Spectral characteristics of X-ray
flashes and X-ray rich Gamma-Ray
Bursts observed by HETE-2
Takanori Sakamoto
Department of Physics. Graduated School of Science,
Tokyo Institute of Technology, Tokyo, Japan

Submitted to the Department of Physics,
Tokyo Institute of Technology on January 5, 200X,
in partial fulfillment of the requirements forthe degree of Doctor of Philosophy

January 29, 2004

Abstract
We present the detail and the systematic study of the spectral characteristics of the X-ray
flashes (XRF) and the X-ray rich GRBs observed by HETE. 18 XRFs and X-ray rich GRBs
are studied in detail. Total 45 GRBs observed from January 2001 to September 2003 are usedin the systematic study of the prompt emission. We performed the joint analysis for both
spectral data of the X-ray instrument called, Wide-field X-ray Monitor (WXM) and the γ-ray
instrument called, FREnch GAmma TElescope (FREGATE) on board HETE.
The spectral characteristics of the XRFs and the X-ray rich GRBs are very similar to thatof hard GRBs except for the lower peak energy in νFν spectrum (Epeak ). The spectrum of both
XRFs and X-ray rich GRBs can be expressed in the empirical GRB models (Band function
or power-law times exponential cutoff model). The XRFs and the X-ray rich GRBs show thesimilar duration as the long GRBs, the complexed time-structures, the spectral softening during
the burst, and a lower Epeak energy comparing to hard GRBs which have typical Epeak energyof ∼ 250 keV. Six XRFs shows Epeak energy of a few keV.

From the systematic study of 45 GRBs, we found; 1) X-ray to γ-ray energy fluence ratio

forms a single distribution form XRF to hard GRBs, 2) the number of XRFs is the same as thehard GRBs, 3) the lower-energy photon index α is centroid around −1 for all GRBs, 4) Epeak

energy has a good positive correlation with the time-average flux, and also with the 1s peak
photon flux in the γ-ray range. This may imply that XRFs are intrinsically weaker than hard
GRBs, and 5) the logN-logP distribution of XRFs is close to the Euclidean geometry. This
may imply XRFs have a closer distance scale than that of ordinary GRBs.
With redshift determined HETE 10 GRBs, the relation between the redshift corrected Epeak
energy and the isotropic-equivalent energy are investigated in the same manner as Amati etal. Our sample includes one XRF, GRB020903, with the redshift of 0.25. We confirmed thecorrelation found by Amati et al. for hard GRBs. Furthermore, the Amati’s relation seems
to be extented for the three orders of magnitude lower in the isotropic-equivalent energy than
hard GRBs.
We discuss the several theoretical XRF models based on the observational results of thisstudy.

Contents
1 Introduction

21

2 Observational properties of GRBs

24

2.1 Prompt emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.1

Spectral parameters of the BATSE GRB sample . . . . . . . . . . . . . . 24

2.1.2

Characteristics of X-ray flashes . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.3

src
Epeak
– Eiso relation (Amati’s relation) . . . . . . . . . . . . . . . . . . . 29

2.1.4

Lag/Variability relation . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1.5

V/Vmax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1.6

Line of Death Problem in low-energy index α . . . . . . . . . . . . . . . 33

2.1.7

Extra high-energy spectral component in GRB941017 . . . . . . . . . . . 35

2.1.8

GRB tail emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.2 Afterglow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1

The supernova-GRB connection . . . . . . . . . . . . . . . . . . . . . . . 37

2.2.2

Optically Dark GRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.3

Standard energy reservoir in GRBs . . . . . . . . . . . . . . . . . . . . . 43

3 GRB theory
3.1 GRB emission models

46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.1.1

Synchrotron shock model (SSM) . . . . . . . . . . . . . . . . . . . . . . . 48

3.1.2

SSM with synchrotron cooling . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Theoretical models for XRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.1

Off-axis jet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.2

Photosphere-dominated fireball . . . . . . . . . . . . . . . . . . . . . . . 54

3.2.3

Dirty fireball model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2.4

Structure jet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1

2

CONTENTS
3.2.5

Relativistic wind with a small contrast of high Lorentz factor . . . . . . . 59

3.2.6High redshift GRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Instruments

61

4.1 HETE-2 Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 FREGATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 WXM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 SXC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Analysis

73

5.1 Data reduction of the WXM data . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Spectral models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3 Selected TAG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.4 Definition of X-ray flash, X-ray-rich GRB, and hard GRB . . . . . . . . . . . . . 75
5.5 “Constrained” Band function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6 HETE X-ray Flashes and X-ray-rich GRBs

77

6.1 GRB010213 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.1.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2 GRB010225 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.2.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.3 GRB010326B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.3.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.4 GRB010629B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.4.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.5 GRB011019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.5.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.5.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.6 GRB011130 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.6.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.6.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

CONTENTS

3

6.7 GRB011212 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.7.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.7.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.8 GRB020317 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.8.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.8.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.9 GRB020903 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.9.1

Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.9.2

Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.10 GRB021021 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.10.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.10.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.11 GRB021104 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.11.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.11.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.12 GRB030416 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.12.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.12.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.13 GRB030418 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.13.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.13.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.14 GRB030429 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.14.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.14.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.15 GRB030528 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.15.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.15.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.16 GRB030723 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.16.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.16.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.17 GRB030823 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.17.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.17.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.18 GRB030824 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

4

CONTENTS
6.18.1 Light curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.18.2 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7 Global characteristics of X-ray Flashes and X-ray-rich GRBs

168

7.1 The X-ray and γ-ray flux and fluence . . . . . . . . . . . . . . . . . . . . . . . . 168
7.2 The distribution of the Band parameters . . . . . . . . . . . . . . . . . . . . . . 171
7.3 Correlation between Epeak and other properties . . . . . . . . . . . . . . . . . . 174
7.3.1

Epeak vs. fluence ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

7.3.2

α and β vs. Epeak

7.3.3

The time-average flux vs. Epeak . . . . . . . . . . . . . . . . . . . . . . . 176

7.3.4

50–300 keV peak flux vs. Epeak . . . . . . . . . . . . . . . . . . . . . . . 176. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

7.4 Comparison with WFC/BATSE XRF sample. . . . . . . . . . . . . . . . . . . 178

7.5 Confirmation and extension of Amati’s relation . . . . . . . . . . . . . . . . . . 179
8 Discussion

183

8.1 The sky distribution and event rate of X-ray flashes . . . . . . . . . . . . . . . . 183
8.2 The spectrum of X-ray flashes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
8.3 The correlation between Epeak and γ-ray peak flux . . . . . . . . . . . . . . . . . 186
8.4 Distance scale of X-Ray flashes . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.5 Theoretical models for X-ray flashes . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.5.1

Off-axis jet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

8.5.2

Structure jet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

8.5.3

Unified jet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

8.5.4

Jet beaming model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

8.5.5

Summary of XRF theoretical models . . . . . . . . . . . . . . . . . . . . 195

9 Conclusion

198

A WXM energy response matrix

200

A.1 The WXM Detector Response Matrix (DRM) Calculation . . . . . . . . . . . . 200
A.1.1 The WXM instrumental effects . . . . . . . . . . . . . . . . . . . . . . . 200
A.1.2 The flow chart of the DRM code

. . . . . . . . . . . . . . . . . . . . . . 204

A.1.3 Comparison with GRMC-flight . . . . . . . . . . . . . . . . . . . . . . . 206
A.2 Crab calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A.3 Cross calibration of WXM and FREGATE DRMs . . . . . . . . . . . . . . . . . 211

CONTENTS

5

B HETE GRB summary

212

C Light curve and Spectrum

218

D The “constrain” Band function

226

List of Figures
2.1 BATSE Epeak distribution of Band function fit [63]. . . . . . . . . . . . . . . . . 25
2.2 BATSE α distribution of Band function fit [63]. . . . . . . . . . . . . . . . . . . 26
2.3 BATSE β distribution of Band function fit [63]. . . . . . . . . . . . . . . . . . . 26
2.4 Left: The low-energy photon index α vs. the break energy E0 (E0 = Epeak /(2 + α)). Open squares are 54 BATSE events and the solid squares are the 22
Ginga events. Right: Distribution of the fluence ratio between X-ray (2–10 keV)
to γ-ray (50–300 keV) [97]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Left: Histogram of T90 for hard GRBs (blue) and XRF(red). Right: The peak
flux in 2–25 keV and the photon index in the power-law spectrum [36]. . . . . . 28
2.6 The distribution of Epeak and α comparing with BATSE sample [42]. . . . . . . 29
2.7 The joint fit spectral parameters of XRF compared with BATSE sample. The
comparison between Epeak versus T50 duration, α, and 1s peak flux [42]. . . . . . 30
2.8 The correlation between the isotropic total energy and Epeak energy at the GRB
source frame [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.9 Left: the correlation of the spectral lag between 25–50 keV (Ch 1) and 100–300
keV (Ch 3) vs. peak luminosity. The dashed line is the relation of equation(2.2). Right: the luminosity range is expanded to include GRB980425 [56]. . . . 32
2.10 Left: Luminosity and variability for BATSE bursts with known redshifts. Right:
Luminosity and variability for BATSE bursts including GRB980425 [20]. . . . . 33
2.11 Lag/Variability correlation for 112 BATSE bursts. The solid line is the predicted−0.46
Lag/Variability relation; V = 0.0021τlag[87]. . . . . . . . . . . . . . . . . . . . 34

2.12 Plot of the low energy index vs. Epeak . The SSM line of death (α = −2/3) isdrawn in dashed line and the accepted region in cooling spectrum (α = −3/2)

is in dotted line [62]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6

LIST OF FIGURES

7

2.13 Left: light curves of GRB941017 a) BATSE-LAD, b) EGRET-TASC 1–10 MeV,
and c) EGRET-TASC 10–200 MeV. Right: time-resolved νFν spectrum of GRB941017.
The data are jointly analyzed with LAD and TASC [28]. . . . . . . . . . . . . . 36
2.14 Left: background subtracted light curve of GRB980923 [27]. Right: Light curvefor 400 long GRBs [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.15 Top: V, Rc , Ic band lingt curves of GRB970228. The dotted curves indicate
power-law decays with −1.51 and redshifted SN 1998bw light curves [25]. Bot-

tom: the R band light curve of GRB980326. Overlaied curves are the power-law
afterglow decline summed with the bright supernova light curve at different redshifts [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.16 Image of the galaxy ESO 184-G82 with (left) and without (right) SN1998bw [24]. 39
2.17 Light curves of three type Ic supernova, SN1998bw, 1997ef, and 1994I. The
solid curves are the models. The light curve of SN1998bw are well fitted in thefollowing parameters: the stellar mass MCO = 13.8 MSolar , the explosion energy
Eexp = 3 × 1052 erg, and the mass of the synthesized 56 Ni M56 = 0.7 MSolar [39].

40

2.18 Spectral evolution of the afterglow of GRB030329 [37]. . . . . . . . . . . . . . . 41
2.19 Left: NH vs. spectral index of X-ray afterglow observed by BeppoSAX NFI. The
filled dots are dark GRBs and empty dots are the optically bright GRBs. There
are no significant difference among them. Right: X-ray vs. optical flux. The
empty dots are the optically bright GRBs. The solid arrows are optically dark
GRBs. [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.20 Light curve of GRB 021211 and other GRBs. The light curve of GRB021211 canbe fitted with two component power-law; an initial steeply declining “flash”, f ∝t−α with α ≈ 1.6 and typical afterglow behavior with α ≈ 1 [21].

. . . . . . . . 43

2.21 Near infrared and optical afterglow spectrum (K, H, J, i∗ , and r∗ band) of
GRB030115. The solid curve is the best fit model assuming extinction by dust
for the data [48]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.22 Left: Distribution of the isotropic γ-ray energy (top) vs. the jet opening angle
corrected γ-ray energy (bottom) [22]. Right: Distribution of the jet opening
angle corrected γ-ray energy [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8

LIST OF FIGURES
3.1 Schematic figure of the GRB prompt and afterglow emission model. The collapseof massive star (collapsar) and/or neutron star (NS) marger which finally forma black hole are the most supported central engines for GRBs. In the internal
shock model, the prompt emission is produced by the particles accelerated via
the internal shock which is due to the collision of the relativistic moving shells.
The particles radiating the afterglow are accelerated by the external shock whichis the interaction between the marged shell and the interstellar matters. . . . . . 47
3.2 The spectrum calculated by synchrotron shock model proposed by Tavani. The
spectral shape is the same as “classical” synchrotron radiation with the slopechange at the synchrotron critical frequency νm . The light blue region is theobserving energy band of GRBs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 The synchrotron cooling spectrum proposed by Sari et al. [85]. There are twophases, fast cooling and slow cooling, whether νc < νm or νc > νm . The light
blue region is the observing energy band of GRBs. . . . . . . . . . . . . . . . . . 53
3.4 Left: The schematic figure of the off-axis GRB model. XRF is the hard GRB
observing from the large viewing angle. Right: The peak flux ratio (upper panel)and fluence ratio (lower panel) of 2–10 keV to 50–300 keV as a function of viewing
angle (see Yamazaki et al. [112] for details). . . . . . . . . . . . . . . . . . . . . 55
3.5 The observed Epeak energy as a function of viewing angle assuming the GRB
Epeak = 300 keV and the bulk Lorentz factor of 100. The solid lines correspondto the half opening angle of the jet are 1◦ (black), 2◦ (red), 3◦ (green), 5◦ (blue),and 10◦ (sky blue). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6 Schematic drawing of the photosphere-dominated fireball. rsh is the radius of
the collision of the two shells. r± is the radius of the optical depth of the pairproduction τ± ∼ 1. When rsh < r± , the optically thick pair-production region

exists from rsh to r± . This region could produce X-ray excess GRBs. . . . . . . . 57

3.7 The plot of the photon energy ǫ in the unit of me vs. the spectral power P(t).
The lines correspond to the different values of bulk Lorentz factors. The peak
photon energy ǫp will decrease and the duration will increase when the Lorentz
factor goes down [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.8 Schematic drawing of jet which has an axisymmetric energy distribution. . . . . 59
3.9 Left: The Epeak distribution in the case of x=y=1/4. The dashed line represents
the whole population and the solid line is the bursts which can be detected by
BATSE. Right: The simulated results of Epeak vs. peak flux [54]. . . . . . . . . . 60

LIST OF FIGURES

9

4.1 Left: HETE-2 spacecraft under a ground testing. Right: The Pegasus rocket on
the bottom of the airplane.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2 Schematic drawing of the HETE-2 spacecraft. . . . . . . . . . . . . . . . . . . . 63
4.3 Burst alert network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4 SGS status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5 The picture of the FREGATE detectors before the integration on the spacecraft(figure (a)). The cross-section view of the one FREGATE detector (figure (b)).
◦

◦

◦

◦

4.6 FREGATE effective area of the incident angle in 0 , 30 , 50 and 60 .

66

. . . . . 66

4.7 The photograph of the WXM detector part (figure a) and the coded aperture of
one direction (figure b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.8 The dimension of the whole WXM system. . . . . . . . . . . . . . . . . . . . . . 69
4.9 The cross section of one PSPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.10 The effective area of one PSPC for the boresight incidence. . . . . . . . . . . . . 70
4.11 The picture of SXC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.12 Effective area curves of SXC, WXM and FREGATE at the boresight angle. . . . 72
5.1 Left: Example of the light curves (GRB021112) using the normal TAG data(above) and the selected TAG data (bottom). Right: The wire-position pairs
vs. the cumulated signal to noise ratio. The dashed line corresponds to the
maximum SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 The energy resolved light curves of GRB010213 in 1.23 seconds time resolution.
The three spectral regions are shown in the dotted lines. There is a data gap in
the FREGATE light curves from 40 to 80 seconds from the onset. . . . . . . . . 79
6.2 The WXM and FREGATE spectra of GRB010213. The spectra of region 1,
region 2, region 3 and the whole time region are shown. The model spectrum
is the Band function for region 2, region 3, and the whole time region, whereas
region 1 is the power-law model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3 The hardness ratio between the 5–10 keV and 2–5 keV bands. The upper panel
is the hardness ratio plot, and the middle and the bottom panels are the light
curves in the 2–5 keV and 5–10 keV bands respectively. . . . . . . . . . . . . . . 81
6.4 The energy resolved light curves of GRB010225. The dotted lines indicate thetime regions used as the foreground to construct spectrum. . . . . . . . . . . . . 84
6.5 The WXM and FREGATE spectra of GRB010225. The spectra with the powerlaw model (top) and Band function (bottom) are shown. . . . . . . . . . . . . . 85

10

LIST OF FIGURES
6.6 The energy resolved light curves of GRB010326B at 0.1 s time bin. The dottedlines correspond to the foreground interval used for accumulating the spectrum.

88

6.7 The WXM and FREGATE spectra of GRB010326B. The model spectrum are
the power-law model, the cutoff power-law model and the Band function from
top to bottom.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.8 The hardness ratio between the FREGATE band C (32–400 keV) and the band
A (6–40 keV). The top panel is the harness ratio. The middle and the bottom
panels are the FREGATE light curves of band A and C respectively.

. . . . . . 90

6.9 The energy resolved light curves of GRB010629B at 1.23 s time bin. The dottedlines correspond to the two foreground intervals used for creating the spectra. . . 93
6.10 The WXM and FREGATE spectra of GRB010629B. The spectra of region 1,
region 2, and all region are shown from top to bottom. The left and right plots
are fitting with the power-law model and cutoff power-law model, respectively. . 95
6.11 The energy resolved light curves of GRB011019 at 1.23 s time bin. The dottedlines correspond to the foreground spectral region. . . . . . . . . . . . . . . . . . 98
6.12 The WXM and FREGATE spectra of GRB011019. The spectral model is thepower-law (top) and the cutoff power-law (bottom). . . . . . . . . . . . . . . . . 100
6.13 The energy resolved light curves of GRB011130 at 1 s time bin. The dotted lines
correspond to the foreground regions of the spectra. . . . . . . . . . . . . . . . . 102
6.14 The WXM and FREGATE spectra of XRF011130. The spectra of region 1,
region 2, and all region are shown from top to bottom. The spectral model isthe power-law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.15 The posterior probability density distribution as a function of Epeak (Epivot =3.4 keV). The highest probability is 2.7 keV. The solid line, the dashed line andthe dashed-dotted line correspond to the 68%, 95% and 99.7% confidence region
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.16 The energy resolved light curves of GRB011212 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum. . . . . . . . . . . . . . . . 110
6.17 The WXM and FREGATE spectrum of XRF011212. The spectral model is thepower-law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.18 The energy resolved light curves of GRB020317 at 0.3 s time bin. The dottedlines represent the foreground region of the spectrum. . . . . . . . . . . . . . . . 114

LIST OF FIGURES

11

6.19 The WXM and FREGATE spectra of GRB020317. The spectra of the wholeburst region with a spectral model of the power-law (top) and the cutoff powerlaw (bottom) are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.20 The hardness ratio between WXM 10–25 keV and 2–10 keV is in the top panel.
The second and the third panels are the WXM light curves of 2–10 keV and
10-25 keV respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.21 The Palomar and HST images of the transient (label OT) discovered within
the error-box of GRB020903. The HST image reveals a complicated galaxy
morphology for G1, suggesting a system of at least four interacting galaxies [95]. 118
6.22 The energy resolved light curves of GRB020903 in 1.0 second resolution. The
two spectral regions are shown in the dotted lines. . . . . . . . . . . . . . . . . . 119
6.23 The time-average spectrum of GRB020903.

. . . . . . . . . . . . . . . . . . . . 121

6.24 The posterior probability density distribution as a function of Epeak . The solidlines define the 68% probability interval for Epeak , while the dashed and dottedlines show the 95% and 99.7% probability upper limits on Epeak . . . . . . . . . . 121
6.25 The energy resolved light curves of GRB021021 in 1.23 second time-bins. . . . . 125
6.26 The time-average spectra of GRB021021 in the power-law model (upper) andthe cutoff power-law model (bottom). . . . . . . . . . . . . . . . . . . . . . . . . 126
6.27 The energy resolved light curves of GRB021104 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum. . . . . . . . . . . . . . . . 129
6.28 The WXM and FREGATE spectra of GRB021104. The top and bottom figures
are fitting with the power-law model and the cutoff power-law model, respectively.131
6.29 The energy resolved light curves of GRB030416 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum. . . . . . . . . . . . . . . . 135
6.30 The time-average spectrum of GRB030416. . . . . . . . . . . . . . . . . . . . . . 136
6.31 The posterior probability density distribution for Epeak . The solid, the dashed,
and the dot-dashed lines show the 68%, 95%, and 99% probability upper limits
on Epeak . Epivot energy is 1.4 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.32 The hardness ratio between 5–25 keV and 2–5 keV band. The middle and thebottom panels are the light curves of the WXM 2–5 keV and 5–25 keV band. . . 137
6.33 The energy resolved light curves of GRB030418 at 1.23 s time bin. The dottedlines correspond to the two foreground intervals used for creating the spectra. . . 140

12

LIST OF FIGURES
6.34 The WXM and FREGATE spectra of GRB030418. The spectra of region 1,
region 2, and all region are shown from top to bottom. The left and right plots
are fitting with the power-law model and cutoff power-law model, respectively. . 141
6.35 The energy resolved light curves of GRB030429 at 1.23 s time bin. The dottedlines correspond to the foreground spectral regions. . . . . . . . . . . . . . . . . 144
6.36 The WXM and FREGATE spectrum of GRB030429. The spectrum of the firstpeak, the second peak and the whole burst region are shown from top to bottom.
The model spectrum is the power-law and the cutoff power-law model from left
to right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.37 The energy resolved light curve of GRB030528 at 1.23 s time bin. The dottedlines correspond to the foreground spectral region. There were data gaps due tothe uncomplete downlink in several places. . . . . . . . . . . . . . . . . . . . . . 149
6.38 The WXM and FREGATE spectra of GRB030528. The model spectrum is thepower-law model, the cutoff power-law model and the Band function from top
to bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.39 The energy resolved light curves of GRB030723 at 1 s time bin. The dotted lines
correspond to the foreground spectral region. . . . . . . . . . . . . . . . . . . . . 154
6.40 The WXM and FREGATE spectrum of GRB030723. The spectral model is thepower-law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.41 The energy resolved light curves of GRB030823 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum. . . . . . . . . . . . . . . . 159
6.42 The WXM and FREGATE spectrum of GRB030823. The spectral model is thepower-law (top) and the cutoff power-law (bottom). . . . . . . . . . . . . . . . . 160
6.43 The energy resolved light curves of GRB030824 in 1.23 s time bin. . . . . . . . . 164
6.44 The WXM and FREGATE spectrum of GRB030824. The spectrum model isthe power-law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.45 The posterior probability density distribution as a function of Epeak . Epivot is
8.1 keV. The 68% confidence range (solid line) of Epeak is 4.1 keV < Epeak < 7.4
keV. The 95% confidence range (dashed line) is 0.9 keV < Epeak < 8.1 keV. The
99.7% upper limit (dash-dotted line) of Epeak is 8.7 keV. . . . . . . . . . . . . . 167
7.1 Distribution of the fluence ratio of 2–30 keV to 30–400 keV in the logarithmic
scale. The dashed lines are the borders of hard GRB/XRR, and XRR/XRF. . . 169
7.2 The scatter plot of the 2-30 keV and the 30-400 keV energy fluence. . . . . . . . 170

LIST OF FIGURES

13

7.3 The time-average flux in 2-30 keV (F2−30 ) and 30-400 keV (F30−400 ). The corre1.14
lation can be expressed as F30−400 ∝ F2−30. . . . . . . . . . . . . . . . . . . . . . 170

7.4 Distribution of the low-energy photon index α for all GRB classes (top) and foreach three different classes (bottom). . . . . . . . . . . . . . . . . . . . . . . . . 172
7.5 Distribution of Epeak for all GRB classes (top) and for three different classes(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.6 Distribution of β for all GRB classes. . . . . . . . . . . . . . . . . . . . . . . . . 174
7.7 Left: The observed Epeak vs. X-ray to γ-ray fluence ratio. Right: The calculated
Epeak vs. X-ray to γ-ray fluence ratio assuming the Band function with α = −1. 175
7.8 α (left) and β (right) vs. Epeak . Each colors correspond to the GRB classes(XRF: black, XRR: red, and hard GRB: blue) and markers correspond to thebest fit spectral models (square: cutoff power-law model, star: Band function).
There are also plotting the XRFs with the fixed values of α (green). . . . . . . . 175
7.9 The time-average flux in 2-30 keV flux vs. Epeak . . . . . . . . . . . . . . . . . . . 176
7.10 The time-average flux in 2-400 keV flux vs. Epeak . . . . . . . . . . . . . . . . . . 177
7.11 The time-average flux in 30-400 keV flux vs. Epeak . . . . . . . . . . . . . . . . . 177
7.12 1-second peak photon flux in 50-300 keV vs. Epeak .

. . . . . . . . . . . . . . . 178

7.13 1-second peak flux in 50-300 keV vs. Epeak . The samples are BATSE bursts(black), WFC/BATSE bursts (red and green), and HETE bursts (blue). . . . . . 179
7.14 1-second peak flux in 50-300 keV vs. Epeak . The samples are WFC/BATSE
bursts (red and green), and HETE bursts (blue). . . . . . . . . . . . . . . . . . . 180
7.15 The Epeak distribution of HETE bursts (top panel) and WFC/BATSE bursts(bottom panel). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.16 The plot of the isotropic-equivalent energy Eiso between 1–10000 keV and Epeak
energy at the GRB source frame. The black points are the BeppoSAX sample inAmati et al. [1]. The red points are the HETE GRB sample. The dashed line is
src
Epeak
= 89 (Eiso / 1052 erg)0.5 .

. . . . . . . . . . . . . . . . . . . . . . . . . . . 181

8.1 The sky distribution of the HETE XRFs (triangle), X-ray rich GRBs (square),and hard GRBs (cross) in the galactic coordinate. The light blue circles represent
the field of view of WXM (60◦ × 60◦ ) for each months assuming the anti-solar

pointing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

14

LIST OF FIGURES
8.2 Left: the best fit νFν spectra of XRFs (black), XRRs (red), and hard GRBs
(blue). Right: the scatter plot of Epeak and the normalization at 15 keV (XRF:
black, XRR: red, hard GRB: blue). . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.3 The schematic figure of νFν spectra of XRFs, XRRs, and hard GRBs. . . . . . . 186
8.4 The 1-second peak photon flux in 50–300 keV and Epeak relation including theHETE and BeppoSAX/BATSE samples. The dashed line is Epeak = (48.51 ±0.46) P0.379±0.003 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

8.5 logN-logP for XRFs (black), XRRs(red), and hard GRBs(blue). The verticalaxis is the cumulative number of the bursts. The horizontal exis is 1s peak fluxin 2–30 keV. See text for the details. . . . . . . . . . . . . . . . . . . . . . . . . 190
8.6 logN-logP for XRFs (black) and GRBs with Epeak > 50 keV. See text for thedetails about the plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.7 The schematic figure of the jet beaming model. The left (right) panel is in thecase of the low (high) bulk Lorentz factor Γ. . . . . . . . . . . . . . . . . . . . . 196
src
8.8 The predicted Epeak-Eiso relations for the unified jet model (red), the off-axis jet

model (green), and the structure jet model (blue). Note that the structure jetmodel is in the case of the same dependence in the viewing angle for the energy
per solid angle and the bulk Lorentz factor.

. . . . . . . . . . . . . . . . . . . . 197

A.1 The gain measurement of the XA detector at Cu K energy (∼ 8 keV). Left top:a contour plot of the gas gain, bottom: the gain distribution along the A–A′ andB–B′ , and right: the gain distribution along the C–C′ [92]. . . . . . . . . . . . . 201
A.2 The gas gain profile inside PSPC at bias voltage of 1700 V. The right contour
plot shows the pulse height distribution around the wire. The left plot is thepulse height distribution as a function of the depth of PSPC [91]. . . . . . . . . 202
A.3 The energy resolution at energies from 6 to 24 keV for bias voltage form 1400 to
1700 V. The WXM bias voltage of the normal operation is 1650 V [92]. . . . . . 203
A.4 Energy and pulse height relation for several bias voltages. The bias voltages are
1299, 1361, 1599, 1618, 1649, 1699 from left to right respectively [91]. . . . . . . 204
A.5 The coordinate system using in the DRM code. . . . . . . . . . . . . . . . . . . 205
A.6 The flow chart of the main part of the DRM calculation code. . . . . . . . . . . 207
A.7 The WXM DRM of XA0 wire. The horizontal axis is the input energy and thevertical axis is the output ADC channels. . . . . . . . . . . . . . . . . . . . . . . 208

LIST OF FIGURES

15

A.8 Modeling two major characteristics of the WXM detector; “M” curve (left) and“∼” curve (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
A.9 The effective areas with the calculation by GRMC flight and our method areoverlaied. Left: the conditions are θx = 0◦ , θy = 0◦ , and XA0 wire. Right: theconditions are θx = 0◦ , θy = 30◦ , and XA0 wire. . . . . . . . . . . . . . . . . . . 209
A.10 The WXM Crab spectrum at the incident angle of 1.6◦ (Left) and 27.3◦ (Right). 210
A.11 The Crab spectral parameters in the various incident angles. Top left: photon
index vs. incident angles, Top right: NH vs. incident angles, Bottom: 2–10 keVenergy flux vs. incident angles, Each colors represent the individual wires. . . . . 210
A.12 The Crab spectrum of WXM (black) and FREGATE (red). Left: boresightangle, right: incident angle of 21-22◦ . . . . . . . . . . . . . . . . . . . . . . . . . 211
C.1 GRB010612 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
C.2 GRB010613 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
C.3 GRB010921 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
C.4 GRB010928 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
C.5 GRB011103 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.6 GRB020124 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.7 GRB020127 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.8 GRB020331 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.9 GRB020531 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
C.10 GRB020625 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
C.11 GRB020801 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
C.12 GRB020812 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
C.13 GRB020813 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C.14 GRB020819 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C.15 GRB021004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C.16 GRB021112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C.17 GRB021211 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
C.18 GRB030115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
C.19 GRB030226 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
C.20 GRB030323 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
C.21 GRB030324 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.22 GRB030328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

16

LIST OF FIGURES
C.23 GRB030329 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C.24 GRB030519 (WXM:1.23s, FREGATE 82ms) . . . . . . . . . . . . . . . . . . . . 224
C.25 GRB030725 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
C.26 GRB030821 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
C.27 GRB030913 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

D.1 Constrained Band functions, with β = −2.5 and Epivot = 4 keV, for different
values of Epeak . All functions have been normalized to 1 keV−1 at 10 keV. The
two vertical lines at 2 keV and at 25 keV show the WXM bandpass. The spectra
shown are (decreasing monotonically from the top at low energy), Epeak =1 keV,
2 keV, 4 keV, 6 keV, and 8 keV, respectively. As Epeak increases, Ebreak also
necessarily increases, so that E0 is forced to smaller and smaller values by theconstraint, increasing the curvature and the value of α.

. . . . . . . . . . . . . 230

D.2 Constrained Band functions, with Epeak = 4 keV and Epivot = 4 keV, for different
values of β. All functions have been normalized to 1 keV−1 at 10 keV. The twovertical lines at 2 keV and at 25 keV show the WXM bandpass. The spectra
shown are for β = -2.0, -2.5, -3.0, -3.5, and -4.0, which can be distinguished by theincreasing steepness of their slopes at high energy. The progression from somecurvature at low energy (β = −2.0) to almost none (β = −4.0) is evident, as is

the fact that as the curvature disappears, the resulting power-law is producedby the high-energy part of the Band function. . . . . . . . . . . . . . . . . . . . 231
D.3 Constrained Band functions, with Epeak = 4 keV and β = 2.0, for different
values of Epivot . All functions have been normalized to 1 keV−1 at 10 keV.
The two vertical lines at 2 keV and at 25 keV show the WXM bandpass. The
spectra shown are (increasing monotonically at low energy) for Epivot = 2 keV,
4 keV, 6 keV, and 8 keV, respectively. Once again, as the low-energy curvature
disappears, the resulting power-law is produced by the high-energy part of theBand function. Note also that the shape of the constrained Band function isinsensitive to the specific choice of Epivot within a reasonable range. . . . . . . . 232

LIST OF FIGURES

17

D.4 Constrained Band functions with parameters that best fit the 13 s spectrum of
XRF020903, for different fixed values of Epivot . The two vertical lines at 2 keV
and at 25 keV show the WXM bandpass. All functions have been normalized sothat the integral from 2 keV to 25 keV is one photon. The five spectra shownin the plot corresponding to Epivot = 4 keV, 5 keV, 6 keV, 7 keV, and 8 keV(the 7 keV and 8 keV largely overlap each other). This figure illustrates a robust
aspect of the constraint procedure: the best-fit model is essentially unchangedin the WXM spectral band despite a factor-of-two change in the value of Epivot . 233

List of Tables
4.1 HETE satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 FREGATE performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 FREGATE data type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4 WXM performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.5 Data products of WXM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 SXC performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.1 The afterglow search for GRB010213 . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 The fluxes and fluence of GRB010213 in the Band function. . . . . . . . . . . . 81
6.3 The spectral parameters of GRB010213 for the power-law model (PL), the cutoff
power-law model (Cutoff PL), and the Band function (Band). . . . . . . . . . . 82
6.4 The fluxes and fluence of GRB010225 in the cutoff power-law model. . . . . . . 86
6.5 The spectral parameters of GRB010213 in the power-law, the cutoff power-law,
and the Band function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.6 The fluxes and fluence of GRB010326B in the cutoff power-law model. . . . . . . 91
6.7 The spectral parameters of GRB010326B in the power-law model (PL), the cutoff
power-law model (Cutoff PL), and Band function (Band). . . . . . . . . . . . . . 91
6.8 The afterglow search for GRB010629B . . . . . . . . . . . . . . . . . . . . . . . 92
6.9 The fluxes and fluences of GRB010629B. The spectral model is the cutoff powerlaw model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.10 The spectral parameters of GRB010629B in the power-law (PL), the cutoff
power-law (Cutoff PL), and the Band function (Band). . . . . . . . . . . . . . . 96
6.11 The afterglow search for GRB011019 . . . . . . . . . . . . . . . . . . . . . . . . 97
6.12 The fluences of GRB011019 in the cutoff power-law. . . . . . . . . . . . . . . . . 99
6.13 The spectral parameters of GRB011019 in the power-law (PL) and the cutoff
power-law model (Cutoff PL). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.14 The afterglow search for GRB011130 . . . . . . . . . . . . . . . . . . . . . . . . 106
18

LIST OF TABLES

19

6.15 The fluxes and fluences of GRB011130. The spectral model is the power-law
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.16 The spectral parameters of GRB011130 in the power-law model (PL). . . . . . . 107
6.17 The afterglow search for GRB011212 . . . . . . . . . . . . . . . . . . . . . . . . 108
6.18 The fluxes and fluences of GRB011212. The spectral model is the power-law
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.19 The spectral parameters of GRB011212 in the power-law model (PL). . . . . . . 111
6.20 The afterglow search for GRB020317 . . . . . . . . . . . . . . . . . . . . . . . . 112
6.21 The fluxes and fluences of GRB020317. The spectral model is the cutoff powerlaw model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.22 The spectral parameters of GRB020317 in the power-law model (PL) and thecutoff power-law model (Cutoff PL). . . . . . . . . . . . . . . . . . . . . . . . . 116
6.23 The afterglow search for GRB020903 . . . . . . . . . . . . . . . . . . . . . . . . 122
6.24 The fluxes and fluences of GRB020903. The spectral model is the power-law
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.25 The time-average spectral parameters of GRB020903. . . . . . . . . . . . . . . . 123
6.26 The fluxes and fluences of GRB021021. The spectral model is the cutoff-law
power-law model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.27 The time-average spectral parameters of GRB020903. . . . . . . . . . . . . . . . 127
6.28 The afterglow search for GRB021104 . . . . . . . . . . . . . . . . . . . . . . . . 128
6.29 The fluxes and fluences of GRB021104. The spectral model is the cutoff powerlaw model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.30 The spectral parameters of GRB021104. . . . . . . . . . . . . . . . . . . . . . . 132
6.31 The afterglow search for GRB030416 . . . . . . . . . . . . . . . . . . . . . . . . 133
6.32 The time-average fluxes and fluences of GRB030416. The spectral model is thepower-law model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.33 The spectral parameters of GRB030416. . . . . . . . . . . . . . . . . . . . . . . 137
6.34 The afterglow search for GRB030418 . . . . . . . . . . . . . . . . . . . . . . . . 138
6.35 The fluences of GRB030418. The spectral model is the cutoff power-law model. . 142
6.36 The spectral parameters of GRB030418 in the power-law (PL) and the cutoff
power-law (Cutoff PL). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.37 The afterglow search for GRB030429 . . . . . . . . . . . . . . . . . . . . . . . . 146
6.38 The time-average fluxes and fluences of GRB030429. The spectral model is thecutoff power-law model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

20

LIST OF TABLES
6.39 The spectral parameters of GRB030429. . . . . . . . . . . . . . . . . . . . . . . 147
6.40 The afterglow search for GRB030528 . . . . . . . . . . . . . . . . . . . . . . . . 151
6.41 The fluxes and fluences of GRB030528. The spectral model is the Band function. 152
6.42 The spectral parameters of GRB030528. . . . . . . . . . . . . . . . . . . . . . . 152
6.43 The afterglow search for GRB030723 . . . . . . . . . . . . . . . . . . . . . . . . 156
6.44 The fluxes and fluences of GRB030723. The spectral model is the power-law
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.45 The spectral parameters of GRB030723. . . . . . . . . . . . . . . . . . . . . . . 157
6.46 The afterglow search for GRB030823 . . . . . . . . . . . . . . . . . . . . . . . . 161
6.47 The fluxes and fluences of GRB030823. The spectral model is the cutoff powerlaw model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.48 The spectral parameters of GRB030823. . . . . . . . . . . . . . . . . . . . . . . 162
6.49 The afterglow search for GRB030824 . . . . . . . . . . . . . . . . . . . . . . . . 165
6.50 The fluxes and fluences of GRB030824. The spectral model is the power-law
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.51 The spectral parameters of GRB030824. . . . . . . . . . . . . . . . . . . . . . . 166
7.1 Esrc
peak and Eiso of the HETE known redshift GRBs . . . . . . . . . . . . . . . . . 182
A.1 The joint fit results of the WXM and FREGATE Crab data. The quoted error
is 90% confidence region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
B.1 The HETE GRBs summary table . . . . . . . . . . . . . . . . . . . . . . . . . . 213
B.2 The HETE GRBs spectral parameters . . . . . . . . . . . . . . . . . . . . . . . 214
B.3 The HETE GRBs time-average photon flux and fluence . . . . . . . . . . . . . . 215
B.4 The HETE GRBs time-average energy flux and fluence . . . . . . . . . . . . . . 216
B.5 The HETE GRB 1s peak flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

Chapter 1
Introduction
It has been thirty years since Gamma-Ray Bursts (GRBs) were first reported in 1973 by Klebesadel et al. [43]. There are two breakthroughs in the GRB research. The first step was provided
by the Burst And Transient Source Experiment Burst (BATSE) instrument on-board Compton
Gamma-Ray Observatory. BATSE consists of eight scintillators with 51 cm in diameter placedat four corners of the spacecraft and possible to determine the direction of GRB in the accuracyof few degrees. BATSE observed 2704 GRBs in 9 year mission and found that the distribution of GRBs is isotropic. The lack of very faint GRBs compared with the Euclidean space
distribution suggest that the GRB population is distorted from the Euclidean geometry [58].
Both observational properties may indicate that the distance scale for GRB is cosmological,
however, we had to wait for the direct measurement of the distance (see a lively debate of thecosmological and Galactic hypotheses by Paczyński [59] and Lamb [45]).
The second breakthrough is the discovery of the afterglow. This revolution conducted by
the BeppoSAX satellite. BeppoSAX has two X-ray telescopes; Wide Field Camera (WFC) andNarrow Field Instruments (NFI). WFC was observing the 40◦ × 40◦ sky to find the transient
sources and localize them in the accuracy of few tens of arcminues. NFI composed of the X-ray

detectors (proportional counters) and the X-ray mirrors. On February 28, 1997, WFC observed
the Gamma-ray burst (GRB970228) and NFI was pointed to the burst position 8 hours after
the trigger. NFI detected an uncatalogued X-ray source with a 2–10 keV flux of several 10−12
erg cm−2 s−1 at the edge of the WFC error box. Four days later, the flux of this source wasdecreasing by a factor of ∼ 20 [12].
The exciting discovery did not end with this. The optical counterpart for GRB970228 was
also detected. Groot et al. [31] discovered a decaying 21st magnitude object with the William
Herschel and Isaac Newton Telescope. The deeper images made with the ESO New Technology
21

22

CHAPTER 1. INTRODUCTION

Telescope [32] and the Keck Telescope [53] showed an ∼ 1′′ extended object at the locationof the optical transient, likely the host galaxy of the GRB with the redshift of z = 0.695.
GRB970228 was the first GRB which determined the distance directly from the observationand its distance was cosmological. After the success of GRB970228, more afterglows in various
wavelengths were detected for the BeppoSAX GRBs. We now know that the distances to mostof the long GRBs are cosmological (z ∼ 1).
The prompt GRB emission in X-ray range was observed in the very beginning of the discovery. The earliest reports of the prompt X-ray emission of GRBs were events occurring 1972
April 27 ([52], [104]) and 1972 May 14 [111]. The April 27 event was observed by the X-ray(2.0–7.9 keV) and γ-ray (0.067–5.1 MeV) spectrometers on board Apollo 16 and also by the
Vela 6A satellite. The authors performed the detail spectral and temporal studies combining
the X-ray/γ-ray data. They found the similar time variability in X-ray data and successfullycollected the spectrum ranging from 4 order of magnitude. In the May 14 event, six different
X-ray/γ-ray instruments observed simultaneously. They are the γ-ray detectors (∼ 0.1–1.5
MeV) on three Vela satellites, the solar-flare γ-ray detector (∼ 0.1–1.5 MeV) on the IMP-6
satellite, and two X-ray telescopes (7–500 keV) on board the OSO-7. The authors mention thehard-to-soft spectral evolution during the burst using the X-ray data. These early observations
confirmed that GRBs produce a significant amount of X-ray emissions.
In the early 1980s, the unidentified X-ray transient sources called “fast X-ray transients”
were argued by several authors. The Sky Survey Instrument (SSI) on Ariel V (15 October 1974
- 14 March 1980) scanned the sky for 5.5 yr in the energy band 2–18 keV with a time resolutionof ∼ 100 minutes. Pye and McHardy [67] performed the systematic search of SSI databaseand found 27 candidates including one coincident event with the GRB (GB 751102). Althoughmost of these events might be nearby RS CVn-like system, it has a possibility of including thetransient source related to GRBs.
HEAO-1 (12 August 1977 - 9 January 1979) A-1 experiment (Large Area Sky Survey experiment; 0.25–25 keV) had a complete coverage of the entire sky. Ambruster and Wood [3]searched for the first 7 months of the A-1 data and found 10 fast transients. Although the error
boxes of three sources included M dwarf flare stars and one source was identified with RS CVn
system, six sources remained unidentified. One source, H0547–14, could be a weak GRB withthe spectral characteristics of the photon index α = 1.65 ± 0.14, with a high hydrogen column

density NH = (9.2 ± 1.7) × 1022 cm−2 [2].

