Energy [keV]
5.3 Gamma-ray Prompt Emissions
5.3.2 The Light Curves & The Spectra of 77 Bursts
[sec]
T90
10-3 10-2 10-1 1 10 102 103
Number of Bursts
0 2 4 6 8 10 12 14 16 18
Figure 5.7: Distribution of the burst durationT90 for the 77Swift GRBs.
[sec]
T90
0.001 0.01 0.1 1 10 100 1000
hardness ratio
0 0.5 1 1.5
2 2.5 3 3.5 4 4.5 5
Figure 5.8: The hardness ratio of flux in 50–150 keV over that in 15–50 keV is plotted against the burst duration T90.
have the duration less than 1 s, and hence being categorized to the short GRBs. Unlike the T90 distribution obtained with BATSE (Fig. 2.6left), theSwift GRBs do not show a clear bimodal distribution. On the other hand, the peak of the distribution at ∼ 30 s, which is comparable to the peak of long bursts at∼50 s for the BATSE samples. Fig. 5.8 shows the hardness ratio against the burst duration. Unlike the BATSE result (Fig. 2.6 right) again, we do not find a clear difference of spectral hardness between short “hard”
bursts and long “soft” bursts. We note that it is not an easy question how to compare the relative sensitivity of different detectors for detecting gamma-ray bursts, for which the difference in trigger systems must be taken into account. Although the BAT use shorter rate triggers than BATSE to increase the sensitivity for short bursts, it is also indicated that the BAT softer energy band relative to BATSE could decrease the fraction of short, hard bursts to long, soft bursts (see Band (2006)). With the small sample of short bursts at the moment, we need to further investigate the real GRB populations and if the short burst is really hard or not.
Fig. 5.9 shows the distribution of photon index obtained by the fit with a single power law model, having a sharp peak around ∼ −1.5 ( softest: −3.0; hardest∼ −0.67).
However, the typical photon indices of BATSE GRBs are αB ∼ −1 and βB ∼ −2.2 for lower and higher energy band (Preece et al. 2000). The photon index obtained from the
Power Law Index
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1
Number of Bursts
0 2 4 6 8 10 12 14 16 18
Figure 5.9: Distribution of photon index obatained by the fit with a single power law model.
Swift samples are distributed right in the middle. While it is possible that the source spectra intrinsically extend with a single power law with a photon index of∼1.5, we can also consider that we are observing a middle part of the Band function and obtaining a middle value of photon index between αB∼ −1 and βB ∼ −2.2.
In order to investigate if the spectra of Swift GRBs are really straight in the BAT energy range or not, we first plot the energy fluence in 15–150 keV againstT90in Fig. 5.10.
We can recognize the difference between the bursts where the best fit is provided by the cut-off power law model (closed circles), and the bursts where that is provided by the single power law model (open circles). The lines drawn in the same figure represents the levels of time averaged flux of 10−7 and 10−8 erg cm−2 s−1. The cut-off power law model is preferable for brighter bursts in flux.
To confirm this tendency we also perform a spectral simulation. Using Xspec ran-domization function (fakeit command), we generate a spectrum from the Band function with αB =−1.0, βB=−2.5 with a flux from 10−8 to 3×10−7 erg cm−2 s−1. By varying Epeakobs from 10 to 1000 keV, we also investigate an effect ofEpeakobs on detecting a curvature, The background noise is taken into account based on the level of actual observations.
[sec]
T90
0.001 0.01 0.1 1 10 100 1000 ]-2 Fluence in 15-150 keV [erg cm
10-8
10-7
10-6
10-5
10-4
Figure 5.10: The fluence in 15–150 keV against the burst durationT90. The events where the best fit is provided by the cut-off power law model are shown byclosed circles. The events where the best fit is provided by the single power law model are shown byopen circles. The two lines are drawn to indicate the levels of time averaged flux of 10−7 (left) and 10−8 (right) erg cm−2 s−1.
