Global Properties of X-Ray Flashes and X-Ray-Rich Gamma-Ray Bursts Observed by Swift
T. Sakamoto, D. Hullinger, G. Sato, R. Yamazaki, L. Barbier, S. D. Barthelmy, J. R. Cummings, E. E. Fenimore, N. Gehrels, H. A. Krimm, D. Q. Lamb, C. B. Markwardt, J. P. Osborne, D. M. Palmer, A. M. Parsons, M. Stamatikos, J. Tueller
aa r X i v : . [ a s t r o - ph ] J a n Not to appear in Nonlearned J., 45.
Global Properties of X-Ray Flashes and X-Ray-Rich Gamma-RayBursts Observed by
Swift
T. Sakamoto , , D. Hullinger , G. Sato , , R. Yamazaki , L. Barbier , S. D. Barthelmy , J.R. Cummings , , E. E. Fenimore , N. Gehrels , H. A. Krimm , , D. Q. Lamb C. B.Markwardt , , J. P. Osborne , D. M. Palmer , A. M. Parsons , M. Stamatikos , , J.Tueller , ABSTRACT
We describe and discuss the spectral and temporal characteristics of theprompt emission and X-ray afterglow emission of X-ray flashes (XRFs) and X-ray-rich gamma-ray bursts (XRRs) detected and observed by
Swift between De-cember 2004 and September 2006. We compare these characteristics to a sampleof conventional classical gamma-ray bursts (C-GRBs) observed during the sameperiod. We confirm the correlation between E obspeak and fluence noted by othersand find further evidence that XRFs, XRRs and C-GRBs form a continuum. Wealso confirm that our known redshift sample is consistent with the correlationbetween the peak energy in the GRB rest frame ( E srcpeak ) and the isotropic radi-ated energy ( E iso ), so called the E srcpeak - E iso relation. The spectral properties of NASA Goddard Space Flight Center, Greenbelt, MD 20771 Oak Ridge Associated Universities, P.O. Box 117, Oak Ridge, TN 37831-0117 Joint Center for Astrophysics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore,MD 21250 Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM, 87545 Department of Physics, University of Maryland, College Park, MD 20742 Universities Space Research Association, 10211 Wincopin Circle, Suite 500, Columbia, MD 21044-3432 Institute of Space and Astronautical Science, JAXA, Kanagawa 229-8510, Japan Department of Physics, Hiroshima University, Higashi-Hiroshima, Hiroshima, 739-8526, Japan Moxtek, Inc., 452 West 1260 North, Orem, UT 84057 Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, 60637 Department of Physics and Astronomy, University of Leicester, LE1, 7RH, UK
Subject headings: gamma rays: bursts – X-rays: bursts
1. Introduction
Despite the rich gamma-ray burst (GRB) sample provided by BATSE (e.g., Paciesas et al.1999; Kaneko et al. 2006), Beppo
SAX (e.g., Frontera 2004),
Konus - W ind (e.g., Ulanov et al.2004), and
HET E -2 (e.g., Barraud et al. 2003; Sakamoto et al. 2005), the emission proper-ties of GRBs are still far from being well-understood. In recent years, however, another phe-nomenon that resembles GRBs in almost every way, except that the flux comes mostly fromX rays instead of γ rays, has been discovered and studied. This new class of bursts has beendubbed “X-ray flashes” (XRFs; Heise et al. (2003); Barraud et al. (2003); Sakamoto et al.(2005)), and there is strong evidence to suggest that “classical” GRBs (hereafter C-GRBs)and XRFs are closely-related phenomena. Understanding what physical processes lead totheir differences could yield important insights into their nature and origin.Strohmayer et al. (1998) identified 22 bursts observed by Ginga that occurred betweenMarch of 1987 and October of 1991, and for which the spectra could be reliably analyzed.About 36% of GRBs observed by
Ginga had very soft spectra. They noted that thesebursts resembled BATSE long GRBs in duration and general spectral shape, but the peakenergies of the ν F ν spectrum, E obspeak , extended to lower values than those of the BATSEbursts (Preece et al. 2000; Kaneko et al. 2006). Heise et al. (2003) reported that amongthe sources imaged by the Wide Field Cameras (WFCs) on board Beppo
SAX was a classof fast X-ray transients with durations less than 1000 s that were not “triggered” (that is,detected) by the Gamma Ray Burst Monitor (GRBM). This became their working defini-tion of XRFs. Kippen et al. (2003) searched for C-GRBs and XRFs which were observedsimultaneously by WFC and BATSE. They found 36 C-GRBs and 17 XRFs in a 3.8-yearperiod. Joint WFC and BATSE spectral analysis was performed for the sample, and theyfound that XRFs have a significantly lower E obspeak compared with C-GRBs. They also found 3 –that there is no systematic difference between XRFs and C-GRBs in their low-energy photonindices, high-energy energy photon indices, or durations. The systematic spectral analysisof a sample of 45 HETE-2
GRBs confirmed these spectral and temporal characteristics ofXRFs. It is worth noting that nine out of sixteen XRF samples of
HETE-2 have E obspeak < Swift (Gehrels et al. 2004), only a handful of X-ray afterglows associated with XRFs werereported. D’Alessio et al. (2006) studied the prompt and afterglow emission of XRFs andX-ray-rich GRBs (XRRs) observed by
Beppo
SAX and
HETE-2 . They found that the XRFand XRR afterglow light curves seem to be similar to those of C-GRBs, including the breakfeature in the light curves. They also investigated the off-axis viewing scenarios of XRFsfor the top-hat shaped jet (Yamazaki et al. 2002, 2004), the universal power-law shapedjet (Rossi et al. 2002; Zhang & M´esz´aros 2002; Lamb et al. 2005), and the Gaussian jet(Zhang et al. 2004), and concluded that these models might be consistent with the data.Their sample, however, only contains 9 XRFs/XRRs with measured X-ray afterglows. Fur-thermore, the data points in the X-ray light curves were not well sampled, so that thereare large uncertainties in the decay indices and the overall structures of the light curve inmost cases. Moreover, since the X-ray afterglow observations began > seconds afterthe trigger, their sample is able to say little about the early afterglow properties, whichcontain rich information that can constrain jet models for XRFs. Other XRF theoreticalmodels are the inhomogeneous jet model (Toma et al. 2005), the internal shock emission fromhigh bulk Lorentz factor shells (Mochkovitch et al. 2003; Barraud et al. 2005), the externalshock emission from low bulk Lorentz factor shells (Dermer et al. 1999; Dermer and Mitman2003), and the X-ray emission from the hot cocoon of the GRB jet if viewed from off-axis(M´esz´aros et al. 2002; Woosley, Zhang, & Heger 2003).Because of the sophisticated on-board localization capability of the Swift
Burst AlertTelescope (BAT; Barthelmy et al. (2005)) and the fast spacecraft pointing of
Swift , morethan 90% of
Swift
GRBs have an X-ray afterglow observation from the
Swift
X-Ray Telescope(XRT; Burrows et al. (2005a)) within a few hundred seconds after the trigger. Due to thefact that BAT is sensitive to relatively low energies (15-150 keV) and also a large effectivearea ( ∼ at 20 keV for a source on-axis), BAT is detecting also XRFs and XRRs.However, because of the BAT’s lack of response below 15 keV, it is very challenging to detectXRFs with E obspeak of a few keV which dominated the XRF samples of the Beppo
SAX and
HETE-2 (e.g., Kippen et al. 2003; Sakamoto et al. 2005). Nonetheless,
Swift has an uniquecapability for studying the detailed X-ray afterglow properties just after the burst for XRFsand XRRs with E obspeak &
20 keV for the first time. 4 –The systematic study of the X-ray emissions of GRBs observed by XRT reveals a verycomplex power-law decay behavior consisting typically of an initial very steep decay (t α with − . α . −
2) (e.g., O’Brien et al. 2006; Sakamoto et al. 2007), followed by a shallowdecay ( − . α . − . α . −
1) (e.g., Nousek et al.2006; O’Brien et al. 2006; Willingale et al. 2007), sometimes followed by a much steeperdecay ( α . −
2) (e.g., Willingale et al. 2007) and, in some cases (about 50%), overlaid X-ray flares (e.g. Burrows et al. 2005b; Chincarini et al. 2007; Kocevski et al. 2007). Althoughthere is increasing evidence that the initial very steep decay component α is a tail of theGRB prompt emission (e.g., Liang et al. 2006; Sakamoto et al. 2007), the origin of thephase from a shallow α to a steeper decay α (hereafter a shallow-to-steep decay) is stilla mystery. Moreover, not all GRBs have a shallow-to-steep decay phase in their X-rayafterglow light curves. Thus, it is very important to investigate the X-ray afterglow lightcurves of bursts along with their prompt emission properties to find a difference in theircharacteristics between C-GRBs and XRFs.In this paper, we report the systematic study of the prompt and afterglow emission of10 XRFs and 17 XRRs observed by Swift from December 2004 through September 2006.Although the data from
Swift
BAT is the primary dataset for investigation of the promptemission properties, we also use information from
Konus - W ind and
HETE-2 as reported onthe Gamma-ray burst Coordinate Network or in the literature, when available, to obtainbetter constraints on E obspeak . We focus on X-ray afterglow properties observed by Swift
XRTin this study. In §
2, we discuss our classification of GRBs, the analysis methods of the BATand the XRT data, and the selection criteria of our sample. In § §
4, we show the resultsof the prompt emission and the X-ray afterglow analysis, respectively. We found distinctdifferences between XRFs and C-GRBs in the shape and in the overall luminosity of X-rayafterglows. We discuss the implications of our results in §
5. Our conclusions are summarizedin §
6. We used the cosmological parameters of Ω m = 0.3, Ω Λ = 0.7, and H = 70 km s − Mpc − . The quoted errors are at the 90% confidence level unless we state otherwise.