Gotthelf et al. [33] searched for the X-ray counterparts of GRBs in the data from theEinstein (12 November 1978 - April 1981) Imaging Proportional Counter (IPC; 0.2–3.5 keV).

23
They found 42 candidates including 18 hard and 24 soft sources (the definition of hard (soft)is the count-ratio between 0.2–1.3 keV and 1.3–3.5 keV is smaller (larger) than unity). The
authors suggested that the hard 18 sources might be the X-ray counterparts of GRBs.
The ROSAT (1 June 1990 - 12 February 1999) all-sky survey data were investigated byGreiner et al. [34] for the X-ray afterglow search. Although they found 23 candidates of Xray afterglows, the expected numbers in RASS was ∼ 4 events. The search for the opticalcounterparts for randomly selected six X-ray sources were conducted. Five out of six X-ray
error circles contained M stars.
With these high attention of the GRB observation in X-ray region, the Ginga (February
5, 1987 - November 1, 1991) gamma-ray burst detector (GBD) was specifically designed toinvestigate burst spectra in the X-ray regime. The success of the Ginga GBD observation of
GRBs made a stream for the next generation GRB satellite, High Energy Transient Experiment(HETE) mission. The details about the GBD observation are summarized in chapter 2.
In this thesis, we focus on the characteristics of the prompt emission of the unique GRBs
called X-ray flashes (XRFs) and X-ray rich GRBs. These GRBs have a high fluence in the
X-ray range (e.g. 2–30 keV) unlike the BATSE GRBs. XRFs and X-ray rich GRBs are firststudied in detail by the Ginga satellite [97] and the spectral characteristics are investigated by
BeppoSAX ([36], [42]). From the recent result form Kippen et al. [42], there is a indicationthat XRFs and X-ray rich GRBs are the same phenomenon as ordinary GRBs.
This thesis includes the detail studies of 18 XRFs and X-ray rich GRBs, and total 45
XRFs/X-ray rich GRBs/GRBs observed by HETE from February 2001 to September 2003.
The thesis consists as following. The review of GRB observations for both prompt emission andafterglow are given in chapter 2. The theoretical XRF/GRB emission models are summarized inchapter 3. The detail description about the HETE satellite is in chapter 4. The data reduction
and analysis method are described in chapter 5. The individual prompt emission characteristics
of 18 XRFs and X-ray rich GRBs are in chapter 6. The systematic study of XRFs and X-ray
rich GRBs are shown in chapter 7. We discuss the sky distribution and event rate of XRFs,
logN-logP of XRFs, the magnetic field strength at the shocked region, and theoretical models
of XRFs based on our observational results in chapter 8. Conclusion is given in chapter 9. The
development and calibration of the WXM detector response matrix, HETE GRB summary
tables, the figures of the all spectra and light curves, and the description about the constrainedBand function are presented in appendix.

Chapter 2
Observational properties of GRBs
2.1

Prompt emission

2.1.1

Spectral parameters of the BATSE GRB sample

The spectral characteristics of the prompt emission of GRBs are studied in detail with the
Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory[63]. The BATSE 156 bright bursts selected by the fluence of 30–1000 keV larger than 4 × 10−5

ergs cm−2 or by the 1s peak flux of 50–300 keV exceeding 10 photons cm−2 s−1 are investigated.

Each GRB spectra are divided by several time intervals, and there are 5500 spectra in total.
The BATSE GRB spectra are well fitted with the Band function [6]. The Band function is anempirical spectral model described as following:

fGRB (E) = A(E/100)α exp(−E(a + α)/Epeak )if

E < (α − β)Epeak /(2 + α) ≡ Ebreak ,andf (E) = A(α − β)Epeak /[100(2 + α)]α−β exp(β − α)(E/100)βif

E ≥ (α − β)Epeak /(2 + α),

where the four model paramters are
1. the amplitude A in photons s−1 cm−2 keV−1
2. a low-energy spectral index α
3. a high-energy spectral index β, and
24

(2.1)

2.1. PROMPT EMISSION

25

Figure 2.1: BATSE Epeak distribution of Band function fit [63].
4. a νFν “peak” energy Epeak .
The distributions of the BATSE spectral parameters (Epeak , α, and β) in the Band function
are at the figure 2.1, 2.2, and 2.3 respectively. As seen in figure 2.1, Epeak is tightly concentrated
around 250 keV. The power-law indices α and β are around −1 and −3 respectively. This result

suggests that the spectra of the prompt emission has a “universal” shape for most of the bursts.

26

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.2: BATSE α distribution of Band function fit [63].

Figure 2.3: BATSE β distribution of Band function fit [63].

2.1. PROMPT EMISSION

27

Figure 2.4: Left: The low-energy photon index α vs. the break energy E0 (E0 = Epeak / (2 +α)). Open squares are 54 BATSE events and the solid squares are the 22 Ginga events. Right:
Distribution of the fluence ratio between X-ray (2–10 keV) to γ-ray (50–300 keV) [97].

2.1.2

Characteristics of X-ray flashes

There are unique group of the GRBs which shows a high fluence in the X-ray range (2–30
keV). These GRBs are called X-ray flashes (XRFs). BATSE did not have a good sensitivity for
detecting XRFs due to the lower threshold energy of 30 keV. To investigate XRFs, we definitely
need the X-ray instrument. The detail studies of XRFs were performed by the GINGA [97]and by the BeppoSAX satellite [36] both of which possessed the X-ray instrument.

GINGA XRF sample
Since the Ginga gamma-ray burst detector (GBD) consisted of a proportional counter (PC; 2–
25 keV) and a scintillation counter (SC; 15–400 keV), GBD had a good capability of observing
XRFs. According to Strohmayer et al. [97], GBD observed the GRBs which show a high X-rayto γ-ray fluence ratio (figure 2.4 right). About 36% of the bright bursts observed by GBD have
Epeak energy around a few keV (figure 2.4 right). This Ginga result is not consistent with the
BATSE Epeak distribution which is concentrated around 250 keV. The Ginga sample indicatesthat GRB has a much broader population especially in a lower energy region.

28

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.5: Left: Histogram of T90 for hard GRBs (blue) and XRF(red). Right: The peak fluxin 2–25 keV and the photon index in the power-law spectrum [36].
BeppoSAX XRF sample
The BeppoSAX satellite had the Wide field X-ray instrument called Wide Field Camera (WFC)
which covers an energy range from 2 to 25 keV and a field of view of 40◦ × 40◦ . The definition

of XRF in BeppoSAX team was GRB which is seen in WFC but not in the γ-ray instrument

called Gamma Ray Burst Monitor (GRBM; 40–7000 keV). WFC observed 17 XRFs in 5 years[36]. The durations of XRFs are from 10 s to 200s, and similar to the long duration GRBs
(figure 2.5 left). The peak fluxes in 2–25 keV were in the range of 10−8 and 10−7 erg s−1 cm−2 .
The spectra in WFC energy range were described by simple power-law model with the photon
indices of −3 to −1.2 (figure 2.5 right).
WFC+BATSE XRF sample
Kippen et al. [42] searched for the GRBs and XRFs which were observed in both WXC and
BATSE. 36 hard GRBs and 17 XRFs are found in 3.8 years when WXM and BATSE wereoperated simultaneously. The WFC and BATSE joint spectral analysis of XRF shows that
their Epeak energies are significantly lower than those of the BATSE sample (figure 2.6). The
low and the high energy photon indices are the same as the hard GRB (α ∼ −1 and β ∼ −2.5).

Epeak has a good correlation with the 1s peak flux in 50–300 keV, but not with the T50 duration

2.1. PROMPT EMISSION

29

28 XRF+GRB
18 GRB
Bright GRB

Number of Bursts

8
6
4
2
0
1

10
100
Epeak (keV)

1000

Number of Bursts

8
6
4
2
0
-3

-2
-1
0
Low-Energy Index α

1Figure 2.6: The distribution of Epeak and α comparing with BATSE sample [42].

and the low-energy photon index α (figure 2.7).

2.1.3

src
Epeak
– Eiso relation (Amati’s relation)

Amati et al. [1] studied the spectral properties of the BeppoSAX GRBs with known redshifts(12 GRBs). They investigated the spectral parameters of time-average spectra at the GRB
source frame (redshift corrected spectrum) and found a good correlation between Epeak at the
0.52±0.06
src
source frame and the isotropic equivalent energies in 1–10000 keV; Epeak∼ Eiso(figure2.8). Atteia [5] applied this relation with combining the duration of the bursts and proposed
the empirical redshift indicator.

Comptonized Epeak (keV)30

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Epeak vs. Duration

Epeak vs. Index

Epeak vs. Intensity

1000

100

10

XRF
GRB
(Long)

XRF
GRB

0.1

1
10
Duration T50 (s)

100

-2

-1

0

1

Comptonized α

XRF
GRB(Long)

0.1
1
10Peak Flux P1024 (ph · cm-2· s-1)

Figure 2.7: The joint fit spectral parameters of XRF compared with BATSE sample. The
comparison between Epeak versus T50 duration, α, and 1s peak flux [42].

Figure 2.8: The correlation between the isotropic total energy and Epeak energy at the GRB
source frame [1].

100

2.1. PROMPT EMISSION

2.1.4

31

Lag/Variability relation

Norris et al. [56] investigated the spectral lags between two energy bands (25–50 keV and
100-300 keV or > 300 keV) of two samples: the 174 brightest BATSE bursts with durations
longer than 2s and six GRBs with known redshifts. The anti-correlation is found between γ-ray
hardness ratio or peak flux and the spectral lag for the bright BATSE GRB sample (figure 2.9).
For the GRBs with known redshift, the relationship between peak luminosity (L) and spectral
lag (τ ) is well fitted with a power law,L1053 erg∼ 1.3 × (

τ −1.15
)
.
0.01s

(2.2)

Fenimore and Ramirez-Ruiz [20] (see also [68]) investigated the correlation between the time
variability (V) and the luminosity of GRBs (7 GRB with redshifts). They found that high (low)variable GRBs are intrinsically more (less) luminous (figure 2.10),

L= 3.1 × 1056 V 3.35 erg s−1 .
dΩ

(2.3)

Schaefer et al. [87] performed a severe test for the lag/variability relation. If both thespectral lag and the variability have correlations with the luminosity, we should see a correlation
between the spectral lag and the variability. Since the lag and variability are possible to measureusing a large number of BATSE GRBs without the information of redshift, the validity ofboth relations can be examined in a good precision. Figure 2.11 shows the plots of lag andvariability for 112 BATSE bursts. The correlation coefficient is r = −0.45 (7.6 × 10−7 forchance occurrence), and the lag/variability has a good correlation. Thus both Lag-Luminosity
and Variability-Luminosity relation is valid in a high significance.

2.1.5

V/VmaxTne V/Vmax test [90] provides a quantitative evaluation of the uniformity of the radial distribution of the objects.
Assuming the Euclidean space, the observed peak count (background subtracted peakcounts) of a source will depend on its distance as r−2 , so thatrmax = r(

Cp 1
)2 .
Clim

(2.4)

32

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.9: Left: the correlation of the spectral lag between 25–50 keV (Ch 1) and 100–300
keV (Ch 3) vs. peak luminosity. The dashed line is the relation of equation (2.2). Right: theluminosity range is expanded to include GRB980425 [56].

2.1. PROMPT EMISSION

33

Figure 2.10: Left: Luminosity and variability for BATSE bursts with known redshifts. Right:
Luminosity and variability for BATSE bursts including GRB980425 [20].
We characterize the radial location of the source by the ratio of the volume V contained within
the radius r to the volume Vmax contained within the radius rmax . The ratio is (r/rmax )3 , so
V /Vmax = (Cp − 3
) 2.
Clim

(2.5)

If the sources are have a uniform distribution in space, the distribution of V /Vmax should be
uniform over the range 0–1. In this case, < V /Vmax > = 0.5. Since for sources with a uniform
space distribution, V /Vmax has a uniform distribution between 0 and 1, the r.m.s. error of< V /Vmax > will be (12n)−1/2 , where n is the number of objects. If the minimum signal-tonoise ratio is set at k, then the limiting count Clim is
Clim = kB 0.5 ,(2.6)

assuming Poisson statistics for the background count B.
Pendleton et al. [60] applied the V /Vmax test to the BATSE burst and found that <V /Vmax > is 0.329 ± 0.011, which is 15.5 σ away from a homogeneous distribution.

2.1.6

Line of Death Problem in low-energy index α

Preece et al. [62] investigated the low energy spectral index of the BATSE GRBs. The synchrotron shock model (SSM) predicts that the low energy photon index should not exceed −2/3

(e.g. [100]). Sari et al. [84] and Sari et al. [85] claimed that the time scale for synchrotron
cooling of the particles may be shorter than the duration of the pulses. In this “fast cooling”
case, the low energy photon index will be −3/2. Figure 2.12 shows the results from the BATSE

34

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.11: Lag/Variability correlation for 112 BATSE bursts. The solid line is the predicted−0.46
Lag/Variability relation; V = 0.0021τlag[87].

2.1. PROMPT EMISSION

35

Figure 2.12: Plot of the low energy index vs. Epeak . The SSM line of death (α = −2/3) isdrawn in dashed line and the accepted region in cooling spectrum (α = −3/2) is in dotted line
[62].

catalog of time-resolved spectroscopy of bright bursts overlaying the α = −2/3 (“death line”,
dashed line) and the lower boundary of the cooling spectrum (α = −3/2, dotted line). It isclear that the observed α is inconsistent with SSM.

Preece et al. [64] applied the additional test for SSM using the observed low and highphoton index (α and β) of BATSE data. Even in this study, Preece et al. [64] claimed that it
is not possible to explain the prompt emission of GRB with only SSM.

2.1.7

Extra high-energy spectral component in GRB941017

González et al. [28] analyized the EGRET’s calorimeter TASC (Total Absorption Shower
Counter) data of GRB941017 and found the extra high energy component expressed as thephoton index −1 up to ∼ 200 MeV. Its fluence is greater than the lower-energy component
observed by BATSE. This high-energy power-law does not show the cutoff, meaning more

36

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.13: Left: light curves of GRB941017 a) BATSE-LAD, b) EGRET-TASC 1–10 MeV,
and c) EGRET-TASC 10–200 MeV. Right: time-resolved νFν spectrum of GRB941017. The
data are jointly analyzed with LAD and TASC [28].
energy is radiated above 200 MeV (figure 2.13). González et al. [28] argued that possibility of
the ultra-relativistic hadrons producing the MeV γ-rays by inducing electromagnetic cascades
through photomeson and photo-pair production.

2.1.8

GRB tail emission

Connaughton [11] developed the sophisticated way of subtracting the background in BATSE
data and studied the weak GRB emission on a longer time scale. Connaughton [11] summed
and averaged the 400 BATSE long GRBs and found the statistically significant tail emissionin γ-ray lasting for 1000–2000 seconds after the trigger. The author also found that this tailemission is independent with the duration of the prompt emission and also with burst intensity.
Although it is not clear whether the emission is coming from the prompt or the afterglow, some2.2. AFTERGLOW

37

Figure 2.14: Left: background subtracted light curve of GRB980923 [27]. Right: Light curvefor 400 long GRBs [11].
signature of the external shock might be seen in the γ-ray region.

2.2

Afterglow

2.2.1

The supernova-GRB connection

Supernova Bump
GRB970228 is the first GRB for which an optical/X-ray counterpart was found. However,the story did not end with this excitement. The optical afterglow of GRB970228 showed thesignificant deviation from the pure power-law decay about 1–2 weeks after the burst [25]. Thismight be the evidence for the presence of a supernova component in the light curve. The
first suggestion of the supernova bump in the GRB afterglow was made by Bloom et al. [8]of GRB980326. This was the very important observational indication about the association
between a supernova and a GRB.
SN1998bw/GRB980425
The most suggestive evidence for the supernova and GRB connection before the HETE-2 era
is SN1998bw/GRB980425. The BeppoSAX detected the GRB980425 and the WFC error box
contained the supernova SN1998bw located in a spiral arm of the nearby galaxy ESO184-G82
with a distance of 40 Mpc (z=0.0085) [24] (figure 2.16). The chance probability of detecting
any supernova with peak optical flux a factor of 10 below that of SN1998bw in the error box is

38

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.15: Top: V, Rc , Ic band lingt curves of GRB970228. The dotted curves indicate
power-law decays with −1.51 and redshifted SN 1998bw light curves [25]. Bottom: the R band
light curve of GRB980326. Overlaied curves are the power-law afterglow decline summed withthe bright supernova light curve at different redshifts [8].

2.2. AFTERGLOW

39

N
W

Figure 2.16: Image of the galaxy ESO 184-G82 with (left) and without (right) SN1998bw [24].
10−4. The optical spectrum indicated that SN1998bw is a type Ic supernova.
Iwamoto et al. [39] performed the model fitting to the light curve and the spectrum of
SN1998bw. They found that SN1998bw can be well reproduced by an extremely energetic
explosion of a massive star composed on mainly of carbon and oxygen (figure 2.17). And the
kinetic energy of the ejecta is calculated to be (2–5) × 1052 erg. They argued that this extremely

large energy could produce the relativistic shock which is required for a GRB.
Supernova association with GRB030329

HETE-2 observed the one of the brightest GRB, GRB030329 [107]. Its optical afterglow was
12.4th magnitude at 67 minutes after the burst [86]. The redshift of z=0.167 [30] is the closest
GRB except GRB980425/SN1998bw.
About ten days after the burst, the spectral signature of type Ic supernva emerged in theafterglow ([96] and [37]; figure 2.18). This supernova is named as SN2003dh. As seen in the
figure 2.18, the spectrum of SN2003dh is very similar to the type Ic supernova SN1998bw. The
expansion velocity is estimated to be 36,000 ± 3,000 km s−1 (0.12 ± 0.01c). GRB030329 shows
the direct observational evidence that indeed core-collapse event produces the GRB.

2.2.2

Optically Dark GRB

Only 50% of the GRB well-localized by BeppoSAX had optical transients (afterglow), whereas
an X-ray afterglow is present in 90% of cases. De Pasquale et al. [17] compared with the X-ray
afterglow and optical bright/dark GRBs observed by BeppoSAX (figure 2.19). The optical dark

40

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Luminosity ( erg sec-1 )

1043

56

Co decay

CO138 & SN 1998bw
42

10

1041

CO60 & SN 1997ef
CO21 & SN 1994I

0

50

100

150

200

time since the GRB ( days)

Figure 2.17: Light curves of three type Ic supernova, SN1998bw, 1997ef, and 1994I. The solid
curves are the models. The light curve of SN1998bw are well fitted in the following parameters:
the stellar mass MCO = 13.8 MSolar , the explosion energy Eexp = 3 × 1052 erg, and the mass ofthe synthesized 56 Ni M56 = 0.7 MSolar [39].

2.2. AFTERGLOW

Figure 2.18: Spectral evolution of the afterglow of GRB030329 [37].

41

42

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.19: Left: NH vs. spectral index of X-ray afterglow observed by BeppoSAX NFI.
The filled dots are dark GRBs and empty dots are the optically bright GRBs. There are no
significant difference among them. Right: X-ray vs. optical flux. The empty dots are theoptically bright GRBs. The solid arrows are optically dark GRBs. [17]GRBs are GRBs without the optical transient detection. They found that X-ray afterglow of
the optical dark GRBs has about 5 times lower flux. Under the assumption that the optical to
X-ray spectrum is the same, the optical flux could be ∼ 2 magnitude lower than the opticallybright GRBs. They argued that the highly absorbed environment of the optical light might becausing the optically dark GRBs.

Faint optical afterglow: GRB 021211

The nearly real-time localization of GRB021211 [15] provided by HETE-2 makes it possible
to solve the problem of “optically dark” GRB. The early optical observation had started 90,
108, and 143 seconds after the burst. The optical afterglow of GRB 021211 is intrinsicallymuch fainter than other GRB afterglow (figure 2.20). This burst would have been classified as“optically dark” GRB without the rapid follow-up observation.

2.2. AFTERGLOW

43
10

12

14

R (mag)

16

18

20

22

24

0.001

0.01

0.1
1
Time After the Burst (Days)

10

Figure 2.20: Light curve of GRB 021211 and other GRBs. The light curve of GRB021211 canbe fitted with two component power-law; an initial steeply declining “flash”, f ∝ t−α with α ≈1.6 and typical afterglow behavior with α ≈ 1 [21].

Extinction by dust; GRB 030115
Rapid follow-up observations of GRB 030115 which was localized by HETE-2 show the convincing signature that the optical afterglow is extinguished by dust. Figure 2.21 shows the nearinfrared and optical afterglow spectrum and the best fit model, assuming the dust extinction[48]. The afterglow property of GRB 030115 provides a good case of “optically dark” GRB
caused by dust absorption.
High redshift GRBs
Fynbo et al. [23] suggests one of the implications for dark GRBs as a large fraction of GRBs
occur at redshifts z ≥ 7 and are hence invisible in the optical due to Ly-α blanketing andabsorption by intervening Lyman-limit systems. Authors suggest that it is essential to conduct
deep (Rlim ≥ 24 at less than 1 day after the trigger) follow-up imaging at optical and infrared

wavelength to answer the question why some bursts are darker than others.

2.2.3

Standard energy reservoir in GRBs

Interpreting the break in the afterglow light curve as the conical jet structure of GRBs, we
can correct the geometry and calculate the “true” released energy in γ-ray. In this conical jet

44

CHAPTER 2. OBSERVATIONAL PROPERTIES OF GRBS

Figure 2.21: Near infrared and optical afterglow spectrum (K, H, J, i∗ , and r∗ band) of
GRB030115. The solid curve is the best fit model assuming extinction by dust for the data
[48].

2.2. AFTERGLOW

45

Figure 2.22: Left: Distribution of the isotropic γ-ray energy (top) vs. the jet opening angle
corrected γ-ray energy (bottom) [22]. Right: Distribution of the jet opening angle corrected
γ-ray energy [9].
picture, the break in the afterglow light curve can happen for two reasons. First, when therelativistic shell has slowed down and the bulk Lorentz factor Γ reached to Γ ≈ θj (where θj is

the opening angle of the jet), the flux drops suddenly. Second, the side-way expansion of thejet makes the deceleration of the ejecta much faster.
Frail et al. [22] calculated the jet opening angle for 17 GRBs with known redshifts using
the jet break times tj . The formula is:tjθj = 0.057
1day!3/8 

1+z2

−3/8 "

Eiso (γ)
1053 ergs#−1/8 ηγ0.2

1/8 

n0.1cm−3

1/8

,

(2.7)

where ηγ is the efficiency of the fireball in converting the energy in the ejecta into γ-rays andn is the mean circumburst density and assuming the constant values for these paramters.
The result is surprising. As you can see in figure 2.22, the jet opening angle corrected total
γ-ray energy Eγ is tightly concentrated around 5 × 1050 ergs. Bloom et al. [9] calculated theEγ for a larger GRB sample and much reliable value of the ambient density. Bloom et al. [9]confirmed the tight Eγ value of Eγ = (1.33 ± 0.07) × 1051 ergs. This energy is comparable toordinary supernovae.

Chapter 3
GRB theory
3.1

GRB emission models

The dynamics of GRB is well described in the framework of the “fireball” model (the details
about the fireball model is in the review by Piran [61]; we refere the review by Van Paradijs
et al. [106] here). In this model, a large amont of energy is released into a small volume andthe explosion will follow. The key is a large fraction of the energy is transformed into a small
fraction of the unit mass of matters. Let us consider the release of an energy E = 1052 E52
ergs into a sphere with radius rin . A rest mass M0 of baryons is contained in the volume, andthe energy-to-mass ratio in the initial fireball is thus η = E/M0 c2 . The evolution of the fireballfrom these initial condition depends on one other paramter, the optical depth. If the primarily
photon energies in MeV, the optical depth is very high due to the photon-photon scatteringand pair production. Thus, the internal energy can only be converted into kinetic energy
with an adiabatic expansion. Adiabatic expansion can be describied from thermodynamics,
T ′ V γa −1 = const., where T ′ is the rest-frame temparature, V is the source volume, and γa isthe adiabatic index of the gas; γa = 4/3 for an ultrarelativistic gas. If we convert V into theradius of the volume R and substitute γa = 4/3, T ′ ∝ R−1 . The total internal plus kinetic

energy in the frame of an external observer is E = ΓM0 (kT ′ /mp + c2 ), where Γ is bulk Lorentz

factor of the fireball and mp is the proton mass. For relativistic temperatures, the first term
dominates, so E ∝ ΓT ′ = const. Combined with the previous thermodynamic relation, we haveΓ ∝ R. The bulk Lorentz factor of the gas thus increases linearly with radius, until it saturates

at a value Γ0 ∼ η, at a radius rc ∼ ηrin . Because all the matter has moved with v ≃ c beyond

rc , it is all piles up in a thin shell with thickness R/Γ2 . This is the picture how Γ evolves in
the fireball model.
463.1. GRB EMISSION MODELS

Slow shellCore collapse SNe

47
External
shock(interaction with ISM)

Internal
shock(shell collision)

Fast shell

X-ray/Optical/Radio

γ-raysISM

GRB
central engine

NS-NS marger∼1017 cm

∼1014 cm
Prompt emission

Afterglow

Figure 3.1: Schematic figure of the GRB prompt and afterglow emission model. The collapseof massive star (collapsar) and/or neutron star (NS) marger which finally form a black hole
are the most supported central engines for GRBs. In the internal shock model, the prompt
emission is produced by the particles accelerated via the internal shock which is due to thecollision of the relativistic moving shells. The particles radiating the afterglow are accelerated
by the external shock which is the interaction between the marged shell and the interstellar
matters.

When the relativistic fireball expands and achieves the optically thin, its kinematic energy
translates to thermal energy via shock. And finally, the thermal energy will be radiated as
Synchrotron radiation. There are two types of the shock (see figure 3.1). First is internal shock
which is due to the internal collisions of various speeds of shells. Another shock is originatedfrom the collision between the expanding shell and the surrounding inter-stellar matters called
external shock. The prompt emission of GRB is considered as the result of the internal shock,whereas the afterglow is caused by the external shock.
Here, we review the two GRB prompt emission models proposed by Tavani [100] and Sari
et al. [84]. These models give us the explanation for how to produce the Synchrotron radiation
through the shock and how to reproduce the observed GRB spectrum.

48

CHAPTER 3. GRB THEORY

3.1.1

Synchrotron shock model (SSM)

Tavani [100] shows that the synchrotron shock model (SSM) predicts a specific shape of GRB
spectrum in agreement with broadband GRB spectra (e.g. Band function).
The environment of the GRB site is assumed to be surrounded by an optically thin nebular
medium (a low-density ISM, a SNR, or a mass outflow from a companion star in a binary
system). An MHD relativistic wind is a mixture of electromagnetic fields, e± -pairs, andbaryons. A relativistic wind is assumed to be produced by a compact star. If the relativistic
wind interacts with a nebula not in pressure equilibrium with MHD outflow, the relativistic
motion of the resulting shock front is characterized by a bulk Lorentz factor Γ.
Before the relativistic MHD plasma interacts with a shock front, the particle distributionfunction is assumed to be completely thermalized and characterized by a single (relativistic)
particle energy or temperature. Three-dimensional distribution of the radiating particle number
per energy interval dγ and solid angle dΩ is described by a relativistic Maxwellian distribution:of particles
n3D
th (γ, α) dγ dΩ =N±M γ 2 −γ/γ∗edγ dΩ,
8π γ∗3(3.1)

where γ = E± /m± c2 , γ∗ = kB T ∗ /m± c2 , with T∗ the preshock distribution temperature ofradiating particles of energy E± , kB the Boltzmann constant, and c the speed of light, dΩ =d cos αdφ the solid angle with α the pitch angle of the particle trajectory with respect to the
local magnetic field direction, φ the azimuthal angle, and N±M a normalization constant.
The postacceleration particle energy distribution function can be drastically altered by theformation of a suprathermal component when the acceleration process takes place at the shock
front. The altered postshock distribution function with a suprathermal power-law tail of indexp:

fα N±  γ 2 −γ/γ∗
+K
e
n3D
(γ,
α)
=
ps
4π
γ∗3
!

γ
γ∗

!−p 
,

(3.2)

where N± and K are normalization constants, and fα takes into account the possible spatial
nonuniformity of the pitch angle distribution with respect to the pitch angle. The energy rangeof the power-law distribution is γ∗ ≤ γ ≤ γm , where γm , which is to be determined by balancing

acceleration and cooling loss in the shock frame, is a maximum energy of shock-accelerated
particles.
The most efficient acceleration process will be at a condition for K = 1 / (eγ∗ ). Thiscondition is achieved at γ = γ∗ when the particles at the initial average energy γ∗ and thermal

3.1. GRB EMISSION MODELS

49

low-energy tail is modified at the top of the distribution resulting from fast acceleration. The
condition τa′ ≤ τr′ , where τa′ and τr′ are the acceleration and radiating timescale at the rest
frame, is the crucial requirement for a suprathermal component in GRB spectra.

The synchrotron spectral energy emissivity per unit volume and solid angle Jνs (α) isJνs (α)Z ∞=1psν (γ, α) n3D
ps (γ, α) dγ

31/2
16π 2

=

!

N±
c2

′3



!





q
ν 
fα Bps sin α F  ∗2m± cν⌋ sin α(3.3)

with νc∗ the critical frequency corresponding to the preshock temperature γ∗ of particles ofcharge e′ , psν (γ, α) the single-particle synchrotron power, N± the local q± -pair number density,
1−pc2 a normalization constant, c2 = 2 − 5/e + [1 − ym]/[e(p − 1)], and F (w) a dimensionlessspectral function given by

F (w ) ≡

Z 1
0

2 −y

′

y e F

!

1
w
dy +
2
y
e

!

(3.4)

ym = γm /γ∗

(3.5)

Z ym
1

−p

′

y F

w
dy
y2

where we denotedw = ν/(νc∗ sin α),

y = γ/γ∗ ,with′F (x) ≡ x

Z ∞x

K5/3 (x′ ) dx′(3.6)

the synchrotron spectral function, and K5/3 (x′ ) the modified Bessel function of order 5/3. The
differential proper intensity in the shock comoving frame (proper intensity) ISν is obtained after
an intergration of JνS over the solid angle dΩ(α) and emission volume dV
IνS =

Z Z

Jνs (α) dΩ(α) dV(3.7)

The observed flux FνS can be obtained from the proper intensity IνS by dividing by thesquare of the source distance D, and by taking into account the possible effect of relativistic
beaming and possible cosmological effects.
In this SSM, Epeak corresponds to the synchrotron critical frequency νc = 3γ∗2 eB sin α/(4πmc).
The electron spectral index p has to be less than 3 for Epeak to be the synchrotron critical frequency (figure 3.2).

50

CHAPTER 3. GRB THEORY

4
ν3

−

ν

(p−3)
2

νFν

E

1
ν3

ν

−

(p−1)
2

Fν

ν

E

−2
3

Nν

ν

−

(p+1)
2

νm
Figure 3.2: The spectrum calculated by synchrotron shock model proposed by Tavani. The
spectral shape is the same as “classical” synchrotron radiation with the slope change at thesynchrotron critical frequency νm . The light blue region is the observing energy band of GRBs.

3.1. GRB EMISSION MODELS

3.1.2

51

SSM with synchrotron cooling

There are several reasons that the simple SSM [100] is not the appropriate model for GRB
prompt emission. First, as seen in figure 3.2, the low energy photon index α is constant value−2/3, so the observed α value should be narrow distribution around −2/3. However, according
to the BATSE results, α is scattered from −2 to 0 (see figure 2.2). Second, since Epeak isconcentrated around 250 keV in BATSE data, magnetic fields will be 107 G if we use thetypical value for electron Lorentz factor γ ∼ 100 and bulk Lorentz factor Γ ∼ 100. Then, thesynchrotron cooling time tcool at the observer’s frame is tcool ∼ (1 + z) / (ΓγB 2 ) ≤ 10−6 s. So
the synchrotron loss effects should be apparent in the GRB spectrum.

Sari et al. [84] proposed a SSM taking into account the effect of the synchrotron cooling.
They consider two possibilities depending on the cooling timescale tcool and the hydrodynamic
timescale of the expanding shell thyd . The total duration of the burst is due to the time forconverting the bulk of the kinetic energy of expanding shell into thermal energy via shocks,
on the other hand, the individual peaks of GRB is because of the shotlike thermalization.
The width of the individual peaks represent the cooling time scale. So, the burst having acomplicated time structure is in the case of thyd > tcool (so called “fast cooling”). In thyd < tcool(so called “slow cooling”), the kinetic energy of the shell is turned rapidly into thermal energy,
but the electrons loose their energy via radiation in much slower timescale. This regime cancreate the burst with a smooth single-hump and an afterglow emission.
Sari et al. [85] calculated the spectrum in SSM model including the cooling effect. Assuming
the electron distribution of N(γ) ∝ γ −p , the spectrum has three characteristic frequencies; thesynchrotron self absorption frequency νa , the synchrotron critical frequency at electrons withminimum Lorentz factor νm , and the synchrotron cooling frequency νc (figure 3.3). The lowerand higher end of the spectrum is the same for both “fast cooling” and “slow cooling” process.
At the higher frequency range (ν > νm for “fast cooling” and ν > νc for “slow cooling”), thenumber of the electrons with Lorentz factor of ∼ γ is proportional to γ 1−p due to the power-law
assumption of the electron distribution. Their energy is proportional to γ 2−p . As the electronscool, they deposit most of their energy into a frequency range νsyn (γ) ∝ γ 2 , hence Fν ∝ γ −p

∝ ν −p/2 . On the other hand, at the frequency below νa , the spectrum is the Rayleigh-Jeans

portion of the blackbody spectrum Fν ∝ ν 2 γ(νtyp ) where γ(νtyp ) is the typical Lorentz factorof the electrons. If we assume that γ(νtyp ) ∝ ν 0 , Fν ∝ ν 2 . In the range of νc < ν < νm in the“fast cooling” spectrum, all the electrons cool down on the dynamical timescale tdyn . Since theenergy of an electron is ∝ γ and its typical frequency is νsyn ∝ γ 2 , Fν ∝ γ −1 ∝ ν −1/2 . The

52

CHAPTER 3. GRB THEORY

spectral shapes in other frequency ranges are same as the Tavani’s simple SSM (this argument
refers to Granot et al. [29]).
In this cooling SSM, the prompt emission is in the “fast cooling” phase, and peak energy inνFν spectrum corresponds to νm . Whether Tavani’s SSM or Sari’s SSM, Epeak is synchrotron
critical frequency of Lorentz factor of γm .