The spectra are then fitted with a single power law model and cut-off power law model in the same manner with the analysis of actual observations. We repeated this procedure for 100 times for each parameter set. Fig. 5.11 shows F-test probability for the improvement in χ2 fit from the power law model to the cut-off power law model. We find that the curvature is detectable only for the spectra simulated with Epeakobs within or close to the BAT energy range and with relatively high flux. The photon index obtained from a single power law fit is also shown in Fig. 5.12. When the Epeakobs is higher enough, let us say higher than ∼ 300 keV, the photon index becomes close to the input αB =−1. On the other hand, when the Epeakobs is lower than∼ 30 keV, the photon index gets close the input βB = −2.5. For the case with Epeakobs ∼ 100 keV, the photon index becomes an intermediate value of ∼ −1.5 between the inputαB and βB.
Overall, it is likely that theSwiftGRBs exhibit spectral curvatures like BATSE GRBs, but the curvatures are detectable only when the GRBs are bright andEpeakobs fall inside the BAT energy range. We therefore conclude here that no differences are found in spectral properties between the previous GRBs and Swift GRBs.
[keV]
obs
Input Epeak
10 100 1000
]-1 s-2Input Flux [erg cm
10-8
10-7
Figure 5.11: F-test probability of an improvement inχ2fit of simulated spectra from the single power law model to the cut-off power law model. The contours represnt 60, 70, 80, 90, 95.45 (2σ), and 99.73 (3σ)% levels from bottom to top. The two vertical dashed lines indicate the BAT energy range from 15 to 150 keV.
[keV]
obs
Input Epeak
10 100 1000
]-1 s-2Input Flux [erg cm
10-8
10-7
-2.6 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8
Figure 5.12: The spectral simulation is performed withαB =−1, βB =−2.5, and the parameters (Epeakobs and flux) indicated at each grid. The gray scale indicates the photon index obtained from the simulated spectra fitted with a power law model.
Table 5.2. Characteristics of the 77 Swift GRBs.
GRB Redshift BAT location T90 Power Law Cutoff Power Law χ2ν Fluence Hardness RA DEC [sec] Photon Index αB Eobspeak[keV] [erg/cm2] Ratio 041217 164.79 -17.95 9.9 −1.61+0.07−0.06 1.50 3.60+0.15−0.14×10−6 1.45+0.11−0.11
041219a 6.51 62.85 520 N/A1
041219b 167.67 -33.46 30 N/A2
041219c 343.97 -76.8 40 N/A3