2. Analysis2.1. Working Definition of
Swift
GRBs and XRFs
The precise working definitions adopted by others who have studied XRFs have tended(understandably) to be based on the characteristics and energy sensitivities of the instru- http://gcn.gsfc.nasa.gov/gcn main.html S X (2– 30 keV)/ S γ (30 – 400 keV) and C-GRBs, XRRs, and XRFs were classified according tothis fluence ratio. Sakamoto et al. (2005) noted a strong correlation between the observedspectral peak energy E obspeak and the fluence ratio. They found that the border E obspeak betweenXRFs and XRRs is ≈
30 keV, and the border E obspeak between XRRs and C-GRBs is ≈ S (25 – 50 keV)/ S (50 – 100 keV) is morenatural and easier to measure with confidence. We therefore chose our working definitionin terms of this ratio. In order to ensure that our definition is close to that adopted bySakamoto et al. (2005), we calculated the fluence ratio of a burst for which the parametersof the Band function (Band et al. 1993) are Γ = −
1, Γ = − .
5, and E obspeak = 30 keV. Thesevalues of Γ and of Γ are typical of the distributions for XRFs, XRRs, and C-GRBs foundby BATSE (Preece et al. 2000; Kaneko et al. 2006), Beppo
SAX (Kippen et al. 2003) and
HETE-2 (Sakamoto et al. 2005). The ratio thus found is 1.32. We likewise calculated thefluence ratio of a burst for which Γ = −
1, Γ = − .
5, and E obspeak = 100 keV, which wasfound to be 0.72. Our working definition of XRFs, XRRs, and C-GRBs thus becomes: S (25 – 50 keV) /S (50 – 100 keV) ≤ .
72 C − GRB0 . < S (25 – 50 keV) /S (50 – 100 keV) ≤ .
32 XRR (1) S (25 – 50 keV) /S (50 – 100 keV) > .
32 XRFTo check the consistency of our definition, we calculated S (25 – 50 keV) and S (50 – 100 keV)of the HETE-2 sample using the best fit time-averaged spectral parameters reported onSakamoto et al. (2005). The 90% error in the fluences is calculated by scaling the associatederror in the normalization of the best fit spectral model. As shown in Figure 1, our definitionis consistent with the
HETE-2 definition of XRFs, XRRs, and C-GRBs (Sakamoto et al.2005). f ( E ) = K E Γ exp[ − E (2 + Γ ) /E peak ] if E < (Γ − Γ ) E peak / (2 + Γ ) and f ( E ) = K E Γ if E ≥ (Γ − Γ ) E peak / (2 + Γ ). Swift
BAT Data Analysis
All the event data from
Swift
BAT is available through HEASARC at Goddard SpaceFlight Center. We used the standard BAT software (HEADAS 6.1.1) and the latest calibra-tion database (CALDB: 2006-05-30). The burst pipeline script, batgrbproduct , was usedto process the BAT event data. The xspec spectral fitting tool (version 11.3.2) was used tofit each spectrum.For the time-averaged spectral analysis, we use the time interval from 0% to 100% of thetotal burst fluence ( t interval) calculated by battblocks . Since the BAT energy responsegenerator, batdrmgen , performs the calculation for a fixed single incident angle of the source,it will be a problem if the position of the source is moving during the time interval selectedfor the spectral analysis due to the spacecraft slew. In this situation, we created the responsematrices for each five second period during the time interval taking into account the positionof the GRB in detector coordinates. We then weighted these response matrices by the fivesecond count rates and created the averaged response matrices using addrmf . Since thespacecraft slews about one degree per second in response to a GRB trigger, we chose fivesecond intervals to calculate the energy response for every five degrees.We fit each spectrum with a power-law (PL) model and a cutoff power-law (CPL)model . The best fit spectral model is determined based on the difference in χ between aPL and a CPL fit. If ∆ χ between a PL and a CPL fit is greater than 6 (∆ χ ≡ χ − χ > t duration of the BAT GRBs (e.g., Sakamoto et al.2008), and determined how many cases a CPL fit gives χ improvements of equal or greaterthan 6 over a PL fit. We used the best fit normal distribution for the power-law photonindex centering on 1.65 with σ of 0.36. The best fit log-normal distribution is used for thefluence centering on S(15–150 keV) = 10 − . erg cm − with σ of S(15–150 keV) = 10 . ergcm − . Also, the best fit log-normal distribution is used for the t duration centering on t = 10 . s with σ of t = 10 . s. The BAT energy response matrix used in the simulationcorresponds to an incident angle of 30 ◦ which is the average of the BAT GRB samples. Wefound equal or higher improvements in χ in 62 simulated spectra out of 10,000. Thus, thechance probability of having an equal or higher ∆ χ of 6 with a CPL model when the parent f ( E ) = K ( E/ Γ where K is the normalization at 50 keV in units of photons cm − s − keV − . f ( E ) = K ( E/ Γ exp( − E (2 + Γ) /E peak ). E obspeak measured from theBAT spectral data are based on a CPL fit, but not on the Band function fit. For XRFs, weapply a constrained Band (C-Band) function method (Sakamoto et al. 2004) to constrain E obspeak . However, there is a systematic problem in the E obspeak values derived by different spectralmodels. In particular, for the bursts for which the true spectral shape is the Band function,there is a known effect that E obspeak derived from a CPL model fit has a systematically highervalue than E obspeak derived from a Band function fit (e.g., Kaneko et al. 2006; Cabrera et al.2007). To investigate this effect, we fit all the BAT GRB spectra for which E obspeak are derivedonly from the BAT data with a Band function with the high-energy photon index fixed atΓ to − .