3.1. GRB EMISSION MODELS

Fast cooling((p−2)
2

4
ν3

νFν

ν

ν

ν

p
−
ν 2

Fν

ν

ν

ν

−3
2

ν

ν

ν

νc

νm

−

1
3

ν

ν

ν

−

−

(

)

ν

−

ν

νa

p
2

Ε

(p+2)
2

Ε

Ε

ν

−2
3

Nν

(p−2)
2

( −1)
2

2

Ε

−2
3

−

ν3

−1
ν 2

2

νa

(p−3)
2

−

Ε

1
3

Fν

Nν

−

3

νFν ν

ν

Slow cooling

1
2
ν

4
3

ν

53

νm

νc

(p+2)
2

Ε

Figure 3.3: The synchrotron cooling spectrum proposed by Sari et al. [85]. There are twophases, fast cooling and slow cooling, whether νc < νm or νc > νm . The light blue region is theobserving energy band of GRBs.

54

CHAPTER 3. GRB THEORY

3.2

Theoretical models for XRF

There are key phenomena which could be a breakthrough to understand the prompt emissionof GRBs. They are X-ray flash (XRF) and X-ray rich GRB. XRF and X-ray rich GRB are the
GRBs having a high fluence in the X-ray range. We review several theoretical models of XRF
which attempt to explain in the unified physical picture from XRFs to ordinary GRBs.

3.2.1

Off-axis jet model

Yamazaki et al. [112] proposed the XRF model that the viewing angle is much larger than thecollimation angle of the jet (left panel of figure 3.4). In this model, the high X-ray to γ-ray
fluence ratio is due to the relativistic beaming factor δ ≡ Γ[1 − β cos(θv − ∆θ)] in the case ofobserving the GRB from the off-axis direction (right panel of figure 3.4). Both the peak flux
ratio and the fluence ratio increase as the viewing angle increases.
According to the model, Epeak energy of GRB (∼ 250 keV) will be shifted to low energy
range because of the smaller relativistic beaming effect. So Epeak can be estimated as ∼ ν0′ /δ, where δ ≡ Γ[1 − β cos(θv − ∆θ)] ≃ [1 + Γ2 (θv − ∆θ)2 )]/2Γ and θv > ∆θ. Epeak of XRF asa function of the viewing angle is plotted in figure 3.5 assuming the GRB Epeak energy of 300
keV and the bulk Lorentz factor of 100. Epeak energy of a few keV could be achieved at theviewing angle larger than 5◦ in the case of the half opening angle of the jet ∼ 1◦ .

In this original model, since the fluence at the Epeak is proportional to δ −3 , XRFs should

not be at high redshift. However, the BeppoSAX team revisited the XRF data and updated
the value of < V /Vmax > from 0.56 to 0.27. This number is very close to the hard GRB. The
BeppoSAX XRF observation suggests that the XRF could be at large cosmological distances.
Yamazaki et al. [113] changes some model parameters of off-axis model, and found that thehard GRB at the viewing angle of 0.05 radian (∼ 2.9◦ ) with the half opening angle of 0.03
radian (∼ 1.7◦ ) could be XRF in the redshift of 1.5.

3.2.2

Photosphere-dominated fireballMészáros et al. [51] studied the photosphere of smaller radius than the radius where the internal
shock is occurring (1012 −1014 cm). The flow starts from a minimum radius r0 = ctv,min = 107 r0,7cm, and the Lorentz factor accelerates as Γ ∝ r up to a coasting (or saturation) radius rc ∼r0 Γf . The shells with Lorentz factors of ΓM and Γm eject from a starting radius r0 and collide

at radius rsh . The energy radiated in the shock by this merged shells can be enough to create3.2. THEORETICAL MODELS FOR XRF

55

Figure 3.4: Left: The schematic figure of the off-axis GRB model. XRF is the hard GRB
observing from the large viewing angle. Right: The peak flux ratio (upper panel) and fluence
ratio (lower panel) of 2–10 keV to 50–300 keV as a function of viewing angle (see Yamazaki etal. [112] for details).

56

CHAPTER 3. GRB THEORY

Figure 3.5: The observed Epeak energy as a function of viewing angle assuming the GRB Epeak= 300 keV and the bulk Lorentz factor of 100. The solid lines correspond to the half opening
angle of the jet are 1◦ (black), 2◦ (red), 3◦ (green), 5◦ (blue), and 10◦ (sky blue).

pairs to be optically thick to Thomson scattering. The radius r± is defined as the pair comoving
scattering depth τ ∼ 1.
For shocks occurring at rsh < r± , the scattering optical depth of the shocked shells canbecome τ ′ ≥ 1 (the prime corresponds to the value at the rest frame). It is expected that pair-

production acts as a thermostat, and for comoving compactness parameters (parameter for
judging whether the source is optically thick for γγ interaction or not) 10 – 103 , the comoving
pair temperature T±′ is 3 – 30 keV. For a center of mass bulk Lorentz factor Γc = (ΓM Γm )1/2
= 300Γc,2.5 , the observer-frame pair-producing shock radiation peak is at′′−2hνx,sh ∼ 100 T±,10
τ±,3
ζ0.2 Γc,2.5 [2/(1 + z)] keV.

(3.8)

Since the term Γc [2/(1 + z)] depend on z and Γ, the typical peak energy is 20 – 100 keV. Notethat because the pair-production is needed in this model, Γc can not be too low. Therefore thepeak energy of ∼ 20 keV could be achieved in the case of a very high redshift (z∼ 10).

3.2. THEORETICAL MODELS FOR XRF

57

Optically thickpair region

Central Engine

r0

rsh

rr

Figure 3.6: Schematic drawing of the photosphere-dominated fireball. rsh is the radius of thecollision of the two shells. r± is the radius of the optical depth of the pair-production τ± ∼ 1.

When rsh < r± , the optically thick pair-production region exists from rsh to r± . This region

could produce X-ray excess GRBs.

3.2.3

Dirty fireball model

The small bulk Lorentz factor GRBs called dirty fireball model [16] could produce XRFs. The
hard GRBs observed with BATSE have a bulk Lorentz factor from 100 to 1000 (the authors
called “clean fireball” as Γ0 ≫ 300). On the other hand, the dirty fireball has a bulk Lorentz

factor Γ0 ≪ 300. In their model, the spectrum is extremely sensitive to Γ0 . Since the peakenergy is ∝ Γ40 , it changes by 8 orders of magnitude between Γ0 = 3000 and Γ0 = 30. The−8/3

duration of peak power output is just the deceleration timescale which is ∝ Γ0

. The dirty

fireball produces transient emissions that are longer lasting and most luminous at X-ray energies
and below (figure 3.7).

3.2.4

Structure jet model

Rossi et al. [79] investigated the jet which has a beam pattern where the luminosity per unit
solid angle decreases smoothly away from the axis (figure 3.8). Both the energy per unit solid
angle (ǫ) and the bulk Lorentz factor (Γ) depend as power laws:ǫc0 ≤ θ ≤ θcǫc ( θθc )−2 θc ≤ θ ≤ θj

(3.9)

Γc
0 ≤ θ ≤ θcΓc ( θθc )−αΓ , αΓ > 0 θc ≤ θ ≤ θj

(3.10)

ǫ=
and
Γ=

(

(

where θj is the opening angle of the jet, θc is introduced to avoid a divergence at θ = 0. The
power-law index of −2 is assumed in this model, however, this is not a necessary ingredient ofCHAPTER 3. GRB THEORY

52
6

48

10 s

44

Γ =
0

40

1 s

3000

p

-1

log [ P ( ε ,t) (ergs s ) ]

58

36
32

Γ = 300

Γ = 30

0

0

28
-1 2

-9

-6

-3

0

3

6

log [ ε (t) ]pFigure 3.7: The plot of the photon energy ǫ in the unit of me vs. the spectral power P(t). Thelines correspond to the different values of bulk Lorentz factors. The peak photon energy ǫp will
decrease and the duration will increase when the Lorentz factor goes down [16].

3.2. THEORETICAL MODELS FOR XRF

59

ObserverFigure 3.8: Schematic drawing of jet which has an axisymmetric energy distribution.
the model.
In this model, Γ tends to be lower when the viewing angle increases. This kind of “structure”
jet is predicted by the Collapsar model [116] and XRF could be the off-axis viewing of thestructure jet.

3.2.5

Relativistic wind with a small contrast of high Lorentz factor

Mochkovitch et al. [54] investigated the internal shock model which a central engine generates
a relativistic wind with a non uniform distribution of the Lorentz factor. In their two shell toy
model, Epeak can be express as,
Ė x ϕxy (κ)
Ep ∝ 2x 6x−1 ,τ Γ̄

(3.11)

where Ė is the average injection power into the wind, κ is the ratio of Lorentz factor of 1st(Γ1 ) and 2nd (Γ2 ) shell (κ = Γ2 /Γ1 ), τ is the time difference between 1st and 2nd shell, Γ̄ isthe average Lorentz factor (Γ̄ = (Γ1 + Γ2 )/2), and ϕxy (κ) is an increasing function of κ for all
reasonable value of x and y. According to this equation, Epeak is a decreasing function of Γ̄ aslong as x > 1/6. XRFs are obtained with “clean fireballs” (large Γ̄) while winds with large
baryon loads (“dirty fireballs”) lead to a harder spectrum because internal shocks occur closer
to the source at a higher density.
The excellent agreement with the observed Epeak distribution could be achieved in the case ofx = y = 1/4 (figure 3.9 left). According to Mochkovitch et al. [54]; 1) the redshift distributionof XRFs are identical to the hard GRBs, 2) the duration and injected power are not very
different between XRFs and hard GRBs, and 3) the most effective way of producing XRFs isa reduction of the constant κ = Γ2 /Γ1 and an increase of the average Lorentz factor Γ̄.

60

CHAPTER 3. GRB THEORY

Figure 3.9: Left: The Epeak distribution in the case of x=y=1/4. The dashed line represents
the whole population and the solid line is the bursts which can be detected by BATSE. Right:
The simulated results of Epeak vs. peak flux [54].

3.2.6High redshift GRB

Heise et al. [36] proposed that XRFs could be GRBs at the high redshift. According to Lamband Reichart [46], if many GRBs are produced by the collapse of massive stars and/or theneutron star margers and their evolution rate is proportional to the star formation rate ([101],[102]), GRBs could occur out to at least z ∼ 10, and possibly to z ∼ 15–20. If this is the casefor XRFs, the observed spectrum of the prompt emission is highly redshifted. For example, theEpeak energy of 300 keV at the source frame is observed as ∼ 30 keV in the case of redshift of

10. However, there are several observational evidences that the XRF is not a very high redshift(e.g. GRB011030, GRB020427 [10], GRB020903 [95] and so on).

Chapter 4
Instruments
4.1

HETE-2 Satellite

The High Energy Transient Explorer 2 (HETE-2; [78]) is the first astronomical satellite dedicated to observe the GRBs. The HETE-2 (hereafter HETE) satellite was successfully launchedon October 9, 2000 using a Pegasus rocket. There are two unique features in HETE. First,
HETE can provide the location of GRBs with localizations of a few tens of arcminutes to a
few tens of arcseconds, with delay times of 10 s to a few hours, to the ground observers. This
capability gives us the opportunity to observe GRB afterglows in multi-wavelengths from avery early phase. Second, broad-band spectroscopy (2–400 keV) of GRBs are possible with the
combination of the X-ray and γ-ray instruments. This ensures us not only to detect the various
classes of GRBs, but also to determine the spectral parameters of the prompt emission. The
information about the prompt emission is essential for study of the central engine which evenexcellent observations of the afterglows can provide limited information.
The FREnch GAmma TElescope (FREGATE; [4]), which gives the trigger to GRBs, are thethree scientific instruments on-board HETE, the Wide-field X-ray Monitor (WXM; [41], [92]),
which is the key instrument to localize GRBs in ∼ 10′ accuracy within a few tens of seconds,

and the Soft X-ray Camera (SXC; [109], [55]), which localized the GRB in a few arcsecond
accuracy. The details about each instruments are described in the next section.

There are three primary ground station (PGS; [13]) located at Singapore, at the Kwajalein
Atoll in the Republic of the Marshall Islands, and at Cayenne, French Guinea. The commanding
and the downloading the data from the spacecraft are possible with these three PGSs. The
S-band is used in the communication, and the data rates are 31.25 kbps for uplink and 250kbps for the downlink. The burst alert network (BAN) consists of fourteen burst alert stations
61

62

CHAPTER 4. INSTRUMENTS

Table 4.1: HETE satelliteMass
124 kgEnvelope
89 cm × 66 cm
Orbit
625 km circular, 0-2 degree inclination
Mission Life> 2 years
Attitude
Instruments are pointing at the anti-solar direction
Data Processing 4 T805 transputers, 8 DSP56001
Downlink
S-band (2.272 GHz) 250 kbps
VHF (137.96 MHz) 300 bps
UplinkS-band (2.092 GHz) 31 kbps

Figure 4.1: Left: HETE-2 spacecraft under a ground testing. Right: The Pegasus rocket on
the bottom of the airplane.
([14]; [108]; figure 4.4). Information about GRBs detected by HETE is transmitted to BAN
in real time at a frequency of 137.96 MHz 300 bps, immediately relayed to the HETE Mission
Control Center at MIT, and then sent to the GRB Coordinates Distribution Network (GCN).
Then the GCN send the information in the various forms (email, pager and/or internet socket
messages) to the observers around the world (figure 4.3).

4.2. FREGATE

63

ACS camera
WXM
SXC

FREGATE

Boresight
cameraFigure 4.2: Schematic drawing of the HETE-2 spacecraft.

4.2

FREGATEThe french gamma telescope (FREGATE) [4] plays the essential role in triggering the GRB
events. Thanks to its wide energy coverage, FREGATE is also a key instrument for the spectroscopic study of GRB prompt emission. Even the bursts outside of the field of view of WXM
can be studied with FREGATE, and their positions can be determined the IPN collaboration.
The FREGATE detector consists of a cleaved NaI crystal (a cylinder of 10 mm thick and 71
mm in diameter) read by a photomultiplier (Hamamatsu 1848, figure 4.5). The cleaved crystals
with no dead layer are used to extend the spectral coverage in the low energy band (∼ 6 keV),
together with the beryllium window in front of the crystal. The geometrical area of the sum offour detectors is ∼ 160 cm2 . To monitor the gain of the detector, the two radioactive sourcesof 133 Ba are placed outside of the detector. The effective area curve at several incident angle
is in figure 4.6
The detectors are guarded by a graded shield made of lead, tantalum, tin, copper, andaluminum which stops the photons from the outside of the field of view (e.g. the diffuse X-ray
background).
The data product of FREGATE is summarized in table 4.3. There is a two type of the

64

CHAPTER 4. INSTRUMENTS

HETE-2GRB

S band- Uplink commands- Downlink data
- Burst alart message- GRB location

VHF- BurstClart message- GRB Location

Primary
GroundStations

Ground Observers

Burst Alert Stations

Internet

Internet

GRB Coordinate
Distribution Network (GCN)

Mission Control Center(MIT)

Figure 4.3: Burst alert network

Maui
Bangalore
CayenneKiritimati

Bohol
Palau

Galapagos
Marquesas

Natal

Gabon

MalindiAscension

Figure 4.4: SGS status

Singapore

Kwajalein4.3. WXM

65

Table 4.2: FREGATE performance
Energy range
6–400 keV
Effective area (4 detectors, on axis)
160 cm2
Field of view
70◦
Energy Resolution∼ 12 % @122 keV
Table 4.3: FREGATE data type
Data type
HK
TH

SP
PH

time resolution description–
The house keeping data.
Available for all time.
0.16 s / 0.32 s The time history data in 4 energy bands(approximately 6–40 keV, 6–80 keV, 32-400 keV,and > 400 keV) for each detectors.
5 s / 10 s
128 channel energy spectral data for eachdetectors.
6.4 µsThe photon data available when triggered the event.
The time and 256 channel energy spectrum information
is available for every photons.

data like WXM. One is the survey data (TH and SP) which is always available when the highvoltage is on, and the other is the burst photon data (PH) which is only produced when thetrigger occurred.
The energy response matrix of FREGATE was calculated using the GEANT Monte Carlopackage [57]. More than 50 parts of the detector components are included in the simulation.
This simulation code is examined before launch with the ground calibrations using a large set ofradioactive sources and various incident angles. In-orbit calibration of the FREGATE response
matrix is performed using the Crab data occulted by the earth. It successfully represents the
Crab nebula spectrum with the photon index of (2.16 ± 0.03) (χ2ν = 1.19 / 84 D.O.F.). Details

about the cross calibration of WXM and FREGATE response matrix is in Appendix A.

4.3

WXM

The wide-field camera (WXM) is located in the center of the spacecraft and the key instrument for localizing the GRBs. The WXM consists of the one-dimensional position sensitive
proportional counters (PSPC) and the coded mask aperture. The one-dimensional coded mask
located on 187 mm above PSPCs (figure 4.8). There are two units of counters called X-camera
and Y-camera. And each camera has two PSPCs. The PSPCs in the X-camera are referred to

66

CHAPTER 4. INSTRUMENTS(b) The cross-section of the FREGATE detector.

(a) Picture of the FREGATE detector

Figure 4.5: The picture of the FREGATE detectors before the integration on the spacecraft(figure (a)). The cross-section view of the one FREGATE detector (figure (b)).

Figure 4.6: FREGATE effective area of the incident angle in 0◦ , 30◦ , 50◦ and 60◦ .

4.3. WXM

67

as XA and XB, while those in the Y-camera are referred to as YA and YB. The orientation of
the X-camera is perpendicular to the Y-camera, the X and Y locations of GRBs are determined
separately (see figure 4.7).
The area of each coded mask is twice that of the total detector area, to ensure a wide fieldof view. The masks are supported by an aluminum support structure. The mask is composedof a plate of aluminum (0.5 mm thickness) plated with gold (50.8 µm). The width of the slit
are randomly varying integer multiples of 2 mm (figure 4.7). The open fraction of the mask
is 0.33. A 7.6 µm thickness aluminum-coated kapton foil is placed in front of the mask, asa thermal shield. The location of the GRB is calculated from the shift distance of the mask
shadow on the X and Y camera independently.
The cross-section view of PSPC is shown in figure 4.9. The PSPC has three anode wires
which are made by a carbon fiber 10 µm in diameter and 120 mm in length. The counteris divided into an upper layer with three anode cells and a lower veto layer. The veto layer
is to distinguish the charged particles from the X-ray photons. The counters are filled withxenon (97%) and carbon dioxide (3%) at 1.4 atm pressure at room temperature. The beryllium
windows of 100 µm thickness is placed at the front of the detector. The detector body ismade of titanium. The geometrical area of the entrance window is 88 cm2 . The effective
are curve of WXM is shown in figure 4.10 in the case of the boresight incident angle. The
55

Fe radioisotopes are attached at the top of the support structure of the coded mask. The

radioisotope is contained in a slit case and both sides of each counter at 40 mm distance fromthe center of the counter are irradiated.
One of the key feature of WXM is on-board triggering and localization of GRBs. There
are 68 trigger criteria with time scales from 80 ms to 27 s, and the threshold levels from 4.7
to 8.0 sigma depending on their time scales. There are also “bracket-type” triggers which have
two background regions taken before and after the foreground region. This trigger reduces thenumber of false triggers due to increase of the background. As of November 2003, 32 on-board
triggers are working. When a GRB triggers WXM or FREGATE, the position histograms of the
X and Y cameras for the optimized foreground and background regions are extracted from thememory, and the histogram is cross-correlated with the templates for all the incidence angles.
Even localization is completed, the trigger process continues to search for better time intervals
based on the signal-to-noise ratio, and localization is performed for each updated foregroundand background regions. The cross-correlation scores between the position histogram data
and the Monte Carlo simulated templates of various incident angles are calculated to findthe template which matches best with the data. The GRB location in the WXM detector

68

CHAPTER 4. INSTRUMENTS

Table 4.4: WXM performance
Energy range
2–25 keV
Effective area (1 PSPC, without coded mask, on axis)∼ 80 cm2
Position Resolution∼ 1 mm @ 8 keVEnergy Resolution (FWHM)∼ 20 % @ 8 keV
Angular Resolution∼ 10′
Table 4.5: Data products of WXM
Data typeHK

Time resolution
4s

RAW

1µs

TH

1.2 s

POS

6.6 s

PHA

4.9 s

TAG

256 µsDescription
House Keeping data. Power status, HV setting
temperatures of an electronic board and the wall of
the support structure.
The unprocessed photon data. This data is used as thehealth check of the instrument and the calibration of theenergy response.
The time history data for 4 energy bands (approximately
2–5 keV, 5–10 keV, 10–17 keV and 17–25 keV) andfor 4 counters.
The position histogram data in two energy bands(approximately 2–7 keV and 7–25 keV).
4.9 s time-binned energy spectrum. Available for eachanode wires. The position information is not available.
This data is generated when the trigger is occurred. The
photon data with the information of time, position, energy
and wire ID are available.

coordinate is converted to the celestial coordinate using the aspect information of the spacecraft.
A conservative error (90% confidence radius) is 30′ in flight. More sphesiticated ground analysis
gives ∼ 10′ accuracy.
Details about the WXM characteristics and the energy response matrix are in Appendix A.
The data products of WXM is summarized in table 4.5. The data using for the scientificstudy are TAG, POS, TH and PHA.

4.4

SXC

The soft X-ray camera (SXC) is designed to provide a few arcsecond location of the GRB. SXC
consists of X-ray CCDs and a fine coded mask. The coded mask is located 95 mm above the
CCD chips with the mask element size of 45µm. This corresponds to the characteristic angular4.4. SXC69

HETE2 Wide Field X-ray Monitor (WXM)(a) The WXM detector. The left side is the X(b) The coded aperture of WXM.

camera, while the right side is the Y camera.

Figure 4.7: The photograph of the WXM detector part (figure a) and the coded aperture of
one direction (figure b).

Coded Mask

427
208

208

5
6.4

+40.05

6

1

84

2

0

10

1

84

Right

Left

35

120

0

35

6

Proportional Counters

Electronics Box

190

1

84

Right

YB

YA

X

2

6

-39.40187.37XB

XA
0-46.24+39.05

Support Structure+44.16-44.16+43.21-38.02

0

2

10

1

84

2

6

40

35

Y
120

113

380

Figure 4.8: The dimension of the whole WXM system.

190

Left
35

70

CHAPTER 4. INSTRUMENTS

Figure 4.9: The cross section of one PSPC.

2

Effective Area (cm ) for 1 PSPC

100

10

1

for on-axis incidence
Thermal Shield (Kapton, 7.62µm)
PSPC Window (Be, 100µm)
Gas Absorption(Xe, 1.36atm, 293K, 25.5mm)

0.1

2

3

4

5

6

7 8 9

1

2

3

10
Energy (keV)

Figure 4.10: The effective area of one PSPC for the boresight incidence.

4.4. SXC

71

Table 4.6: SXC performance
Energy range
Effective area
Field of view
Energy Resolution

2–14 keV
7.4 cm2 per SXC
0.91 sr46 eV @ 525 eV, 129 eV @ 5.9 keV

resolution of 96′′ .
The size of the SXC coded mask is 10 cm × 10 cm. The deviations of the slit edges ofthe mask is less than 5µm rms and this is an ideal performance to achieve the SXC angularresolution. The pattern consisted of 2100 coded elements. The open fraction of the mask is ∼0.2.

The X-ray CCDs are front-side CCID-20 2048 × 4096 arrays (15 × 15 µm pixels; 6.1 cm

× 3.1 cm size) fabricated at MIT Lincoln Labs. The device operates as a collection of 2048
long and narrow detectors. The integration time is 1.2 s. To minimize the power, the CCDs
are passively cooled to −50◦ C in flight using a radiator plate attached to the baseplate.

Two optical blocking filters (OBF) are mounted in SXC. The OBF works for preventing

from the non X-ray photons like moonlight. One is 0.05 µm aluminized plastic films, covering
the whole aperture. Another is 25 µm Be foil filters, covering one half of the CCD area.
Unfortunately, due to the increase of the density of atomic oxygen by the intense solar flaresin the period of the late year 2000 to the early year 2001, the outer OBFs were lost. Polyimide(OBF) was eroded by unexpected high flux of atomic oxygen. Since then, SXC is not operated
at the bright moon phases.
To monitor the gain variation in orbit, 55 Fe radioactive source is attached to the mask frame.
The localization procedure of SXC is restricted for the search region to ± 1◦ of the best WXM

location to avoid the false localization. With this restriction, there is only a 1% chance thatthe location is a false detection. Empirical measurements show a 20′′ radius RMS localization
accuracy in the X and Y directions. This corresponds to a 90% confidence, two-dimensional
error circle of 43′′ radius [55].

72

CHAPTER 4. INSTRUMENTS

Figure 4.11: The picture of SXC.

Figure 4.12: Effective area curves of SXC, WXM and FREGATE at the boresight angle.

Chapter 5
Analysis
5.1

Data reduction of the WXM data

In the spectral analysis of WXM, we used the photons within the wire range of ± 50 mm (fullwire range is ± 60 mm) when the WXM photon data (TAG data) are available in order toavoid the gain variations of the both ends of the wires (see Appendix A, “∼“ curve). Since theposition information is not available in the spectral survey data (PHA data), this reduction is
only applied to the TAG data.
The WXM spectrum is constructed by the summing the photons of the wires illuminatedby the source using a FTOOLS command mathpha.

5.2

Spectral models

Three spectral models are used in fitting the GRB spectrum. The first model is the power-law
model:fGRB (E) = A(E/15)α ,(5.1)

where the normalization A in photons cm−2 s−1 keV−1 , and the photon index α. The normalization is selected to be at 15 keV, because both the WXM and FREGATE spectra areoverlapped at this energy.
The second model is the cutoff power-law model:
fGRB (E) = A(E/15)α exp(−E(2 + α)/Epeak ),(5.2)

where the normalization A, the photon index α, and the peak energy in νFν spectrum Epeak .
73

74

CHAPTER 5. ANALYSISThe third model is the Band function [63]:fGRB (E) = A(E/15)α exp(−E(2 + α)/Epeak )if

E < (α − β)Epeak /(2 + α) ≡ Ebreak ,andf (E) = A(α − β)Epeak /[15(2 + α)]α−β exp(β − α)(E/15)βif

E ≥ (α − β)Epeak /(2 + α),(5.3)

where the four parameters are the normalization A, a low-energy spectral index α, a high-energy
spectral index β, and a peak energy Epeak in νFν spectrum.
All the spectral analyses are performed in XSPEC v11.2.0 software package.

5.3

Selected TAG data

Due to the coded aperture, the signal to noise ratio (SNR) of the WXM data are usually low(the open fraction of the mask is ∼ 30% at the boresight incident angle). However, it is possible

to increase the SNR of the WXM data using its imaging capability. We apply the following
steps to maximize the SNR of the WXM data:
1. Simulate positional distribution of the burst photons due to the mask shadows.
2. Sort the position bins according to the simulated counts in decreasing order.
3. Find the foreground/background time regions which maximize the SNR (They usuallyagree with the foreground/background time regions used in the localization of the burst).
4. Cumulate the foreground/background counts and compute the SNR for the position bins.
5. Choose N which shows the highest SNR.
6. Select the wire-position pairs from 1 to N.
The new data set created in this method called “selected TAG data.” The resulting improvement of SNR is demonstrated in figure 5.1. All the bursts which the TAG data are
available, are creating the selected TAG data. The selected TAG data are using in both thetemporal and the spectral analysis. Note that since the selected TAG data are “artificially”
selecting the illuminated position bins from the burst, we have to correct the effective area
for the spectral analysis. We are multipling the fraction to the response matrix of each wires
defined as (simulated counts of selected bins)/(total simulated counts).

5.4. DEFINITION OF X-RAY FLASH, X-RAY-RICH GRB, AND HARD GRB

75

Figure 5.1: Left: Example of the light curves (GRB021112) using the normal TAG data (above)and the selected TAG data (bottom). Right: The wire-position pairs vs. the cumulated signal
to noise ratio. The dashed line corresponds to the maximum SNR.

5.4

Definition of X-ray flash, X-ray-rich GRB, and hard
GRB

Our definitions of X-ray-flash, X-ray-rich GRB, and hard GRB 1 are:log(SX /Sγ ) > 0
X-ray flash−0.5 < log(SX /Sγ ) ≤ 0 X-ray-rich GRB
log(SX /Sγ ) ≤ −0.5
hard GRB
where SX and Sγ are the fluence of 2–30 keV and 30–400 keV in the best fit spectral model
respectively.

5.5“Constrained” Band function

In some XRFs, we confronted by the difficulty of determining the four spectral parameters in
the Band function due to the low statistics. Moreover, since XRFs are intrinsically weak andthe break energy is close to the lower boundary of the observable energy band of HETE, thesimple power-law will be the acceptable model for many cases. If we assume that XRF has thesimilar spectrum as hard GRB, the power-law index < −2 is the high energy photon index βof the Band function. The break energy Ebreak = (α − β)E0 which separates the low and highenergy part of the Band function is near or below the lower boundary of the energy range of a1

We call the BATSE-like GRBs as “hard GRBs” for the clarification.

76

CHAPTER 5. ANALYSIS

detector.
When we try to fit this kind of XRF spectrum with the Band function, a problem arises.
Since the Band function is a combination of the two power-law spectrum, both the low energy
index α and the high energy index β can make the pure power-law spectrum.
To handle this situation, we develop the new spectral model called a constrained Band
function. The constrained Band function has three spectral parameters (β, Epeak , and A) and
one fixed parameter Epivot . The constrained Band function is perfectly able to make both pure
power-law spectra and the cutoff power-law spectra of the required curvature in the detector
range. And only the high-energy part of the Band function is allowed to produce a pure
power-law spectrum. We described this model in detail at Appendix D.

Chapter 6
HETE X-ray Flashes and X-ray-rich
GRBs
In this chapter, we show the detail spectral and temporal analysis of 18 X-ray flashes (XRF)
and X-ray rich GRBs (XRR) selected by the X-ray to γ-ray fluence ratio of larger than 0.751 .
Each sections consist of the brief summary of the event, the afterglow status, the temporal,
and the spectral characteristics. From these detail studies of the individual properties of XRFs
and XRRs, we found 1) duration of the XRFs and XRRs are similar to hard GRBs, 2) most of
the XRFs and XRRs show complex time-structures like hard GRBs, 3) the spectral softening
is seen during the burst for most of the XRFs and XRRs, 4) their Epeak energies are generally
lower than those of hard GRBs, 5) there are six events which showed the Epeak energy of afew keV and 6) the afterglows were found only for a few XRF, and this may imply that theafterglows of XRFs are generally very faint.

6.1

GRB010213

The bright X-ray Flash was detected on 13 February 2001 at 12:35:35 UTC [69]. Since HETE
was in the performance verification phase at that period, the localization was performed by theground analysis. The celestial coordinate of this source is (R.A., Dec.) = (10h 31m 36s , 5◦ 30′ 30′′ )(J2000) with a 95% error radius of 30′ . This large uncertainty is due to the unstable attitudeof the spacecraft.
1

GRB020625, which has the X-ray to γ-ray fluence ratio of 20.5, is not included in this study. Because thisfluence ratio value is derived from the possible second peak of the burst and might not be a “actual” fluence
ratio of this event.

77

78

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS
The status of the afterglow search of this X-ray flash is summarized in table 6.1. No afterglow

candidate has been found for GRB010213.
Table 6.1: The afterglow search for GRB010213
Timea
Telescope & Instruments
OT
1.48 days HETE GCN notice
38 hours Automatic 25 cm telescope
N
TAROT (Nice, France)
1.57 days 0.57m f/5.2 Telescope (unfiltered)
N
Klet Observatory (Czech Republic)
1.89 days ASTROCAM IR cameraN
USNOFSc 1.55 m
1.90 days VLAd (1.43 GHz)Ne
2 daysBAOf 0.6 m Schmit Telescope(BATC-i filter)

N

Lim. Mag.b

GCN
#934
17 mag. (USNO A2.0) Boer et al.
(#936)∼ 20.5 mag. (DSS2)
Hudec et al.
(#941)
POSS-IIF limit
Henden et al.
(#940)
Berger et al.
(#945)∼ 22 mag.
Zhu et al.
(#946)a Time after the trigger
b Limiting magnitude
c U.S. Naval Observatory Flagstaff Station (Arizona, USA)d Very Large Array (New Mexico, USA)e Berger et al. reported the afterglow candidate in GCN #945, however, they rejected in GCN #947.
f Beijing Astronomical Observatory

6.1.1

Light curve

As we can see in Figure 6.1, two peaks are see in the WXM energy range. The first peak isvisible for all four WXM energy bands. On the other hand, the second peak is only seen in theenergy range below 10 keV. The double peak structure is also seen in the FREGATE 6-40 keVlight curve. There is no significant excess in the FREGATE 32–400 keV band. The durationin 2–25 keV is ∼ 40 seconds.

6.1.2

SpectrumThe spectral analysis is performed for the four time intervals including the whole burst region(Fig. 6.1). The fluxes and fluences derived with the Band function are summarized in table 6.2.
The energy fluence ratio of 2–30 keV to 30–400 keV is 11.4, qualifying this event as an X-ray

6.1. GRB010213

79

Figure 6.1: The energy resolved light curves of GRB010213 in 1.23 seconds time resolution.
The three spectral regions are shown in the dotted lines. There is a data gap in the FREGATE
light curves from 40 to 80 seconds from the onset.

80

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.2: The WXM and FREGATE spectra of GRB010213. The spectra of region 1, region
2, region 3 and the whole time region are shown. The model spectrum is the Band function forregion 2, region 3, and the whole time region, whereas region 1 is the power-law model.

flash in our definition. The spectra for the second, the third, and the whole region apparently
require a break within the observed energy range. For the first region, however, a simple powerlaw model provides an acceptable fit. The outstanding characteristics of the prompt emissionof GRB010213 is the low Epeak energy (a few keV) for the second and the third time intervals.
Softening of Epeak is observed between these two time intervals.

We investigate the spectral evolution during the burst with the hardness ratio between 5–10
keV and 2–5 keV energy band. As you can see in figure 6.3, the spectral softening started justafter the first peak at t = 5 sec.

6.1. GRB010213

81

Figure 6.3: The hardness ratio between the 5–10 keV and 2–5 keV bands. The upper panel isthe hardness ratio plot, and the middle and the bottom panels are the light curves in the 2–5
keV and 5–10 keV bands respectively.

Table 6.2: The fluxes and fluence of GRB010213 in the Band function.
energy range [keV]
Duration [sec.]
Photon flux
−1
[10 ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−9Photon fluence[ph cm−2 ]Energy fluecne[10−8 erg cm−2 ]2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400

region 1
10.5
1.8±1.6
2.7±1.9
1.4±1.2
4.1±2.2
1.4±1.1
4.0±2.3
14.7+14.4−10.7
32.3+39.2
−23.4
+1.8
1.9−1.5
2.9±2.0+1.4
1.5−1.1
4.3±2.3+1.2
1.5−1.1
4.2±2.4
15.4+15.1−11.2
33.9+41.2−24.6

region 2
region 3
10.5
10.5
30.1±2.059.8±3.0
33.4±2.2
61.0±3.0+0.5
0.7−0.1(31.7±17.9) × 10−334.1±2.3
61.0±3.0
19.6±1.333.5±1.727.9±2.335.8±2.3+6.1+2.0
6.7−4.7(1.3−0.6) × 10−1+7.8
34.6−6.6
35.9±2.631.7±2.862.8±3.1
35.1±2.2
64.0±3.1+0.5
0.7−0.1(3.3±1.9) × 10−235.8±2.464.1±3.1
20.6±1.3
35.2±1.729.3±2.437.6±2.4+6.4+2.1
7.1−5.0
1.3−0.6
× 10−1+8.2
36.4−7.0
37.7±2.7all
31.5
30.4±1.532.3±1.5
0.2±0.1
32.5±1.6
18.4±0.8+0.7
22.9−1.6+1.7
2.0−0.924.9±2.895.9±4.5
101.8±4.7+0.5
0.7−0.3
102.5±4.8
58.0±2.6+2.2
72.2−5.0+5.3
6.3−2.9+9.2
78.5−8.6

82

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.3: The spectral parameters of GRB010213 for the power-law model (PL), the cutoff
power-law model (Cutoff PL), and the Band function (Band).
Model
PL

parametersαK15 aχ2ν /DOF
Cutoff PL
αEpeak [keV]K15
χ2ν /DOF
Band
αβ
Epeak [keV]K152χν /DOFregion 1+0.54−1.23−0.51+2.99
5.65−3.19 ×10−3
0.964/19

region 2+0.10−2.19−0.10+0.35
2.64−0.34 × 10−2
1.293/41−1.00 (fixed)+0.82
5.45−0.69+0.04
0.29−0.04
1.057/41−1.00 (fixed)+0.22−2.55−0.60+1.06
4.81−0.78+0.06
0.32−0.06
0.949/40

a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

region 3
all
+0.08
−2.89
−2.47−0.09+0.23−21.85 ×10
1.75−0.21 ×10−2
2.363/36
1.561/45−1.00 (fixed) −1.00 (fixed)
+0.22
+0.34
2.57−0.21
3.60−0.31
+0.18
+0.06
1.26−0.17
0.42−0.05
1.114/36
1.144/45−1.00 (fixed) −1.00 (fixed)+0.23< −3.61−2.96−0.53
+0.22
+0.35
2.56−0.23
3.41−0.40
+0.21
+0.07
1.26−0.15
0.45−0.06
1.120/35
0.940/44

6.2. GRB010225

6.2

83

GRB010225

The FREGATE instrument triggered on 25 February 2001 at 16:52:11.2 UTC on this event.
The trigger occurred in 5–120 keV band on the 1.3 second time scale. Since the attitude control
camera was not operational, the celestial coordinate of this burst was not distributed to the
GRB community.
The photon data of WXM (TAG data) are not available due to the corruption of the data.
The survey data (TH (time resolution of 1.2 s) and PHA (time resolution of 5.6 s) data) areused in the temporal and the spectral analysis instead.

