GRB PLE PL

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

E (keV)

PLE

PL

Models of fitsFirst question: why this increasing shape in Konus spectra, in terms of

E2N(E) for high energy range ?

4

Baring & Braby Apj 2004

Tavani (1996) electron distribution:

TTTe

Tenn /2

,

ThermalNon Thermal

Pure Synchrotron model

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Both pure Synchrotron and Inverse Compton models can’t explain the increasing part in E2N(E) of Konus-Wind spectra, even with

two components for electron distribution ne(E) = NT+TH.

Baring & Braby Apj 2004

Pure Inverse Compton modelFor external monoenergetic soft photons

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354 GRBs KONUS-Wind spectra for the years 2002, 2003 and 2004 are analyzed.

Model of fits

The sum of two components

i) PLE component, dominant at low energies

ii) a PL component, dominant at high energies

keVEB

E

EkeVEAEN 1/exp1/

0

7

The spectra are presented and fitted in terms of S(E):

2

0

2

2

1/exp1/

keVEBE

EkeVEA

ENEES

We put

2

2'

'

1st Step► It becomes very easy to fit the data in term of )( ii SLnY

to have a linear problem.

► In first time we consider a limit energy EL for the low energy range to fit only by using the PLE component. We can write:

iii

iii

EaEaEa

EE

ELnALnY

32211

0

' 1)()(

8

101 102 103 104

10-4

10-3

10-2

GRB20040324 GRB PLE PL

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

E (keV)

EL

9

► The problem become linear, and we have

and for functions we have

30

2

03

'2

1

1

2

1

)( 1

aE

a

eA

Ea

a

ALna a

k

EE

ELnE

E

3

2

1 1

2 The function

LN

iiii EYY

1

22

10

iwhere is the weight of the ith point, given by

121

11 1-N2,ifor

NN

iii

and

EE

We finally obtain the linear system LPM

L

L

N

iikiik

N

iijikikj

kEYL

jkEEM

1

1

3,1;

3,1&3,1;

2nd Step

►After having the parameters we introduce the PL component: 0,, EA '1/ keVEB

►We consider the data:

0

exp1/'

E

EkeVEASG i

ii

11

As for the 1st step we can have

ii

ii

EaEa

ELnBLnG

2211

' )()(

2

)(

2'

2

1 1

a

eB

a

BLna a

Where

and

ELnE

E

2

1 1

► For this step we refine our parameters to minimize the . We define: 2

3rd Step

'1/' keVEBSS iii

► We omit the points whose . 0' iS

► We continue as for the 1st step

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♦ The final result depend on the value of the energy EL.

♦ we repeat this procedure for many values of the energy EL in some range of low energies LE2

Results and discussion

For a sample of 354 GRB we find:► 6 XRFs (1.7%) (bad statistics)► 214 XRRs (60.5%) 26.1% with► 134 GRBs (37.8%) 36.1% with

Why not all GRBs with

3/23/2

3/2 ?

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-2 -1 0 1 20

10

20

30

40

50

alpha

alpha distribution Gaussian Fit

<alpha> = -0.914

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

0

10

20

30

40

50

60

70

Log(Ep) distribution

Gaussian Fit <log(E

p)> = 1.877

Log(Ep)

Lac because of the range of Konus spectrometers: 13.12 keV – 9.17 MeV

(Low energy index)(Epeak of E2N(E))

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-1,6 -1,2 -0,8 -0,4 0,0

0

20

40

60

80

100

120 Gamma distribution Gaussian Fit

<gamma> = -1.098

Gamma

-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

10

20

30

40

50

60 Log(H) distribution Gaussian Fit

<log(H)> = 0.385

Log(H)

(High energy index) (Hardness)

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Class distributionsIt’s interesting to present the parameter distributions for each class of gamma-

ray bursts to more investigate results and to show if they exist important differences between the three classes.

-2,5 -2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,50

5

10

15

20

25

30

3/2

ondistributiindex

index

▶ GRBs: 26.1% ▶ XRRs: 36.1% ▶ XRFs: (bad statistics)

For 3/2

Two remarks: 1. GRB% < XRR% for: 3/2

2. Values of alpha around zero

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1,0 1,5 2,0 2,5 3,0 3,5-2,0

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

GRB XRR XRF

log(Ep)

inde

x

3/2Now, Lets focusing on bursts whose

Lac of data

For Konus spectra 13.12 keV < EKONUS < 9.17 MeV

1. Determinations of slop alpha depends on the range 13.12 keV < E < Epeak,i.e. when Ep is close to 13.12 keV, the value of index-alpha is more uncertain.