3. Figure 2 shows E obspeak derived by the Band function fixing Γ = − . E obspeak derived by a CPL or a C-Band function. The E obspeak values derived by the Band functionwith fixing Γ = − . E obspeak values derivedby a C-Band function also agree with E obspeak derived by the Band function with fixing Γ = − . E obspeak derived bydifferent spectral models is negligible compared to that of the statistical error assigned to E obspeak derived from the BAT spectral data alone. Note that the BAT spectral data includethe systematic errors which are introduced to reproduce the canonical spectrum of the Crabnebula observed at various incident angles (Sakamoto et al. 2008).To perform the systematic study using the BAT data, we only selected bursts for whichthe full BAT event data are available . Swift
XRT Data
We constructed a pipeline script to perform the XRT analysis in a systematic way. Thispipeline script analysis is composed of four parts: 1) data download from the
Swift
ScienceData Center (SDC), 2) an image analysis to find the source (X-ray afterglow) and backgroundregions, 3) a temporal analysis to construct and fit the light curve, and 4) a spectral analysis.The screened event data of the Window Timing (WT) mode and the Photon Counting (PC)mode are downloaded from the SDC and used in our pipeline process. For the WT mode,only the data of the first segment number (001) are selected. All available PC mode dataare applied. The standard grades, grades 0-2 for the WT mode and 0-12 for the PC mode,are used in the analysis. The analysis is performed in the 0.3–10 keV band. The detection We exclude bursts such as GRB 050820A, GRB 051008, and GRB 060218 because of incomplete eventdata. ximage assuming that an afterglow is thebrightest X-ray source located within 4 ′ from the BAT on-board position. However, in caseswhere a steady cataloged bright X-ray source is misidentified as an afterglow, we specify thecoordinates of the X-ray afterglow manually. The source region of the PC mode is selectedas a circle of 47 ′′ radius. The background region of the PC mode is an annulus in an outerradius of 150 ′′ and an inner radius of 70 ′′ excluding the background X-ray sources detectedby ximage in circular regions of 47 ′′ radius. For the WT data, the rectangular region of1 . ′ × . ′ is selected as a foreground region using an afterglow position derived from thePC mode data as the center of the region. The background region is selected to be a squareregion of 6 . ′ on a side excluding a 2 . ′ × . ′ rectangular region centered at the afterglowposition. The light curve is binned based on the number of photons required to meet atleast 5 σ for the PC mode and 10 σ for the WT mode in each light curve bin. The light curvefitting starts with a single power-law. Then, additional power-law components are added tominimize χ of the fit. Complicated structures such as X-ray flares are also well fitted withthis algorithm. Although our pipeline script fits the XRT light curve automatically for everyGRB trigger by this algorithm, we excluded the time intervals during the X-ray flares fromthe light curve data by visual inspections before doing the fit by our method because theunderstanding of the overall shape of the light curve is the primary interest in our study.The ancillary response function (ARF) files are created by xrtmkarf for the WT and thePC mode data individually. The spectral fitting is performed by xspec 11.3.2 using anabsorbed power-law model for both the WT and the PC mode data. For an absorptionmodel, we fix the galactic absorption of Dickey and Lockman (1990) at the GRB location,and then, add an additional absorption to the model. We use xspec zwabs model for knownredshift GRBs applying the measured redshift to calculate the absorption associated to thesource frame of GRBs. The spectra are binned to at least 20 counts in each spectral bin by grppha . The conversion factor from a count rate to an unabsorbed 0.3–10 keV energy fluxis also calculated based on the result of the time-integrated spectral analysis.A “pile-up” correction (e.g., Romano et al. 2006; Nousek et al. 2006; Evans et al. 2007)is applied during our pipeline process. It assumes a “pile-up” effect exists whenever theuncorrected count rate in the processed light curve exceeds 0.6 counts/s and 100 counts/sfor the PC and the WT modes respectively. Only the time intervals which are affected bythe “pile-up” as described in our definition above have corrections applied. Although thearea of the spectral region affected by pile-up depends on its count rate, the script alwayseliminates a central area within 7 ′′ radius for the PC data and a 14 ′′ × . ′ box region forthe WT data. The count rate derived from the region excluding the central part is corrected wabs ∗ wabs ∗ pegpwrlw or wabs ∗ zwabs ∗ pegpwrlw model in xspec < < ∼ ′′ and ∼ ′′ , respectively, from the position of the afterglow. Since it is difficultto exclude the contamination from the very closely located background source, we excludedthe last portion of the light curves which have a flattening that is very likely due to thecontamination from the background source. We calculated the fluence ratio between the 25–50 keV and the 50–100 keV bands derivedfrom a PL model using the BAT time-averaged spectrum for all
Swift bursts detected betweenDecember 2004 and September 2006. Then we classified these GRBs using the definitiondescribed in § HETE-2 results (Sakamoto et al.2005), the figure clearly shows that
Swift’s
XRFs, XRRs, and C-GRBs also form a singlebroad distribution. This figure also clearly shows that the ratio of the number of BAT XRFsto BAT XRRs is smaller than that of the
HETE-2
XRF samples. As discussed in Band(2006), the numbers of each GRB class strongly depend on the sensitivity of the instrument.This problem becomes more serious for the instruments which do not cover a wide energyrange, such as the BAT. Thus, we will not discuss the absolute numbers of each GRB classin this paper.Since the determination of E obspeak is crucial for our study, we only select GRBs havingvalues for E obspeak that can be determined from the BAT data alone or from using the datafrom other GRB instruments ( Konus - W ind and
HETE-2 ). Since we can use the C-Bandfunction method for XRFs to constrain E obspeak if the photon index Γ in a PL fit is much steeperthan − < − Konus - W ind (Golenetskii et al. 2006b). Based on these selection criteria, a total of 41GRBs are selected, including 10 XRFs, 17 XRRs, and 14 C-GRBs. 10 –
3. Prompt Emission
The spectral properties of the prompt emission for our 41 GRBs are summarized in Table1. Figure 4 shows the S (25 – 50 keV)/ S (50 – 100 keV) fluence ratio verses E obspeak . As seen inthe figure, E obspeak of the BAT GRBs ranges from a few tens of keV to a few hundreds of keV.This broad continuous distribution of E obspeak is consistent with the Beppo
SAX (Kippen et al.2003) and the
HETE-2 (Barraud et al. 2003; Sakamoto et al. 2005) results. The BAT GRBsfollow well on the curve calculated assuming Γ = − = − . S (25 – 50 keV)/ S (50 – 100 keV) fluence ratio from 0.8 to 1.2 in our sample islikely due to a selection effect. Essentially, we selected bursts based on the measurement of E obspeak for XRRs and C-GRBs. This criterion is more or less equivalent to selecting the burstsbased on their brightness. On the other hand, most of the XRFs were selected based onthe photon index value in a PL fit (Γ < − E obspeak in a CPL fit and the low energy photon indices Γ for theBAT, the HETE-2 and the BATSE samples. For both the
HETE-2 (Sakamoto et al. 2005)and the BATSE (Kaneko et al. 2006) samples, we only plotted GRBs with a CPL modelas the best representative model for the time-averaged spectrum to reduce the systematicdifferences in both Γ and E obspeak due to the different choices of spectral models (Kaneko et al.2006). As seen in the figure, the range of Γ values derived from the BAT data alone areconsistent with the HETE-2 and the BATSE results. In addition, we have confirmed thatthe Γ values for XRFs and XRRs (GRBs with E obspeak <
100 keV) cover the same range as forC-GRBs (GRBs with E obspeak >
100 keV) (Sakamoto et al. 2005).The top panel of Figure 6 shows E obspeak and the 15 – 150 keV fluence, S(15–150 keV), forthe BAT GRBs. We note a correlation between E obspeak and S(15–150 keV). For the purposeof the correlation study, we assigned the median of the 90% confidence interval to be thebest fit value of E obspeak , so that the errors would be symmetric. For cases in which we onlyhave upper limits for E obspeak , we assigned the best fit values of E obspeak to be the median of0 and 90% upper limit, and we assigned the symmetric error to be half that value. Thelinear correlation coefficient between log[S(15 - 150 keV)] and log( E obspeak ) is +0.76 for asample of 41 GRBs using the best fit values. The best fit functions with and without takinginto account the errors are log( E obspeak ) = 3 . +0 . − . + (0 . ± .