6.2.1

Light curve

A burst consisting of a single peak is visible below 85 keV. The duration of the burst is ∼10 seconds. The fast rise and exponential decay (FRED) -like temporal structure is seen in
the FREGATE lower energy bands. The peak width becomes broader as the energy ranges golower. A same trend has been seen in many bright BATSE long GRBs [19].

6.2.2

SpectrumThe spectrum is investigated using the whole burst region. The spectral parameters, fluxes andfluence are summarized in table 6.4 and 6.5. The X-ray to γ-ray fluence ratio of 1.4 qualifies
this burst as an X-ray flash.
We obtained a χ2 of 43.9 for d.o.f. of 40, which is formally acceptable. However, with anaddition of one parameter, the cutoff power-law model yielded a χ2 of 36.1 for d.o.f. of 39.
The F-test probability for this improvement is 6.06 × 10−3 . The Band function also provides

a significant improvement over the simple power-law model, but it is no better than the cutoff

power-law model, and the addition of two more parameters is not justified. From this reason,
we decided that the cutoff power-law model is the best representative model for this burst.
The Epeak energy is around 30 keV. This value lies in the low-end tail of the BATSE Epeak
distribution [63] (see also figure 2.1).

84

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.4: The energy resolved light curves of GRB010225. The dotted lines indicate the time
regions used as the foreground to construct spectrum.

6.2. GRB010225

85

Figure 6.5: The WXM and FREGATE spectra of GRB010225. The spectra with the power-law
model (top) and Band function (bottom) are shown.

86

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.4: The fluxes and fluence of GRB010225 in the cutoff power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−8 erg cm−2 ]2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400

9.8
2.2±0.4
2.9±0.4
0.3±0.1
3.2±0.4
1.6±0.2
3.6±0.4+1.8
2.5−1.0+1.7
6.0−1.1
21.1±3.7
28.3±3.8+1.0
2.7−0.831.0±3.915.4±2.234.8±3.6
24.0+17.2−9.5
58.8+16.9−10.6

Table 6.5: The spectral parameters of GRB010213 in the power-law, the cutoff power-law, andthe Band function.
Model
PL

Cutoff PL2

Bandparametersα−1.71±0.1
aK15(4.05 ±0.45) × 10−32χν /DOF
1.098/40
0.30
α−1.31−0.26+26.50
Epeak [keV]
31.57−9.17
+2.93
K15
6.75−1.87
× 10−2χ2ν /DOF
0.925/39+0.30
α−1.31−0.26+7.31
β−9.21−0.79
Epeak [keV]
31.55+26.65
−9.07
+2.93
K15
6.72−1.87
× 10−2χ2ν /DOF
0.950/38

a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

6.3. GRB010326B

6.3

87

GRB010326B

The FREGATE instrument triggered on this event in the 6–120 keV band on the 160 ms
timescale on 26 March 2001 at 08:33:12 UTC [70]. The celestial coordinates of the burst are
R.A. = 11h 24m 23.36s , Dec. = −11◦ 09′ 57′′ (J2000) with the 90% error radius of 21′ which
includes statistical and systematic errors.

Although the optical observation of this field was performed at 6 hours after the trigger withthe robotic 50-inch telescope at Mount Stromlo Observatory, no optical transient was found in
the comparison with the DSS-2 plates [65].

6.3.1Light curve

The burst is visible in the all energy bands. The spiky structures are clearly seen at the FREGATE light curve. There are at least three peaks. The middle peak is the hardest component
and the peaks at the both sides are softer. The duration of the burst is > 3 seconds and it isa long burst.

6.3.2

Spectrum

The results of the spectral analysis of the time average spectrum are summarized in table
6.6 and 6.7. For some unknown reason, we have to multiply the normalization of the model
function for WXM by a constant factor 0.47 to fit the WXM and the FREGATE spectra. The
improvement of χ2 is quite significant when we fit with the cutoff power-law model. We obtained
the fairly acceptable χ2 for the simple power-law model is 120.3 for d.o.f. of 112. However,the cutoff power-law model provides a χ2 of 95.0 for d.o.f. 111. The F-test probability for thisimprovement is 3.5 × 10−7 . Although the Band function also provides a significant improvement
over the simple power-law model, it is not better than the cutoff power-law model. We decided

the cutoff power-law model is the acceptable model from these reasons. The X-ray to γ-ray
fluence ratio is 0.75 which qualifies this event as an X-ray rich GRB.
To investigate the spectral evolution during the burst, the hardness ratio between the FREGATE band C (32–400 keV) and band A (6–40 keV) are plotted in figure 6.8. The gradualsoftening is seen after the sharp peak of the band C. The highest peak at band A is very soft.
The photons at the one second before the trigger are the relatively soft. The hard to soft
spectral evolution is seen at the prompt emission of GRB010326B and this characteristic iscommon in long GRBs.

88

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.6: The energy resolved light curves of GRB010326B at 0.1 s time bin. The dottedlines correspond to the foreground interval used for accumulating the spectrum.

6.3. GRB010326B

89

Figure 6.7: The WXM and FREGATE spectra of GRB010326B. The model spectrum are thepower-law model, the cutoff power-law model and the Band function from top to bottom.

90

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.8: The hardness ratio between the FREGATE band C (32–400 keV) and the band
A (6–40 keV). The top panel is the harness ratio. The middle and the bottom panels are the
FREGATE light curves of band A and C respectively.

6.3. GRB010326B

91

Table 6.6: The fluxes and fluence of GRB010326B in the cutoff power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−8 erg cm−2 ]2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400
2 – 102 – 3030 – 400
2 – 400

3.5
3.2±0.7
4.8±0.8
0.9±0.2
5.7±0.8
2.5±0.5
6.9±0.8+2.6
9.2−2.2+2.7
16.1−2.3
11.3±2.6
16.8±2.8
3.2±0.5
20.0±2.88.7±1.7
24.0±2.7+9.2
32.2−7.6+9.5
56.2−8.9

Table 6.7: The spectral parameters of GRB010326B in the power-law model (PL), the cutoff
power-law model (Cutoff PL), and Band function (Band).
Model
PL

parametersα
K15 a
Cb (WXM)
χ2ν /DOF
Cutoff PL
αEpeak [keV]
K15
C (WXM)χ2ν /DOF
Band
αβ
Epeak [keV]
K15
C (WXM)χ2ν /DOF−1.62±0.07(8.23±0.84) ×10−2
0.47 (fixed)
1.073/112+0.25−1.08−0.22
51.8+18.61−11.25+0.31
1.32−0.23
× 10−10.47 (fixed)
0.856/111+0.23−1.08−0.19+7.35−9.33−0.67+12.5951.70−10.98(1.32±0.18)×10−1
0.47 (fixed)
0.864/110

a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1
b Constant parameter of WXM. The constant parameter of FREGATE is fixed to 1.

92

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

6.4

GRB010629B

The WXM and FREGATE instruments detected this event on 29 June 2001 at 12:21:08 UTC[71]. The position of the burst is R.A. = 16h 32m 38.3ss , Dec. = −18◦ 43′ 24′′ (J2000) with the

90% error radius of 15′ . This event was also observed by Ulysses and the BeppoSAX GRBM
[38].
The status of the afterglow search is summarized in table 6.8. No afterglow was found for
GRB010629B.
Table 6.8: The afterglow search for GRB010629B
Timea
Telescope & Instruments
OT
8.95 hours HETE GCN notice11.68 hours DFOSCc 1.54 m TelescopeN
La Silla Observatory (Chile)
15.2 hours 1.3 m Telescope (R band)N
MDM Observatory (Arizona, USA)19 hours
USNOFSd 1.0 m TelescopeN(Arizona, USA)

Lim. Mag.b
20.5 mag. (I band)
deeper than DSS
19 mag. (I band)

GCN
#1075
Andersen et al.
(#1080)Halpern et al.
(#1079)Henden et al.
(#1077)

a Time after the trigger
b Limiting magnitudec Danish Faint Object Spectrograph and Camera
d U.S. Naval Observatory Flagstaff Station

6.4.1

Light curve

The two peaks are seen in all the energy bands (figure 6.9). The shape of the both peaks isthe fast-rise and the exponential decay (FRED) type in the FREGATE band B and C. The
duration of the burst is shorter in the high energy band. It is possible to see that the second
peak is much softer than the first peak.

6.4.2

Spectrum

The prompt emission of GRB010629 is studied with the spectra of individual peaks and thatof the whole burst region. Due to the corruption of the burst data in WXM, PHA data areused for the analysis.

6.4. GRB010629B

93

Figure 6.9: The energy resolved light curves of GRB010629B at 1.23 s time bin. The dottedlines correspond to the two foreground intervals used for creating the spectra.

94

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS
The time-averaged fluxes and fluences in the various energy bands are summarized in table

6.9. The fluence ratio of 2–30 keV to 30–400 keV is 0.9 which qualifies this event as an X-ray
rich GRB. The fluence in the 30–400 keV band decreased from region 1 to region 2, while thatin the 2–30 keV band increased, indicating the spectral softening during the burst.
The spectral parameters are shown in table 6.10. The power-law model is rejected forthe region 1 and for the whole burst region with the null hypothesis probability of 1.2 ×

10−10 and 1.7 × 10−8 respectively. For the region 2, the F test probability is 1.9 × 10−9 fromthe improvement of the cutoff power-law model over the power-law model. There was no
improvement in χ2 to justify the Band function over the cutoff power-law model. Thus, thespectra of all spectral regions requires the cutoff in the power-law spectrum. Since the highenergy photon index β is not well determined for all spectral regions, we decided that the cutoff
power-law model is the best model for GRB020629B.
The hard to soft spectral evolution is observed from region 1 to region 2. The low-energy
power-law slope becomes steeper, and Epeak decreased between these two intervals. The Epeak
energy of the time-averaged spectrum is ∼ 45 keV.
Table 6.9: The fluxes and fluences of GRB010629B. The spectral model is the cutoff power-law
model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

region 1 region 2
9.8
14.7
+0.8
2.5−0.77.5±1.4+0.9
4.6−0.89.9±1.4
1.6±0.1
0.9±0.1+0.9
6.2−0.810.9±1.4+0.6+0.7
2.1−0.5
5.6−1.0
8.0±0.9 12.1±1.0+1.9
1.5
16.3−1.7
8.2−1.2+1.924.3±2.1 20.3−1.6+8.0
24.9−6.8
110.5+20.9
−19.8
+9.2
44.8−8.1
146.5+21.3
−20.3
+1.8
16.3−1.713.8±1.4+9.2
60.8−8.2
160.4+21.4
−20.5
+0.6
+1.0
2.1−0.5
8.2−1.4
7.8±0.9 17.8±1.4
+1.8
+2.3
16.1−1.6
12.1−1.7+2.8
23.9±2.1 29.9−2.4

all
24.5
5.1±0.8
7.4±0.8
1.2±0.1
8.7±0.9
3.9±0.5
10.3±0.7
11.6±1.0
22.0±1.3
126.2+20.1−18.9
182.9+21.3−20.3
30.0±1.7
212.9+21.3−20.3
9.6±1.3
25.4±1.7+2.7
28.6−2.5+3.3
54.0−3.1

6.4. GRB010629B

95

Figure 6.10: The WXM and FREGATE spectra of GRB010629B. The spectra of region 1,
region 2, and all region are shown from top to bottom. The left and right plots are fitting withthe power-law model and cutoff power-law model, respectively.

96

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.10: The spectral parameters of GRB010629B in the power-law (PL), the cutoff powerlaw (Cutoff PL), and the Band function (Band).
Model
PL

Parameters Region 1
α
−1.63
K15 a
0.13
2
χν /DOF
2.481/69+0.26
Cutoff PLα−0.66−0.22+7.81
Epeak [keV] 60.47−6.11K15
0.18±0.02
χ2ν /DOF
1.006/68
+0.61
Band
α
−0.52−0.33+0.52
β−2.80−7.20
Epeak [keV] 55.47+11.14−11.98+0.06
K15
0.19−0.03
χ2ν /DOF
1.008/67
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

Region 2−1.87±0.05
0.14±0.01
1.112/82+0.21−1.35−0.18+5.22
31.29−3.90+0.04
0.22−0.03
0.719/81+0.21−1.35−0.18+6.96−9.35−0.65+5.12
31.39−4.02+0.04
0.22−0.03
0.730/80

All−1.79±0.03
0.14±0.01
1.924/111+0.14−1.13−0.13+4.61
45.57−3.84
0.20±0.02
0.817/110+0.20−1.13−0.13+2.31−4.84−5.16+4.59
45.56−6.39
0.20±0.02
0.825/109

6.5. GRB011019

6.5

97

GRB011019

The faint GRB was observed on 19 October 2001 at 8:42:50 UT [72]. The burst position was
R.A.= 00h 42m 50.23s , Dec. = −12◦ 26′ 58′′ (J2000) . One sigma uncertainty radius for thislocation was 21′ (7.5′ statistical error combined in quadrature with 19.8′ systematic error).

This large systematic error is due to the uncertainty of the aspect because the star camera wasradiated by the bright earth at the burst time. This burst was an untriggered event.
The status of the afterglow search is summarized in table 6.11. No afterglow was found forthis burst.
Table 6.11: The afterglow search for GRB011019
Timea
Telescope & Instruments
OT
12.12 hours HETE GCN circular
13.3 hours automated 600 mm telescopeN
Kosmoten Observatory (Russia)
17.6 hours ROTSE-III (0.45 m)
N(New Mexico, USA)20.9 hours NOFSc 1.0 m telescopeN(Arizona, USA) V band
1.03 days 50 inch robotic telescopeNdMount Stromlo Observatory
1.06 days Subaru 8.2 m telescope
N
SuprimeCam
1.85 days 48 inch NEAT automated telescope N
Mt. Palomar Observatoryg

Lim. Mag.b

GCN
#1109
15.5 mag. (R)Bondar et al.
(#1130)19.5 mag. (R)Akerlof et al.
(#1115)
deeper than DSS Henden et al.
(#1110)19.5 mag. (R)Price et al.
(#1112)e22.5 mag. (R)Komiyama et al.
25.0f mag. (R)(#1128)19.5 mag. (R)Fox et al.
(#1116)a Time after the trigger
b Limiting magnitude
c U.S. Naval Observatory Flagstaff Stationd Australia e limiting magnitude of the first exposure
f limiting magnitude of the second exposureg California, USA

6.5.1

Light curve

The energy resolved light curves of WXM and FREGATE are shown in figure 6.11. The
apparent signal is seen in only below 10 keV in WXM. There is no signal in the FREGATE
32-400 keV band which is the typical energy band for hard GRBs.

98

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.11: The energy resolved light curves of GRB011019 at 1.23 s time bin. The dottedlines correspond to the foreground spectral region.

6.5. GRB011019

99

Table 6.12: The fluences of GRB011019 in the cutoff power-law.
Energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

6.5.2

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

All
26.2
0.9±0.2
1.1±0.2+5.0
5.7−3.6×10−2
1.2±0.26
0.6±0.1
1.2±0.2+0.6
0.4−0.3+0.6
1.7−0.5+5.2
21.9−4.8+5.7
27.5−5.6+1.2
1.4−0.929.0±5.6
1.5±0.3
3.0±0.6+1.4
1.1−0.7+1.5
4.1−1.1

SpectrumThe spectrum of the whole burst interval is investigated. The power-law model gave an acceptable fit. However, the cutoff power-law model improved the χ2 by ∆χ2 = 4.6 with 1 additionalparameter. This corresponds to the probability of 2.3 ×10−2 with the F test. Following thisstatistical test, we choose the cutoff power-law model as a suitable model for this burst. The
fluxes and fluences in the cutoff power-law model are summarized in table 6.12. The fluence
ratio of 2–30 keV and 30–400 keV of 2.7 qualifies this event as an X-ray flash. The Epeak energy
is ∼ 20 keV.

100

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.13: The spectral parameters of GRB011019 in the power-law (PL) and the cutoff
power-law model (Cutoff PL).
Model
PL

Parameters+0.18
α−1.93−0.21
+0.28
K15 a
1.23−0.29
χ2ν /DOF
0.909/68
Cutoff PLα−1.43 (fixed)
Epeak [keV]
18.71+18.33
−8.72
0.82
K15
2.46−0.63
χ2ν /DOF
0.854/68
a Normalization at 15 keV in the unit of 10−2 photon cm−2 s−1 keV−1

Figure 6.12: The WXM and FREGATE spectra of GRB011019. The spectral model is thepower-law (top) and the cutoff power-law (bottom).

6.6. GRB011130

6.6

101

GRB011130

The WXM observed the GRB on 6:19:35 on 30 November 2001. This event occurred before theorbital dusk, and the uncertainty of spacecraft aspect is larger than usual. The celestial coordinates of this burst were R.A. = 02h 58m 09.1s , Dec. = 07◦ 24′ 40′′ (J2000) with 90% error radiusof 60′ including the statistical and the systematic error [73]. The revised WXM localization is
R.A. = 03h 05m 36.45s , Dec. = 3◦ 48′ 37′′ (J2000) with 90% error radius of 8.0′ [74].
The status of the afterglow search is summarized in table 6.14. Although there was theafterglow candidate which was found by VLA, this source might be an AGN. The Chandra
observed the HETE error circle and found 43 X-ray sources. The Chandra observation of the
2nd epoch (about two months after the trigger) found that two X-ray sources faded to thebackground level. Further investigation of these X-ray sources has not been reported in GCN
and their nature is still unknown.

6.6.1

Light curve

The light curve shows the double peak structure with no signal above 10 keV. The duration of
the burst is ∼ 50 seconds in the 2–5 keV band.

6.6.2

Spectrum

The prompt emission of GRB011130 is investigated for the three time intervals; the first peak,the second peak and the whole burst. The fluxes and fluences at the several energy bands areshown in table 6.15. Since the fluence ratio of 2–30 keV to 30–400 keV is 5.8, this event isclassified as X-ray flash.
The spectral parameters are summarized in table 6.16. The simple power-law model gives
an acceptable fit for all intervals. The steepening in the photon index is seen from region 1 toregion 2, however, it is not statistically significant.
If there is a spectral break (peak energy at νFν spectrum) within or below the WXM energy
band, the photon index of power-law model must be < −2. The data suggest that the photon

index of the power-law model is < −2 for all regions. This is the solid evidence that WXM

and FREGATE are observing the high-energy photon index β of the Band function. Following
this argument, we tried to constrain the time-average Epeak energy using the constrained Band
function. The posterior probability density distribution as a function of Epeak is shown in figure
6.15. The 68% confidence range is 0.6 < Epeak < 3.5 keV. The 95% and 99.7% upper limit is

102

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.13: The energy resolved light curves of GRB011130 at 1 s time bin. The dotted lines
correspond to the foreground regions of the spectra.

6.6. GRB011130
4.1 keV and 4.9 keV respectively.

103

104

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.14: The WXM and FREGATE spectra of XRF011130. The spectra of region 1, region
2, and all region are shown from top to bottom. The spectral model is the power-law.

6.6. GRB011130

105

Figure 6.15: The posterior probability density distribution as a function of Epeak (Epivot = 3.4
keV). The highest probability is 2.7 keV. The solid line, the dashed line and the dashed-dottedline correspond to the 68%, 95% and 99.7% confidence region respectively.

106

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.14: The afterglow search for GRB011130
Timea5.71 hours
16.5 hours
18.78 hours
23.45 hours
3.47 days
1.13 days
1.94 days
2.04 days
4.97 days
5.11 days
5.73 days
5.89 days
6.89 days
9.76 days
5.92 days
6.98 days
9.01 days
Feb. 20

Telescope & Instruments
HETE GCN circular
1.23 telescope (R&I band)
Calar Alto Observatory (Spain)
HETE GCN circular (2nd)
48 inch NEAT automated telescope
Mt. Palomar Observatoryc
VLAd (4.86 GHz)
Wide-Field Infrared Camera
Palomar Hale Telescope
SDSSf 0.5 m
Photometric Telescope at APOg
1.3 m Telescope
MDM Observatioryh
Magellan 6.5 m Baade Telescope
Las Campanas Observatoryj
3.0 m telescopeNASA IRTFk + NSFCAM
HETE GCN circular (3rd)Magellan 6.5 m Baade Telescope
Las Campanas Observatory
Magellan 6.5 m Baade Telescope
Las Campanas Observatory
Chandra ACIS-I (1st)

OT
N

N
Y(N)e
N
VLA src.
VLA src.
VLA src.
VLA src.

VLA src.
VLA src.
20 src.

1.3 m telescope
MDM Observatory

notem

Chandra (2nd)two src.

Milagro GeV/TeV Telescope

noten

Lim. Mag.b

GCN
#1165
18.5–19 mag. Greiner et al.
(R&I)(#1171)#1169
18.5 mag. (R) Fox et al.
(#1170)Berger et al.
(#1173)18.5 (K’)
Fox et al.
(#1174)20.5±0.5 (i*) Lee et al.
(#1175)inote
Mirabal et al.
(#1177)22.8 (R)Jha et al.
(#1179)18.1 (K)
Rhods et al.
(#1180)#1178
23.0 (R)
Garnavitch et al.
(#1181)z=0.5lJha et al.
(#1183)
Ricker et al.
(#1185)
Mirabal et al.
(#1186)
Butler et al.
(#1227)
McEnery et al.
(#1212)a Time after the trigger
b Limiting magnitudec California, USA
d Very Large Array (New Mexico, USA)e They reported the unknown source at R.A. = 03h 05m 24.71s , Dec. = 03◦ 46′ 13.1′′ . However, this source might be an AGN witha flat spectrum (#1207). Here after this source called “VLA src.”.
f Sloan Digital Sky Survey
g Apache Point Observatory (New Mexico, USA)h Arizona, USA
i OT reported on #1175 has the offset of 4.5′′ from the VLA source.
j Carro Las Campanas, Chilek NASA Infrared Telescope Facility (Hawai, USA)l Strong calcium break (600 nm). No significant [OII].
m No optical counter part for CXOU J0306458+034702.
n The upper limit: J(E > 2 TeV) < 6 × 10−7 erg cm−2 , J(100–150 GeV) < 5 × 10−4 erg cm−2

6.6. GRB011130

107

Table 6.15: The fluxes and fluences of GRB011130. The spectral model is the power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

region 125.0
1.8±0.3
1.9±0.3+2.1
2.1−1.2×10−2
1.9±0.3
1.0±0.2
1.3±0.2+2.6
2.1−1.4×10−1+0.4
1.5−0.344.5±7.2
47.3±7.2+5.2
5.3−3.1×10−1
47.8±7.2
2.5±0.4
3.2±0.6+6.4
5.3−3.4
×10−1+1.1
3.7−0.8

region 225.0
1.5±0.3
1.6±0.3−3
6.4+14.4−5.3 ×10
1.6±0.3
0.8±0.1
0.9±0.2−2
5.7+15.9−4.9 ×10+0.3
1.0−0.2+7.6
37.6−7.4+7.5
38.9−7.4+3.6
1.6−1.3 ×10−1+7.5
39.0−7.4
2.0±0.4
2.3±0.5+4.0
1.4−1.2×10−1+0.8
2.5−0.6all
50.0
1.6±0.3
1.7±0.3+1.9
2.0−1.1×10−2
1.7±0.26
0.9±0.1
1.2±0.2+0.2
0.2−0.1+0.4
1.4−0.380.9±12.886.0±12.8+0.9
1.0−0.686.9±12.8
4.6±0.65.8±1.0+1.2
1.0−0.6+1.9
6.8−1.5

Table 6.16: The spectral parameters of GRB011130 in the power-law model (PL).
Model Parameters
Region 1+0.27
PLα−2.66−0.34
+3.25
K15 a
7.48−2.93
× 10−3
χ2ν /DOF
1.000/55
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

Region 2+0.44−3.01−0.68+3.11
3.64−2.36
× 10−30.779/40

All+0.26−2.65−0.33+2.92
6.86−2.64
× 10−31.016/40

108

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

6.7

GRB011212

The WXM and FREGATE observed the burst on 04:04:02 UT on 12 December 2001 [75]. The
position of the burst was reported to be R.A. = 05h 00m 05s , Dec. = 32◦ 07′ 39′′ with a 90% total
error radius of 11′ . This event is also detected by RXTE ASM. The error box corners combining
the RXTE ASM and HETE WXM is (R.A., Dec.) = (05h 00m 00s , 31◦ 55′ 48′′ ), (05h 00m 05s ,32◦ 08′ 24′′ ), (04h 59m 43s , 32◦ 22′ 48′′ ), and (04h 59m 22s , 32◦ 13′ 12′′ ) (J2000). This event was an
untriggerd event.
The status of the afterglow search of GRB011212 is summarized on table 6.17. The Magellan
6.5 m telescope and the 2.2 m telescope on Maunakea observed the four fading sources, however,the further observations have not been reported.
Table 6.17: The afterglow search for GRB011212
Timea
8.3 hours
9.1 hours
1.4 days
14.7 hours
0.7 days

Telescope & Instruments
HETE GCN Position Notice
1.5 m Telescope (R)Gunma Astronomical Observatory
RXTE ASM Position Notice0.25 m F/4.2 Telescope

OT

Lim. Mag.b

GCN

N

20.5 mag. (R)Kinugasa et al.
(#1210)N

18.5 mag. (R)

0.7 days

2 m Telescope
Peak Terskal Observatory (Russia)
Mt. Ekar 1.8 m Telescope
Asiago Observatoryc
1.3 m Telescope (Ic)
USNO Flagstaff Station
Magellan 6.5 m Baade Telescope
Las Campanas Observatoryj
2.2 m on Maunakea (VR)U. of Hawai

N

21.5 mag. (R)N

22.7 mag. (R)N

20.0-20.1 mag. (R) dY

4 sourcese

Trondal et al.
(#1201)
Sergeev et al.
(#1206)
Saracco et al.
(#1205)
Vrab et al.
(#1216)Dullighan et al.
(#1324))

1.0 days
1.2 days
2.0 days
3.0 days
4.2 days
5.2 daysa Time after the trigger
b Limiting magnitude
c Cima Ekar-Asiago, Italyd extinction-corrected magnitude
e 4 fading sources

Epoch 1 m(R)Epoch 2 m(R)Epoch 3 m(VR)1

4:59:58.1 +32:02:57

RA

Dec

23.14 +/- 0.12

23.89 +/- 0.22

24.08 +/-0.24

2

4:59:59.4 +32:03:43

23.80 +/- 0.18

24.65 +/- 0.39

> 24.5

3

4:59:59.0 +32:09:04

23.75 +/- 0.18

24.80 +/- 0.48

> 24.5

4

4:59:39.5 +32:08:34

23.38 +/- 0.12

24.41 +/- 0.38

> 24.5

6.7. GRB011212

6.7.1

109

Light curve

The duration of this burst is > 60 seconds in 2–5 keV band . Some structures in the light curve
might be seen in the WXM 2-5 keV energy band. The burst signal is not seen above 17 keV.

6.7.2

Spectrum

The fluence ratio of 2–30 keV to 30–400 keV is 1.2 qualifying this burst as an X-ray flash. The
prompt emission is well fitted in the power-law model with the photon index of ∼ −2. However,

it is not possible to reject a photon index larger than −2 with a high significance (i.e. the peakenergy Epeak cannot determined reliably). Thus it is not possible to fit the spectrum with theconstrained Band function for calculating the Epeak .
Table 6.18: The fluxes and fluences of GRB011212. The spectral model is the power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ 10−1 ph cm−2 ]Energy flux
[10−9 erg cm−2 ]Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

57.6
7.1±1.2
8.2±1.2+0.3
0.4−0.2
8.7±1.2
4.5±0.77.3±1.1+4.4
5.8−2.9+5.0
13.2−3.741.1±6.847.3±7.0+1.5
2.6−1.1
49.9±7.0
2.6±0.4
4.2±0.6+2.5
3.4−1.7+2.9
7.6−2.2

110

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.16: The energy resolved light curves of GRB011212 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum.

6.7. GRB011212

111

Figure 6.17: The WXM and FREGATE spectrum of XRF011212. The spectral model is thepower-law.

Table 6.19: The spectral parameters of GRB011212 in the power-law model (PL).
Model Parameters
+0.19
PL
α
−2.07−0.22
+1.74
K15 a
7.18−1.78
× 10−32
χν /DOF
0.795/54
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

112

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

6.8

GRB020317

The GRB was observed by WXM and FREGATE on 18:15:31.4 UT on 17 March 2002 [76].
According to the ground analysis, the position of the source is R.A. = 10h 23m 21s , Dec. =12◦ 44′ 38′′ (J2000) with a 90% total error radius of 18′ .
The afterglow search for GRB020317 is summarized in table 6.20. The first two reports(GCN #1277 and #1278) about the suspicious object could be just minor planets which are
not in the DSS-2 image (GCN #1282). The nature of four suspicious sources reported by the
KISO observatory are still unknown.

Table 6.20: The afterglow search for GRB020317
Timea
Telescope & Instruments
52 minutes HETE GCN Position Notice57.8 minutes BART robotic telescope

OT

Lim. Mag.b

Y(?)c

15.5 mag. (R)2 hours0.38 m Cassegrain telescopeY(?)d0.77 days
0.96 days
1.15 days

1.05 m telescope (R)
KISO observatory
1.52 m telescope (R)4 src.e

1.93 days

1.2 m telescope (IR)Mt. Abu IR Observatoryf

N
N

GCN

Jelinek et al.
(#1278)18.2±0.3
Pavlenko et al.
(#1277)20.8 mag. (R)Tomita et al.
18.1 mag. (R)(#1282)
18.7/17.0 mag. (R) Guarnierie al.
(#1287)
not reported
Baliyan et al.
(#1297)

a Time after the trigger
b Limiting magnitudec Position is RA.(J2000) = 10h 23m 25s , Dec. (J2000) = 12◦ 51′ 36′′ . Could be a minor planet reported by GCN #1282.
d Position is RA.(J2000) = 10h 24m 27.99s , Dec. (J2000) = 12◦ 36′ 5.6′′ . Could be a minor planet reported by GCN #1282.
e 6 suspicious sources are reported including the two minor planets.

Dec

Mag. (R)1

10:24:25

RA+12:51:55

18.0 (minor planet)

2

10:24:09+12:48:33

17.3 (minor planet)

3

10:23:10+12:33:17

19.6

4

10:22:40+12:32:02

18.5

5

10:22:39+12:44:02

19.0

6

10:22:20+12:36:55

19.1

f MIRO, operated by the Physical Reaserch Laboratory, Ahmedabad, India

6.8. GRB020317

6.8.1

113

Light curve

The energy resolved light curves are shown in figure 6.18. The duration of the burst is around∼ 10 seconds.

6.8.2

Spectrum

The fluence ratio of 2–30 keV to 30–400 keV in the cutoff power-law model is 1.8. This burst
is classified as X-ray flash. The cutoff power-law model with the Epeak energy ∼ 30 keV is theacceptable model for the time-average spectrum.

The spectral evolution of the burst is investigated by the hardness ratio between 10–25 keV
and 2–10 keV. As seen in the figure 6.20, there is a global trend of the softening during the
burst. And also it is possible to see the hard-to-soft spectral evolution for the individual pulses.
Table 6.21: The fluxes and fluences of GRB020317. The spectral model is the cutoff power-law
model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

7.3
1.1±0.3
1.8±0.3
0.2±0.1
2.0±0.4
0.9±0.2
2.8±0.4+1.2
1.6−0.9+1.2
4.4−1.0
8.2±2.2
13.2±2.4
1.6±0.8
14.8±2.6
0.7±0.2
2.1±0.3+0.8
1.2−0.7+0.9
3.2−0.8

114

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.18: The energy resolved light curves of GRB020317 at 0.3 s time bin. The dotted lines
represent the foreground region of the spectrum.

6.8. GRB020317

115

Figure 6.19: The WXM and FREGATE spectra of GRB020317. The spectra of the wholeburst region with a spectral model of the power-law (top) and the cutoff power-law (bottom)
are shown.

116

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.20: The hardness ratio between WXM 10–25 keV and 2–10 keV is in the top panel. The
second and the third panels are the WXM light curves of 2–10 keV and 10-25 keV respectively.

Table 6.22: The spectral parameters of GRB020317 in the power-law model (PL) and the cutoff
power-law model (Cutoff PL).
Model
PL

Parametersallα−1.60±0.11
K15 a(2.86±0.44) × 10−2χ2ν /DOF
1.420/40+0.56
Cutoff PLα−0.56−0.45
Epeak [keV]
27.3+12.0
−7.7
−2
K15
10.22+12.6−4.26 × 10
2
χν /DOF
0.944/39a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

6.9. GRB020903

6.9

117

GRB020903

This event was detected by WXM and SXC at 10:05:37.96 UT on 2002 September 3 [77].
Although the WXM flight location was correct, it was not sent to the GCN, because HETE
was pointed to the Galactic Bulge region at this time and the automatic transmission of theflight location was turned off at that time. The WXM location, which was sent to GCN 3.8hours after the trigger, based on the ground analysis can be express as a 90% confidence circle
that is 16.6◦ in radius and is centered at (R.A., Dec.) = (22h 49m 25s , −20◦ 53′ 59′′ ) (J2000). The
one-dimensional localization was possible using the SXC data. The combined the SXC and the

WXM localization, which was sent to GCN 6.9 hours after the trigger, can be described as a
90% confidence quadrilateral that is 4′ in width and ∼31′ in length. It is centered at R.A. =22h 49m 01s , Dec. = −20◦ 55′ 47′′ (J2000), and its four corners lie at (R.A., Dec.) = (22h 48m 48.00s ,−20◦39′ 36.0′′ ), (22h 48m 33.60s , −20◦ 42′ 36.0′′ ), (22h 49m 10.80s , −21◦ 10′ 12.0′′ ), and (22h 49m 30.00s ,−21◦10′ 48.0′′ ) (J2000).

Detection of the optical and radio afterglow, and the host galaxy have been reported byseveral authors (table 6.23). Soderberg et al. [95] discovered an optical transient within the
HETE-2 SXC + WXM localization region at R.A. = 22h 48m 42.34s , Dec = −20◦ 46′ 09.3′′ , using
the Palomar 200-inch telescope. They report that the optical transient brightened by ∼ 0.3−0.4

magnitudes between about 7 and 24 days after the XRF, and suggest that the re-brightening
might be due to an associated supernova. However, the optical transient apparently faded byover a magnitude only three days later. Spectroscopic observations of the optical transient,using the Magellan 6.5 m Baade and Clay telescopes, detected narrow emission lines from anunderlying galaxy at a redshift z = 0.25 ± 0.01, suggesting that the host galaxy of the opticaltransient is a star-forming galaxy. A fading bright radio source at the position of opticaltransient was detected using the Very Large Array. Hubble Space telescope observations of
the GRB 020903 field reveal the optical transient and show that its host galaxy is an irregulargalaxy, possibly with four interacting components. These detections likely represent the first
discoveries of the optical and radio afterglows, together with the host galaxy, of an XRF.

6.9.1

Light curve

The energy resolved light curves are shown in figure 6.22. There is no signal above 10 keV. The
double peak structure is seen in the light curve.

118

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

HST/ACS
G1

Palomar 200"/LFC
OT
3 asecG3

G2

1 arcminN

Figure 6.21: The Palomar and HST images of the transient (label OT) discovered within theerror-box of GRB020903. The HST image reveals a complicated galaxy morphology for G1,
suggesting a system of at least four interacting galaxies [95].

6.9. GRB020903

119

Figure 6.22: The energy resolved light curves of GRB020903 in 1.0 second resolution. The two
spectral regions are shown in the dotted lines.

120

6.9.2

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Spectrum

The X-ray to the γ-ray fluence ratio of 5.6 qualifies this burst as an X-ray flash. Although thepower-law model is the acceptable model for the prompt emission, the photon index is < −2 ina high significance (99% confidence level). If we assume that this XRF has the same spectral
shape as ordinary GRBs, WXM and FREGATE observed the high energy portion of the Band
function (photon index β). We applied the constrained Band function to calculate the upper
limit of the Epeak energy. The posterior probability density distribution is shown in the figure
6.24. We find a best-fit value Epeak = 2.7 keV, and the confidence limits of 1.1 keV < Epeak< 3.6 keV with 68% probability, and that Epeak < 4.1 keV with 95% and 5.0 keV with 99.7%
probabilities.
There is evidence of spectral softening between the first and second time intervals. To
investigate the spectral evolution, we perform the spectral analysis for the first and the second
peaks which are seen in the WXM 2–5 keV band (see figure 6.22). We treat each individual
WXM wires separately in order to extract the strongest possible constraints on the spectral+0.5parameters. A power-law fit to the sum of the first time interval gives α1 = −2.4−0.6
and χ2min,1 =+1.1
75.1, while a power-law fit to the second time interval gives α2 = −4.2−3.7
and χ2min,2 = 71.1.
+0.44
In contrast, a power-law fit to the first and second time intervals, gives α = −2.86−0.82
andχ2min = 152.2. The first (more complicated) model includes the second model as a special case.

Comparing χ2min for the two models, we find that ∆χ2 = 6.0 for one additional parameter.
Thus, there is evidence of spectral softening at the 98.6% confidence level.

6.9. GRB020903

121

Figure 6.23: The time-average spectrum of GRB020903.

Figure 6.24: The posterior probability density distribution as a function of Epeak . The solidlines define the 68% probability interval for Epeak , while the dashed and dotted lines show the
95% and 99.7% probability upper limits on Epeak .