041220 291.24 60.69 5.1 −1.65+0.10−0.09 0.72 5.06+0.28−0.28×10−7 1.37+0.14−0.14 041223 100.12 -37.03 108.3 (−1.15+0.03−0.03) −0.96+0.12−0.13 364.0+572.6−121.6 0.49 2.03+0.03−0.03×10−5 2.47+0.09−0.09 041224 56.19 -6.62 176.6 (−1.79+0.06−0.05) −1.04+0.28−0.24 68.2+9.3−6.0 0.83 9.61+0.34−0.33×10−6 1.14+0.08−0.08 041226 79.63 73.33 89.1 −1.53+0.40−0.40 1.52 3.44+0.87−0.85×10−7 1.56+0.72−0.68 041228 336.64 5.04 61.8 −1.72+0.08−0.08 0.99 3.74+0.16−0.16×10−6 1.26+0.11−0.11 050117 358.48 65.94 167.0 (−1.54+0.04−0.04) −1.09+0.20−0.18 115.3+38.7−18.1 0.64 9.67+0.24−0.24×10−6 1.56+0.08−0.08 050124 192.88 13.03 4.0 (−1.53+0.08−0.08) −0.64+0.39−0.36 85.7+22.1−11.5 0.86 1.21+0.06−0.06×10−6 1.56+0.16−0.16 050126 1.29 278.11 42.39 39.7 −1.37+0.15−0.15 1.09 1.03+0.10−0.10×10−6 1.88+0.32−0.32 050128 219.59 -34.76 25.3 (−1.47+0.07−0.07) −0.69+0.36−0.30 99.9+26.7−13.5 0.83 5.03+0.21−0.21×10−6 1.75+0.15−0.15 050202 290.58 -38.73 0.1 −1.43+0.29−0.31 0.77 2.85+0.55−0.54×10−8 1.73+0.61−0.59 050215a 348.40 49.33 85.2 −1.34+0.24−0.24 0.81 8.13+1.11−1.11×10−7 1.95+0.50−0.50 050215b 174.49 40.79 7.8 −2.03+0.19−0.20 1.02 2.41+0.30−0.29×10−7 0.88+0.21−0.20 050219a 166.45 -40.69 25.6 (−1.40+0.05−0.05) −0.19+0.29−0.28 91.2+9.9−7.1 0.86 4.30+0.15−0.15×10−6 1.89+0.13−0.13 050219b 81.26 -57.76 31.8 (−1.59+0.05−0.05) −1.13+0.24−0.21 112.8+44.0−18.3 0.98 1.56+0.05−0.05×10−5 1.52+0.09−0.09 050223 271.40 -62.47 17.0 −1.84+0.16−0.16 0.80 5.50+0.55−0.54×10−7 1.10+0.21−0.21 050306 282.32 -9.15 160.8 (−1.56+0.06−0.06) −1.19+0.28−0.25 133.3+144.8−31.7 0.94 1.19+0.04−0.04×10−5 1.56+0.12−0.09 050315 1.949 306.47 -42.59 98.3 −2.17+0.09−0.09 0.87 3.45+0.15−0.15×10−6 0.75+0.07−0.07 050318 1.44 49.68 -46.40 29.1 (−1.92+0.10−0.09) −1.16+0.45−0.42 50.4+11.1−6.8 0.96 1.13+0.08−0.08×10−6 0.87+0.13−0.12 050319 3.24 154.16 43.57 151.4 −1.99+0.17−0.17 0.73 1.36+0.14−0.14×10−6 0.93+0.19−0.18 050326 6.84 -71.37 29.5 (−1.29+0.03−0.04) −1.00+0.13−0.16 227.3+174.6−57.3 0.73 9.14+0.17−0.16×10−6 2.11+0.08−0.09 050401 2.9 247.88 2.18 34.3 (−1.54+0.07−0.06) −1.26+0.25−0.29 >113.3 0.70 8.46+0.32−0.32×10−6 1.58+0.13−0.12 050406 34.44 -50.18 6.0 −2.50+0.36−0.32 1.32 8.76+1.94−1.80×10−8 0.53+0.26−0.22 050410 89.77 79.60 47.2 (−1.74+0.07−0.07) −0.84+0.38−0.35 67.8+11.8−7.0 1.31 4.19+0.21−0.21×10−6 1.18+0.11−0.12 050412 181.12 -1.25 27.9 −0.67+0.16−0.15 0.70 7.35+0.59−0.58×10−7 4.15+0.69−0.70 050416a 0.6535 188.47 21.04 2.4 (−3.00+0.18−0.19) −0.75+1.26−0.41 16.6+6.2−14.9 0.79 3.36+0.34−0.32×10−7 0.12+0.08−0.05 050416b 133.85 11.17 3.3 (−1.42+0.12−0.11) −0.40+0.67−0.53 92.3+38.9−15.0 0.90 1.13+0.09−0.08×10−6 1.85+0.28−0.27 050418 44.34 -18.54 82.5 (−1.69+0.06−0.05) −1.37+0.25−0.24 112.7+183.3−28.2 0.72 5.45+0.20−0.19×10−6 1.31+0.09−0.09 050421 307.24 