03) log[ S (15 −
150 keV)] andlog( E obspeak ) = (5 . ± .
80) + (0 . ± .
14) log[ S (15 −
150 keV)], respectively. 11 –Since the fluence in the 15 – 150 keV band is not a good quantity to examine thecorrelation with E obspeak because of its narrow energy range of integration, we also investigatethe correlation between E obspeak and the fluence in the 1 – 1000 keV band, S(1–1000 keV). ForGRBs which have the measurement of E obspeak by the BAT data alone, we calculate S(1–1000keV) directly from a spectral fitting process using the Band function. Therefore, uncertaintyin the spectral parameters in the Band function, especially in the high-energy photon indexΓ is also taken into account in an error calculation of the fluence. For GRBs for which we use E peak from the literature, we calculated the fluence using the spectral parameters presentedin the literature, and the error associated in the normalization of the best fit spectral modelis used to calculate an error of the fluence. If the reported best fit model is a CPL for theseGRBs, we use Γ = − . E obspeak and S(1–1000 keV).To take into account the errors associated with E obspeak and S(1–1000 keV) in our calcula-tion of the correlation coefficient, we generate 10,000 random numbers assuming a Gaussiandistribution in E obspeak and S(1–1000 keV) of the central value and the error for each GRBin the sample. For GRBs only having the upper limits in E obspeak and/or S(1–1000 keV), weuse an uniform distribution to generate the random numbers. Then, we calculate the linearcorrelation coefficient for the 10,000 burst sample in log[ E obspeak ]-log[S(1–1000 keV)] space, andmake a histogram of the calculated correlation coefficient. The highest peak and 68% pointsfrom the highest value of the histogram are assigned as the central value and 1 σ interval ofthe correlation coefficient. We investigate the correlation coefficient for 1) GRBs with E obspeak from a CPL model (sample A; total 32 GRBs), 2) GRBs with a constrained E obspeak from aC-Band model and a CPL model (sample B; total 37 GRBs), and 3) all 41 GRBs (sampleC) to evaluate the systematic effect of E obspeak due to the different spectral models (C-Bandvs. CPL). The calculated correlation coefficients are +0 . +0 . − . , +0 . +0 . − . , and +0 . +0 . − . (all in 1 σ error) for samples A, B and C respectively. The probabilities of such a correlationoccurring by chance in each sample size are 3 . × − – 2 . × − , 5 . × − – 5 . × − ,and 4 . × − – 2 . × − in the 1 σ interval for samples A, B and C respectively. Thus,the correlation between E obspeak and the fluence is still significant even if we use the fluence inthe 1–1000 keV band, and also take into account the E obspeak derived by the different spectralmodels.The histograms of E obspeak for the Swift /BAT, the
HETE-2 (Sakamoto et al. 2005) andthe BATSE (Kaneko et al. 2006) samples are shown in Figure 7. We notice a difference inthe distributions of E obspeak for the three GRB instruments, especially between the BAT (orthe HETE-2 ) and the BATSE distributions. Applying the two-sample Kolmogorov-Smirnov(K-S) test to the E obspeak distributions for the BAT and the HETE-2 samples, the BAT and theBATSE samples, and the
HETE-2 and the BATSE samples, we find K-S test probabilities 12 –of 0.44, 2 . × − , and 4 . × − respectively. Based on these tests, we may conclude thatthe BATSE GRB samples have a systematically higher E obspeak than the BAT and the HETE-2 samples. This is probably because not only the BATSE energy range is higher than thoseother instruments but also the current BATSE spectral catalog only contains the brightGRBs, therefore systematically selecting higher E obspeak GRBs in the catalog (Kaneko et al.2006).Figure 8 shows E obspeak and S(15–150 keV) of the BAT, the HETE-2 and the BATSEsamples. The fluence in the 15–150 keV band for the
HETE-2 and the BATSE samples iscalculated using the best fit spectral model reported in the catalog (Sakamoto et al. 2005;Kaneko et al. 2006). The error in the fluence for the
HETE-2 and the BATSE samples iscalculated by scaling the error in the normalization of the best fit spectral model. As clearlyseen in the figure, S(15–150 keV) and E obspeak of the BAT GRBs are consistent with boththe HETE-2 and the BATSE samples. The strong correlation between E obspeak and S(15–150keV) still exists by combining the BAT and the HETE-2 samples. The correlation coefficientcombining the BAT and the
HETE-2
GRBs is +0.685 for 83 samples. The probability ofsuch a correlation occurring by chance is < − . The best fit correlation function between E obspeak and S(15–150 keV) with and without taking into account the errors are log( E obspeak ) =2 . +1 . − . + (0 . ± .
02) log[ S (15 −
150 keV)] and log( E obspeak ) = (4 . ± .
63) + (0 . ± .
11) log[ S (15 −
150 keV)], respectively. However, as clearly shown in both Figure 7 and8, the BAT XRFs are not softer (or weaker) than the
HETE-2 sample. This is because ofthe higher observed energy band of the BAT compared to that of the
HETE-2
Wide-fieldX-ray Monitor (WXM; 2–25 keV) (Shirasaki et al. 2003). Thus, caution might be neededfor comparing the BAT and the
HETE-2
XRF samples. It is also clear from the figuresthat the E obspeak distribution of the BATSE sample is systematically higher compared with theGRB samples of the HETE-2 and the BAT because of lacking sensitivity below 20 keV forBATSE.Figure 9 shows the correlation between the peak energy in the GRB rest frame E srcpeak ( ≡ (1+z) E obspeak ) and the isotropic radiated energy E iso . We calculated E srcpeak and E iso for thenine known redshift GRBs in our sample using the BAT data (Table 2). For these GRBs, E iso is derived directly from the spectral fitting using the Band function and integrating from1 keV to 10 MeV at the GRB rest frame. E srcpeak is calculated from E obspeak based on a CPL fit. E srcpeak and E iso values for the remaining Swift
GRBs are extracted from Amati (2006). Thevalues for the pre-
Swift
GRBs are also extracted from Amati (2006). Although our sampleof known redshift GRBs is small, we have confirmed the existence and the extension of the We exclude GRB 060512 because of a less secure measurement of its redshift.
13 – E srcpeak − E iso relation to XRFs and XRRs (GRBs with E srcpeak <
100 keV) for the
Swift
GRBs(Amati et al. 2002; Lamb et al. 2005; Sakamoto et al. 2004, 2006).
4. X-ray Afterglow Emission
The spectral and temporal properties of the 41 X-ray afterglows are summarized inTables 3 and 4.Figure 10 is a composite plot of the X-ray afterglow light curves. Figures 11, 12, and 13show the light curves in each GRB class. As we subsequently discuss in detail, we find thatC-GRBs in our sample tend to have afterglows with shallow decay indices at early timesfollowed by steeper indices at later times, and that the breaks between these two indicesoccur at about 10 − seconds. On the other hand, XRF afterglows show a fairly shallowdecay index until the end of the XRT observation without any significant break. XRRs inour sample were split between these two behaviors, with some manifesting a pattern like theXRF sample and others a pattern like the C-GRB sample.Figure 14 shows the distribution of best-fit excess neutral hydrogen column densities N H over the galactic N H (Dickey and Lockman 1990) and photon indices Γ in the PC modefor our sample of bursts. For known redshift GRBs, the excess N H is calculated in the GRBrest frame. Also shown are the Beppo SAX values gathered and cited by Frontera (2003) forcomparison. There is no systematic differences in N H and Γ between either the BAT andthe pre- Swift
GRBs or between the individual classes of the BAT GRBs. We also confirmeda significant amount of an excess N H for most of our sample (e.g. Campana et al. 2006;Grupe et al. 2007).Figure 15 shows the X-ray temporal index in the 0.3–10 keV band taken 1 day afterthe burst ( α ) plotted against E obspeak for 36 bursts . There is a systematic trend in α ofXRFs, in that they are concentrated around − − . α of XRRs and C-GRBs are much more widely spread. Moreover,there might be a hint that XRRs and C-GRBs have a systematically steeper α thanXRFs. The correlation coefficient between α and E obspeak has been calculated using thesame method for which we apply to calculate the correlation coefficient between E obspeak andthe fluence in the 1–1000 keV band (section 3). We investigate the correlation coefficientfor 1) GRBs without XRFs and GRB 050717 which is outlier with E obspeak of 2 MeV (sample We exclude GRB 050124, GRB 050128, GRB 050219A, GRB 050815, and GRB 060923B for this studybecause there are no X-ray data around 1 day after the burst.