122

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.23: The afterglow search for GRB020903
Timea3.84 hours
6.91 hours
4.15 hours
1 day
12.46 hours
4.18 hours
0.88 days
6.88 days
24.9 days
24.7 days
23.8 days
25.7 days
16.3 hours
5.68 days
26.5 days
5.45 hours
28.5 days
34.6 days
36.8 days
3 months

Telescope & Instruments
HETE GCN position notice (WXM)
HETE GCN position notice (SXC)
0.6 m (wide B and wide R)
Mt. John Obs.c
50-inch Telescope (R-MACHO)Mount Stromlo Obs.d
0.38 m Cassegrain Telescope
Crimean Astrophysical Obs.e
25 cm Telescope
Kyoto University
5 m Telescope + LFCf (R)Palomar Obs.h
MDMi 1.3 m Telescope (R)Magellanj 6.5 m (spectroscopy)
VLA (8.46 GHz)
CTIOk 4 m Telescope (BRI)(R only)
182 cm Telescope (VRI)
Cima Ekar Observatorym
0.25 cm Telescope
RIKEN
3.5 m TNGn Telescope (BVRI)
ORMoKeck I 10 m Telescopeb Limiting magnituded Weston, Australiae Ukraine

Lim. Mag.b

GCN

N

DSS-2 lim.

NR∼19.8NR∼17.4NR∼17.5#1531
Tristram et al.
#1533
Price et al.
#1535
Pavlenko et al.
#1537
Uemura et al.
#1554
Soderberg et al.

Yg
host
Y
Y
Y
N
Y
hostp

1.54 m Danish Telescope (BVR)
La Silla Obs.r
HST/ACS F606W

a Time after the trigger

OT

Y
host

g The position of OT is (R.A., Dec.) = (22h 48m 42.34s , −20◦ 46′ 09.3′′ ) (J2000)

j Las Campanas Observatory, Cerro Las Campanas, Chile
k Cerro Tololo Inter-American Observatory, La Serena, Chilel re-brightening

m Cima Ekar-Asiago, Italyn Telescopio Nazionale Galileoo Observatorio del Roque de los Muchachos, Palma, Italyp low metallicity, high excitation starburst galaxy
q same magnitude as #1563

r La Silla, Chile#1555
Berger et al.
#1557
ց 0.2 mag.
Fruchter et al.
18.6±0.2l#1561
Stefanon et al.
unresolved obj.
#1562
Torii et al.
ց 0.2 mag. (VRI) #1563
Covino et al.
#1609
Chornock et al.
noteq
#1631
Gorosabel et al.
#1761
Levan et al.

c Lake Tekapo, New Zealandf Large Format Camerah San Diego, CA i MDM Observatory, Tucson, AZ

z=0.25±0.02
1.1 mJy
0.7 mJy

6.9. GRB020903

123

Table 6.24: The fluxes and fluences of GRB020903. The spectral model is the power-law model.
energy range [keV]
Duration [sec.]
Photon flux
−1
[ 10 ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−9Photon fluence[ph cm−2 ]Energy fluecne[10−8 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

13.0
9.3±1.99.9±2.0+2.6
1.2−1.0×10−1
10.0±2.1
5.3±1.5
6.8±2.0+3.4
1.3−1.0+5.1
8.1−2.912.1±2.512.9±2.7+3.3
1.6−1.3×10−1
13.0±2.7
6.9±1.58.9±2.7+4.4
1.6−1.4+6.7
10.5−3.8

Table 6.25: The time-average spectral parameters of GRB020903.
Model Parameters all (WXM+FREGATE)
+0.42
PL
α
−2.62−0.55
+3.40
K15 a
4.14−2.47
× 10−3
χ2ν /DOF
0.845/26
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

124

6.10

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

GRB021021

WXM and FREGATE detected a faint and untriggered burst at 18:43:00.00 UTC on 21 Oct
2002 [81]. The ground localization result was distributed 16 hours after the event. The WXM
location can be expressed as a 90% confidence circle that is 20′ in radius and is centered at(R.A., Dec.) = (00h 17m 23s , −01◦ 37′ 00′′ ) (J2000). There is no report about the afterglow search

for this burst.

6.10.1

Light curve

As seen in the figure 6.25, there is no obvious signal in the typical GRB energy band 32–400
keV. Although the signal to noise ratio is quite low, the burst seems to be lasting for ∼ 50
seconds.

6.10.2

Spectrum

The calculated fluxes, fluences and the spectral parameters are shown in table 6.26 and 6.27.
The X-ray to γ-ray fluence ratio is 4.0, so this event is classified as an X-ray flash. Although
the significance is not high, the acceptable model of the time-average spectrum is the cutoff
power-law model. If we apply the F test for the cutoff power-law model against the simple
power-law model, the probability is 4.46 × 10−2 . To constrain the Epeak energy in the cutoff

power-law model, the photon index α is fixed to the best fit value −1.33. The Epeak energy is

15.4 keV.

6.10. GRB021021

Figure 6.25: The energy resolved light curves of GRB021021 in 1.23 second time-bins.

125

126

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.26: The time-average spectra of GRB021021 in the power-law model (upper) and thecutoff power-law model (bottom).

6.10. GRB021021

127

Table 6.26: The fluxes and fluences of GRB021021. The spectral model is the cutoff-law powerlaw model.
energy range [keV]
Duration [sec.]
Photon flux
[ 10−1 ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−9Photon fluence[ph cm−2 ]Energy fluecne[10−8 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

49.2
3.8±1.0
4.7±1.1+2.3
1.8−1.4×10−1
4.9.0±1.2
2.7±0.7
5.1±1.3+2.2
1.3−1.0+2.8
6.4−2.2
18.6±4.923.1±5.6−1
8.8+11.1−6.7 ×10
24.0±5.7
13.0±3.3
25.1±6.3
6.2+10.6−4.9
31.3+13.9−10.6

Table 6.27: The time-average spectral parameters of GRB020903.
Model
PL

Parameters+0.24
α−2.04−0.34
+1.63
K15 a
4.30−1.71
× 10−3
χ2ν /DOF
0.974/41
Cutoff PLα−1.33 (fixed)
Epeak [keV]
15.38+14.24
−7.47
+0.50
K15 a
1.24−0.37
× 10−220.879/41
χν /DOFa Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

128

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

6.11

GRB021104

At 07:01:02.9 UTC on 4 Nov 2002, FREGATE and WXM detected the burst [98]. The signal to noise ratio in WXM was ∼ 5. The position of the burst can be expressed as a 90%

confidence rectangle that is approximately 24′ in width and 42′ in length. The four corners of

the rectangle are (R.A., Dec.) = (3h 52m 40.3s , 38◦ 19′ 26′′ ), (3h 54m 44.6s , 38◦ 17′ 10′′ ), (3h 54m 56.2s ,37◦ 34′ 59′′ ), and (3h 52m 52.6s , 37◦ 37′ 12′′ ) (J2000). Although the afterglow was searched by several observers within 4 hours after the trigger (see table 6.28), no optical transient has beenfound for GRB021104.
Table 6.28: The afterglow search for GRB021104
Timea2.76 hours
2.78 hours
2.78 hours
3.93 hours

Telescope & Instruments
HETE GCN position notice
Automatic 0.76 m telescope
KAITc
1.2 m Telescope (unfiltered)
Oschin NEAT camerae
Automatic 0.6 m telescope
Super-LOTISf
Milagro GeV/TeV Telescope

OT

Lim. Mag.b

Nd
N∼ 21 mag.

N

DSS limit

N

conf.gGCN
Li et al.
(#1668)Fox et al.
(#1671)
Bradshaw et al.
(#1677)
McEnery et al.
(#1724)a Time after the trigger
b Limiting magnitudec Katzman Automatic Imaging Telescope, Lick Observatory, San Jose, CA
d They reported the candidate of OT, however, this source is seen in DSS2 plate (#1669, #1670).
e Mt. Palomar, San Diego, CA
f Livermore Optical Transient Imaging System, located on Kitt Peak National Observatory (Tucson, AZ)
g J(0.2-20 TeV) < 3.4 × 10−6 erg cm−2

6.11.1

Light curve

The energy resolved light curves are shown in figure 6.27. The duration is ∼ 30 seconds. The

duration in 2–10 keV band could have a longer duration. Due to the low signal to noise ratio,
it is hard to say about the structure of the time profile.

6.11. GRB021104

129

Figure 6.27: The energy resolved light curves of GRB021104 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum.

130

6.11.2

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Spectrum

The X-ray to γ-ray fluence ratio of 1.7 qualifies this burst as an X-ray flash. Although the powerlaw model shows an acceptable fit for the time-average spectrum, the χ2 value is improved in
the cutoff power-law model. ∆χ2 is 6.62 for one extra degree of freedom (F test probabilityof 5.78 × 10−3 ) between the power-law model and the cutoff power-law model. Hence, themodel with a spectral break is requested from the data statistics. We decided that the cutoff
power-law model is the acceptable model for the prompt emission. Epeak lies around 30 keV.

Table 6.29: The fluxes and fluences of GRB021104. The spectral model is the cutoff power-law
model.
energy range [keV]
Duration [sec.]
photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

31.4
+0.9
1.8−0.6+1.0
2.5−0.7
2.4±1.0 ×10−1+1.0
2.7−0.7
1.4±0.5
3.3±0.7+1.4
2.0−0.9+1.6
5.2−1.1
56.5+29.2−19.6
78.7+29.9
−20.9
+3.0
7.5−2.6
86.3+30.4
−21.3
+1.8
4.3−1.3+2.1
10.3−1.8+4.4
6.1−2.7+5.0
16.4−3.3

6.11. GRB021104

131

Figure 6.28: The WXM and FREGATE spectra of GRB021104. The top and bottom figures
are fitting with the power-law model and the cutoff power-law model, respectively.

132

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.30: The spectral parameters of GRB021104.
Model
PL

Parametersα−1.82±0.18
aK15(4.19±0.66) × 10−2
+0.16b
C (WXM)
0.34−0.11
χ2ν /DOF
0.924/39+0.54
Cutoff PLα−1.11−0.46+17.4
Epeak [keV]28.2−7.9+5.31
K15
7.59−2.55
× 10−2+0.20
C (WXM)
0.48−0.15
0.774/38
χ2ν /DOF
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1
b Constant parameter of WXM. The constant parameter of FREGATE is fixed to 1.

6.12. GRB030416

6.12

133

GRB030416

At 11:03:59.00 UTC on 16 Apr 2003, the FREGATE and WXM observed the untriggered burst[40]. Although FREGATE 6–80 keV triggered this event, the trigger process of WXM had been
turned off in order to avoid false triggers by Sco X-1. Consequently, the burst did not produce
an on-board localization. The position of the burst by the ground analysis is centered at (R.A.,
Dec.) = (11h 06m 51s , −02◦ 52′ 58′′ ) (J2000) with a 90% radius of 7′ .
There are two reports about the afterglow search for this event (table 6.31). However, noafterglow has been found.
Table 6.31: The afterglow search for GRB030416
Timea
Telescope & Instruments
OT
15.74 hours HETE GCN position notice15.4 hours USNO
N
1.38 days

0.23 m Telescope
MASTER systemd

N

Lim. Mag.b

GCN

BVRcIcc

Henden et al.
(#2250)∼ 15.0 mag. (R) Lipunov et al.
(#2154)a Time after the trigger
b Limiting magnitudec Limiting magnitude:

Start
Date

Start Time Filter Integration Limiting
Since GRB

Time (sec)(hours)x Pointings (3 sigma)

Magnitude

Telescope

Calibration
Catalog

Apr 17.103 15.391

Rc

6000 x 1

19.8

0.6-m RBO* USNO A2.0

Apr 17.143 16.361

B

300 x 120.1

1.3-m USNO USNO A2.0

Apr 17.149 16.502

V

300 x 120.9

1.3-m USNO ACT

Apr 17.155 16.643

Rc

300 x 120.4

1.3-m USNO USNO A2.0

Apr 17.160 16.784

Ic

300 x 119.9

1.3-m USNO USNO B1.0

Apr 20.143 88.454

Rc

2160 x 1

22.3

1.3-m USNO USNO A2.0

* RBO = Red Buttes Observatoryd Alexander Kryolov Observatory, Moscow, Russia

6.12.1

Light curve

The duration is ∼ 80 seconds at the WXM 2–5 keV energy band. The slow increase of thesignal is lasting about 30 seconds. The high flux part continues about 20 seconds, and then the

134

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

signal decayed in 30 seconds. The burst signal is very weak in the WXM 17–25 keV band.

6.12.2

Spectrum

The time-average fluxes and the fluences are summarized in table 6.32. Since the X-ray to
γ-ray fluence ratio is 2.4, this burst is classified as X-ray flash.
Table 6.32: The time-average fluxes and fluences of GRB030416. The spectral model is thepower-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10−9 erg cm−2 s−1 ]Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2-30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

78.6
1.3±0.1
1.4±0.1+1.7
4.1−1.3×10−2
1.5±0.1
7.9±0.7
11.4±1.1+2.4
4.7−1.7+3.1
16.1−2.6
102.9±9.8113.7±10.0
3.2±1.3
116.9±10.1
6.2±0.5
9.0±0.9+1.9
3.7−1.4+2.5
12.7−2.1

The power-law model is acceptable for the time-averaged spectrum of GRB030416. The
photon index is well steeper than < −2. The constrained Band function is applied to constrain

the Epeak of this event. The probability density distribution as a function of Epeak is shown infigure 6.31. The 68%, 95% and 99.7% upper limit of Epeak are 3.1, 3.3 and 3.8 keV respectively.
To investigate the spectral evolution, the hardness ratio between 5–25 keV and 2–5 keV isplotted in figure 6.32. It is possible to see two hard-to-soft evolutions during the burst. The
first part is from T0 + 10 s to T0 + 20 s, and the second part is from T0 + 20 s to T0 + 35 s

(T0 is the trigger time). The soft tail is lasting for T0 + 60s.

6.12. GRB030416

135

Figure 6.29: The energy resolved light curves of GRB030416 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum.

136

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.30: The time-average spectrum of GRB030416.

Figure 6.31: The posterior probability density distribution for Epeak . The solid, the dashed,
and the dot-dashed lines show the 68%, 95%, and 99% probability upper limits on Epeak . Epivot
energy is 1.4 keV.

6.12. GRB030416

137

Figure 6.32: The hardness ratio between 5–25 keV and 2–5 keV band. The middle and thebottom panels are the light curves of the WXM 2–5 keV and 5–25 keV band.

Table 6.33: The spectral parameters of GRB030416.
Model Parameters
+0.13
PL
α
−2.32−0.15
aK15(9.23±1.72) ×10−3
χ2ν /DOF
0.870/54
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

138

6.13

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

GRB030418

FREGATE detected this event in the 32–400 keV band on 18 April 2003 at At 09:59:18.85
UTC [93]. The correct WXM flight localization was reported in a GCN Notice at 215 seconds
after the trigger. The WXM localization in the ground analysis can be expressed as a 90%
confidence circle that is 9′ in radius and is centered at: R.A. = 10h 54m 53s , Dec. = −06◦ 59′ 22′′

(J2000).

The status of the afterglow search is summarized in table 6.34. The candidate of the opticaltransient (OT) was reported by Price et al. (GCN 2148) at 2.26 hours after the trigger. The
decline of the optical flux of this OT candidate was observed by the same authors (GCN 2150).
The Magellan 6.5 m telescope also observed this OT and confirmed the decrease in the flux atthe power-law decay of t−1.2±0.1 (Dullighan et al.; GCN 2168 and GCN 2236).
Table 6.34: The afterglow search for GRB030418
Timea
215 seconds
1.73 hours
2.26 hours
4.66 hours
69 minutes
238 seconds

Telescope & Instruments
OT
HETE flight location
HETE ground location
40-inch Telescope
Yc
Siding Spring Observatory (Chile)
40-inch Telescope (2nd epoch)
Y

Lim. Mag.b

GCN

18.8 mag. (R)

1.05 m Telescope (J)Kiso Observatory
ROTSE-IIIaN

13 mag.d (J)Y

18.7 - 17.4 mag.
(360 s. - 2.3 h)
16.5 mag. (R)Price et al.
(#2148)
Price et al.
(#2150)Mito et al.
(#2151)
Smith et al.
(#2153)
Lipunov et al.
(#2158)Dullighan et al.
(#2168)Dullighan et al.
(#2236)

11-12.5 hours MASTER systemN2.59 days

Magellan 6.5 m (R, I)

Y

6.58 days

Magellan 6.5 m (R, I, V)(2nd epoch)Y9.53 hours

152 cm Telescope (R)Y

a Time after the trigger
b Limiting magnitudec (R.A., Dec.) = (10h 54m 33.69s , −7◦ 01′ 40.8′′ )d 3 sigma upper limit

19.8 mag. (R)

23.3±0.1 (R)
23.0±0.1 (I)24.9±0.4 (R)>24 (I)
25.1±0.5 (V)20.50±0.30 (9.53h) Ferrero et al.
20.65±0.29 (10.18h) (#2284)

6.13. GRB030418

6.13.1

139

Light curve

The double peak structure was observed in the FREGATE energy bands, whereas, this time
profile was closer to the single peak in the WXM 2–10 keV band (figure 6.33). Although thesignificant decreasing trend of the background started around t=100 (this event occurred about
10 minutes before the SAA), the duration was ∼ 130 seconds in the FREGATE bands and could
be much longer in the WXM 2–10 keV band.

6.13.2

SpectrumDue to the incomplete downlink of the data, we used the SP data for the spectral analysis of
FREGATE. The photon data (TAG data) were available for WXM.
The spectral analysis is performed for the three time intervals including the whole burst
region (figure 6.33). Since this event occurred 10 minutes before the SAA and the decreasing
trend of the background was observed just after the burst, we choose t ∼ 100 as the end of

the foreground time region for creating the spectra. The cutoff power-law model is the best

representative model for all time regions. The F test probabilities of the cutoff power-law modelover the simple power-law model are 1.73 × 10−11 , 2.22 × 10−2 , and 3.78 × 10−4 respectively.

The X-ray to γ-ray fluence ratio is 0.99 qualifies this burst as an X-ray rich GRB. The spectrum

in the first region has a harder photon index and also a higher Epeak energy than that of thesecond region. The time-average Epeak energy is 46 keV.

140

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.33: The energy resolved light curves of GRB030418 at 1.23 s time bin. The dottedlines correspond to the two foreground intervals used for creating the spectra.

6.13. GRB030418

141

Figure 6.34: The WXM and FREGATE spectra of GRB030418. The spectra of region 1, region
2, and all region are shown from top to bottom. The left and right plots are fitting with thepower-law model and cutoff power-law model, respectively.

142

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.35: The fluences of GRB030418. The spectral model is the cutoff power-law model.
energy range [keV]
Duration [sec.]
Photon flux
−1
[10 ph cm−2 s−1 ]Energy flux
[10−8 erg cm−2 s−1 ]Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

region 152.4
3.5±0.8
6.9±0.9
2.3±0.4
9.2±1.0(3.1±0.6) × 10−1
1.3±0.1
2.0±0.5
3.3±0.5
18.6±4.1
36.0±4.7
12.0±2.1
60.8±5.2
1.6±0.3
6.7±0.7
10.7±2.6
17.4±2.7

region 257.7
15.7±1.0
18.7±1.0
0.8±0.4
19.5±1.2(10.5±0.6) × 10−1
1.8±0.1+0.7
0.7−0.3+0.7
2.5−0.490.5±5.8
107.8±6.1
4.6±2.2
112.4±6.7
6.0±0.3
10.6±0.7+3.9
3.9−1.8+3.9
14.5−2.2all
110.1
9.9±0.8
13.0±0.8
1.5±0.4
14.6±0.9(7.1±0.5) × 10−1
1.6±0.1+0.7
1.6−0.5+0.7
3.1−0.5
109.0±8.8143.1±8.8
16.5±3.9
160.7±9.4
7.8±0.617.1±1.1+7.3
17.3−5.2+7.2
34.5−5.5

Table 6.36: The spectral parameters of GRB030418 in the power-law (PL) and the cutoff
power-law (Cutoff PL).
Model
PL

Parameters
Region 1α−1.41 ± 0.07
aK15
(1.36±0.14) × 10−22χν /DOF1.720/69+0.31
Cutoff PLα−0.43−0.27+11.19Epeak [keV]
48.62−8.03
+0.99
K15
(3.35−0.69) × 10−2
χ2ν /DOF
0.893/68
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

Region 2−1.95±0.08(1.90±0.18) × 10−2
1.133/54+0.19−1.75−0.16+12.3713.74−4.89+0.94(2.69−0.63) × 10−2
1.045/53

All−1.70±0.06(1.76±0.13) × 10−2
1.104/69+0.14−1.46−0.13+31.9646.10−13.70+0.47(2.43−0.37) × 10−2
0.929/68

6.14. GRB030429

6.14

143

GRB030429

At 10:42:22.68 UTC on 29 April 2003, FREGATE, WXM, and SXC observed the γ-ray burst[18]. The burst triggered in the 32–400 keV energy band. The flight position was not sent out
to GCN due to the low signal to noise ratio in WXM. The WXM ground localization can be
expressed as 90% confidence rectangle, whose center is at (R.A., Dec.) = (12h 13m 18s , −20◦

51′ 09′′ ) (J2000), and whose corners lie at (R.A., Dec.) = (12h 13m 32s , −21◦ 01′ 55′′ ), (12h12m 50s , −20◦ 59′ 56′′ ), (12h 13m 03s , −20◦ 40′ 26′′ ), (12h 13m 46s , −20◦ 42′ 22′′ ) (J2000). The

SXC position is centered at (R.A., Dec.) = (12h 13m 06s , −20◦ 56′ 00′′ ) (J2000) with the 90%

confidence circle of 2′ radius.

The afterglow of GRB030429 was discovered in the optical band at 3.5 hours after the trigger.
Several authors reported the confirmations of the optical transient and also the redshift of 2.56
is measured by VLT for this burst (see table 6.37).

6.14.1

Light curve

The duration of the burst is ∼ 20 seconds. Although it is hard to see the structure of the light

curve in the WXM energy band, the two peaks are clearly visible in the FREGATE light curve.

6.14.2

SpectrumThe spectral analysis is performed for the each peaks. Since there is a problem in photon data,
the survey data are used in the analysis.
The time-averaged flux and fluence are in table 6.38. Since the fluence ratio of 2–30 keV to
30–400 keV is 1.23, this burst is classified as an X-ray flash.
The spectral parameters are summarized in table 6.39. The time-resolved spectral analysis
is performed for the first peak, the second peak, and the whole burst region (see figure 6.35).
The cutoff power-law model is the acceptable model for all spectral regions. Even at the second
time region, the F test probability between the power-law model and the cutoff power-law
model is 5.41 × 10−3 . So, the improvement of the fitting is significant. It is possible to see thedecrease of the Epeak energy from the first to the second peak.

144

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.35: The energy resolved light curves of GRB030429 at 1.23 s time bin. The dottedlines correspond to the foreground spectral regions.

6.14. GRB030429

145

Figure 6.36: The WXM and FREGATE spectrum of GRB030429. The spectrum of the firstpeak, the second peak and the whole burst region are shown from top to bottom. The model
spectrum is the power-law and the cutoff power-law model from left to right.

146

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.37: The afterglow search for GRB030429
Timea1.87 hours
1.87 hours

2.65 days

Telescope & Instruments
OT
HETE GCN position notice
ROTSE-IIIaN
cSiding Spring Ovservatory
0.6 m (unfil.)and 1.55 m (Rc) Tel. Yd
Mt. John Obs.e and USNOFS
AT-64 TelescopeY
CrAOf
VLT (ISAAC and FORS2)
Y
gParanal Obervatory
SIRIUShYi
1.4 m Telescope (J H Ks)
VLT (FORS1;spectrum)Y
3800–8000 Å
VLA (8.46 GHz)N

3.43 days

1.5 m RTTj

3.5 hours
8.98 hours
12.6 hours
6.74 hours
2.75 days

Y

Lim. Mag.b
18∼19 (R)Smith et al.
(#2178)Gilmore et al.
(#2184)20.20±0.15 (R)Rumyantsev et al.
(#2190, #2218)∆m ∼ 0.43 (V) in 5.5 h Fynbo et al.
(#2185)
Nishiyama et al.
(#2195)z=2.65
Weidinger et al.
(#2195, #2215)
J(3σ)=0.18 mJy
Berger et al.
(#2197)23.5±0.5(R)Khamitov et al.
(#2208)a Time after the trigger
b Limiting magnitudec New South Wales, Australia
d OT position: 12:13:07.50 -20:54:49.7 J2000 (err: +/- 0.3arcsec)

UTmid

CRmag

CRerr

Apr 29.591

19.34

0.11

Apr 29.600

19.43

0.13

Apr 29.616

19.71

0.16

Apr 29.660

19.87

0.19

e Lake Tekapo, New Zealandf Crimean Astrophysical Observatory, Nauchny, Ukraine
g Cerro Paranal, Chileh Simultaneous three-color InfraRed Imager for Unbiased Survey

South Africa Astronomical Obsevatory(SAAO), Sutherland, South Africa
i OT info:

UTmid

J

H

Ks

Apr 29.727

18.8

17.8

17.0

Apr 29.873

19.2

18.3

17.5

Apr 30.005

18.9

18.1

17.4

---------------------------Apr 30.768

19.0

18.4

17.8

j Russian-Turkish Telescope (Bakyrlytepe, Turkey)

GCN6.14. GRB030429

147

Table 6.38: The time-average fluxes and fluences of GRB030429. The spectral model is thecutoff power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

Energy flux
[10−8 erg cm−2 s−1 ]Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

reg.1
14.8
1.0±0.2
1.5±0.2(2.4±0.6) ×10−1
1.8±0.2
0.8±0.1
2.2±0.3
2.1±0.7
4.3±0.715.1±3.2
22.6±3.3
3.6±0.826.2±3.4
1.2±0.2
3.3±0.4
3.1±0.1
6.4±1.1

reg.2
9.8
1.0±0.3
1.3±0.3+6.9
5.3−4.8×10−2
1.4±0.3
0.7±0.2
1.5±0.3+8.1
3.7−3.4×10−1
1.9±0.7
10.0±3.0
12.8±3.0+6.8
5.2−4.7×10−1
13.3±3.3
0.7±0.2
1.5±0.3+7.9
3.6−3.4×10−1
1.8±0.7all
24.6
1.0±0.2
1.4±0.2(1.8±0.4) ×10−1
1.6±0.2
0.8±0.1
1.9±0.2
1.5±0.6
3.5±0.624.9±4.435.2±4.5
4.4±1.1
39.6±4.7
1.9±0.3
4.7±0.5
3.8±1.3
8.5±1.4

Table 6.39: The spectral parameters of GRB030429.
Model
PL

Parameters
region 1α−1.68±0.09
K15 a
2.30±0.28
2χν /DOF1.270/70+0.28
Cutoff PLα−0.99−0.24
Epeak [keV]
39.1+11.6
−8.1
+1.55
K15
4.91−1.08
2χν /DOF0.804/69
a Normalization at 15 keV in the unit of 10−2 photon cm−2 s−1 keV−1

region 2+0.18−1.95−0.23
1.41±0.36
0.787/69+1.44−1.19−0.61
16.5+19.8−6.7
4.18+36.38−2.38
0.712/68

all−1.72±0.08
2.02±0.22
1.108/69−1.13±0.24
35.0+11.8
−7.9
+1.32
4.05−0.90
0.720/68

148

6.15

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

GRB030528

FREGATE triggered on this event in 32–400 keV energy band [110]. The WXM flight location
was distributed to the GCN at 37 seconds after the trigger. The ground localization by SXC
was reported to the GCN at 107 minutes after the trigger. The SXC position was expressed as a
90% confidence circle in a radius of 2′ with a center of (R.A., Dec.) = (17h 04m 02s , −22◦ 38′ 59′′ )(J2000).

The afterglow was detected in X-ray and infrared, but not in optical band. The status of theafterglow search is summarized in table 6.40. The earliest optical observation was reported in
2.5 minutes after the trigger by Torii at RIKEN (GCN #2252). The Chandra X-ray observation
was performed at 5 days after the trigger. Four X-ray afterglow candidates were reported within
the SXC error circle (GCN #2269). Greiner et al. (GCN #2271) searched in the near infrared
bands of these X-ray sources, and found that only the Chandra source #1 showed the decay inthe magnitude. The second epoch of the Chandra X-ray observation confirmed the source #1
was indeed the afterglow of GRB030528 (GCN #2279).

6.15.1

Light curve

As seen in figure 6.37, the light curves show the strong hard-to-soft evolution during the burst.
The duration of the burst could be ∼ 100 seconds in the lower energy bands. On the other
hand, in the γ-ray energy band (32-400 keV), the duration is ∼ 20 seconds.

The additional peak is seen around 250 seconds after the trigger. Since this peak was notpossible to be localized by WXM, we can not confirm the origin of this peak.

6.15.2

SpectrumDue the problem of the primary ground station, the several data were not properly downlinked.
There were gaps in various data. For the WXM, the photon data (TAG data) is not possible
to use. The PHA data is only available every 10 seconds (a half of the data was missing). We
use PHA data and multiply the constant factor in the model. Because of this incomplete data
downlink problem, it is difficult to perform the time-resolved spectral analysis.
The X-ray to γ-ray fluence ratio of 1.1 qualifies this event as an X-ray flash. However, it isfair to classify this event as the border of X-ray flash and X-ray-rich GRB. The Epeak energy ∼30 keV is the good evidence that this event is in the border of these two GRB classifications.

6.15. GRB030528

149

Figure 6.37: The energy resolved light curve of GRB030528 at 1.23 s time bin. The dottedlines correspond to the foreground spectral region. There were data gaps due to the uncomplete
downlink in several places.

150

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.38: The WXM and FREGATE spectra of GRB030528. The model spectrum is thepower-law model, the cutoff power-law model and the Band function from top to bottom.

6.15. GRB030528

151

Table 6.40: The afterglow search for GRB030528
Timea
37 seconds
1.78 hours
105 seconds
148 seconds
252 seconds
2.3 hours
0.5 days
4.97 days-5.30 days
4.78 days

Telescope & Instruments
HETE flight location
HETE SXC ground loc.
0.2 m telescope0.25 m telescope (RIKEN)
25 cm telescope
Kyoto U.
1.01 m telescope (R)Bisei Observatory
unfil. 0.72 m TNT telescope
Astro. Obs. of Colluraniac
Chandra X-ray Obs.

OT

Lim. Mag.bN

VLA (8.46 GHz)

N(#2253)∼ 15.8 mag.
Torii
∼ 16 mag.
(#2252)
Uemura et al.
∼ 18.7(#2257)
Ayani et al.
∼ 20.5(#2258)
Valentini et al.
(#2269)Butler et al.
∼350µJy(#2270)
Frail et al.
Chandra src.#1 (#2271)
Greiner et al.

N
N
N
Yd

0.66 days
1.66 days
2.63 days
6.74 daysnear-IR NTTe SOFI camera
La Silla Obs.f

Y (Ks)

MDMg 1.3 m telescope (I)Nh

4.81 daysnear-IR (Ks) WIRC camera
Palomar 5 m telescope
Chandra X-ray Obs. (2nd)Ni

10.8 days

Y(#2273)
Mirabal et al.
(#2275)
Bogosavljevic et al.
Chandra src.#1 (#2279)
Butler et al.

a Time after the trigger
b Limiting magnitudec Teramo, Italyd Chandra src. within the SXC error region:#

Chandra Name

RA

DEC
0.31

-22 37dR(s) dD(") Cts

1 CXOU J170400.3-223710

17 4

4 CXOU J170348.4-223826

17 3 48.39-22 38 25.93

0.054

0.92

30

9 CXOU J170400.1-223548

17 4

0.11

-22 35 48.10

0.053

0.92

11

10 CXOU J170354.0-223654

17 3 53.95-22 36 53.67

0.054

0.93

9

e The ESO New Technology Telescope, 3.58 m
f La Silla, Chileg Tucson, AZ
h No Chandra src.#1 in I band imagei No Chandra src.#1 in Ks band image

9.99

0.053

0.91

GCN

39

152

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.41: The fluxes and fluences of GRB030528. The spectral model is the Band function.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10−8 erg cm−2 s−1 ]Photon fluence[ 10 ph cm−2 ]Energy fluecne[10−6 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400

all
83.6
4.6±0.5
6.1±0.5(6.4±0.4) ×10−1
6.8±0.5
3.3±0.3
7.5±0.3
6.7±0.914.2±0.938.4±3.951.2±4.0
5.4±0.356.7±4.0
2.8±0.2
6.3±0.3
5.6±0.7
11.9±0.8

Table 6.42: The spectral parameters of GRB030528.
Model
PL

Parametersα−1.87±0.03
K15 a
8.62±0.30 × 10−2
C (WXM)
0.5 (fixed)χ2ν /DOF
1.946/111
Cutoff PLα−1.39±0.10+3.68
Epeak [keV]
34.95−3.10K151.30±0.10 × 10−1
C (WXM)
0.5 (fixed)χ2ν /DOF
0.835/110
+0.15
Band
α
−1.33−0.12+0.29
β−2.65−0.98+4.67
Epeak [keV]
31.84−4.97
+0.24
K15
1.39−0.15
×10−1
C (WXM)
0.5 (fixed)χ2ν /DOF
0.809/109
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1
b Constant parameter of WXM. The constant parameter of FREGATE is fixed to 1.

6.16. GRB030723

6.16

153

GRB030723

FREGATE, WXM and SXC observed the γ-ray burst at 06:28:17.45 UTC on 23 July 2003[66]. The burst triggered on the WXM 2–25 keV band. The correct flight location was send 42
seconds after the trigger. The 90% confidence circle of the WXM position based on the ground
analysis was centered at (R.A., Dec.) = (21h 48m 52s , −27◦ 41′ 16′′ ) (J2000) with 9.4′ radius.

The SXC localization was expressed as the center of (R.A., Dec.) = (21h 49m 27.4s , −27◦ 42′ 01′′ )(J2000) with 2′ radius in the 90% confidence circle.

The optical and infrared afterglow was found in 21.3 and 18.7 magnitude respectively at
1.1 days after the trigger. The temporal behavior of the optical afterglow showed the different
decay slope from −1 to −2 around 30–50 hours after the burst (GCN #2336). The spectroscopic
observation was performed by VLT. There were no absorption lines and a Lyman-α Forest in
the spectrum. This result suggests a redshift was less than 2.1.

6.16.1

Light curve

The duration of the burst is ∼ 20 seconds. The burst signal is not seen in the WXM 17–25

keV band. The duration of the burst could be much longer at the lower energy band (e.g. 2–5
keV). Because of the low signal to noise ratio, it is hard to see the temporal structure of the
burst.

6.16.2

Spectrum

The X-ray to γ-ray fluence ratio of 0.9 qualifies this event as an X-ray-rich GRB. However, it ispossible to classify this event as the border of X-ray flash and X-ray-rich GRB. The power-law
is the acceptable model. If we tried the cutoff power-law model, ∆χ2 = 1.43 in one additional
degree of freedom and this is not a significant improvement. The photon index is ∼ −2 and it isdifficult to show that the photon index is steeper than −2 in a high significance. Unfortunately,
it is not possible to constrain the Epeak energy of this burst applying the constrained Band

function.

154

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.39: The energy resolved light curves of GRB030723 at 1 s time bin. The dotted lines
correspond to the foreground spectral region.

6.16. GRB030723

155

Figure 6.40: The WXM and FREGATE spectrum of GRB030723. The spectral model is thepower-law.

156

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.43: The afterglow search for GRB030723
Timea41.6 s2.90 hours
7.49 hours
47 s

Telescope & Instruments
S/C position
HETE GCN position notice (WXM)
HETE GCN position notice (SXC)
ROTSE-IIIb
McDonald Ovservatoryc
KAITd

OT

Lim. Mag.b

N

18∼19 (R)

0.6 m Telescope (MOA)
Mt. John Obs.e
12.9 hours
0.3 m Telescope (unfil.)Bronberg observatoryf
19.7/21.8 hours SMARTS Consortium 1.3 m Tel. (R)
1.02 days
Cerro Tololo inter-American Obs.g
1.04 days
1.5 m Telescope
2.04 days
La Silla Observatoryh
1.14 days
1.5 m (R)& 5 m (Ks) Telescope
2.14 days
Palomar Observatoryi
1.03 days
LDSS2 6.5 m Magellan Tel.
1.05 days
Las Campanas Obs.k
2.99 days
VLT FORS1/UT1, spectrum
3650–7500 Å
2.14 days
Chandra X-ray Obs.
– 2.46 days
2.15 days
SMARTS 1.3 m Tel.
(re-analysis)
3.16 days
VLA (8.46 GHz)N

1.2 hours
3.3 hours
7.6 hours

5.13 days
10.9 days
14.0 days
12.66 days
– 13.67 days

N

N
N
N
Yj
Y
Y
Yl
Y
N

LDSS2 6.5 m Magellan Tel.
Las Campanas Obs.
VLTY

Chandra X-ray Obs.

Yma Time after the trigger

Y

Smith et al.
(#2318, #2338)
19–20 (R)
Chornock et al.
(#2315)
DSS lim.
de Ugarte et al.
(#2314)
CR=20
Monard et al.
(#2312)
DSS lim.
Bond et al.
(#2316)24 (R)
Jensen et al.
(#2321)
21.3/ 22.4 (R)Fox et al.
18.65 / no detection (Ks) (#2323)
R=21.13±0.05
Dullighan et al.
(#2326)z<2.1
Fynbo et al.
(#2327)
Butler et al.
(#2328)R=21.0 (1.91 days)
Bond et al.
R=20.9 (1.02 days)(#2329)180 mJy (3σ)
Soderberg et al.
(#2330)24.2±0.3 (R)Dullighan et al.
(#2336)re-brightening 1 mag.
Fynbo et al.
(#2345)
Butler et al.
(#2347)b Limiting magnitudec Davis Mountains, Austin, TX
d Katzman Automatic Imaging Telescope (Lick Observatory, San Jose, CA)e Lake Tekapo, New Zealandf Pretoria, South Africa

g La Serena, Chileh La Silla, Chile

j OT pos: R.A. 21:49:24.40, Dec. -27:42:47.4 (J2000)

i San Diego, CA
k Carro Las Campanas, Chilel 3 X-ray sources:#

Chandra Name

RA

DEC

Cts

1 CXOU J214924.4-274248

21 49 24.421-27 42 48.00

78

3 CXOU J214926.9-274146

21 49 26.891-27 41 45.92

19

4 CXOU J214928.7-274211

21 49 28.724-27 42 11.47

16

GCN

m 0.5–8.0 keV flux in the power-law model with the index of 1.9 is (2.2 ± 0.3) × 10−14 erg cm−2 s−1 and(3.5 ± 0.5) × 10−15 erg cm−2 s−1 for the 1st epoch and the 2nd epoch respectively.

