analysis of grbs konus/wind spectra from 2002 to 2004 : the correlation r-h ?
DESCRIPTION
Analysis of GRBs KONUS/Wind Spectra from 2002 to 2004 : The correlation R-H ?. Gamma Ray Bursts & Neutron Stars March 30 - April 4, 2009 Cairo & Alexandria, Egypt. Mourad FOUKA CRAAG, Algiers Observatory, Algeria. ► Model of fit : PLE+PL ► Results and discussion: - PowerPoint PPT PresentationTRANSCRIPT
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
2
► 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)
3
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
5
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
6
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
12
♦ 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 ?
13
-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))
14
-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)
15
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:
17
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
18
-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
19
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 ?
20
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
21
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 /
22
► 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
23
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.
24
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)
26
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
27
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)
28
Thank you for your attention
CRAAG, Algiers Observatory, Algeria