14 –A; total 26 GRBs), 2) GRBs without GRB 050717 (sample B; total 35 GRBs), and 3)all 36 GRBs (sample C) to evaluate the systematic effect due to significantly low or high E obspeak values compared with the rest of the samples. We find the correlation coefficients of − . +0 . − . , − . +0 . − . , and − . +0 . − . (all 1 σ errors) for samples A, B, and C respectively.The probabilities of a chance occurrence in each sample size are 7 . × − − . × − ,2 . × − − . × − , and 5 . × − − . × − in the 1 σ interval for samples A, B, andC respectively. Therefore, if we include the XRF sample, the correlation between α and E obspeak is significant at the > E obspeak is shown in Figure 16. We calculate the correlation coefficient between the X-ray flux and E obspeak by the same method and also for the same three samples as we usedin the correlation study between α and E obspeak (Figure 15). The calculated correlationcoefficients are +0 . +0 . − . , +0 . +0 . − . , and +0 . +0 . − . (all 1 σ errors) for samples A, B, and Crespectively. The chance probabilities are 3 . × − − . × − , 1 . × − − . × − and1 . × − − . × − in 1 σ interval for samples A, B, and C respectively. Therefore, there isno significant correlation between the X-ray flux and E obspeak if we investigate for the whole 36bursts (sample C). However, the correlation becomes significant if we exclude GRB 050717,which is an outlier with E obspeak of 2 MeV. Therefore, there might be a hint of a correlationbetween the X-ray flux at 1 day after the burst and E obspeak .Figure 17 shows the composite X-ray luminosity light curves for the known redshiftGRBs in our sample. The k-correction has been applied to derive the 0.3–10 keV lumi-nosities from the X-ray fluxes of each light curve bin using the best fit PL photon indexof the WT and the PC mode spectra. The time dilation effect of the cosmic expansion istaken into account in these light curves. The colors in the light curves are coded in thefollowing ways: E srcpeak <
100 keV in red (hereafter, XRF src , as XRF in the GRB rest frame),100 keV < E srcpeak <
300 keV in green (hereafter, XRR src , as XRR in the GRB rest frame),and E srcpeak >
300 keV in blue (hereafter, C-GRB src , as C-GRB in the GRB rest frame). Asillustrated in the figure, there are clear separations between XRF src , XRR src and C-GRB src in the overall luminosities of the X-ray light curves. XRFs src have less luminosity by a factorof two or more compared to XRRs src and C-GRBs src . Figure 18 and 19 show the X-raytemporal index and the luminosity respectively at 10 hours after the burst in the GRB restframe as a function of E srcpeak . As seen in the observer’s frame (Figure 15 and 16), there areweak correlations between E srcpeak and the temporal index and the luminosity. The correlation The 0.3–10 keV luminosity, L . − , is calculated by L . − = 4 πd L (1 + z ) − Γ − F . − , where d L is theluminosity distance, Γ is the photon index of the XRT spectra (Table 3) and F . − is the observed flux inthe 0.3-10 keV band.
15 –coefficients between E srcpeak and the temporal index, and between E srcpeak and the luminosity at10 hours are − .
53 and +0 .
72 in both samples of 12 . The chance probabilities are 0.075and 0.008. The global trend in the X-ray luminosity light curve is that XRFs src have atemporal index of α ∼ − src and C-GRBs src .
5. Discussion5.1. Characteristics between the prompt emission and the X-ray afterglow
The results of our analysis strengthen the case that XRFs and long-duration C-GRBs arenot separate and distinct phenomena, but instead are simply ranges along a single continuumdescribing some sort of broader phenomenon. As Figure 4 illustrates, XRFs, XRRs and C-GRBs form a continuum in peak energies E obspeak , with XRF E obspeak values tending to be lowerthan those of XRRs, which in turn are lower than those of C-GRBs. Further evidence of thecontinuous nature of these phenomena comes from the continuity in the fluences of XRFs,XRRs, and C-GRBs, with XRFs tending to manifest lower fluences than XRRs, which tendto have lower fluences than C-GRBs. This is illustrated by the correlation between fluencesand E obspeak shown in Figure 6. We also confirmed the existence of the extension of the E srcpeak - E iso relation (Amati et al. 2002) to XRFs using our limited sample of known redshift GRBs.As we examine the X-ray afterglow properties of XRFs, XRRs and C-GRBs, we notethat their spectral indices and natural hydrogen column densities show no strong correlationto indicate that the spectra of XRF afterglows are distinctly different from those of XRRsor C-GRBs. We do, however, note a possible distinction in the shape of the afterglow lightcurves among XRFs, XRRs, and C-GRBs.We find that the C-GRBs in our sample tend to have afterglows with shallow decayindices ( − . < α < − .
2) at early times followed by steeper indices ( − . < α < − .
2) atlater times, and that the breaks between these two indices occur at about 10 − seconds.XRF afterglows, on the other hand, seem to follow a different pattern. They often show afairly shallow decay index ( − . < α <
0) until the end of the XRT observation without anysignificant break to α < − .
2. The afterglows of the XRRs in our sample were split betweenthese two behaviors, with some manifesting a pattern like the XRF sample and others apattern like the C-GRB sample (Figure 10–13). It is possible that these two patterns form acontinuum, with the break between shallow index and steep index occurring at later times for We exclude GRB 060927 because there is no X-ray data around 10 hours at the GRB rest frame.