6.16. GRB030723

157

Table 6.44: The fluxes and fluences of GRB030723. The spectral model is the power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

18.7
1.1±0.2
1.3±0.2(1.1±0.5) ×10−1
1.5±0.2
0.7±0.1
1.3±0.2
1.5±0.8
2.8±0.921.2±2.925.2±3.1
2.0±0.827.2±3.2
1.4±0.2
2.4±0.3
2.8 .6±1.4
5.2±1.7

Table 6.45: The spectral parameters of GRB030723.
Model
PL

Parameters+0.15
α−1.93−0.17
K15 a(1.39±0.28) × 10−2χ2ν /DOF
1.117/40

a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

158

6.17

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

GRB030823

FREGATE triggered on this event at 08:52:40.64 UTC on 23 August 2003 in the 6–80 keV energy band [94]. Since the WXM Y-location was extreme edge of the FOV, the flight localization
was not send to the ground. The WXM localization could be expressed as a 90% confidence rectangle, whose center was at (R.A., Dec.) = (21h 30m 46s , 21◦ 55′ 43′′ ) (J2000), and whose corners layat (R.A., Dec.) =(21h 31m 02.6s , 21◦ 37′ 55′′ ), (21h 30m 21.1s , 21◦ 37′ 23′′ ), (21h 30m 29.0s , 22◦ 13′ 30′′ )and (21h 31m 10.6s , 22◦ 14′ 02′′ ) (J2000). The SXC Y-camera detected the burst, but the Xcamera did not. The joint WXM and SXC location of the burst could be expressed at a90% confidence rectangle, whose center was at (R.A., Dec.) = (21h 30m 47s , 21◦ 59′ 46′′ ) (J2000),
and whose corners lay at (R.A., Dec.) = (21h 30m 26.9s , 22◦ 01′ 44′′ ), (21h 30m 25.9s , 21◦ 57′ 14′′ ),(21h 31m 07.4s , 22◦ 02′ 17′′ ), (21h 31m 06.5s , 21◦ 57′ 50′′ ) (J2000).
Although there were several deep optical investigations, no afterglow has been found forthis burst (table 6.46).

6.17.1

Light curve

The signal is clearly visible in the FREGATE 6–40 keV band and not in the 32–400 keV band.
The rising background counts were due to the high energy particles (this event occurred ∼ 20
minutes before the SAA). The burst might be started ∼ 25 seconds before the trigger time,

however, the particle background was also starting to increase around that period. The burst
signal is seen in all WXM energy bands. The low signal to noise ratio in the WXM data wasdue to the large incident angle of the event (∼ 35◦ ). The temporal structure of this burst is

characterized in a large single pulse with the duration of ∼ 50 seconds.

6.17.2

Spectrum

The X-ray to γ-ray fluence ratio of 1.8 qualifies this burst as an X-ray flash. Since there isa large improvement of χ2 in the cutoff power-law model against the simple power-law model(∆χ2 = 35.23 with 1 degree of freedom), the cutoff power-law model is the best model for thetime-average spectrum. The Epeak energy is 26.6 keV.

6.17. GRB030823

159

Figure 6.41: The energy resolved light curves of GRB030823 at 1.23 s time bin. The dottedlines represent the foreground region of the spectrum.

160

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.42: The WXM and FREGATE spectrum of GRB030823. The spectral model is thepower-law (top) and the cutoff power-law (bottom).

6.17. GRB030823

161

Table 6.46: The afterglow search for GRB030823
Timea2.28 hours
3.19 hours
1.82 hours

Telescope & Instruments
WXM ground analysis
SXC ground analysis
30cm Telescope (un fil.)Titech2.28 hours RAPTOR

OTLim. Mag.b

GCN

N∼ 16.5N∼ 16.03.50 hours 1.0m Telescope (PI1300)
Lulin Obs.
6.86 hours 1.5m Telescope
Mavidanak high-altitude Obs.(UBAI)
AT-64 and K-380 telescopes
Crimean Astrophysical Obs.(CrAO)
0.78 days 5m Hale Telescope
1.86 days Mt. Palomar Obs.
1.24 days 0.60 m Telescope (Rc)
Ouda Obs.

N

18.8 (R)N

notec(#2362)
Suzuki et al.
(#2361)
Wren et al.
(#2360)Huang et al.
(#2366)
Ibrahimov et al.

N

R>22.5N

20.5 (Rc)a Time after the trigger
b Limiting magnitudec Limiting magnitude of various observations are following:#

Mid. Time

Telescope

Exposure(UT)

Limiting
magnitude(R)1

23.6651

1.5m (UBAI)

300s

19.5

2

23.7805

1.5m (UBAI)

300s

20.5

3

23.7826

AT-64 (CrAO)

7x180s20.5

4

23.8131K-380 (CrAO)

6x300s19.0(#2365)Fox et al.
(#2370)Imada et al.

162

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.47: The fluxes and fluences of GRB030823. The spectral model is the cutoff power-law
model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[10 ph cm−2 ]Energy fluecne[10−6 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

55.6
2.6±0.3
3.4±0.3(2.8±0.6) ×10−1
3.7±0.3
1.9±0.2
4.1±0.3
2.3±0.7
6.4±0.814.5±1.8
19.1±1.8
1.5±0.3
20.7±1.8
1.1±0.1
2.3±0.2
1.3±0.4
3.6±0.5

Table 6.48: The spectral parameters of GRB030823.
Model
PL

Cutoff PL

Parametersα−1.82±0.06
K15 a(4.41±0.31) ×10−2
χ2ν /DOF
1.019/111+0.20
α−1.31−0.18+7.45
Epeak [keV]
26.57−5.03
+2.34
K15
8.26−1.59
×10−2
2
χν /DOF0.708/110

a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

6.18. GRB030824

6.18

163

GRB030824

FREGATE triggered on the 6–40 keV band at 16:47:35.10 UTC on 24 August 2003 [26]. The
WXM flight location was correct, however, it was not distributed to the GCN due to the low
signal-to-noise ratio and the burst location at the edge of the FOV. The WXM location basedon the ground analysis could be expressed as a 90% confidence circle, whose radius was 11.2′
and whose center was at: (R.A., Dec.) = (00h 05m 02s , +19◦ 55′ 37′′ ) (J2000).
The afterglow search is summarized at table 6.49. Although there was the optical observation starting 76 minutes after the burst, no afterglow has been found. There was an observation∼ 1 month after the burst in searching for the supernova signal of this burst. Two transientssources were reported in GCN, however, the nature of these sources are still unclear (very red
objects, very faint in R band but clearly visible in i′ band, GCN #2418).

6.18.1

Light curve

The burst signal is seen in the soft energy bands of both WXM and FREGATE (figure 6.43).
The several spikes are observed in the FREGATE 6–40 keV band, whereas they are hard tosee in the WXM 2–10 keV band due to the low signal to noise ratio. This low signal to noise
ratio in the WXM data is mainly due to the large incident angle of the burst (∼ 40◦ ). Almost
no detection of the photons in the WXM 10–25 keV indicate that this burst is very soft. The
duration of the burst is ∼ 15 seconds.

6.18.2

Spectrum

The time-average spectrum is well described in the simple power-law model with the photon
index of −2.1. The X-ray to γ-ray fluence ratio of 1.5 qualifies this event as an X-ray flash.

The the photon index greater than −2 is rejected in a high significance if we use the FRE-GATE data only (> 99.9% confidence level). Thus, this burst is also a good event to apply

the constrained Band function to calculate the upper limit of Epeak . The posterior probability
density distribution as a function of Epeak is shown in figure 6.45. The highest probability
is in 6.1 keV and the 99.7% upper limit is 8.1 keV. The Epeak energy ∼ 10 keV is a typicalcharacteristics of X-ray flashes.

164

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 6.43: The energy resolved light curves of GRB030824 in 1.23 s time bin.

6.18. GRB030824

165

Table 6.49: The afterglow search for GRB030824
Timea
1.0 hours
2.43 hours
76-153 min.
3.87 hours
4.52 hours
0.55 days
1.72 days
27.63 days

Telescope & Instruments
OT
WXM ground analysis
WXM ground analysis (2nd)0.6m Telescope
Y→Nc
Morehead Obs.d
1.05m Schumidt Telescope
N
Kiso Obs.
0.4m Telescope (Rc)N
Nyrola Obs.e
1.5m TelescopeNf
Maidanak Obs.
5m Hale Telescope
N
Palomar Obs.
3.6m CFHT Megaprimeg (i′ ) 2 src.h
Mt. Mauna Kea, Hawaii

Lim. Mag.b

GCN(#2363)
Moran et al.
∼ 17 (R)(#2407)
Urata et al.
17.5-19.0 (Rc) (#2379)
Oksanen et al.
∼ 19.5 (R)(#2368)Ibrahimov et al.
22.5 (R)(#2364, #2369)
Fox et al.
(#2406, #2418)
Klotz et al.

a Time after the trigger
b Limiting magnitude
c The suspicios object was reported in R∼17, however, this transient was an instrumental noise (GCN Circ.#2373).
d Chapel Hill, NC
e Jyvaskyla, Finlnad
f Mt. Maidanak, the Republic of Uzbekistan (altitude, 2000m)
g Canada-France-Hawaii Telescope, 1◦ × 1◦ FOV with 0.7′′ seeing.
h 2 new sources are reported;

Object 1: 0h05m12.30s, +20d06’29.4" +-0.2", i’=22.7+-0.2;(no host galaxy detected)
Object 2: 00h05m06.82s +20d05m00.4s +-0.4", i’=22.6+-0.4;(offset from apparent host anonymous galaxy 0.56"W and 0.55"N,host magnitude i’ = 21.5+-0.2)

166

CHAPTER 6. HETE X-RAY FLASHES AND X-RAY-RICH GRBS

Table 6.50: The fluxes and fluences of GRB030824. The spectral model is the power-law model.
energy range [keV]
Duration [sec.]
Photon flux
[ph cm−2 s−1 ]Energy flux
[10 erg cm−2 s−1 ]−8Photon fluence[10 ph cm−2 ]Energy fluecne[10−7 erg cm−2 ]

2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–400
2–400
2–10
2–30
30–4002–400

15.7
5.8±0.9
6.6±1.0(3.0±0.9) ×10−1
6.9±1.0
3.6±0.5
5.7±0.7
3.7±1.4
9.4±1.6
9.1±1.4
10.3±1.5
4.6±1.4
10.8±1.5
5.7±0.88.9±1.1
5.8±2.1
14.7±2.6

Table 6.51: The spectral parameters of GRB030824.
Model Parameters
+0.13
PL
α
−2.14−0.14
K15 a(5.25±0.77) ×10−2
χ2ν /DOF
0.813/53
a Normalization at 15 keV in the unit of photon cm−2 s−1 keV−1

6.18. GRB030824

167

Figure 6.44: The WXM and FREGATE spectrum of GRB030824. The spectrum model is thepower-law.

Figure 6.45: The posterior probability density distribution as a function of Epeak . Epivot is
8.1 keV. The 68% confidence range (solid line) of Epeak is 4.1 keV < Epeak < 7.4 keV. The
95% confidence range (dashed line) is 0.9 keV < Epeak < 8.1 keV. The 99.7% upper limit(dash-dotted line) of Epeak is 8.7 keV.

Chapter 7
Global characteristics of X-ray Flashes
and X-ray-rich GRBs
We investigated the time-average spectral characteristics of the HETE GRB sample. The HETE
GRB sample is selected to satisfy the following criteria: 1) the burst signal is seen in both WXM
and FREGATE, and 2) both WXM and FREGATE data have a enough statistics to carry out
the spectral analysis. The 45 GRBs satisfy this criteria from January 2001 to September 2003.
The summary status of the bursts, the best fit spectral parameters, the photon and energy
flux/fluence, and 1-second peak flux in 50–300 keV are summarized in Appendix B. The light
curves and the spectrum of the bursts which are not shown in chapter 6 are shown in Appendix
C.

7.1

The X-ray and γ-ray flux and fluence

The fluence ratio distribution between 2–30 keV (SX ) and 30-400 keV (Sγ ) is shown in figure7.1. The definitions of X-ray flashes (XRFs), X-ray rich GRBs (XRRs), and hard GRBs arelog(SX /Sγ ) > 0, −0.5 < log(SX /Sγ ) ≤ 0, and log(SX /Sγ ) ≤ −0.5 respectively. The boundaries

between hard GRBs and XRRs, and XRRs and XRFs are in the dashed lines. The figure clearlyshows that XRFs, XRRs, and hard GRBs form a single broad distribution. The number of the
bursts are 15, 20, and 10 for XRF, XRR, and hard GRB respectively. The small fraction of
hard GRBs could be due to the selection effect that the really hard GRB does not produce thesignal in WXM.
The scatter plot of 2–30 keV and 30–400 keV energy fluence is shown in figure 7.2. Eachcolors correspond to the GRB classes (XRF: black, XRR: red, and hard GRB: blue). The
168

7.1. THE X-RAY AND γ-RAY FLUX AND FLUENCE

169

Figure 7.1: Distribution of the fluence ratio of 2–30 keV to 30–400 keV in the logarithmic scale.
The dashed lines are the borders of hard GRB/XRR, and XRR/XRF.
different markers represent the best fit spectral models (triangle: power-law model, circle:
cutoff power-law model, star: Band function). The dotted line represents the border between
hard GRBs and XRRs, and the dashed line is the border between XRRs and XRFs. As wealready see in the figure 7.1, these three GRB classes seem to be a single phenomenon. There isa good positive correlation between 2–30 keV and 30–400 keV fluence. This implies that there
is no GRB with a high X-ray fluence and a low γ-ray fluence, and vice versa.
The time-average flux of 2–30 keV and 30–400 keV are plotted in figure 7.3. These twovalues also has a good positive correlation. The 2–30 keV flux (F2−30 ) and the 30–400 keV flux
1.1
(F30−400 ) can be expressed as F30−400 ∝ F2−30.

170CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.2: The scatter plot of the 2-30 keV and the 30-400 keV energy fluence.

Figure 7.3: The time-average flux in 2-30 keV (F2−30 ) and 30-400 keV (F30−400 ). The correlation
1.14
can be expressed as F30−400 ∝ F2−30.

7.2. THE DISTRIBUTION OF THE BAND PARAMETERS

7.2

171

The distribution of the Band parameters

Figure 7.4 shows the distribution of the low-energy photon index α. The bursts for which theBand function or the cutoff power-law model are required to represent their energy spectra arein this figure, but not included are the bursts whose spectra can be well represented by simple
power-law models. This is due to the fact that the photon index of the simple power-law model
could be observing the high-energy photon index β in the Band function.
The low-energy photon index α is well concentrated around −1 and similar to the BATSE α

distribution (see figure 2.2). The small number of α > −0.5 in the HETE sample as comparedwith BATSE’s could be due to two reasons: the first is the selection effect that our HETE
sample might be lacking the real hard GRBs, and second is that the BATSE α distribution
is not the time-average but the time-resolved spectral fitting result. Since the GRB spectrum
shows the time evolution and has a harder spectrum around the peak of the light curve, theharder α distribution of BATSE sample might be the contribution of the spectra at the peak.
There is no difference in the α between GRB classes (figure 7.4 bottom). From this α
distribution, we conclude that XRFs and XRRs have a similar α value as hard GRBs.
Figure 7.5 shows the Epeak distribution. The events shown as left arrows 99.7% upper limits
for the Epeak derived by using the constrained Band function. As seen in this figure, Epeak showsa broader distribution than the BATSE sample, especially for the extension to the lower energy
range. If we investigate with the GRB classes (figure 7.5 bottom), there are clear separation
between XRF and XRR around 30 keV. This is simply because of the fact that we are classifying
the GRBs for 30 keV as a boundary. The Epeak distributions of the XRRs and the hard GRBs
are quite similar.
The distribution of β is shown in figure 7.6. Because of the small number of GRBs withsignificantly constrained β, only the distribution for all the GRB classes are plotted. The
distribution of β is similar to the BATSE GRBs (see figure 2.3).

172CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.4: Distribution of the low-energy photon index α for all GRB classes (top) and foreach three different classes (bottom).

7.2. THE DISTRIBUTION OF THE BAND PARAMETERS

173

Figure 7.5: Distribution of Epeak for all GRB classes (top) and for three different classes (bottom).

174CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.6: Distribution of β for all GRB classes.

7.3

Correlation between Epeak and other properties

7.3.1

Epeak vs. fluence ratio

The Epeak energy and the fluence ratio of 2–30 keV to 30–400 keV are plotted in figure 7.7 (left).
Since the fluence ratio is independent of the normalization parameter of the model spectrum, it
is possible to calculate the relationship between the fluence ratio and Epeak . The right of figure
7.7 is the calculated relation assuming the Band function with α = −1. The curves correspondto the different values of β (β = −2.5 (black), −3.0 (red), and −10.0 (blue)). The fluence ratio
dependence of β is small in the case of Epeak > 30 keV. However, this dependence increases

when the Epeak is less than 30 keV. It implies that the choice of the proper spectral model isneeded especially for the XRF in our criteria of GRB classes.

7.3.2

α and β vs. Epeak

The scatter plots of α and β with Epeak are shown in figure 7.8. Both α and β do not show agood correlation with Epeak and also with the GRB classes. Kippen et al. [42] also do not findany correlation between α and Epeak in XRF/GRB sample of WFC/BATSE (see figure 2.7).

7.3. CORRELATION BETWEEN EPEAK AND OTHER PROPERTIES

175

Figure 7.7: Left: The observed Epeak vs. X-ray to γ-ray fluence ratio. Right: The calculated
Epeak vs. X-ray to γ-ray fluence ratio assuming the Band function with α = −1.

Figure 7.8: α (left) and β (right) vs. Epeak . Each colors correspond to the GRB classes (XRF:
black, XRR: red, and hard GRB: blue) and markers correspond to the best fit spectral models(square: cutoff power-law model, star: Band function). There are also plotting the XRFs withthe fixed values of α (green).

176CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.9: The time-average flux in 2-30 keV flux vs. Epeak .

7.3.3

The time-average flux vs. Epeak

The correlation between the time-average flux in 2–30 keV, 2–400 keV, and 30–400 keV andEpeak are shown in figure 7.9, 7.10, and 7.11 respectively. Each colors correspond to the GRB
classes (XRF: black, XRR: red, and hard GRB: blue) and markers correspond to the best fit
spectral models (circle: cutoff power-law model, star: Band function). The Epeak energy ofthe four XRFs (green) is calculated by the constrain Band function and their fluxes are in the
power-law model. The sample correlation coefficients are 0.193, 0.590, and 0.772 between theflux in 2–30 keV, 2–400 keV, and 30–400 keV and Epeak respectively. Thus, the time-average
flux in 2–400 keV and 30–400 keV have a good correlation with Epeak .

7.3.4

50–300 keV peak flux vs. Epeak

As was studied for WFC/BATSE sample by Kippen et al. [42], we investigate the correlation
between 1s peak photon flux and Epeak . To calculate the peak photon flux in the HETE burst
sample, we perform the following steps. 1) find time of the peak counts (Tp ) in the light
curve, 2) create the 5s WXM and FREGATE spectrum from Tp − 2.5 to Tp + 2.5, 3) performthe spectral fitting in this 5s spectrum and calculate the flux in the best fit spectral model, 4)
calculate the counts from Tp − 2.5 to Tp + 2.5, and Tp − 0.5 to Tp + 0.5 using the background7.3. CORRELATION BETWEEN EPEAK AND OTHER PROPERTIES

Figure 7.10: The time-average flux in 2-400 keV flux vs. Epeak .

Figure 7.11: The time-average flux in 30-400 keV flux vs. Epeak .

177

178CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.12: 1-second peak photon flux in 50-300 keV vs. Epeak .
subtracted light curve, 5) calculate the ratio of 1s counts to 5s counts, 6) multiply this ratio tothe flux value calculated in 3), and this is 1s peak photon flux. This procedure is performed forthe both the WXM and the FREGATE light curve and we selected the most reliable value forthe bursts (most of the case, the peak flux of the XRF is the value using the WXM light curve
and the peak flux of XRR and hard GRB are the value using the FREGATE light curve).
The result of 1s peak flux in 50–300 keV (BATSE’s trigger band) and Epeak are shown infigure 7.12. Each colors correspond to the GRB classes (XRF: black, XRR: red, and hard GRB:
blue) and markers correspond to the best fit spectral models (triangle: power-law, circle: cutoff
power-law model, star: Band function). The summary table of the peak flux is in Appendix
B. There is a good correlation between these two quantities (sample correlation coefficients,
r=0.811). This is a similar trend as seen for the WFC/BATSE sample, and we will investigate
this correlation in detail at the next section.

7.4

Comparison with WFC/BATSE XRF sample

Figure 7.13 shows 1-second peak flux in 50–300 keV and Epeak of the 523 triggered BATSE
bursts, the 29 WFC/BATSE bursts (20 GRBs and 9 XRFs; [42]), and the 41 HETE bursts.
Figure 7.14 is 1s peak flux in 50–300 keV and Epeak plot with the WFC/BATSE and the HETE

7.5. CONFIRMATION AND EXTENSION OF AMATI’S RELATION

179

Figure 7.13: 1-second peak flux in 50-300 keV vs. Epeak . The samples are BATSE bursts(black), WFC/BATSE bursts (red and green), and HETE bursts (blue).
bursts only. It can be seen that HETE is more sensitive to XRFs with much lower peak flux
than WFC/BATSE sample (figure 7.14). The Epeak distribution are compared in figure 7.15.
The Epeak distributions are generally consistent with a possible deficit of high Epeak events andpossible excess of low Epeak events in the HETE sample.

7.5

Confirmation and extension of Amati’s relation

Redshifts have been measured for 10 HETE GRBs/XRFs with Epeak energy. These events aretested for relation proposed by [1] (see section 2.1.3). Figure 7.16 is the plot of Epeak at thesrc
GRB source frame (Epeak) and the isotropic-equivalent energy Eiso between 1–10000 keV. The

HETE GRBs (red marks) are overlaid with the BeppoSAX sample (black marks) in Amati etal. [1]. As seen in this figure, HETE GRBs/XRFs follows this relation remarkably well.
Furthermore. we find that one data point around Eiso ∼ 1049 erg falls on the extensionof this relation, despite the fact that its isotropic-equivalent energy is smaller by a factor of
300 than the smallest value in the BeppoSAX sample. This data point is the softest XRF,
XRF020903. The discovery of the extension of Amati’s relation to XRF region has a great
impact on the interpretation of XRF phenomenon as a uniform physical picture with GRBs.

180CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Figure 7.14: 1-second peak flux in 50-300 keV vs. Epeak . The samples are WFC/BATSE bursts(red and green), and HETE bursts (blue).

Figure 7.15: The Epeak distribution of HETE bursts (top panel) and WFC/BATSE bursts(bottom panel).

7.5. CONFIRMATION AND EXTENSION OF AMATI’S RELATION

181

Figure 7.16: The plot of the isotropic-equivalent energy Eiso between 1–10000 keV and Epeak
energy at the GRB source frame. The black points are the BeppoSAX sample in Amati et al.
src[1]. The red points are the HETE GRB sample. The dashed line is Epeak= 89 (Eiso / 1052

erg)0.5.
We will discuss this issue in the next chapter.

182CHAPTER 7. GLOBAL CHARACTERISTICS OF X-RAY FLASHES AND X-RAY-RICH GRBS

Table 7.1: Esrc
peak and Eiso of the HETE known redshift GRBs
GRB

redshiftEsrc
peak [keV]

GRB010921
GRB020124
GRB020813
GRB020903
GRB021004
GRB021211
GRB030226
GRB030323
GRB030328
GRB030329
GRB030429
GRB030723

0.45
3.2
1.25
0.25
2.3
1.01
1.98
3.37
1.52
0.168
2.65
∼ 0.5

150.0+27.35−16.97342.2+135.86−91.77319.4+33.04−30.07< 6.25234.7+223.21−156.82
91.0+11.359−9.936290.4+98.54−53.76–276.4+27.91−27.14+2.85
78.91−2.76
119.0+34.58−29.19–a Eiso at z = 0.5

b The spectral model used for the calculation of Eiso

Eiso [1052 erg]

Modelb+0.556
0.954−0.063
Band+12.6536.85−11.84
Band
153.5+10.24
Band−10.40−3
1.4+18.0
Power-law−0.7 ×10+5.022
4.395−2.383
Band+0.3171.684−0.267
Band+3.951
6.766−1.049
Band
19.20+63.70
Power-law−13.0
33.10+10.24
Band
−8.03
+0.07
1.795−0.071
Band+0.8923.084−0.686
Band
+14.0
−2
6.07−2.29 ×10 (z=0.5) Power-law

Chapter 8
Discussion
In chapter 6, we investigated the individual characteristics of the prompt emission of the HETE
XRFs1 and XRRs2 . We found the several similarities between XRFs/XRRs and hard GRBs in
the spectral and the temporal characteristics. We will discuss the properties of XRFs/XRRs
based on these individual characteristics and the global characteristics of XRFs/XRRs which
are studied in chapter 7.

8.1

The sky distribution and event rate of X-ray flashes

Figure 8.1 shows the sky distribution of HETE XRFs, XRRs, and hard GRBs. The all GRBs
are populated uniformly in the sky. There is no difference in the GRB classes. This result
provides a strong support for XRFs as the same origin of the ordinary GRBs.
As we summarized in chapter 7, the numbers of each GRBs are 15, 20, and 10 for XRFs,
XRRs, and hard GRBs respectively. The total observation time when the WXM high voltage
was on from February 2001 to September 2003 was 1.1 years3 . When we take into accountthe WXM field of view of 60◦ × 60◦ , the event rates of each GRBs are estimated to be 160,
220, and 110 events year−1 for XRFs, XRRs, and hard GRBs respectively. BeppoSAX reports

the number of XRFs of ∼ 100 year−1 [36]. Since both WXM and FREGATE have a goodsensitivity for detecting XRFs comparing to the BeppoSAX instruments, the XRF event ratesof ∼ 100 year−1 could be underestimated. According to HETE sample, XRFs occupy one third
1

X-ray flashes

2

X-ray rich GRBs
There are two main reasons for not operating WXM. The first reason is turning off the high voltage during

3

the orbit day (while HETE is pointing the earth). The second reason is due to the automatic high voltage
turning off mechanism when the count rates go high (e.g. SAA, Ecuador anomaly [99])

183

184

CHAPTER 8. DISCUSSION

X-ray flash
X-ray rich GRB
Hard GRB

Figure 8.1: The sky distribution of the HETE XRFs (triangle), X-ray rich GRBs (square), andhard GRBs (cross) in the galactic coordinate. The light blue circles represent the field of viewof WXM (60◦ × 60◦ ) for each months assuming the anti-solar pointing.
of the whole GRB population. Note that the number of the XRFs is almost the same as thatof the hard GRBs.

8.2

The spectrum of X-ray flashes

The low Epeak energy is the most noticeable spectral characteristics of XRFs (section 7.2). The
correlation between Epeak and the energy flux becomes tighter when we measure the flux inthe γ-ray range (section 7.3). Almost no correlation has found between Epeak and 2–30 keVenergy flux (figure 7.9). The left panel of figure 8.2 shows the best fit spectral models in νFνspectrum. Although there are variations for each GRBs, the flux at the lower energy range
is almost consistent with all GRB classes. However, the flux at the γ-ray range is smaller
for XRFs. This trend becomes much clear when we investigated the correlation between thenormalization of the spectrum and Epeak energy. The figure 8.2 (right) shows the correlation
between the normalization at 15 keV and Epeak energy. 15 keV is close to the Epeak energy
for XRFs, whereas below the Epeak energy for XRRs and hard GRBs. The values of the8.2. THE SPECTRUM OF X-RAY FLASHES

185

Figure 8.2: Left: the best fit νFν spectra of XRFs (black), XRRs (red), and hard GRBs (blue).
Right: the scatter plot of Epeak and the normalization at 15 keV (XRF: black, XRR: red, hard
GRB: blue).
normalization are clustering for the Epeak energy around 30–100 keV.
From these properties, the spectral shape from XRFs to GRBs can be expressed as figure8.3. When the Epeak energy goes lower, the flux at the Epeak energy becomes lower. In thispicture, it is possible to explain the good correlation between Epeak and the energy flux in
γ-ray, and the less correlation between Epeak and the energy flux in the X-ray range. XRFs are
intrinsically fainter than XRRs/hard GRBs.

186

CHAPTER 8. DISCUSSION

νFν
Hard GRB

XRF

XRR

EnergyFigure 8.3: The schematic figure of νFν spectra of XRFs, XRRs, and hard GRBs.

8.3

The correlation between Epeak and γ-ray peak flux

HETE GRB sample confirmed the correlation between Epeak and γ-ray peak flux from hard
GRBs to XRFs suggested by Kippen et al. [42] (figure 8.4). Even more, HETE is observing
much weaker XRFs than the WFC/BATSE XRF sample. The relationship between Epeak andγ-ray peak flux P is Epeak ∝ P0.379 .

We will extend the discussion done by Schaefer [89] to XRFs. The two kinematic effect willchange the characteristic energy, Erest , to the observed energy, Epeak . They are relativistic
beaming effect and the cosmological expansion of the universe. The relativistic beaming effectwill blueshift the Erest energy by the factor of the bulk Lorentz factor Γ. The cosmologicaleffect will redshift the energy by a factor of (1 + z)−1 . Epeak can be expressed as,
Epeak = Erest Γ(1 + z)−1 .

(8.1)

The Epeak can vary from pulse to pulse and burst to burst. In general, Erest might have apower-law dependence on Γ.
Erest = E0 ΓM ,(8.2)

where M is the power-law index.
In general internal shock model, the burst isotropic luminosity, L, varies as some power of
Γ. The index of Γ is model dependent. We will express in a general formula of,
L = L0 ΓN ,(8.3)

8.3. THE CORRELATION BETWEEN EPEAK AND γ-RAY PEAK FLUX

187

where N is the power-law index.
Using (8.1)-(8.3), Epeak can be expressed as,
Epeak = E0 (L M+1
) N (1 + z)−1 .
L0

(8.4)

So, Epeak is
M+1

Epeak ∝ L N (1 + z)−1 .

(8.5)

If we assume z ≃ 1, the peak luminosity L corresponds to the peak flux P. Equation (8.5) canbe expressed as,

M +1

Epeak ∝ P N .

(8.6)

From HETE and WFC/BATSE sample, (M + 1)/N is 0.379. In the same manner as [89],the variability/luminosity relation (section 2.1.4) is used to constrain the value of N. Since thevariability (V) is the “spikeyness” of the GRB light curve, V varies as the inverse of the risetimes in the light curve. The rise time will be limited by the geometric delays that scale as Γ−2(see [80] problem 4.1), so V ∝ Γ2 . According to the variability/luminosity relation [88], L ∝V1.57±0.17 . Thus, L ∝ Γ3.14±0.34 and N = 3.14.

Now it is possible to calculate M value using N = 3.14. M is 0.19 ∼ 0. This implies that thevariation of Epeak from a few keV to MeV is only depending on two effects; the cosmologicalredshift and the relativistic beaming effect.
Thanks to GRB020903 with the redshift measurement, we have the redshift corrected Epeak
relation (extended Amati’s relation; figure 7.16). This extended Amati’s relation indicates that
Epeak still has a variation from a few keV to MeV even if the redshifts of Epeak are corrected.
So, we may conclude that the variation of Epeak energy is mainly due to the relativistic beaming
effect. Finally, Epeak can be written as,(1 + z) Epeak = E0 Γ.

(8.7)

Epeak can be interpreted as the synchrotron critical frequency νm with a minimum Lorentz
factor of electrons (section 3.1). νm can be expressed as,
νm =

2
3eBγm
,
4πmc

(8.8)

where γm is the minimum Lorentz factor of electrons, m is the mass of electron, e is theelementary electric charge, c is the speed of light, and B is the magnetic field. If we use the188

CHAPTER 8. DISCUSSION

relation, E0 = hνm , where h is Plank constant, the magnetic field B can be written as,
4πmcE02h3eγm−2= 5.76 × 1010 γm
E0 .

B =

(8.9)

On the other hand, the cooling time of electrons can be written as,
γm mc2
tc = 4 22 ,γ σ cB
3 m T 8π(8.10)

where σT is the Thomson cross section. Then γm is,
6π mc
tc σT B 2
= 7.75 × 108 B −2 t−1
c .

γm =

(8.11)In the internal shock model, the cooling time corresponds to the individual spikes in the light
curve. The duration of each spike is < ms. If we assume tc < ms and substitute equation (8.11)
to equation (8.9), magnetic field will be,
B > 2.18 × 10

4



E0
1 keV

− 13 

tc
1 ms

− 2

3

[G].

(8.12)

Although we assume E0 = 1 keV from the extended Amati’s relation, this minimum energy
could be much smaller.
In the unified picture from XRFs to GRBs, the magnetic field at the shock region is estimated to be > 104 gauss. It is very important to constrain E0 energy from the observation of
XRFs to estimate the magnetic field at the shock region in much higher precision.

8.4. DISTANCE SCALE OF X-RAY FLASHES

189

Figure 8.4: The 1-second peak photon flux in 50–300 keV and Epeak relation including theHETE and BeppoSAX/BATSE samples. The dashed line is Epeak = (48.51 ± 0.46) P0.379±0.003 .

8.4

Distance scale of X-Ray flashes

To discuss the distance scale of XRF, we investigate the logN-logP for HETE GRBs. Figure
8.5 shows the logN-logP plot for each GRB classes. The cumulative numbers of each GRBs arenormalized to the total numbers of events. Note that this logN-logP plot is not corrected forthe trigger efficiency.
From the BATSE/PVO GRBs, we already know that the slope of logN-logP of hard GRBs
changes from −3/2 to −0.8 ([35], [50]). The slope of −3/2 is derived from the Euclidean space.

Based on this result, we tried to compare the logN-logP distribution of XRFs and hard GRBs.
We select the HETE GRBs with Epeak greater than 50 keV as hard GRB sample (total 22
bursts). Figure 8.6 shows the overlaied logN-logP distribution of XRF (black) and hard GRBs
(red). The peak flux is calculated in 2–30 keV. The logN-logP distribution of hard GRBs (redline) is normalized to adjust for that of XRFs around the peak flux of 3 photons cm−2 s−1 .
The vertical dot-dot-dashed lines are the sensitivity limits as a function of Epeak (10 keV, 30
keV, and 100 keV from right to left) calculated by Band [7] assuming the Band function of α =190

CHAPTER 8. DISCUSSION

Figure 8.5: logN-logP for XRFs (black), XRRs(red), and hard GRBs(blue). The vertical axis
is the cumulative number of the bursts. The horizontal exis is 1s peak flux in 2–30 keV. See
text for the details.
−1, β = −3. Since the peak flux less than 3 photons cm−2 s−1 might suffer from the threshold
effect, we will discuss the region larger than this peak flux. The dashed lines are the slope of−3/2.

The logN-logP distribution of hard GRBs shows a clear offset from the −3/2 around peak

flux of 10 photons cm−2 s−1 . Whereas, the logN-logP distribution of XRFs follows on the slopeof −3/2. This might indicate that the distace scale of XRFs are different from that of hard
GRBs. The distance of XRFs are close to the Euclidean geometory which means z ∼ 0.2.

8.4. DISTANCE SCALE OF X-RAY FLASHES

191

Figure 8.6: logN-logP for XRFs (black) and GRBs with Epeak > 50 keV. See text for the details
about the plot.

192

8.5

CHAPTER 8. DISCUSSION

Theoretical models for X-ray flashes

We will discuss in details for three promising theoretical models of XRFs; the off-axis jet model([112]; [113]; see also section 3.2.1), the structure jet model ([79]; see also section 3.2.4), theunified jet model ([47]) and the jet beaming model which is based on the result on this paper.

8.5.1

Off-axis jet model

In this model, XRF is a collimated GRB jet with a large viewing angle (see figure 3.4). Their
original model [112] can explain the low Epeak energy, the peak flux and flunece of XRF basedon BeppoSAX observation. This model also predicted the distance scale of XRF is z < 0.2 tomatch with the observed event rate of XRFs.
The redshift corrected Epeak energy of GRB020903 is ∼ 5 keV (see section 6.9). If weestimate the viewing angle, θv , with Epeak energy of 5 keV assuming the Epeak energy in the

on-axis jet of 300 keV and the bulk Lorentz factor of 100, θv is 8 degrees with the jet half
opening angle, ∆θ, of 1 degree. Yamazaki et al. [112] discuss the event rate of XRF in a
3
formula of RXRF = rGRB ng (4πDXRF/3)(fXRF /fGRB ), where rGRB and ng are the event rate of

the GRBs and the number density of galaxies, resectively. The DXRF (DGRB ) is the distance ofXRF (GRB). The fXRF (fGRB ) is the fraction of the solid angle observed as XRF (GRB). Sinceθv ∼ 8∆θ in the case of GRB020903, fXRF /fGRB ∼ (82 − 12 )/12 = 63.

From HETE observation, the event rate of XRFs and hard GRBs are about the same. If

the event rates of XRFs and GRBs are the same, as observed by HETE, the distance of XRF
will be calculated as,


!−1

1
fXRF
DXRF 3
=
=
DGRB
fGRB
63
DXRF ∼ 0.25 DGRB .


(8.13)

If GRBs are z ∼ 1, XRFs have to be populated around 1.8 Gpc. This is consistent with our
discussion of the distance scale of XRFs based on the logN-logP distribution.

On the other hand, the authors also proposed the cosmological off-axis jet model for XRFs
[113]. It is possible to produce XRFs in a viewing angle of 2.9 degrees with the jet half opening
angle of 1.7 degrees at the redshift of 1.5. In this case, Epeak will be around 30 keV. Because
the viewing angle is much closer to the jet opening angle, the distance scale of XRFs will besimilar to that of GRBs.
The most plausible way of explaining the all observations of XRFs, XRRs, and hard GRBs
in the off-axis model will be the combination of the above two models. Epeak above ∼ 30 keV

8.5. THEORETICAL MODELS FOR X-RAY FLASHES

193

will be a cosmological off-axis GRB jet and a few keV events will be a off-axis jet with z <src
0.2. This off-axis jet model has a unique prediction to Epeak- Eiso relation (extended Amati’s
src
relation). When the viewing angle is larger than the jet opening angle, Eiso ∝ δ 3 and Epeak
∝
1/3

src
δ, where δ is the Doppler factor δ −1 ≡ Γ[1 − β cos(θv − ∆θ)]. Thus, Epeak∝ Eiso . The Eiso

dependence of δ will be Eiso ∝ δ 2 when the viewing angle is within the jet opening angle ([115],
1/2src[49]). In this case, Epeak∝ Eiso .