73.67 13.5 −1.61+0.38−0.39 0.71 1.41+0.36−0.35×10−7 1.43+0.66−0.62 050422 324.45 55.80 57.3 −1.37+0.19−0.19 0.77 6.38+0.78−0.77×10−7 1.88+0.41−0.41 050502b 142.55 17.01 17.3 −1.61+0.13−0.13 1.00 4.91+0.42−0.42×10−7 1.42+0.22−0.22 050505 4.27 141.78 30.26 63.1 (−1.53+0.10−0.10) −0.96+0.51−0.41 100.2+70.7−22.7 0.71 2.67+0.17−0.18×10−6 1.56+0.20−0.20 050507 48.06 -11.07 26.0 (−1.63+0.16−0.17) 0.63+1.18−0.93 56.0+9.2−6.5 1.15 4.60+0.62−0.59×10−7 1.03+0.28−0.27 050509a 310.59 54.07 10.8 −2.06+0.15−0.17 1.04 3.54+0.33−0.32×10−7 0.85+0.16−0.16 050509b 189.06 29.00 0.04 −1.54+0.34−0.36 0.74 1.32+0.33−0.34×10−8 1.56+0.68−0.67 050525a 0.606 278.14 26.34 8.9 N/A4 −0.98+0.12−0.11 78.2+3.6−3.0 0.26 1.62+0.02−0.02×10−5 1.29+0.04−0.04 050528 353.53 45.94 10.8 −2.42+0.24−0.27 1.03 4.48+0.65−0.64×10−7 0.56+0.18−0.17 050603 2.821 39.98 -25.20 22.1 −1.25+0.07−0.07 1.26 6.86+0.26−0.27×10−6 2.15+0.16−0.17 050607 300.17 9.14 26.2 −1.91+0.15−0.15 1.09 6.37+0.56−0.55×10−7 1.01+0.17−0.17 050701 227.29 -59.42 32.1 −1.69+0.08−0.08 0.96 1.54+0.07−0.07×10−6 1.30+0.12−0.12 050712 77.69 64.90 49.7 −1.53+0.17−0.18 1.25 1.06+0.11−0.11×10−6 1.56+0.31−0.31 050713a 320.54 77.07 97.6 −1.57+0.07−0.07 1.17 5.39+0.21−0.21×10−6 1.49+0.12−0.12 050713b 307.82 60.94 128.3 −1.57+0.13−0.13 1.12 4.86+0.37−0.37×10−6 1.50+0.22−0.22 050714b 169.69 -15.53 48.3 −2.60+0.29−0.33 1.03 6.05+1.04−1.01×10−7 0.46+0.19−0.17 050715 155.67 -0.06 49.8 −1.68+0.11−0.11 1.28 1.41+0.09−0.09×10−6 1.33+0.16−0.16 050716 338.60 38.70 67.7 (−1.45+0.06−0.05) −0.83+0.27−0.24 113.7+41.1−18.8 0.77 6.50+0.23−0.23×10−6 1.74+0.12−0.12 050717 214.33 -50.54 68.6 −1.39+0.04−0.06 0.83 6.29+0.15−0.15×10−6 1.81+0.09−0.09 050721 253.45 -28.39 44.1 −1.84+0.11−0.13 0.85 3.23+0.21−0.21×10−6 1.09+0.14−0.14
Table 5.2—Continued
GRB Redshift BAT location T90 Power Law Cutoff Power Law χ2ν Fluence Hardness RA DEC [sec] Photon Index αB Eobspeak[keV] [erg/cm2] Ratio 050724 246.18 -27.52 2.5 −1.99+0.20−0.20 1.20 1.16+0.13−0.13×10−6 0.93+0.22−0.21 050726 200.06 -32.09 33.7 −1.04+0.16−0.15 1.35 1.80+0.15−0.15×10−6 2.71+0.47−0.48 050730 3.97 212.06 -3.74 197.6 −1.56+0.10−0.12 0.76 2.80+0.18−0.17×10−6 1.50+0.18−0.18 050801 204.14 -21.95 19.2 −2.10+0.21−0.26 1.22 3.16+0.45−0.44×10−7 0.80+0.24−0.22 050802 1.71 219.29 27.81 31.3 −1.67+0.14−0.14 0.83 2.09+0.17−0.17×10−6 1.33+0.21−0.21 050803 350.65 5.80 92.6 −1.51+0.10−0.10 0.88 2.42+0.14−0.15×10−6 1.60+0.19−0.18 050813 242.01 11.25 0.4 −1.07+0.39−0.36 1.29 4.63+1.09−1.08×10−8 2.65+1.14−1.14 050814 264.20 46.33 135.4 −1.94+0.16−0.18 1.07 1.91+0.20−0.20×10−6 