16 –XRFs (sometimes after the afterglow has faded below our detection threshold) and at earliertimes for C-GRBs (Figure 15). There is, however, another possibility that this shallow-to-steep decay only exists in high E peak GRBs. Furthermore, using our limited known redshiftGRB sample, we confirmed our findings of the global features of the X-ray afterglows in theX-ray light curves in the GRB rest frame (Figure 18 and 19). Thus, the transition from ashallow to steep decay around 10 − seconds commonly seen in XRT light curves mightsomehow be related to the E peak of its prompt emission (Figure 20). Note that, however,two C-GRBs, GRB 050716 and GRB 060908, show a relatively shallow decay index withoutbreaks up to 10 − seconds after the trigger, and thus have the same afterglow behaviorsas XRFs. As noted by Gendre et al. (2007), we also found differences in the luminosity of theX-ray light curves measured in the GRB rest frame. The luminosity of the global X-raylight curve is brighter when E srcpeak is higher (Figure 17). According to Liang and Zhang(2006), there are two categories in the luminosity evolution of the optical afterglow. Theyfound that the dim group (having optical luminosities at 1 day of ∼ . × ergs s − )all appear at redshifts lower than 1.1. Motivated by their finding, we investigated E srcpeak ofthe Liang and Zhang (2006) sample using the values quoted in Amati (2006). We noticedthat the E srcpeak values from their dim group are <
200 keV. The average E srcpeak of their dimgroup is 96 keV which would be XRFs , src in our classification. On the other hand, theaverage E srcpeak values from the bright group in their sample is 543 keV. Therefore, the trendwhich we found in the overall luminosity of the X-ray light curves might be consistent withthe optical light curves. However, the break from a shallow-to-steep decay in the X-raylight curve which preferentially we see in C-GRBs is not usually observed in the opticalband (e.g., Panaitescu et al. 2006). These similar and distinct characteristics in the X-rayand the optical afterglow light curves, together with the correlation in E srcpeak , are importantcharacteristics in seeking to understand the nature of the shallow-to-steep decay componentin the X-ray afterglow data. There are several theoretical models which explain a shallow-to-steep decay break.They are 1) the energy injection from the central engine or late time internal shocks (e.g.,Nousek et al. 2006; Zhang et al. 2006; Ghisellini et al. 2007; Panaitescu 2007), 2) the geo- 17 –metrical jet models (e.g. Eichler and Granot 2006; Toma et al. 2006), 3) the reverse shock(Genet et al. 2007; Uhm & Beloborodov 2007), 4) time-varying micro-physical parame-ters of the afterglow (Ioka et al. 2006), or 5) the dust scattering of prompt X-ray emission(Shao & Dai 2007). Here we focus on the geometrical jet models which have a tight con-nection between the prompt and afterglow emission properties. Eichler and Granot (2006)investigated a thick ring jet (cross section of a jet in the shape of a ring) observed at slightlyoff-axis from the jet. They can reproduce the shallow-to-steep decay feature in the X-rayafterglow with their thick ring jet model with the appearance of an off-axis afterglow emis-sion at late times. Because of the relativistic beaming effect in this model, the observer,who is observing the ring jet from an off-axis direction, should see a softer prompt emission.Therefore, we would expect to see a shallow-to-steep decay in the X-ray light curve morefrequently for XRFs and rarely for C-GRBs. Our findings contradict this prediction of themodel. Another jet model which can produce a shallow-to-steep decay light curve is aninhomogeneous jet model (Toma et al. 2006). A shallow-to-steep decay phase of the lightcurve may be produced by the superposition of the sub-jet emissions which are launchedslightly off-axis from the observer. The prediction of this jet model is that a shallow-to-steepdecay should co-exist with high E srcpeak in GRBs (an observer has to observe the prompt sub-jet emission from on-axis), and XRFs will have a conventional afterglow light curve. Ourresults agree quite nicely with this prediction. However, considering the non-existence of ashallow-to-steep phase in the optical light curve, it is hard to understand why this shallow-to-steep phase only exists in the X-ray band in the framework of these jet models. Furthersimultaneous X-ray and optical afterglow observations along with a detailed modeling ofafterglows taking into account the prompt emission properties such as E peak will be neededto solve the origin of this mysterious shallow-to-steep decay feature.
6. Conclusion
We have seen that the XRFs observed by
Swift form a continuum with the C-GRBsobserved by
Swift and by other missions, having systematically lower fluences and lower E obspeak than C-GRBs.We have noted that the X-ray light curves of XRFs tend to follow a different “template”than those of C-GRBs. The light curves of the C-GRB afterglows show a break to steeperindices (shallow-to-steep decay) at earlier times, whereas XRF afterglows show no such break.This break is evident in the X-ray but not in the optical light curve. Moreover, the overallluminosity of XRF X-ray afterglows is smaller by a factor of two or more compared to thatof C-GRBs. These distinct differences in the X-ray afterglow between XRFs and C-GRBs 18 –are keys to understanding not only the shallow-to-steep decay phase in the X-ray afterglowbut also the nature of XRFs in an unified picture.We have discussed the geometrical jet models based on the trend which we found thatthe shallow-to-steep break in the X-ray afterglow preferentially is seen in the C-GRB sample.We concluded that none of the jet models can explain the behavior of a shallow-to-steep decayphase observed only in the X-ray afterglow. We also emphasize the importance of havingsimultaneous X-ray and optical afterglow observations along with the characteristics of theprompt emission such as E obspeak to constrain the various geometrical jet models.We would like to thank the anonymous referee for comments and suggestions that ma-terially improved the paper. This research was performed while T.S. participated in a NASAPostdoctoral Program administered by Oak Ridge Associated Universities at NASA God-dard Space Flight Center. R. Y. was supported in part by Grants-in-Aid for ScientificResearch of the Japanese Ministry of Education, Culture, Sports, Science, and Technology18740153. The material of the paper has been improved by the discussions during the work-shop “Implications of Swift’s
Discoveries about Gamma-Ray Bursts” at the Aspen Centerfor Physics. 19 –
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This preprint was prepared with the AAS L A TEX macros v5.2.
Table 1. Prompt Emission Properties of 41 Swift Bursts
GRB T
BAT100 ∗ PL CPL Other S(15-150 keV) ¶ SR23 ✸ Γ K ⋆ χ ⊕ Γ E obspeak ⋄ K † χ ⊕ E obspeak ⋄ Mo/Inst ‡ XRF 050406 6.4 − . +0 . − . ± +7 − C-Band 0 . ± .
17 1 . ± . − . ± . ±
17 58.8 – – – – 17 +6 − C-Band 3 . ± . . ± . − . ± . ± +7 − C-Band 6 . ± . . ± . − . ± . ± +6 − C-Band 3 . ± . . ± . − . ± . ± <
19 C-Band 2 . ± . . ± . − . +0 . − . ± <
33 C-Band 4 . ± . . ± . − . ± . ± − . +1 . − . +5 − +210 − . ± . . ± . − . ± . ± +8 − C-Band 2 . ± . . ± . − . +0 . − . ± < . ± . . ± . − . ± . ± <
23 C-Band 2 . ± . . ± . − . ± .
05 224 ± − . ± . +35 − +10 − ± . ± . − . ± .
08 94 ± − . ± . +19 − +13 − ± . ± . − .
76 1350 166.4 − . ± . +4 − +30 − ± − . ± .
08 28 ± +117 − BAT/KW ± . ± . − . ± . ± . +1 . − . +9 − +1390 − . ± . . ± . − . ± .
06 67 ± − . ± . +17 − +4 − . ± . . ± . − . ± .
14 16 ± − . +0 . − . +45 − +7 − . ± . . ± . − . ± .
07 75 ± − . ± . +19 − +8 − . ± . . ± . − . ± . ± − . +0 . − . +36 − +3 − . ± . . ± . − . ± .
08 74 ± − . ± . +38 − +6 − . ± . . ± . − . ± . ± − . +0 . − . +18 − +4 − . ± . . ± . − . ± .
07 362 ±
13 54.0 – – – – 184 +36 − KW . ± . . ± . − . ± . ± − . +0 . − . +21 − +10 − . ± . . ± . − . ± .
03 67 ± +122 − KW ± . ± . − . ± .
07 103 ± − . ± . +28 − +9 − . ± . . ± . − . ± .
04 62 ± ±
31 KW . ± . . ± . − . ± .
08 52 ± − . ± . +25 − +7 − . ± . . ± . − . ± .
08 213 ±
11 58.7 − . ± . +39 − +23 − . ± . . ± . − . ± .
07 172 ± − . ± . +46 − +14 − . ± . . ± . − . ± .
06 123 ± − . ± . +12 − +15 − . ± . . ± . − . ± .
04 216 ± ±
24 KW . ± . . ± . − . ± .
07 231 ± ±
16 KW . ± . . ± . − . ± .
06 289 ±
10 71.1 – – – – 349 ±
28 KW . ± . . ± . − . ± .
06 72 ± − . ± . +61 − +4 − . ± . . ± . Table 1—Continued
GRB T
BAT100 ∗ PL CPL Other S(15-150 keV) ¶ SR23 ✸ Γ K ⋆ χ ⊕ Γ E obspeak ⋄ K † χ ⊕ E obspeak ⋄ Mo/Inst ‡ GRB 050717 209.2 − . ± .