Another interesting prediction of the off-axis jet model is the different behavior of theafterglow light curve. According to [103], when the viewing angle of the collimated jet is larger
than several tens of degrees, the afterglow light curve shows the sharp rise at t > tj 4 , andcontinues to rise till t = tp when Γ = θv (θv is the viewing angle) is achieved. At t > tp , theafterglow light curve becomes similar to that of the on-axis jet, hence starts to fall. Since theviewing angle of the jet will be few tens of degrees in XRFs with Epeak of a few keV at theoff-axis jet model, this rise-and-fall afterglow light curve should be observed.

8.5.2

Structure jet model

In the structure jet model, the bulk Lorentz factor and also the energy per unit solid angle
change by the viewing angle of the jet. XRF can be interpreted as a GRB structured jet witha large viewing angle.
The bulk Lorentz factor dependence of the viewing angle (θv ) can be described as Γ = θv−k([79], [114]). We consider the case of k = 2 as the same manner of Rossi et al. [79]. In the
structure jet model, the jet opening angle which is interpreted in the Frail relation ([22], seealso section 2.2.3) corresponds to the viewing angle θv . According to Zhang and Mészáros [114],k has to be 2 not to violate from the Frail relation. Thus, Eiso ∝ θv−2 . Since the Epeak energy atsrc
the source frame is proportional to Γ, Eiso -Epeak relation should be Epeak∝ Eiso . This relation

is inconsistent with the extended Amati’s relation found by HETE (figure 7.16).

Another difficulty is the event rate of XRFs. Since the Eiso has the variation in five ordersof magnitude, the viewing angle θv has a difference by the factor of 100 (Eiso ∝ θv−2 ). So, theevent rate of the large viewing angle (e.g. XRF) must exceed the on-axis event (e.g. hard
GRBs) by the factor of ∼ 50 if we assume the θv ∼ 2 degrees for the on-axis event. This is also

inconsistent with the observation of HETE.
4−1
tj is the “jet-break time,” the time when Γ = θjetand the observer “sees” the entire jet surface and a breakin the light curve.

194

8.5.3

CHAPTER 8. DISCUSSION

Unified jet modelLamb et al. [47] proposed the GRB jet model which could be explained the observational
characteristics from XRF to hard GRB in the unified picture. Their model is based on two
important observational results; 1) jet opening angle corrected radiation energy is concentrated
src
in 1.3 × 1051 ergs [22], and 2) Eiso − Epeak
relation [1] seems to be valid from XRFs to hard

GRBs [82]. Assuming these two results, it is possible to construct the uniform jet model having
the varieties of the jet opening angles from XRFs to hard GRBs.
When we defined the isotropic-equivalent energy Eiso , the jet opening angle corrected energy
Eγ = 1.3 × 1051 ergs, and the jet opening angle θjet , the relation discovered by Frail et al. [22]is2Eγ ∝ Eiso θjet.

(8.14)

src
0.5
If we substitute eq. (8.14) into Epeak∼ Eiso
,
src
0.5
−1
−1
Epeak
∝ Eiso∝ Eγ0.5 θjet∝ θjet.

(8.15)XRFs (low Epeak energy) are interpreted as the jet with a large opening angle, whereas hard
−2
GRBs as a fine collimated jet. Because of Eiso ∝ θjet
, if the number of the bursts has a−2dependence of ∝ θjet
, this model predict the same amount of the bursts between XRFs andhard GRBs.

One of the difficulty in this model might be following. If the “standard energy” in γ-ray,Eγ ∼ 1051 ergs, is valid, Eiso should not go below this standard energy. However, Eiso of

GRB020903 is ∼ 1049 ergs. Although Lamb et al. [47] claimed that Eγ inferred by Frail et al.

[22] might be too large by the factor of 100, the observed results of Eγ by Bloom et al. [9] seemto be quite solid.

8.5.4

Jet beaming model

Since the unified jet model has a difficulty in explanation of the low isotropic-equivalent energy
in the case of the extremely large jet opening angle, we propose the jet model that the GRB jet
itself is collimated, however, the relativistic beaming angles of γ-rays are different due to thedifference of the bulk Lorentz factors. We interpret the relativistic beaming angle θbeam insteadof the jet opening angle θjet in the unified jet model. So,
src
−1
Epeak
∝ θbeam.

(8.16)

8.5. THEORETICAL MODELS FOR X-RAY FLASHES

195

src
From our study in section 8.3 (see equation 8.7), Epeak
is proportional to the bulk Lorentz

factor Γ. And we have
θbeam ∝ Γ−1 .

(8.17)

This relation is exactly same as the relativistic beaming effect. The produced γ-rays are highly(less) collimated at the shock region in the case of high (low) Lorentz factor due to the relativistic
beaming effect. We assume the similarly collimated jet in the case of both high and low Lorentz
factor.
In the fully adiabatic fireball, the equation of the motion of relativistic ejecta can be writtenas,(γ − 1)M0 c2 + (γ 2 − 1)mc2 = EK0 ,(8.18)

where γ is the Lorentz factor of the materials which are swept up by the shell and has a relation√
with the bulk Lorentz factor Γ in γ = Γ 2, M0 is the rest mass of baryons, m is the rest massof the swept-up materials, and EK0 is the total kinetic energy of the explosion and is a constant[106]. In the ultrarelativistic limit (m ≫ M0 /γ and γ ≫1), γ 2 m = const. Substituting thisrelation to the equation (8.17), we have the relation between the beaming angle and the massof the swept-up materials in the form ofθbeam ∝√

m.

(8.19)

So, the low Γ GRBs (e.g. XRF) have a less beaming effect with larger mass of the swept-up
materials (figure 8.7).

8.5.5

Summary of XRF theoretical models

src
Figure 8.8 summarized the predicted Epeak-Eiso relations for three XRF models. The power-law

dependence in the off-axis jet model will change when the viewing angle becomes larger thansrc
the jet opening angle. The structure jet model has a relation of Epeak∝ Eiso in the case of index

k = 2, and it is inconsistent with the data. The unified jet model is assuming the extended
src
Amati’s relation. As seen in this figure, the key observations will be the Epeak
energies from a

few keV to a few tens of keV.
From the overall characteristics of XRFs, the off-axis jet model might be the most promisingmodel for explaining the observed properties of XRFs. This model has several observational
predictions, and could be investigated by further observations.
When we try to interpret from XRFs to hard GRBs in the unified physical picture, it ispossible to study: 1) kinematic of the relativistic shells (variation of the bulk Lorentz factor),

196

CHAPTER 8. DISCUSSION(a) LowG(b) HighG

g-raysG-1

G-1

Electrons

Collimated jet

Figure 8.7: The schematic figure of the jet beaming model. The left (right) panel is in the caseof the low (high) bulk Lorentz factor Γ.
2) the jet structure of GRBs (whether the jet is the structure jet, the uniform jet, or the off-axisjet), and 3) the magnetic field of the shock region when we observed the minimum Epeak energy
at the source frame. To accomplish these studies, we definitely need the large sample of the
XRFs with the Epeak energy of a few keV and also with the redshift measurements from theafterglow. The afterglow behavior of XRFs is also important to investigate. The simultaneous
operation of HETE and Swift will progress the observation of XRFs which directly reflect theunderstanding of the prompt emission of GRBs.

8.5. THEORETICAL MODELS FOR X-RAY FLASHES

197

Ep ~ Eiso1/2

Ep ~ Eiso1/3
Unified jet model(Lamb et al. 2003)

Ep ~ Eiso1/2

Off-axis jet model(Yamazaki et al. 2002)
Ep ~ Eiso
Structure jet model(Rossi et al. 2002)

src
Figure 8.8: The predicted Epeak-Eiso relations for the unified jet model (red), the off-axis jet

model (green), and the structure jet model (blue). Note that the structure jet model is in thecase of the same dependence in the viewing angle for the energy per solid angle and the bulk
Lorentz factor.

Chapter 9
Conclusion
Based on the detailed study of 17 HETE observed X-ray flashes (XRFs) and X-ray rich GRBs
(XRRs) 1 , we found the following characteristics.
• Duration of the XRFs/XRRs are similar to hard GRBs (few tens of seconds).
• Most of the XRFs/XRRs show complex time-structures like hard GRBs.
• The spectral softening is seen during the burst for most of the XRFs/XRRs.
• Their Epeak energies are generally lower than those of hard GRBs.
• There are six events which showed the Epeak energy of a few keV.
• The afterglows were found for only a few XRFs (e.g. GRB020903, GRB030528, GRB030723).
This may imply that the afterglows of XRFs are generally very faint.

With the systematic study of 45 HETE localized GRBs including 17 XRFs and XRRs, wefound,• The distribution of X-ray to γ-ray fluence ratio has a single profile.
• The numbers of XRFs, XRR, and hard GRBs are roughly comparable: 15, 20, and 10
respectively in our sample.

• HETE XRFs/XRRs/hard GRBs are uniformly distributed in the sky.
1

Our definitions of X-ray flashes (XRFs), X-ray rich GRBs (XRRs), and hard GRBs are the X-ray (2–30

keV; SX ) to the γ-ray (30–400 keV; Sγ ) fluence ratio SX /Sγ of log(SX /Sγ )> 0, −0.5 < log(SX /Sγ ) ≤ 0, andlog(SX /Sγ ) ≤ −0.5 respectively.

198

199
• In the spectral parameters of XRFs/XRRs, the low-energy photon indices are similar to
those of hard GRBs, whereas, Epeak energies are systematically lower than those of hard

GRBs. The Epeak energy seems to be distributed in much lower energy, unlike the BATSE
Epeak distribution.
• The correlation between Epeak energy and the time-average flux becomes tighter when
the flux in higher energy range (i.e. γ-ray) is used. This may imply that the XRFs are

intrinsically fainter than other ordinary GRBs.
• The logN-logP distribution of XRFs is close to the Euclidean geometry. This may imply
XRFs have a closer distance scale than that of weak hard GRBs.

Epeak and γ-ray peak photon flux have a good correlation. Using this correlation and theextended Amati’s relation, we found that the variation of the Epeak energy from a few keV to afew MeV is only due to the relativistic beaming effect. We also estimated the magnetic field at
the shock region to be > 104 gauss assuming Epeak energy as the synchrotron critical frequencyof the minimum energy of electrons.
For 10 HETE GRBs with known-redshifts including one XRF, GRB020903, we confirm andextend the correlation between Epeak energy in the source frame and the isotropic-equivalentenergy (the extended Amati’s relation) to the XRF region. Now, GRBs have a variation of
Eiso in five orders of magnitude. This relation gives a crucial constraint on the theoreticalmodels. For instance, 1) GRBs can produce the different bulk Lorentz factor in three order ofmagnitude (from a few keV to a few MeV Epeak at the source frame), 2) the power-law index of
0.5
0.5 (Epeak ∝ Eiso
) might be valid from XRFs to hard GRBs, and 3) GRBs show the different

isotropic-equivalent energy in the five order of magnitude.

Finally, the observation of XRFs suggests that XRFs, XRRs, and hard GRBs form a continuum and are a single phenomenon. The theoretical model has to explain the all GRBs in a
uniform physical picture. Further progress in observational aspects of XRFs will be achieved
with a larger sample of XRFs with the redshifts. HETE and Swift will lead the observations of
XRFs and progress in understanding the prompt emission of GRBs.

Appendix A
WXM energy response matrix
A.1

The WXM Detector Response Matrix (DRM) Calculation

A.1.1

The WXM instrumental effects

Our DRM is calculated for each GRB event using the formula based on the calibration datataken before launch. The main formulae which we need for creating the WXM DRM arefollowing:
1. The signal pulse height as a function of the three-dimensional location inside the detector
where an X-ray photon is absorbed.
2. The empirical formula of the energy resolution for the mono-chromatic X-rays
3. The empirical formula for the energy and pulse height conversion
4. The X-ray absorption coefficients of PSPC gas (Xe, 1.36 atm, 293 K, 25.5 mm thickness),
PSPC window (Be, 100 µm thickness), and thermal shield (Kapton, 7.62 µm thickness)
5. The mask shadow pattern on the detector surface (specific incident angles θx and θy )Our code is using the various functions created for the ground localization code [92]. Wesummarized the major internal characteristics of the WXM PSPC.
The gain variation at both end of the anode wires (“∼” curve)
Due to the internal mechanical structure of the WXM PSPC, there is a gain variation at bothend of the anode wires. As seen in figure A.1, the gas gain rises steeply at the left side, whereas
200A.1. THE WXM DETECTOR RESPONSE MATRIX (DRM) CALCULATION

Cu
1600

20

10

B'

1600

0 A

w1

y (mm)

20

1600

10 B

A'

0

1600

-10

-10
1600

-20
w0

-20

-30

C-C'

-30
1600

C

-40
-60

PH

30

w2

30

40

Y (mm)C'

XA (Cu)

XA
40

201

-50

-40

-30

-20

-10

-40

0
10
x (mm)

20

30

40

50

60

2000
PH

2400
XA (Cu)

wire1

1500
(x = 0mm)

A-A'
B-B'

2200
2000
1800
1600
1400
1200
1000
-60

-40

-20

0
X (mm)

20

40

60

Figure A.1: The gain measurement of the XA detector at Cu K energy (∼ 8 keV). Left top:a contour plot of the gas gain, bottom: the gain distribution along the A–A′ and B–B′ , andright: the gain distribution along the C–C′ [92].
it drops sharply at the right side. Since the shape of the curve looks like the character “∼”, wecalled “∼” (tilda) curve.
The high gain region surrounding the anode wires (M curve)
Although the physical reason is still unclear, there is the region having the maximum gas gainaround 3 mm away from the anode wires. The gain also has a dip near the on-wires position.
The pulse height distribution for the depth direction resembles to the character “M”, so we callthis effect as “M” curve. According to Sakurai et al. [83], the M curve gain structure traces
the electrical field very well. Thus, the electrical fields may be playing a crucial role for this202

APPENDIX A. WXM ENERGY RESPONSE MATRIX

A
0

0

5

5

ADC
4200

3000

2800

2800

4000

15

15

20

20

2900

3800

3500

4000

4100

10

2800

10

3500

3600
3300

25

A-A' section
4000

ADC

2700

A'

30
3000

2700

2700

25

30

3400

2800
2900

2700

Depth (mm)

3200

10

5

0

3200

3000
-5

-10

Distance Across the Wire (mm)Figure A.2: The gas gain profile inside PSPC at bias voltage of 1700 V. The right contour
plot shows the pulse height distribution around the wire. The left plot is the pulse height
distribution as a function of the depth of PSPC [91].
anomalous gas gain.

The energy resolution
The energy resolutions as a function of incident energies at the various bias voltages are plottedin figure A.3. At the low bias voltage 1400 V, the energy resolution follows the ∼ E−0.5 law,however, it no longer follows the same law at higher voltages due to the space charge effect (seedetails [44]). Shirasaki et al. [91] found the empirical relation which can express the energy
resolution at various operational bias voltages. This empirical relation is used in the WXM
DRM calculations.

The energy and pulse height relation
The relation between the pulse height and the X-ray incident energy at various bias voltages(1300 ∼ 1700 V) is shown in figure A.4. As seen in this figure, the linearity between the theA.1. THE WXM DETECTOR RESPONSE MATRIX (DRM) CALCULATION

203

4Energy Resolution (FWHM %)

3

1700V
1650V

2

1600V
1550V
1500V
10
1400V

9
8

~1/sqrt(E)

7
6
5
5

6

7

8

9

2

3

4

10
Energy (keV)

Figure A.3: The energy resolution at energies from 6 to 24 keV for bias voltage form 1400 to
1700 V. The WXM bias voltage of the normal operation is 1650 V [92].

204

APPENDIX A. WXM ENERGY RESPONSE MATRIX
30

25

Energy (keV)

20

15

10

5
X-ray Fluorescence Experiment
Monochrometer Experiment

0
0

1000

2000
ADC channel

3000

4000

Figure A.4: Energy and pulse height relation for several bias voltages. The bias voltages are
1299, 1361, 1599, 1618, 1649, 1699 from left to right respectively [91].
pulse height and the photon energy is lost above 1600 V. Since WXM is operated with highvoltage ∼ 1650 V, we need a non-linear formula to convert the pulse height to the photon
energy. The experimental result is well represented by the following formula:
E = a · (P H/c) + b · sinh(P H/c) + d · (P H/c)2(A.1)

where PH is the pulse height, a, b, c, and d are the coefficients which are a function of “effective”
bias voltage1 .

A.1.2

The flow chart of the DRM code

The coordinate system used in the code is shown in figure A.5. We assume that the spectrumof the monochromatic X-ray can be expressed as a gaussian. The code calculates a gaussian foreach point at (x, y, z) and sums the individual gaussian for all detector points. This summed
gaussian is the spectrum including the instrumental effects such as an energy resolution, M
curve, and “∼” curve.
The flow chart of the main part of the code is following (see figure A.6):
1“effective” means that it is not the actual operating bias voltage. This “effective” bias voltage is a function of

position inside the detector and also reproduces the internal gain variation of WXM (because the gain variationof WXM can be expressed as the difference of the electrical fields (“effective” bias voltage))A.1. THE WXM DETECTOR RESPONSE MATRIX (DRM) CALCULATION

205

y

x

anode wirez
Figure A.5: The coordinate system using in the DRM code.
1. Input θx , θy , energy, and wire ID. Since the DRM code calculates the input energy from
1.5 keV to 30.0 keV in 0.1 keV step, this routine is executed 286 times.
2. Set the gain parameter (“gc” parameter). This parameter corrects for the gain difference
according to the specific observing period. The gain variation of each wires at the specific observing period is corrected referring the results of 55 Fe gain monitoring which areautomatically processed every week.
3. Calculate the absorption probability of the thermal shield (aluminum coated kapton foil,
7.6 µm), Be window (100 µm), and Xe gas (Xe 97 %/CO2 3 %, 25.5 mm) taking into
account the incidence angle of the source.
4. Start the loop for the x-direction in 1 mm step. The minimum and maximum range ofthe x-direction can be adjusted by the user.
5. Call the function for calculating the mask pattern at the specific θx and θy . And judge
whether the x position is in the shadow of the mask or not. If the position is not illuminated by the source, the position is skipped and calculation is moved the the next x
position.
6. Calculate the “effective” bias voltage, v parameter with function cal v(). cal v() is afunction of wire ID and x position.
7. Start the loop for the y-direction in 1 mm step. The y range depends on the wires (top,middle, or bottom wire).

206

APPENDIX A. WXM ENERGY RESPONSE MATRIX

8. Start the loop for the z-direction in 1 mm step. The z range is from 0 to 25 mm.
9. Call the function for checking the shadow due to the support structure. If this position
is in the shadow of this structure, the calculation of this position is skipped and is moved
to the next position.
10. Calculate the pulse height and the energy resolution at that position. Two function,ene2adc 3d() and adc flc() are used for this purpose. The ene2adc 3d() and adc flc() return the pulse heigh and the 1 sigma energy resolution in ADC channels. The ene2adc 3d()is the function of wire ID, energy, and 3-dimensional position. adc flc() is the function of
the v parameter and the pulse height.
11. Start the loop for the ADC channels. The dynamic range of ADC channels depends onthe data type.
12. Calculate the pulse height distribution in the gaussian with the centroid and sigma as thevalue of step 10. Then multiply the normalization by the Xe gas absorption probability.
The pulse height distributions of all the positions are summed.
13. When all the x, y, z loop calculations are finished, multiply the normalization by theabsorption probability of the thermal shield and Be window and scales by the calculation
steps.
14. The effective area per energy bin will be the multiplication of the geometrical area at one
wire cell and the open fraction of the mask to the result of step 13.
After this DRM calculations, the FITS conversion function is called and generates the FITS
response files.
Figure A.7 shows the 2-dimensional image of the WXM DRMs. The extra tail in the high
ADC channels is seen in the most of the spectra. This is due to the M-curve effect. The widthof the spectrum is almost constant from 2 to 10 keV. The spectrum becomes very broad above
20 keV.
Two major effects, “M” and “∼” curves are also successfully reproduced in our DRMs
(figure A.8).

A.1.3

Comparison with GRMC-flight

GRMC-flight is the Monte Carlo simulation code developed by Edward E. Fenimore (LANL).
This code is used for creating the templates of the mask pattern for the on-board localization.

A.1. THE WXM DETECTOR RESPONSE MATRIX (DRM) CALCULATION

1. input thx, thy, energy, wireID
2. set gain parameter (gc parameter)
3. calculate absorption efficiency:
thermal_shield, Be_window, Xe_gas(z)4. x loop (1 mm step)
5. mask shadow?

YesNo
6. calculate v parameter:
cal_v (wireID, x)
7. y loop (1 mm step)
8. z loop (1 mm step)Yes

9. shadow of support structure?
No
10. calculate ph and σ (energy resolution):ph; ene2adc_3d (wireID, energy, x, y, z)
σ; adc_flc (v, ph)11. from ADC_min to ADC_max
12. calculate ph distribution
prob[ADC] += gaussian (ph, σ) *Xe_gas (z)13. calculate ph distribution with absorbers:
resp_output = prob[ADC] * thermal_shield * Be_window / calc_point
14. calculate effective area
eff_area = resp_output * geometrical_area * mask_open_fraction

Figure A.6: The flow chart of the main part of the DRM calculation code.

207

APPENDIX A. WXM ENERGY RESPONSE MATRIX

Output ADC

208

10

5

15

20

25

Input energy [keV]

Effective area [cm2]

Figure A.7: The WXM DRM of XA0 wire. The horizontal axis is the input energy and thevertical axis is the output ADC channels.

Figure A.8: Modeling two major characteristics of the WXM detector; “M” curve (left) and“∼” curve (right).

A.2. CRAB CALIBRATION

209

Figure A.9: The effective areas with the calculation by GRMC flight and our method areoverlaied. Left: the conditions are θx = 0◦ , θy = 0◦ , and XA0 wire. Right: the conditions areθx = 0◦ , θy = 30◦ , and XA0 wire.

GRMC-flight also has been used for the DRM of Ginga GRBM and various simulations for the
Swift BAT instrument.
We compare the effective area curves of our DRM and GRMC flight DRMs calculation. In
figure A.9, the effective area curves by these two different calculations at the same conditions areplotted. The overall shape and normalization agree quite well. The GRMC flight calculation
seems to have a larger effective area above 15 keV, however, the difference between these two
calculation is less than 5%.

A.2

Crab calibration

The RAW data of the Crab nebula were collected for the purpose of calibration from December
2001 to January 2002. Since we need to check the DRMs with various incident angles, the Crabdata with the different incident angles were recorded.
The Crab spectral parameters in the current DRMs (version 6.1) are shown in figure A.11.
The overall spectral parameters of the Crab are mostly consistent with the known values.
However, there are several problems. The NH values show relatively small value at the large
incident angle. The normalization among the wires are not completely consistent; there are
10–20% uncertainties in the normalization for individual anode wires in the current DRM.

210

APPENDIX A. WXM ENERGY RESPONSE MATRIX

Figure A.10: The WXM Crab spectrum at the incident angle of 1.6◦ (Left) and 27.3◦ (Right).

Figure A.11: The Crab spectral parameters in the various incident angles. Top left: photon
index vs. incident angles, Top right: NH vs. incident angles, Bottom: 2–10 keV energy flux vs.
incident angles, Each colors represent the individual wires.

A.3. CROSS CALIBRATION OF WXM AND FREGATE DRMS

211

Figure A.12: The Crab spectrum of WXM (black) and FREGATE (red). Left: boresight angle,
right: incident angle of 21-22◦ .

A.3

Cross calibration of WXM and FREGATE DRMs

The cross calibration of WXM and FREGATE DRM is performed using the Crab nebula.
The WXM and FREGATE data of the Crab nebula were corrected on December 2001, andDecember 2002 respectively. The data with the Crab at incident angles of the boresight and
20–21◦ are available. The occultations of the Crab are used to accumulate the FREGATE data.
We linked the value of NH and photon index for both the WXM and FREGATE data. The
normalizations of each data are kept as free parameters.
The joint fit spectral parameters of the Crab nebula are summarized in table A.1. The
WXM and FREGATE DRMs can successfully represent the known spectral parameters of the
Crab nebula. There is no systematic difference in the normalization between two instruments.
Table A.1: The joint fit results of the WXM and FREGATE Crab data. The quoted error is
90% confidence region.
Spectral parameters

Incident angle◦∼0
21–22◦+1.9
NH [10 cm ]2.3−1.8
3.0 (fixed)
Photon index
2.09 ± 0.03
2.17 ± 0.02
−2a(3.44 ± 0.09) × 10
(3.10 ± 0.10) × 10−2
K15 (WXM)
K15 (FREGATE)(3.40 ± 0.14) × 10−2 (2.91 ± 0.19) × 10−2
χ2 (D.O.F.)
136.07 (156)108.36 (117)−2 −1−1
a normalization at 15 keV in the unit of photons cm s keV
21−2

Appendix B
HETE GRB summary

212

213

Table B.1: The HETE GRBs summary table
GRB
GRB010213
GRB010225
GRB010326B
GRB010612
GRB010613
GRB010629B
GRB010921
GRB010928
GRB011019
GRB011103
GRB011130
GRB011212
GRB020124
GRB020127
GRB020317
GRB020331
GRB020531
GRB020625
GRB020801
GRB020812
GRB020813
GRB020819
GRB020903
GRB021004
GRB021021
GRB021104
GRB021112
GRB021211
GRB030115
GRB030226
GRB030323
GRB030324
GRB030328
GRB030329
GRB030416
GRB030418
GRB030429
GRB030519
GRB030528
GRB030723
GRB030725
GRB030821
GRB030823
GRB030824
GRB030913

BID
10805
1491
1496
1546
1547
1573
1761
1770
10823
1829
1864
10827
1896
1902
1959
1963
2042
2081
2177
2257
2262
2275
2314
2380
10623
2434
2448
2493
2533
10893
2640
2641
2650
2652
10897
2686
2695
2716
2724
2777
2779
2814
2818
2821
2849

θX
-2.41
-23.107.97
13.81-30.50-26.60-23.95-2.99-18.29-0.32-13.03
-1.60
14.65
-7.51
-17.14
6.91
22.94
5.64
4.73
-15.30
0.04
17.70
4.20
3.92
15.24
22.56
12.24
-12.5513.01-13.004.05-26.35
5.05
26.68
-1.98
7.45
8.88
-41.00
20.66
1.55
18.41
12.13
11.67
-29.79
-2.05

θY
13.60
0.97
-15.02
1.17
25.17
8.29
39.45
35.00
-17.63-10.9422.83
9.71-31.5720.76
15.15-14.33
11.33
10.12
35.44
-12.13-3.81-22.4512.64-12.39
11.92
22.38
27.06
-0.01
-3.11
-16.27
35.06
0.57
7.14
-29.00-11.32
-9.66
11.83
16.18
6.14
10.93
33.10
32.47
-32.65-31.43
4.62

TTa
—
G
G
G
G
G
G
G
—
XG
XG
—
G
G
G
G
G
G
G
G
G
G
XG
G
—
G
G
G
G
—
XG
G
G
G
—
XG
XG
G
G
XG
G
G
G
G
G

TSb
—
1.3s
160ms
160ms
1.3s
1.3s
1.3s
1.3s
—
5.12s
5.12s
—
1.3s
5.12s
1.3s
160ms
20ms
5.2s
1.3s
1.3s
1.3s
160ms
5.12s
5.2s
—
1.3s
1.3s
160ms
1.3s
—
320ms
1.3s
1.3s
1.3s
—
13.280s
6.72s
160ms
1.3s
6.72s
160ms
1.3s
5.2s
1.3s
1.3s

EBc
—
5-120
5-120
30-40030-4005-120
5-120
30-400————30-40030-4005-12030-40030-40030-40030-40030-40030-40030-400—30-400
—
5-120
5-120
30-40030-400——30-400
5-120
5-120
—
—
—
30-40030-400WXM
5-120
30-4005-120
5-120
30-400R.A.
10h31m36s—
11h24m24s
18h03m18s
17h00m40s
16h32m38s
22h55m35s
23h25m52s
00h42m50s
03h20m37s
03h05m36s
05h00m05s
09h32m49s
08h15m06s
10h23m21s
13h16m34s
15h14m45s
20h44m14s
21h02m14s
20h38m48s
19h46m38s
23h27m07s
22h49m25s
00h26m57s
00h17m23s
03h53m48s
02h36m52s
08h09m00s
11h18m30s
11h33m01s
11h06m54s
13h37m11s
12h10m51s
10h44m49s
11h06m51s
10h54m53s
12h13m06s
14h58m18s
17h04m02s
21h49m30s
20h33m47s
21h42m33s
21h30m47s
00h05m02s
20h58m02s

a Triggered type; G: FREGATE triggered, XG: FREGATE triggered by XDSPb Triggered time-scalec Triggered energy band in keV
d Location error radius in (90% confidence)e Whether optical transient was discovered (Y) or not (N)Dec.
+05d30m39s—-11d09m57s-32d08m01s+14d16m05s-18d43m+40d56m+32d47m46s-12d27m
17d40m01s+03d48m36s+32d07m39s-11d27m35s+36d44m31s+12d44m38s-17d52m29s-19d21m35s+07d10m12s-53d46m13s-05d23m34s-19d35m16s+06d21m50s-20d53m59s+18d55m44s-01d37m00s+37d57m12s+48d50m56s+06d44m20s+15d02m17s+25d53m56s-21d51m00s-00d19m22s-09d21m05s+21d28m44s-02d52m58s-06d59m22s-20d56m00s-32d56m57s-22d38m59s-27d42m06s-50d45m49s-45d12m12s+21d59m46s+19d55m37s-02d12m32s

errord
30.2′
—
36′
36′
36′
15′
20d*15′16.4′ x11◦
35′

OTe
N
N
N
N
N
N
Y
N
N

10′
11′
12′
8′
18′
10′
38′
13.8′
13.9′
13.8′
1′ (S)
7′
16.7′
2′ (S)
20′
26′
20′
2′ (S)
2′ (S)
2′ (S)
18′
7′
′
1 (S)
2′ (S)
7′
9′
1′ (S)
30′
2′ (S)
2′ (S)
14.4′
120′ x10′
5.4′
11.2′
30′

N
N
Y
Y
N
Y
N
N
N
N
Y
Y
Y?
Y
N
N
N
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
N
Y
Y
Y
N
N
N
N

214

APPENDIX B. HETE GRB SUMMARY

Table B.2: The HETE GRBs spectral parameters
GRB
GRB010213
GRB010225
GRB010326B†
GRB010612
GRB010613
GRB010629B
GRB010921†
GRB010928†
GRB011019
GRB011103
GRB011130
GRB011212
GRB020124
GRB020127
GRB020317
GRB020331
GRB020531
GRB020625
GRB020801†
GRB020812
GRB020813†
GRB020819
GRB020903
GRB021004
GRB021021
GRB021104†
GRB021112
GRB021211
GRB030115
GRB030226
GRB030323
GRB030324
GRB030328
GRB030329
GRB030416
GRB030418
GRB030429
GRB030519†
GRB030528†
GRB030723
GRB030725
GRB030821
GRB030823
GRB030824
GRB030913

Classa
XRF
XRF
XRR
GRB
XRR
XRR
XRR
GRB
XRF
XRR
XRF
XRF
XRR
XRR
XRF
GRB
GRB
XRF
GRB
XRR
GRB
XRR
XRF
XRR
XRF
XRF
XRR
XRR
XRR
GRB
XRR
XRR
GRB
XRR
XRF
XRR
XRF
GRB
XRF
XRR
XRR
XRR
XRF
XRF
GRB

Modelb
Band
CPL
CPL
CPL
Band
CPL
CPL
CPL
CPL
PL
PL
PL
CPL
CPL
CPL
CPL
CPL
CPL
Band
CPL
Band
Band
PL
CPL
CPL
CPL
CPL
Band
CPL
CPL
PL
CPL
Band
Band
PL
CPL
CPL
Band
Band
PL
CPL
CPL
CPL
PL
CPL

α
−1.00(fixed)+0.30−1.31−0.26+0.25−1.08−0.22+0.19−1.07−0.17+0.33−0.95−0.26+0.14−1.12−0.13+0.08−1.55−0.07+0.10−0.66−0.09−1.43 (fixed)+0.24−1.73−0.29+0.26−2.65−0.33+0.19−2.07−0.22+0.15−0.79−0.14+0.14−1.03−0.13+0.61−0.61−0.52+0.13−0.79−0.12+0.14−0.83−0.13−1.14 (fixed)+0.44−0.32−0.34+0.29−1.09−0.25+0.03−0.94−0.03+0.17−0.90−0.14+0.42−2.62−0.55+0.19−1.01−0.17−1.33 (fixed)+0.54−1.11−0.46+0.42−0.94−0.32+0.10−0.86−0.09+0.14−1.28−0.13+0.17−0.89−0.15+0.24−1.62−0.25+0.14−1.45−0.12+0.03−1.14−0.03+0.01−1.26−0.02+0.13−2.31−0.15+0.14−1.46−0.13+0.25−1.12−0.22+0.07−0.75−0.06+0.15−1.33−0.12+0.15−1.93−0.17+0.04−1.51−0.04+0.13−0.88−0.12+0.20−1.31−0.18+0.13−2.14−0.14+0.28−0.82−0.24

β+0.22−2.96−0.54
—
—
—
+0.09
−2.01−0.15
—
—
—
—
—
—
—
—
—
—
—
—
—
+0.17
−2.01−0.25—+0.03−1.57−0.04+0.18−1.99−0.48
—
—
—
—
—
+0.14
−2.18−0.25
—
—
—
—
+0.19
−2.09−0.40+0.05−2.28−0.06
—
—
—
+0.05
−1.72−0.07+0.29−2.65−0.98
—
—
—
—
—
—

Epeak [keV]+0.35
3.41−0.40
31.57+26.50−9.17
51.77+18.61−11.25244.50+285.07−81.9746.25+17.78−10.38+4.61
45.57−3.84+21.7688.63−13.79
409.50+118.46−74.9818.71+18.33−8.72—< 4.9d—86.93+18.11−12.45104.00+47.00−24.1028.41+12.68−7.41
91.57+20.99−14.09230.60+113.10−58.11+5.44
8.52−2.91
53.35+14.37−11.1287.62+106.03−29.57142.10+14.05−12.9149.90+17.88−12.19< 5.0d79.79+53.35−22.9715.38+14.24−7.47
28.21+17.41−7.88
57.15+38.90−20.70+7.84
45.56−6.23
82.79+52.82−22.2697.12+26.98−17.06—146.80+627.57−65.49126.30+13.89−13.10+2.31
67.86−2.15< 3.8d46.10+31.96−13.7035.04+11.75−7.90
137.60+17.80−15.36+4.67
31.84−4.97—
102.80+19.05−13.7384.26+15.12−10.88+7.45
26.57−5.02< 8.7d119.70+113.25−36.47

a GRB classification; XRF: X-ray-flash, XRR: X-ray-rich GRB, GRB: Hard GRB
b Spectral model; PL: Power-law, CPL: Cutoff power-law, Band: Band function
c Normalization at 15 keV in the unit of 10−2 photon cm−2 s−1 keV−1
d 99.7% upper limit derived by the constrain Band function† The constant factor is multiplied to the spectral model.