0.97+0.20−0.19 050815 293.57 9.17 3.3 −1.79+0.24−0.24 1.44 1.11+0.19−0.19×10−7 1.17+0.37−0.34 050819 358.74 24.85 38.3 −2.63+0.28−0.27 1.14 3.80+0.58−0.55×10−7 0.45+0.17−0.15 050820a 2.612 337.40 19.58 240.4 −1.26+0.10−0.10 0.95 4.23+0.26−0.26×10−6 2.13+0.24−0.24 050820b 135.56 -72.67 12.7 (−1.40+0.05−0.04) −0.59+0.23−0.20 101.5+15.3−10.1 0.67 2.25+0.06−0.06×10−6 1.85+0.10−0.10 050822 51.08 -46.02 104.5 −2.51+0.15−0.12 0.99 2.91+0.18−0.18×10−6 0.52+0.08−0.08 050824 0.83 12.24 22.59 26.9 −2.72+0.33−0.38 0.80 3.21+0.59−0.56×10−7 0.39+0.19−0.16 050826 87.73 -2.68 34.7 −1.24+0.25−0.24 0.74 4.96+0.72−0.71×10−7 2.16+0.58−0.58 050827 64.28 18.22 47.6 −1.38+0.09−0.09 0.71 2.14+0.11−0.11×10−6 1.85+0.19−0.19 050904 6.10 13.67 14.14 229.0 −1.39+0.07−0.07 1.15 5.78+0.21−0.21×10−6 1.83+0.13−0.14 050906 52.80 -14.62 0.1 −1.22+0.97−0.93 0.85 6.25+3.07−2.94×10−9 2.23+2.71−1.92 050908 3.35 20.46 -12.97 21.6 −1.92+0.17−0.17 0.83 5.47+0.57−0.56×10−7 1.01+0.20−0.20 050911 13.72 -38.86 168.7 −2.00+0.50−0.60 0.94 6.62+2.35−2.22×10−7 0.91+0.64−0.55 050915a 81.71 -28.03 28.8 −1.46+0.14−0.14 1.26 7.82+0.68−0.68×10−7 1.69+0.27−0.27 050915b 219.10 -67.40 40.9 (−1.93+0.07−0.05) −1.33+0.26−0.28 58.1+9.7−6.2 0.80 3.49+0.13−0.13×10−6 0.97+0.07−0.07 050916 135.93 -51.40 43.9 −1.61+0.22−0.22 0.96 8.80+1.19−1.18×10−7 1.43+0.36−0.36 050922b 5.78 -5.62 270.0 −2.08+0.24−0.20 0.98 2.81+0.36−0.35×10−6 0.85+0.23−0.21 050922c 2.198 317.39 -8.77 4.6 −1.40+0.05−0.05 0.93 1.70+0.05−0.05×10−6 1.82+0.11−0.11 050925 303.48 34.33 0.2 −1.78+0.18−0.18 0.93 8.98+1.06−1.09×10−8 1.19+0.26−0.26
1,2,3
Event data are unavailable for these bursts.
4Because of the brightness, a curvature is clearly observed in the spectrum. A single power law model does not give a good fit to this data.
Time since trigger [s]
102 103 104 105 106 107
N
0 2 4 6 8 10 12 14 16 18
Time since trigger [day]
10-3 10-2 10-1 1 10 102
Time since trigger [s]
102 103 104 105 106 107 ]-1 s-2 Flux [erg cm
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
Time since trigger [day]
10-3 10-2 10-1 1 10 102
X-ray afterglows observed by SAX, XTE, XMM from ’97 to ’04
Figure 5.13: The left panel shows the distribution of the time at which the Swift XRT started actual observations. The events indicated by filled his-togram are follow-up observations for the bursts detected by HETE and IN-TEGRAL satellites. For comparison, the X-ray observations conducted in pre-Swift era are also shown in the right panel. The light curves are repro-duced from the best fit models reported in Frontera (2003).