05 31 ± +1934 − BAT/KW . ± . . ± . − . ± .
06 247 ± +51 − HETE . ± . . ± . − . ± . ± +224 − KW . ± . . ± . − . ± .
04 191 ± +25 − KW ± . ± . − . ± .
09 17 ± − . ± . +75 − ± . ± . . ± . − . ± .
04 155 ± − . ± . +117 − +5 − . ± . . ± . − . ± .
06 103 ± − . ± . +184 − +5 − . ± . . ± . ∗ in seconds. ⋆ in 10 − photons cm − s − keV − . ⋄ in keV. † in 10 − photons cm − s − keV − . ‡ Spectral fitting model used/GRB instrument which reports E obspeak . ¶ BAT 15-150 keV energy fluence in 10 − ergs cm − s − with the BAT best fit model. ✸ A fluence ratio of S(25-50 keV)/S(50-100 keV) derived from a PL fit. ⊕ The degrees of freedom in a PL fit and a CPL fit are 57 and 56 respectively. Morris et al. 2007; E obspeak derived from a CPL model. Golenetskii et al. 2006a, GCN Circ. 5113. E obspeak derived from a CPL model. Golenetskii et al. 2006c, GCN Circ. 5460. E obspeak derived from a CPL model. Golenetskii et al. 2006d, GCN Circ. 5518. E obspeak derived from a Band model. Golenetskii et al. 2005a, GCN Circ. 3152. E obspeak derived from a Band model. Golenetskii et al. 2005b, GCN Circ. 3179. E obspeak derived from a Band model for the first episode. Golenetskii et al. 2005c, GCN Circ. 3518. E obspeak derived from a Band model. Krimm et al. 2007; E obspeak derived from a CPL model. Crew et al. 2005, GCN Circ. 4021. E obspeak derived from a CPL model. Golenetskii et al. 2005d, GCN Circ. 4238. E obspeak derived from a CPL model. Tashiro et al. 2007; E obspeak derived from a CPL model.
26 –Table 2. E srcpeak and E iso derived from the BAT data. The uncertainty is 1 σ .GRB z E srcpeak E iso Instrument(keV) (10 erg)050401 ±
110 41 ± +6 − . +0 . − . BAT050525A 0.606 131 +4 − . +0 . − . BAT050603 ±
107 70 ± <
35 0 . +0 . − . BAT050922C ±
111 6 . ± . ±
200 7 . ± . +63 − . +4 . − . BAT060206 4.048 394 +82 − . +2 . − . BAT060707 3.425 279 +43 − . +2 . − . BAT060908 +224 − . +1 . − . BAT060926 3.20 < . . +3 . − . BAT060927 5.6 475 +77 − . +2 . − . BAT E srcpeak and E iso values from Amati (2006). The high energy photon index Γ of the Band function isfixed at − . Table 3. XRT X-ray spectral properties of 41 Swift Bursts
GRB WT PCt start t stop N H Γ † χ /d.o.f. t start t stop N H Γ † χ /d.o.f.[s] [s] [10 cm − ] [s] [s] [10 cm − ]XRF 050406 92 1 . × – − . . × . × . +5 . − . − . +1 . − . . × < − . +0 . − . . × . +1 . − . − . ± . . +1 . . − . +0 . − . . × . +1 . − . − . +0 . − . < . − . +0 . − . . × < − . +0 . − . . × . × . +1 . − . − . ± . . × . +6 . − . < − . . × . +1 . − . − . +0 . − . . ± . − . ± . . × < . − . ± . . +0 . − . − . +0 . − . . × . × < . − . +0 . − . . × +2 − − . +0 . − . +28 − − . +0 . − . . × . × < − . +0 . − . . × . × . ± . − . +0 . − . . × . × . +0 . − . − . ± . . × . × +18 − < − . . × . × < − . +0 . − . . × . × ± − . ± . . × . ± . − . +0 . − . . × . × . ± . − . ± . . × < − . +0 . − . . × < . − . +0 . − . . × < − . +0 . − . < − . +0 . − . . × < − . +0 . − . . ± . − . +0 . − . . × . × . +0 . − . − . ± . . × < − . +0 . − . . × < − . +0 . − . . × +8 − − . +0 . − . . × . × +11 − − . +0 . − . . ± . − . ± .
07 162.1/172 662 5 . × . +0 . − . − . ± . − . . × . × < . − . +0 . − . < − . +0 . − . . × ± − . ± . . × . ± . − . ± .
05 363.1/280 1 . × . × . ± . − . ± .
08 169.6/158XRR 060825 199 1 . × < − . +0 . − . . × +4 − − . ± . . × . +0 . − . − . +0 . − . . × . × +2 − − . +0 . − . . × < − . ± . . × . × < . − . +0 . − . . × . × . +0 . − . − . ± . . × . +0 . − . − . ± . . × < − . +0 . − . . × . × . +0 . − . − . +0 . − . . × . × . +0 . − . − . ± . . × ± − . ± .
04 277.1/266 8 . × . × +17 − − . ± . . × . × ± − . +0 . − . Table 3—Continued
GRB WT PCt start t stop N H Γ † χ /d.o.f. t start t stop N H Γ † χ /d.o.f.[s] [s] [10 cm − ] [s] [s] [10 cm − ]GRB 050716 105 7 . × < . − . +0 . − . . × . × . ± . − . ± . . × . +0 . − . − . ± . . × < − . +0 . − . . × < − . ± .
07 107.9/124 3998 5 . × ± − . +0 . − . . × < − . ± . . × . × ± − . ± .
07 130.7/129GRB 060105 97 4 . × . ± . − . ± .
03 527.6/496 1 . × . × . ± . − . ± . . × . ± . − . +0 . − . . × . × . ± . − . +0 . − . . × . ± . − . ± .
08 167.1/163 4 . × . × . ± . − . ± . . × < − . ± . . × . × < − . +0 . − . † The definition of the photon index, Γ, is based on the spectral model: f(E) = KE Γ . Table 4. XRT X-ray temporal properties of 41 Swift Bursts
GRB t min t max α ini ( ⋆ ) t inibr ( ⋄ ) α ini ( † ) α fin , ( ∗ ) t finbr ( ◦ ) α fin , ( • ) χ /d.o.f.[s] [s] [s] [s]XRF 050406 170 1 . × − . ± . − . ± . . × − . ± . ± − . ± .
04 – 7700 ± − . ± .
03 86.2/79XRF 050714B 163 8 . × − . ± . ± − . ± . − . ± .
07 27.1/15XRF 050819 154 4 . × − . ± . ± − . ± . . ± .
50 (2 . ± . × − . ± . . × − . ± . . ± . × − . ± .
09 – – – 36.6/24XRF 060219 129 3 . × − . ± . ± − . ± . ± − . ± . . × − . ± . ± − . ± .
04 – – – 70.3/61XRF 060512 115 2 . × − . ± .
03 – – – – – 14.1/13XRF 060923B 145 5820 − . ± .
07 – – – – – 6.6/8XRF 060926 192 2 . × − . ± . ± − . ± . . × − . ± .
04 – – – – – 37.1/28XRR 050410 246 6 . × − . ± .
09 – – – – – 6.4/4XRR 050525A 77 2 . × − . ± . − . ± .
06 – – – 29.6/27XRR 050713A 330 9 . × − . ± .
00 1450 − . ± .
07 – (4 . ± . × − . ± . . × − . ± . . × − . ± . ± − . ± . − . ± . . ± . × − . ± . . × − . ± . ± − . ± . . × − . ± .
04 – – – – – 27.3/27XRR 060115 122 3 . × − . ± . ± − . ± . − . ± . . ± . × − . ± . . × − . ± . . × − . ± . . × − ± − . ± . ± − . ± .
09 72.1/63XRR 060510A 105 5 . × − ± ± − . ± .
06 – 5500 ± − . ± .