Kc15
+7.63
44.63−5.19+2.93
6.75−1.87+3.07
13.19−2.31+0.37
2.93−0.36+4.37
15.24−2.43+1.77
20.05−1.56+1.75
41.79−1.63+0.55
6.30−0.55+0.82
2.46−0.63+0.88
2.72−0.88+0.29
0.69−0.26+0.17
0.72−0.18+0.98
9.24−0.88+0.58
4.50−0.51+7.73
7.27−3.12+0.46
4.03−0.41+2.31
20.99−2.21+1.05
2.84−0.78+1.92
5.66−1.02+0.61
2.27−0.47+0.51
20.74−0.47+2.47
10.71−1.65+0.34
0.41−0.25+0.60
2.77−0.48+0.50
1.24−0.37+5.31
7.59−2.55+3.47
6.57−1.83+4.16
32.58−3.32+0.53
3.50−0.46+0.42
3.47−0.38+0.64
2.19−0.67+0.72
4.94−0.60+0.20
6.64−0.18+1.70
146.20−1.70+0.17
0.92−0.17+0.48
2.43−0.37+1.32
4.05−0.90+2.06
73.21−1.90+2.44
13.94−1.48+0.28
1.39−0.28+0.54
15.71−0.50+0.77
8.74−0.70+2.34
8.26−1.59+0.76
5.25−0.78+0.75
3.53−0.62

χ2ν
0.940
0.925
0.856
0.884
0.785
0.817
0.939
0.825
0.854
1.266
1.016
0.795
0.710
0.746
0.923
0.732
0.831
0.781
0.638
0.664
1.160
0.945
0.845
0.949
0.879
0.744
1.126
1.149
0.812
0.894
0.835
0.882
0.982
1.537
0.870
0.929
0.720
0.742
0.809
1.117
1.069
0.971
0.708
0.813
0.740

D.O.F.
44
39
111
65
134
110
140
125
68
38
40
54
95
110
53
111
141
55
140
68
140
108
26
68
41
38
61
140
67
139
33
76
140
139
54
68
68
124
109
40
141
98
110
53
53

215

Table B.3: The HETE GRBs time-average photon flux and fluence
GRB
GRB010213
GRB010225
GRB010326B
GRB010612
GRB010613
GRB010629B
GRB010921
GRB010928
GRB011019
GRB011103
GRB011130
GRB011212
GRB020124
GRB020127
GRB020317
GRB020331
GRB020531
GRB020625
GRB020801
GRB020812
GRB020813
GRB020819
GRB020903
GRB021004
GRB021021
GRB021104
GRB021112
GRB021211
GRB030115
GRB030226
GRB030323
GRB030324
GRB030328
GRB030329
GRB030416
GRB030418
GRB030429
GRB030519
GRB030528
GRB030723
GRB030725
GRB030821
GRB030823
GRB030824
GRB030913

Duration[sec.]
34.41
9.76
3.50
47.19
141.56
24.58
23.85
34.55
24.57
14.75
50.00
57.68
40.63
25.63
10.00
75.00
1.04
41.94
117.9760.16
113.00
50.16
13.00
49.70
49.15
31.41
4.00
8.00
36.00
68.81
19.61
15.73
199.2362.94
78.64
110.10
24.58
20.97
83.56
18.70
83.88
21.21
55.56
15.73
9.12

Photon fluxa
2–30 keV 30–400 keV
+0.15
+0.02
3.23−0.14
0.02−0.01
+0.38
+0.10
2.90−0.39
0.28−0.09
+0.81
+0.15
4.79−0.79
0.93−0.16
+0.28
+0.05
1.20−0.25
0.62−0.04
+0.79
+0.04
4.75−0.64
1.19−0.04
+0.87
+0.07
7.44−0.82
1.22−0.07
+2.05
+0.15
25.58−1.92
3.71−0.15
+0.28
+0.09
2.04−0.26
3.03−0.09
+0.23
+0.05
1.12−0.23
0.06−0.04
+0.34
+0.27
2.09−0.34
0.28−0.15
+0.26
+0.02
1.72−0.26
0.02−0.01
+0.12
+0.03
0.82−0.12
0.04−0.01
+0.29
+0.09
2.83−0.29
1.26−0.10
+0.16
+0.07
1.70−0.16
0.61−0.06
+0.35
+0.08
1.38−0.33
0.17−0.07
+0.10
+0.05
1.24−0.09
0.58−0.05
+1.08
+0.46
7.25−1.05
5.94−0.46
+0.10
+0.01
0.59−0.09
0.00−0.00
+0.23
+0.04
1.11−0.20
0.59−0.04
+0.17
+0.06
0.88−0.16
0.26−0.05
+0.20
+0.04
7.48−0.19
4.25−0.04
+0.17
+0.07
3.25−0.18
0.91−0.06
+0.20
+0.03
0.99−0.20
0.01−0.01
+0.10
+0.05
1.00−0.09
0.31−0.06
+0.11
+0.02
0.47−0.11
0.02−0.01
+0.95
+0.10
2.51−0.67
0.24−0.08
+0.52
+0.16
2.12−0.50
0.53−0.16
+0.30
+0.11
9.32−0.30
2.36−0.11
+0.15
+0.04
1.63−0.15
0.35−0.05
+0.15
+0.05
1.16−0.15
0.49−0.04
+0.82
+0.08
1.49−0.64
0.28−0.09
+0.29
+0.08
2.78−0.27
0.57−0.08
+0.06
+0.03
2.79−0.05
0.97−0.02
+0.66
+0.09
65.47−0.66
13.40−0.09
+0.12
+0.02
1.45−0.13
0.04−0.01
+0.08
+0.04
1.30−0.08
0.15−0.03
+0.19
+0.04
1.43−0.18
0.18−0.05
+1.17
+0.11
23.16−1.14
17.05−0.21
+0.48
+0.04
6.13−0.47
0.64−0.04
+0.17
+0.05
1.34−0.16
0.11−0.04
+0.33
+0.05
9.36−0.33
1.51−0.05
+0.29
+0.07
2.86−0.27
1.09−0.07
+0.33
+0.06
3.44−0.31
0.28−0.06
+0.97
+0.09
6.57−0.96
0.30−0.09
+0.20
+0.09
1.15−0.20
0.64−0.09

a The time-average photon flux in the unit of photon cm−2 s−1
b The photon fluence in the unit of photon cm−2

2–400 keV
+0.16
3.25−0.14+0.40
3.18−0.40+0.83
5.71−0.79+0.29
1.82−0.26+0.79
5.94−0.65+0.87
8.66−0.82+2.02
29.30−1.91+0.29
5.06−0.27+0.23
1.18−0.23+0.46
2.37−0.43+0.25
1.74−0.26+0.13
0.86−0.12+0.32
4.08−0.30+0.18
2.31−0.18+0.37
1.55−0.34+0.11
1.82−0.11+1.18
13.19−1.16+0.09
0.60−0.09+0.23
1.70−0.20+0.18
1.14−0.16+0.21
11.73−0.20+0.19
4.16−0.19+0.21
0.98−0.21+0.11
1.31−0.11+0.11
0.49−0.12+0.96
2.75−0.68+0.55
2.65−0.53+0.33
11.68−0.32+0.16
1.98−0.16+0.15
1.66−0.16+0.79
1.77−0.64+0.30
3.35−0.29+0.06
3.77−0.06+0.67
78.86−0.65+0.13
1.49−0.13+0.08
1.46−0.09+0.19
1.61−0.19+1.16
40.21−1.12+0.49
6.77−0.46+0.17
1.45−0.17+0.34
10.87−0.33+0.30
3.95−0.28+0.33
3.72−0.33+0.96
6.86−0.94+0.22
1.79−0.23

Photon fluenceb
2–30 keV 30–400 keV 2–400 keV
+0.52
+0.07
+0.55
11.11−0.48
0.07−0.03
11.18−0.48
+0.37
+0.10
+0.39
2.83−0.38
0.27−0.09
3.10−0.39
+0.28
+0.05
+0.29
1.68−0.28
0.33−0.06
2.00−0.28
+1.32
+0.24
+1.37
5.66−1.18
2.93−0.19
8.59−1.23+0.56
67.24+11.18
16.85−0.57
84.09+11.18
−9.06
−9.20
+2.14
+0.17
+2.13
18.29−2.02
3.00−0.17
21.29−2.02
+4.89
+0.36
+4.82
61.01−4.58
8.85−0.36
69.88−4.55
+0.97
+0.31
+1.00
7.05−0.90
10.47−0.31
17.48−0.93
+0.57
+0.12
+0.57
2.75−0.56
0.15−0.10
2.90−0.56
+0.50
+0.40
+0.68
3.08−0.50
0.41−0.22
3.50−0.64
+1.30
+0.10
+1.25
8.60−1.30
0.10−0.05
8.70−1.30
+0.69
+0.17
+0.75
4.73−0.69
0.23−0.06
4.96−0.69
+1.18
+0.37
+1.30
11.50−1.18
5.12−0.41
16.58−1.22
+0.41
+0.18
+0.46
4.36−0.41
1.56−0.15
5.92−0.46
+0.35
+0.08
+0.37
1.38−0.33
0.17−0.07
1.55−0.34
+0.75
+0.38
+0.83
9.30−0.68
4.35−0.38
13.65−0.83
+0.11
+0.05
+0.12
0.75−0.11
0.62−0.05
1.37−0.12
+0.42
+0.05
+0.38
2.47−0.38
0.02−0.02
2.52−0.38
+2.72
+0.47
+2.72
13.09−2.35
6.96−0.47
20.05−2.35
+1.02
+0.36
+1.08
5.29−0.96
1.56−0.30
6.86−0.96
+2.26
+0.46
+2.40
84.52−2.14
48.02−0.45 132.50−2.20
+0.85
+0.35
+0.95
16.30−0.90
4.57−0.30
20.87−0.96
+0.27
+0.03
+0.27
1.26−0.26
0.02−0.01
1.27−0.27
+0.50
+0.25
+0.55
4.97−0.45
1.54−0.30
6.51−0.55
+0.54
+0.11
+0.54
2.31−0.54
0.09−0.07
2.41−0.59
+2.99
+0.31
+3.01
7.88−2.11
0.75−0.25
8.64−2.14
+0.21
+0.06
+0.22
0.85−0.20
0.21−0.06
1.06−0.21
+0.24
+0.09
+0.26
7.46−0.24
1.89−0.09
9.34−0.26
+0.54
+0.14
+0.58
5.87−0.54
1.26−0.18
7.13−0.58
+1.03
+0.34
+1.03
7.98−1.03
3.37−0.28
11.42−1.10
+1.61
+0.16
+1.55
2.92−1.25
0.55−0.18
3.47−1.26
+0.46
+0.13
+0.47
4.37−0.43
0.90−0.13
5.27−0.46
+1.19
+0.59
+1.20
55.59−1.00
19.33−0.40
75.11−1.20
+4.10
+0.57
+4.30
412.10−4.20
84.34−0.57 496.30−4.00
+0.95
+0.16
+1.02
11.40−1.02
0.31−0.08
11.72−1.02
+0.88
+0.44
+0.89
14.31−0.88
1.65−0.33
16.07−0.99
+0.47
+0.10
+0.47
3.52−0.44
0.44−0.12
3.96−0.47
+2.45
+0.23
+2.43
48.57−2.39
35.75−0.44
84.32−2.35
+4.01
+0.33
+4.09
51.22−3.93
5.35−0.33
56.57−3.84
+0.32
+0.09
+0.32
2.51−0.30
0.21−0.07
2.71−0.32
+2.77
+0.42
+2.85
78.51−2.77
12.67−0.42
91.18−2.77
+0.62
+0.15
+0.64
6.07−0.57
2.31−0.15
8.38−0.59
+1.84
+0.33
+1.83
19.11−1.72
1.56−0.33
20.67−1.84
+1.53
+0.14
+1.51
10.33−1.50
0.47−0.14
10.79−1.48
+0.18
+0.08
+0.20
1.05−0.18
0.58−0.08
1.63−0.21

216

APPENDIX B. HETE GRB SUMMARY

Table B.4: The HETE GRBs time-average energy flux and fluence
GRB
GRB010213
GRB010225
GRB010326B
GRB010612
GRB010613
GRB010629B
GRB010921
GRB010928
GRB011019
GRB011103
GRB011130
GRB011212
GRB020124
GRB020127
GRB020317
GRB020331
GRB020531
GRB020625
GRB020801
GRB020812
GRB020813
GRB020819
GRB020903
GRB021004
GRB021021
GRB021104
GRB021112
GRB021211
GRB030115
GRB030226
GRB030323
GRB030324
GRB030328
GRB030329
GRB030416
GRB030418
GRB030429
GRB030519
GRB030528
GRB030723
GRB030725
GRB030821
GRB030823
GRB030824
GRB030913

2–30 keV+0.07
2.29−0.16+0.37
3.57−0.37+0.77
6.86−0.77+0.29
1.87−0.28+0.46
7.17−0.47+0.68
10.34−0.68+1.44
30.02−1.34+0.36
3.97−0.39+0.24
1.24−0.24+0.53
2.24−0.48+0.20
1.17−0.19+0.11
0.73−0.11+0.34
4.86−0.35+0.20
2.63−0.20+0.37
2.16−0.38+0.14
2.14−0.14+1.35
12.81−1.37+0.13
0.56−0.12+0.24
2.18−0.23+0.18
1.32−0.18+0.24
12.26−0.21+0.22
5.02−0.22+0.20
0.68−0.20+0.14
1.54−0.14+0.13
0.51−0.13+0.66
3.29−0.58+0.62
3.28−0.62+0.36
14.50−0.36+0.17
2.19−0.17+0.17
1.92−0.17+0.66
1.73−0.61+0.28
3.49−0.28+0.07
4.11−0.07+0.48
87.88−0.51+0.11
1.14−0.11+0.10
1.55−0.10+0.20
1.93−0.20+1.16
41.51−1.13+0.34
7.48−0.33+0.18
1.30−0.18+0.27
11.22−0.27+0.30
4.69−0.30+0.28
4.15−0.28+0.68
5.66−0.68+0.26
1.99−0.26

Energy fluxa
30–400 keV
2–400 keV
+0.17
+0.29
0.20−0.09
2.49−0.27
+1.76
+1.73
2.46−0.97
6.03−1.08
+2.64
+2.72
9.20−2.17
16.06−2.31
+1.51
+1.35
10.64−1.31
12.51−1.38
+0.89
+0.97
16.08−0.89
23.27−0.98
+1.10
+1.35
11.62−1.01
21.96−1.28
+3.62
+4.06
47.20−3.52
77.25−3.99
+2.65
+2.66
65.31−2.72
69.26−1.39
+0.56
+0.63
0.45−0.30
1.68−0.46
+5.91
+5.92
4.22−1.92
6.46−2.92
+0.23
+0.38
0.20−0.12
1.37−0.29
+0.44
+0.50
0.58−0.29
1.32−0.37
+2.17
+2.18
15.09−1.87
19.95−1.90
+1.75
+1.73
7.99−1.42
10.62−1.42
+0.88
+0.94
1.29−0.64
3.45−0.79
+1.14
+1.13
7.11−0.99
9.25−0.99+13.00+13.00105.40−12.90 118.20−13.00
+0.08
+0.20
0.03−0.03
0.59−0.14
+0.90
+0.93
8.07−0.89
10.26−0.93
+1.36
+1.35
3.18−0.97
4.50−0.99
+1.09
+1.13
74.30−1.10
86.61−1.13
+1.66
+1.68
12.47−1.85
17.50−1.88
+0.34
+0.48
0.13−0.10
0.73−0.25
+1.41
+1.38
3.58−1.01
5.12−1.01
+0.22
+0.28
0.13−0.10
0.64−0.22
+1.40
+1.59
1.95−0.85
5.21−1.06
+2.71
+2.73
5.34−2.25
8.62−2.31
+2.54
+2.58
29.64−2.51
44.18−2.58
+1.12
+1.10
4.21−0.89
6.40−0.90
+1.00
+1.01
6.24−0.88
8.16−0.89
+1.96
+1.87
4.54−1.78
6.27−1.75
+2.13
+2.12
8.11−1.92
11.59−1.91
+0.69
+0.70
14.43−0.71
18.55−0.71
+2.10
+2.20
171.00−2.20
259.00−2.20
+0.24
+0.31
0.47−0.17
1.61−0.27
+0.66
+0.66
1.58−0.47
3.13−0.50
+0.57
+0.60
1.54−0.48
3.47−0.54
+4.60
+4.80
290.60−4.70
332.20−4.70
+0.85
+0.92
6.74−0.88
14.24−0.93
+0.88
+0.99
1.49−0.63
2.79−0.77
+1.23
+1.26
19.87−1.20
31.09−1.23
+1.58
+1.61
12.95−1.41
17.64−1.44
+0.80
+0.83
2.29−0.64
6.44−0.72
+1.52
+1.74
3.71−1.20
9.37−1.54
+2.95
+2.91
8.82−2.11
10.81−1.90

a The time-average energy flux in the unit of 10−8 erg cm−2 s−1
b The photon fluence in the unit of 10−7 erg cm−2

Energy fluenceb
2–30 keV
30–400 keV
2–400 keV
+0.25
+0.58
+1.01
7.88−0.54
0.69−0.32
8.58−0.94
+0.36
+1.72
+1.69
3.48−0.36
2.40−0.94
5.89−1.06
+0.27
+0.92
+0.95
2.40−0.27
3.22−0.76
5.62−0.81
+1.35
+7.12
+6.37
8.84−1.31
50.23−6.21
59.05−6.53+6.60
101.50−6.54
227.60+12.60
329.40+13.70−12.50−13.80
+1.67
+2.69
+3.32
25.41−1.66
28.56−2.47
53.97−3.13
+3.42
+8.60
+9.70
71.60−3.20
112.60−8.40
184.20−9.50
+1.24
+9.10
+9.20
13.71−1.35
225.70−9.50
239.30−4.80
+0.58
+1.39
+1.54
3.03−0.58
1.10−0.74
4.13−1.14
+0.79
+8.72
+8.73
3.31−0.71
6.22−2.84
9.53−4.30
+0.98
+1.17
+1.90
5.85−0.96
0.98−0.62
6.83−1.46
+0.64
+2.53
+2.90
4.24−0.64
3.37−1.68
7.61−2.16
+1.40
+8.79
+8.86
19.74−1.41
61.33−7.63
81.04−7.70
+0.51
+4.48
+4.43
6.73−0.50
20.49−3.65
27.22−3.63
+0.37
+0.88
+0.94
2.16−0.38
1.29−0.64
3.45−0.79
+1.04
+8.52
+8.45
16.07−1.03
53.32−7.39
69.40−7.45
+0.14
+1.35
+1.35
1.33−0.14
10.96−1.34
12.30−1.35
+0.55
+0.35
+0.83
2.37−0.50
0.12−0.11
2.49−0.58+2.83
25.66−2.72
95.23+10.67
121.00+11.00−10.54−10.90
+1.09
+8.18
+8.11
7.91−1.09
19.15−5.86
27.06−5.98+2.70
138.50−2.30
839.60+12.30
978.70+12.70−12.50−12.80
+1.10
+8.33
+8.39
25.20−1.11
62.53−9.27
87.80−9.47
+0.28
+0.44
+0.62
0.83−0.24
0.16−0.14
0.95−0.33
+0.69
+7.01
+6.85
7.65−0.69
17.79−5.00
25.45−5.04
+0.63
+1.07
+1.39
2.51−0.64
0.62−0.49
3.13−1.06
+2.06
+4.40
+5.00
10.32−1.80
6.13−2.67
16.38−3.34
+0.25
+1.08
+1.09
1.31−0.25
2.14−0.90
3.45−0.93
+0.29
+2.03
+2.07
11.60−0.29
23.71−2.01
35.34−2.06
+0.61
+4.02
+3.98
7.89−0.61
15.17−3.20
23.05−3.23
+1.18
+6.85
+6.93
13.20−1.18
42.92−6.02
56.12−6.14
+1.29
+3.84
+3.68
3.40−1.21
8.91−3.48
12.30−3.43
+0.44
+3.35
+3.34
5.49−0.44
12.75−3.01
18.23−3.01+1.31+13.90+14.0081.86−1.29
287.40−14.10
369.50−14.20+3.10+13.00553.10−3.20 1076.00−14.00 1630.00+14.00−13.00
+0.87
+1.85
+2.47
8.98−0.87
3.72−1.38
12.70−2.09
+1.09
+7.27
+7.23
17.11−1.10
17.34−5.22
34.45−5.48
+0.49
+1.40
+1.48
4.74−0.49
3.80−1.17
8.54−1.32
+2.43
+9.70
+9.90
87.05−2.38
609.30−9.70
696.70−9.90
+2.80
+7.13
+7.60
62.54−2.79
56.34−7.32
119.00−7.80
+0.33
+1.64
+1.86
2.43−0.33
2.79−1.18
5.22−1.44+2.27
94.12−2.25
166.70+10.30
260.80+10.60−10.10−10.40
+0.63
+3.35
+3.41
9.96−0.64
27.47−2.99
37.43−3.07
+1.56
+4.43
+4.63
23.05−1.55
12.74−3.53
35.80−3.97
+1.07
+2.38
+2.72
8.90−1.07
5.83−1.89
14.73−2.42
+0.23
+2.69
+2.66
1.81−0.23
8.04−1.93
9.86−1.73

X/γ ratio
11.38
1.45
0.75
0.18
0.45
0.89
0.64
0.06
2.77
0.53
5.96
1.26
0.32
0.33
1.68
0.30
0.12
20.49
0.27
0.41
0.16
0.40
7.31
0.43
4.03
1.69
0.61
0.49
0.52
0.31
0.38
0.43
0.28
0.51
2.42
0.99
1.25
0.14
1.11
0.87
0.56
0.36
1.81
1.53
0.23

217

Table B.5: The HETE GRB 1s peak flux
GRB
GRB010213
GRB010225
GRB010326B
GRB010612
GRB010613
GRB010629B
GRB010921
GRB010928
GRB011019
GRB011103
GRB011130
GRB011212
GRB020124
GRB020127
GRB020317
GRB020331
GRB020531
GRB020625
GRB020801
GRB020812
GRB020813
GRB020819
GRB020903
GRB021004
GRB021021
GRB021104
GRB021112
GRB021211
GRB030115
GRB030226
GRB030323
GRB030324
GRB030328
GRB030329
GRB030416
GRB030418
GRB030429
GRB030519
GRB030528
GRB030723
GRB030725
GRB030821
GRB030823
GRB030824
GRB030913

Classa
XRF
XRF
XRR
GRB
XRR
XRR
XRR
GRB
XRF
XRR
XRF
XRF
XRR
XRR
XRF
GRB
GRB
XRF
GRB
XRR
GRB
XRR
XRF
XRR
XRF
XRF
XRR
XRR
XRR
GRB
XRR
XRR
GRB
XRR
XRF
XRR
XRF
GRB
XRF
XRR
XRR
XRR
XRF
XRF
GRB

ModelbBand (W)
CPL (F)
CPL (F)
CPL (F)
Band (W)
CPL (F)
CPL (F)
CPL (F)
PL (W)PL (F)PL (F)
PL (W)CPL (F)
CPL (W)
CPL (F)
CPL (F)
CPL (F)
PL (W)
Band (F)CPL (F)
Band (W)Band (F)
PL (W)CPL (F)
PL (W)CPL (F)
CPL (F)
Band (F)CPL (F)
CPL (F)
PL (F)CPL (F)
Band (F)Band (W)
PL (W)CPL (W)
CPL (F)
Band (F)Band (F)
PL (W)CPL (F)
CPL (F)
CPL (F)
PL (W)CPL (F)

5s Photon fluxc(8.50 ± 3.54) × 10−3
(6.58 ± 6.34) × 10−2
(2.85 ± 0.89) × 10−1
(1.33 ± 0.10)(3.77 ± 0.62) × 10−1
(1.04 ± 0.13)(2.78 ± 0.20)(3.84 ± 0.20)(3.73 ± 3.65) × 10−2
(4.71 ± 2.95) × 10−2
(2.52 ± 2.23) × 10−2
< 2.79 ×10−2(9.16 ± 1.55) × 10−1
(7.36 ± 0.98) × 10−1
(9.67 ± 6.52) × 10−2
(9.64 ± 1.06) × 10−1
(9.90 ± 0.10) × 10−1
(8.70 ± 4.42) × 10−2
(5.69 ± 1.12) × 10−1
(3.45 ± 0.94) × 10−1
(7.74 ± 0.19)(2.38 ± 0.14)(1.36 ± 1.23) × 10−2
(2.92 ± 0.92) × 10−1
(7.86 ± 6.07) × 10−2
(1.70 ± 0.89) × 10−1
(2.47 ± 1.19) × 10−1
(2.03 ± 0.13)(9.82 ± 1.01) × 10−1
(4.81 ± 0.95) × 10−1
(1.89 ± 0.91) × 10−1
(5.98 ± 1.29) × 10−1
(2.90 ± 0.10)(28.90 ± 0.42)(1.12 ± 0.46) × 10−1
(9.04 ± 6.62) × 10−2
(1.83 ± 0.68) × 10−1
(5.38 ± 0.25) × 10−1
(1.38 ± 0.50) × 10−1
(1.34 ± 0.65) × 10−1
(5.46 ± 0.22)(9.75 ± 1.17) × 10−1
(1.13 ± 0.93) × 10−1
(8.90 ± 4.66) × 10−2
(6.01 ± 0.92) × 10−1

Count ratiod
1.325 ± 0.097
1.454 ± 0.149
2.576 ± 0.188
2.314 ± 0.171
3.249 ± 0.597
1.792 ± 0.084
1.147 ± 0.056
1.905 ± 0.132
1.984 ± 0.196
1.392 ± 0.229
1.419 ± 0.208
1.754 ± 0.281
1.562 ± 0.129
1.726 ± 0.215
2.093 ± 0.198
1.236 ± 0.092
3.620 ± 0.229
2.015 ± 0.363
1.381 ± 0.139
2.415 ± 0.264
1.074 ± 0.054
1.436 ± 0.071
1.822 ± 0.299
1.458 ± 0.150
2.368 ± 0.490
1.469 ± 0.163
2.220 ± 0.252
2.021 ± 0.069
1.183 ± 0.094
1.305 ± 0.132
1.538 ± 0.226
1.600 ± 0.120
1.145 ± 0.059
1.317 ± 0.051
1.247 ± 0.167
1.481 ± 0.216
1.570 ± 0.157
2.101 ± 0.040
1.082 ± 0.073
1.224 ± 0.208
1.043 ± 0.043
1.222 ± 0.106
1.490 ± 0.150
1.457 ± 0.276
1.485 ± 0.144

a GRB classification; XRF: X-ray-flash, XRR: X-ray-rich GRB, GRB: Hard GRB
b Spectral model; PL: Power-law, CPL: Cutoff power-law, Band: Band function,
W: peak counts using WXM data, F: peak counts using FREGATE datac The photon flux in 50–300 keV using 5s WXM/FREGATE spectrumd Count ratio between 1s and 5s time interval including the highest peake The 1s peak flux in 50–300 keV

1s Peak fluxe(1.13 ± 0.48) × 10−2
(9.57 ± 9.33) × 10−1
(7.33 ± 2.33) × 10−1
(3.07 ± 0.33)(1.23 ± 0.30)(1.87 ± 0.24)(3.19 ± 0.27)(7.31 ± 0.64)(7.40 ± 7.35) × 10−2
(6.56 ± 4.24) × 10−2
(3.58 ± 0.52) × 10−2
< 4.89 ×10−2(1.43 ± 0.27) × 10−1
(1.27 ± 0.23)(2.02 ± 1.38) × 10−1
(1.19 ± 0.16)(3.58 ± 0.44)(1.75 ± 0.94) × 10−1
(7.86 ± 1.73) × 10−1
(8.34 ± 2.46) × 10−1
(8.31 ± 0.47)(3.42 ± 0.27)(2.48 ± 2.28) × 10−2
(4.26 ± 1.41) × 10−1
(1.86 ± 1.49) × 10−1
(2.49 ± 1.33) × 10−1
(5.48 ± 2.72) × 10−1
(4.10 ± 0.30)(1.16 ± 0.15)(6.28 ± 1.40) × 10−1
(2.91 ± 1.47) × 10−1
(9.57 ± 2.18) × 10−2
(3.32 ± 0.20)(38.06 ± 1.58)(1.39 ± 0.60) × 10−1
(1.34 ± 1.00) × 10−1
(2.87 ± 1.10) × 10−1
(11.31 ± 0.57)(1.49 ± 0.55) × 10−1
(1.65 ± 0.84) × 10−1
(5.69 ± 0.33)(1.19 ± 0.18)(1.69 ± 1.39) × 10−1
(1.30 ± 0.72) × 10−1
(8.92 ± 1.61) × 10−1

Appendix C
Light curve and Spectrum

218

219

Figure C.1: GRB010612

Figure C.2: GRB010613

Figure C.3: GRB010921

Figure C.4: GRB010928

220

APPENDIX C. LIGHT CURVE AND SPECTRUM

Figure C.5: GRB011103

Figure C.6: GRB020124

Figure C.7: GRB020127

Figure C.8: GRB020331

221

Figure C.9: GRB020531

Figure C.10: GRB020625

Figure C.11: GRB020801

Figure C.12: GRB020812

222

APPENDIX C. LIGHT CURVE AND SPECTRUM

Figure C.13: GRB020813

Figure C.14: GRB020819

Figure C.15: GRB021004

Figure C.16: GRB021112

223

Figure C.17: GRB021211

Figure C.18: GRB030115

Figure C.19: GRB030226

Figure C.20: GRB030323

224

APPENDIX C. LIGHT CURVE AND SPECTRUM

Figure C.21: GRB030324

Figure C.23: GRB030329

Figure C.22: GRB030328

Figure C.24:

GRB030519 (WXM:1.23s,

FREGATE 82ms)

225

Figure C.25: GRB030725

Figure C.27: GRB030913

Figure C.26: GRB030821

Appendix D
The “constrain” Band function
In the spectral analysis of GRBs, one occasionally encounters events (such as XRF 020903) thatare so soft that they present themselves as pure power-laws with power-law index β < −2 inthe energy range of the detector. The natural interpretation of such spectra is that the breakenergy Ebreak separating the two functional parts of the Band function is near or below thelower boundary of the detector energy range.
This situation creates a problem for fits of the Band function, in that the Band function
has two distinct ways of conforming to a power-law in the detector energy range:
1. Ebreak → 0, so that only the high-energy, pure power-law part of the Band function isvisible in the energy range of the detector.

2. Ebreak → ∞, E0 → ∞, where E0 is the “cutoff energy” of the cutoff power-law that

constitutes the low-energy part of the Band function. In this limit, the limiting powerlaw is actually the cutoff power-law, but the cutoff energy is so large that the curvatureof the model is imperceptible in the detector energy range.

Therefore, despite the fact that the numerical value of the power-law index is such that weare certain that we should be dealing with the high-energy part of the Band function (i.e., theindex is < −2, the low-energy part of the function can “horn in” on the fit, altering the physicalinferences drawn from the spectrum.

This situation is particularly a problem for the estimation of Epeak . Since we know that weare in case 1, we also know that we ought to have at least a firm upper limit on Epeak , since
Epeak is always necessarily less than Ebreak , which is at the low end of the detector energy range.
On the other hand, the case 2 limit implies Epeak → ∞. Unfortunately, the data doesn’t care
226

227
which side of the Band function makes the power-law, so no discrimination is possible between
the two cases. Consequently, we can’t constrain Epeak at all using a normal Band function fit.
The approach we have chosen to deal with this situation in the case of XRF 020903 is tofit a constrained Band function to the data. That is, we consider a three-dimensional subspaceof the full four-dimensional Band function parameter space, choosing the subspace with a viewto satisfying the following criteria:
1. It is perfectly possible to make both pure power-laws and cutoff power-laws of the any
desired curvature in the detector energy range.
2. Only the high-energy part of the Band function is allowed to produce a pure power-law.
We define the three-dimensional subspace in the following way: consider a Band function
parametrized by low- and high-energy indices α and β, and by a cutoff energy E0 . The wellknown relation between E0 and Ebreak is Ebreak = (α−β)E0 . We impose the constraint conditionon our family of fitting functions
Ebreak = Epivot × (E0 /Epivot)−1 ,(D.1)

where Epivot is some suitably chosen energy, in the general neighborhood where the GRB has
appreciable emission. Ebreak and E0 are then inversely related, and are equal to each otherwhen both are equal to Epivot.
When E0 < Epivot , then Ebreak > Epivot , and the function is essentially a cutoff power-law
in the energy range of interest.
On the other hand, when E0 > Epivot , then Ebreak < Epivot , and as E0 → ∞, Ebreak → 0.

In other words, when the low-energy part of the Band function is trying to imitate a powerlaw, the break energy becomes small enough to force the low-energy part of the function below
the energy range of interest, where it cannot be seen and therefore can do no harm. Any pure
power-law work must thus be done by the high-energy part of the Band function.
The resulting spectral function has three parameters (including the scale), rather than four.
The two input shape parameters can be chosen arbitrarily from the set {α, β, E0 , Ebreak , Epeak }.

The remaining parameters may then be determined by algebraic relationships.

We have found it most convenient to adopt Epeak and β as our parameters. The choiceof Epeak is dictated by the necessity of estimating its value, or at least an upper bound on
its value. The choice of β is convenient because one may then impose the parameter boundβ < −2, which guarantees that the formal expression for Epeak may be meaningfully interpreted

228

APPENDIX D. THE “CONSTRAIN” BAND FUNCTION

as the energy of the peak of the νFν distribution. This bound on β is an important part of thespecification of the fitting family of models. Were it not imposed, it would be possible for theformal expression for Epeak to exceed Ebreak , so that at large values of Epeak the fit could always
produce a β >∼ − 2 power-law in the detector energy range. The result would be an extended
tail of constant χ2 for arbitrarily large values of Epeak .
Figure D.1 shows the constrained Band function, with β = −2.5 and Epivot = 4 keV,for different values of Epeak . This figure shows that Epeak increases, Ebreak also necessarily

increases, so that E0 is forced to smaller and smaller values by the constraint, which increases
the curvature (and the value of α).
Figure D.2 shows the constrained Band function, with Epeak = 4 keV and Epivot = 4 keV,for different values of β. The progression from some curvature at low energy (β = −2.0) toalmost none (β = −4.0) is evident, as is the fact that as the curvature disappears, the resulting

power-law is produced by the high-energy part of the Band function.

Figures D.1 and D.2 show that the constrained Band function is perfectly able to makeboth pure power-laws, and cutoff power-laws with any desired curvature in the detector energy
range. Figure D.2 demonstrates that, in the constrained Band function, a power-law spectrum
is always produced by the high-energy part of the Band function.
The choice of Epivot is dictated by the following considerations:
1. Epivot must be low enough to prevent the low-energy part of the Band function frommaking a power-law in the energy range of interest. If Epivot were 1 GeV (say), then theBand function would have no difficulty making E0 large and α <∼ − 2, which is what
we are trying to prevent by introducing the constraint. So Epivot should be “as low as
possible.”
2. Epivot must not be so low that we cannot adequately fit any curvature that may exist in
the spectrum. If Epivot were 1 eV (say), then whenever Ebreak was in or above the energy
range where the spectrum is appreciable, E0 would be so tiny that the curvature of themodel would be huge, much too large to fit the data well.
One way of choosing Epivot is to calculate it’s value using the best-fit parameters from a fitof a free Band function, using Epivot = (E0 Ebreak )1/2 . This choice, which effectively chooses theunique constrained subspace of the full parameter space that contains the best-fit free Band
function, allows the constrained family of functions to optimally fit whatever curvature thedata may seem to hint is required.

229
We must require that the inferences that we draw from the spectral fit should be robust, inthe sense that they should not depend strongly on the specific choice of Epivot . So the properuse of this constrained Band model involves not only choosing a representative value of Epivot ,but also varying Epivot in some reasonable range, to make sure that the conclusions aboutparameter estimates and bounds are unaffected by the choice of Epivot .
Figure D.3 shows the constrained Band function, with Epeak = 4 keV and β = 2.0, fordifferent values of Epivot . Once again, as the low-energy curvature disappears, the resulting
power-law is produced by the high-energy part of the Band function. Figure D.3 also showsthat the shape of the spectrum in the detector energy range is insensitive to the specific choice of
Epivot , within a reasonable range. Thus the conclusions about parameter estimates and bounds
are unaffected by the choice of Epivot .
Figure D.4 shows the constrained Band functions with parameters that best fit the 13 s
spectrum of XRF 020903, for different fixed values of Epivot . This figure illustrates the fact thatthe shape of the best-fit model is essentially unchanged in the energy range of the WXM for
choices of Epivot within a reasonable range.‘
Finally, we give the algebraic relationships necessary to recover the remaining Band function
parameters assuming that Epeak and β are given. Let x ≡ Epeak /Epivot . Then,s

1 4
1x − x2 (β + 2),
α = −2 + x2 +24E0 = (2 + α)Epeak .

(D.2)
(D.3)

In Equation (D.2), we have resolved the ambiguity in the choice of root of a quadratic equation
by requiring that when β + 2 < 0, then α + 2 > 0, so that Epeak is in fact the peak energy ofthe νFν distribution.

230

APPENDIX D. THE “CONSTRAIN” BAND FUNCTION

Figure D.1: Constrained Band functions, with β = −2.5 and Epivot = 4 keV, for different

values of Epeak . All functions have been normalized to 1 keV−1 at 10 keV. The two verticallines at 2 keV and at 25 keV show the WXM bandpass. The spectra shown are (decreasing
monotonically from the top at low energy), Epeak =1 keV, 2 keV, 4 keV, 6 keV, and 8 keV,
respectively. As Epeak increases, Ebreak also necessarily increases, so that E0 is forced to smallerand smaller values by the constraint, increasing the curvature and the value of α.

231

Figure D.2: Constrained Band functions, with Epeak = 4 keV and Epivot = 4 keV, for different
values of β. All functions have been normalized to 1 keV−1 at 10 keV. The two vertical linesat 2 keV and at 25 keV show the WXM bandpass. The spectra shown are for β = -2.0, -2.5,-3.0, -3.5, and -4.0, which can be distinguished by the increasing steepness of their slopes athigh energy. The progression from some curvature at low energy (β = −2.0) to almost none

(β = −4.0) is evident, as is the fact that as the curvature disappears, the resulting power-law

is produced by the high-energy part of the Band function.

232

APPENDIX D. THE “CONSTRAIN” BAND FUNCTION

Figure D.3: Constrained Band functions, with Epeak = 4 keV and β = 2.0, for different values of
Epivot . All functions have been normalized to 1 keV−1 at 10 keV. The two vertical lines at 2 keV
and at 25 keV show the WXM bandpass. The spectra shown are (increasing monotonicallyat low energy) for Epivot = 2 keV, 4 keV, 6 keV, and 8 keV, respectively. Once again, as the
low-energy curvature disappears, the resulting power-law is produced by the high-energy partof the Band function. Note also that the shape of the constrained Band function is insensitive
to the specific choice of Epivot within a reasonable range.

233

Figure D.4: Constrained Band functions with parameters that best fit the 13 s spectrum of
XRF020903, for different fixed values of Epivot . The two vertical lines at 2 keV and at 25 keVshow the WXM bandpass. All functions have been normalized so that the integral from 2 keV
to 25 keV is one photon. The five spectra shown in the plot corresponding to Epivot = 4 keV,
5 keV, 6 keV, 7 keV, and 8 keV (the 7 keV and 8 keV largely overlap each other). This
figure illustrates a robust aspect of the constraint procedure: the best-fit model is essentiallyunchanged in the WXM spectral band despite a factor-of-two change in the value of Epivot .

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Acknowledgments
First of all, I am most grateful to Prof. N. Kawai for his support and concern for my entire
Ph.D. program. I also would like to thank Dr. E. E. Fenimore for giving me a opportunity toworking at Los Alamos National Laboratory for a year. For the scientific guidance and advice
for GRBs, I appreciate the great support from Prof. D. Q. Lamb and Dr. C. Graziani. I
would like to express my deepest gratitude for the first three “senior” members of the WXM
operation, Dr. Y. Shirasaki, Dr. T. Tamagawa, and Dr. K. Torii. Without their supports, I
would not possible to express the great results of HETE.
I express my thank to Dr. J.-L. Atteia and Ms. C. Barraud for teaching and providing
us their spectral analysis software of the FREGATE data. I also would like to thank Dr.
M. Kippen for discussing about the spectral analysis of XRFs/GRBs and providing me the
WFC/BATSE spectral parameters.
HETE is operated by the international collaborations of seven different countries. I am
greatful to the all HETE members for developing and operating the HETE satellite and also
give me the opportunity for joint the team and analyzing the data.
I want to thank Prof. K. Makishima, who is the chief scientist of the cosmic radiationlaboratory at the Institute of Physical and Chemical Research (RIKEN), for supporting mygraduate work. Last but not least, I wish to thank all the staffs, the post doctorates, andthe graduate students of RIKEN, Tokyo Institute of Technology, and Los Alamos National
Laboratory.

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