Two suggested interpretations:

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1,0 1,5 2,0 2,5 3,0 3,50

5

10

15

20

25

30

35

N(

> -

2/3)

log(Epeak

)

N( > -2/3)

Lac of data

Need of soft GRBs

2. Contribution of Inverse Compton for external soft photons ( ):

s2ths

0TH NT,IC for ~ n

s

around zero for low Epeak values

Final GRB spectrum=

Inverse Compton for soft external photons

+GRBs internal photons

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-1,8 -1,5 -1,2 -0,9 -0,6 -0,3 0,00

20

40

60

80

ondistributiindex

index

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,50

10

20

30

40

50

Log(Ep)

Log(Ep) distribution

GRB XRR XRF

GRBsXRRs

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Dispersion in Log(Ep)-Log(H)

It’s interesting to remark and evaluate the dispersion for data:

1,4 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0

-3,5

-3,0

-2,5

-2,0

-1,5

-1,0

Data

Log

(FT)

Log(Ep)

1,6 2,0 2,4 2,8-0,1

0,0

0,1

0,2

0,3

0,4

0,5

y

Data dispersion Linear fit

b0= -0.451

b1= 0.230

Log(Ep)

Is this dispersion a property of Konus spectra or a property of GRBs ?

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Correlation Log(Ftotal)-Log(H)

5,0 5,5 6,0 6,5 7,0 7,5 8,0-0,5

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5 Data Mean Data Linear fit

Log

(H)

Log(Ftotal

)

But a true correlation may be between Esource (intrinsic energy of the source) and hardness H.

FzDzE Ljetsource241cos1 But : 3 problems:

1. Redshift z not measured for all GRBs !

2. Need of true cosmological model to calculate DL(z)

► Apparent correlation Log(Ftotal)-Log(H)

3. Need of jet angle jet

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An apparent correlation R-H:

We defined the parameter R as the ratio of the PLE fluency FPLE (the low energy range) to the PL fluency FPL (high energy range) :

-2 -1 0 1

-1

0

1

2

3

Log

(H)

Log(R)

► The Figure show an apparent correlation between

the ratio R ( defined here) and the hardness H.

PLPLE FFR /

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► This apparent correlation can be easily explained:In fact, In the commoving frame of GRB jet, as the initial flash is rich on soft synchrotron photons (low H=Fgamma /FX ), the inverse Compton scattering is efficient (large SigmaIC). So that, as the jet is reach on hard synchrotron photons (large H=Fgamma /FX), the inverse Compton fluency FIC is much lower than the synchrotron fluency FSy R=FSy /FIC large. As a consequence the more hard GRBs (large H) are more reach on synchrotron photons than inverse Compton ones (large R) .

FinallyWe can conclude that correlation R-H, revealed here, give a direct proof of

contribution of Inverse Compton mechanism in GRB’s jets this favorite the SSC (Synchrotron-Self Compton) mechanism ?

SSC with NT + TH electrons

The high energy part can be interpreted by an SSC Thermal term

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Final GRB spectrum

=

Unified model for all Konus wind spectra may be:

Inverse Compton for soft external photons

GRBs internal photons in the SSC model with NT+TH electrons

+

And, Synchrotron self-absorption can also be involved for low energy photon energies if data are available.

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Typical Konus spectrum

100 101 102 103 104

10-6

10-5

10-4

10-3

E2 N

(E)

(keV

2 .keV

-1.c

m-2

.s-1

)

E (keV)

PLE PL PLE+PL

25

10 100 1000 10000

10-4

10-3

10-2

E2 N

(E)

(k

eV

2 .ke

V -

1 .cm

-2.s

-1)

E (keV)

GRB20030919 XFR

Some XRFs fits in the PLE+PL model

10 100 1000 10000

10-4

10-3

10-2

GRB20020822 XFR

E2 N

(E)

(k

eV

2 .ke

V -

1 .cm

-2.s

-1)

E (keV)

10 100 1000 10000

10-5

10-4

10-3

GRB20030317 XFR

E2 N

(E)

(k

eV

2 .ke

V -

1 .cm

-2.s

-1)

E (keV)

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101 102 103 10410-5

10-4

10-3

10-2

GRB20021027 XRR

E (keV)

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

101 102 103 104

10-4

10-3

10-2

GRB20020620 XRR

E (keV)

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

101 102 103 104

10-4

10-3

10-2

GRB20041202 XRR

E (keV)

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

Some XRRs fits in the PLE+PL model

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Some classical GRBs fits in the PLE+PL model

101 102 103 104

10-4

10-3

10-2

GRB20031214 GRB

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

E (keV)

101 102 103 104

10-5

10-4

10-3

10-2

E (keV)

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

GRB20040329 GRB

101 102 103 104

10-4

10-3

10-2

GRB20040324 GRB

E2 N

(E)

(k

eV2 .k

eV -

1 .cm

-2.s

-1)

E (keV)

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Thank you for your attention

CRAAG, Algiers Observatory, Algeria