04 161.8/156XRR 060707 207 2 . × − . ± . ± − . ± . . ± . × − . ± . . × − . ± .
05 940 ± − . ± . − . ± .
06 (4 . ± . × − . ± .
07 197.9/185XRR 060825 108 4 . × − . ± .
04 – – – – – 10.7/7XRR 060904A 83 1 . × − . ± . ± − . ± . . × − . ± .
06 4400 ± − . ± . . × . × − . ± . . × − . ± . ± − . ± .
04 – – – 138.7/128GRB 050219A 116 2 . × − . ± . ± − . ± .
07 – – – 28.0/11GRB 050326 3350 1 . × − . ± .
05 – – – – – 15.6/21GRB 050401 136 7 . × − . ± .
04 840 ± − . ± .
05 – 3440 ± − . ± . . × . × − . ± . . × − . ± .
04 – – – – – 31.8/34
Table 4—Continued
GRB t min t max α ini ( ⋆ ) t inibr ( ⋄ ) α ini ( † ) α fin , ( ∗ ) t finbr ( ◦ ) α fin , ( • ) χ /d.o.f.[s] [s] [s] [s]GRB 050717 93 5 . × − . ± . ± − . ± .
05 – – – 49.8/49GRB 050922C 119 5 . × − . ± . ± − . ± .
03 – (2 . ± . × − . ± . . × − . ± . ± − . ± . − . ± .
07 (5 . ± . × − . ± .
06 179.5/152GRB 060105 97 3 . × − . ± .
06 199 ± . ± . − . ± . . ± . × − . ± . . × − . ± .
08 5170 ± − . ± .
80 – 6670 ± − . ± .
09 44.4/48GRB 060813 115 1 . × − . ± .
05 1680 ± − . ± .
04 – (5 . ± . × − . ± . . × − . ± .
06 875 ± − . ± .
09 – (1 . ± . × − . ± . ⋆ The decay index of the first power-law component. For most of cases, this component corresponds to the very steep decay α as discussed in § ⋄ The break time of the first component in seconds after the BAT trigger. † The post break decay power-law index of the first component. For most cases, this component corresponds to the shallow decay α as discussed in § ∗ The pre-break decay index of the last component. ◦ The break time of the last component in seconds after the BAT trigger. For most cases, this component corresponds to either the shallow decay α or the steeper decay α , as discussed in § • The post break decay power-law index of the last component. For most cases, this component corresponds to either the steeper decay α or the muchsteeper decay α , as discussed in §
31 –Fig. 1.— S (2–30 keV)/ S (30–400 keV) and S (25–50 keV)/ S (50–100 keV) fluence ratios of HETE-2 bursts. The dashed and dash-dotted lines correspond to the borders between C-GRBs and XRRs, and between XRRs and XRFs, respectively. 32 –Fig. 2.— The relationship between E obspeak derived by the Band function with a fixed high-energy photon index Γ = − . E obspeak derived by the C-Band function or a CPL model. 33 –Fig. 3.— Distributions of the fluence ratio S (25 −
50 keV) /S (50 −
100 keV) for the BAT (top)and the
HETE-2 (bottom). The dashed lines corresponds to the borders between C-GRBsand XRRs, and between XRRs and XRFs. 34 –Fig. 4.— S (25 – 50 keV)/ S (50 – 100 keV) fluence ratios and E obspeak values of BAT-detectedbursts. The dashed line shows the fluence ratios as a function of E obspeak assuming Γ = − = − . E obspeak in a CPL model. Thesamples of BAT, HETE-2 , and BATSE are shown in black circles, red squares, and greentriangles, respectively. 36 –Fig. 6.— A plot of the 15 – 150 keV fluence and peak spectral energy E obspeak of XRFs(red), XRRs (green), and C-GRBs (blue) detected by BAT. The dashed and dash-dottedlines are the best fit to the data with and without taking into account the errors, andare given by log( E obspeak ) = 3 . +0 . − . + (0 . ± .
13) log( S (15 −
150 keV)) and log( E obspeak ) =(5 . ± .
80) + (0 . ± .
14) log( S (15 −
150 keV)). Those bursts for which E obspeak is derivedfrom a constrained Band function, a CPL, and the Band function are marked as squares,circles, and triangles, respectively. 37 –Fig. 7.— Distribution of E peak for the Swift /BAT, the
HETE-2 , and the BATSE samples.The white, blue and red histograms are E peak derived by the constrained Band function, aCPL model, and the Band function respectively. The left side arrows are E peak with upperlimits. 38 –Fig. 8.— Top: A plot of the 15 – 150 keV fluence and peak spectral energy E obspeak for BAT(black) and HETE-2 (red) samples. Bottom: A plot of the 15 – 150 keV fluence and peakspectral energy E obspeak for BAT (black), HETE-2 (red) and BATSE (green) samples. Thedashed and dash-dotted line are the best fit to the BAT and the
HETE-2 data with andwithout taking into account the errors, and are given by log( E obspeak ) = 2 . +0 . − . + (0 . ± .
02) log( S (15 −
150 keV)) and log( E obspeak ) = (4 . ± . . ± .
11) log( S (15 −
150 keV)). 39 –Fig. 9.— Isotropic equivalent energy, E iso vs. the peak energy in the GRB rest frame, E srcpeak for the known redshift BAT GRBs in this work (red circles), pre- Swift
GRBs (black dots)and the known redshift
Swift
GRBs observed by
Konus - W ind or HETE-2 (blue triangles).The dashed line is the best fit correlation reported by Amati (2006) ( E srcpeak = 95 keV × (cid:16) E iso ergs (cid:17) . ). 40 –Fig. 10.— A composite plot of the 0.3 – 10 keV fluxes of the X-ray afterglow light curves ofthe XRFs (red), XRRs (green), and C-GRBs (blue) in our sample. 41 –Fig. 11.— A composite plot of the 0.3 – 10 keV X-ray afterglow light curves of XRFs. 42 –Fig. 12.— A composite plot of the 0.3 – 10 keV X-ray afterglow light curves of XRRs. 43 –Fig. 13.— A composite plot of the 0.3 – 10 keV X-ray afterglow light curves of C-GRBs. 44 –Fig. 14.— A plot of the best-fit neutral hydrogen column densities N H and photon indicesΓ of X-ray afterglows in our sample, along with values taken from Frontera (2003). Thevalues plotted here of the Swift sample are taken from the PC mode spectra.
Swift
XRFs,XRRs, C-GRBs and non-
Swift samples are shown in red circles, green squares, blue trianglesand black dots, respectively. 45 –Fig. 15.— A plot of the temporal decay indices measured 1 day after the burst and E obspeak of XRFs (red), XRRs (green) and C-GRBs (blue). E obspeak values derived from a constrained Band function, a CPL, and the Band function are marked as stars, circles, and squares,respectively. 46 –Fig. 16.— A plot of the X-ray unabsorbed flux measured 1 day after the burst and E obspeak of XRFs (red), XRRs (green) and C-GRBs (blue). E obspeak values derived from a constrained Band function, a CPL, and the Band function are marked as stars, circles, and squares,respectively. 47 –Fig. 17.— The composite X-ray luminosity afterglow light curves for known redshift GRBsin our sample. GRBs with E srcpeak <
100 keV, 100 keV < E srcpeak <
300 keV, and E srcpeak > BAT0 refers to the BAT trigger time. 48 –Fig. 18.— A plot of the X-ray temporal index measured at 10 hours after the burst in theGRB rest frame and E srcpeak . 49 –Fig. 19.— A plot of the 0.3–10 keV luminosity measured at 10 hours after the burst in theGRB rest frame and E srcpeak . 50 – XRFC−GRB Time ν L Fig. 20.— A schematic figure of XRF and C-GRB X-ray afterglow light curves. C-GRBafterglows tend to have a shallow index followed by a steeper index, with a break around10 −4