Distribution of Spectral Lags in Gamma Ray Bursts
a r X i v :a s t r o -p h /0410344v 2 16 O c t 2004
Distribution of Spectral Lags in Gamma Ray Bursts
Li Chen 1
Department of Astronomy,Beijing Normal University,Beijing 100875,P.R.China
chenli@https://www.sodocs.net/doc/bb10225821.html,
Yu-Qing Lou 2
(a)Physics Department and the Tsinghua Center for Astrophysics (THCA),Tsinghua University,
Beijing 100084,China;(b)Department of Astronomy and Astrophysics,The University of Chicago,5640South Ellis Avenue,Chicago,IL 60637USA;(c)National Astronomical Observatories,Chinese Academy of Sciences,A20,Datun Road,Beijing 100012,The People’s
Republic of China
louyq@https://www.sodocs.net/doc/bb10225821.html, and lou@https://www.sodocs.net/doc/bb10225821.html,
Mei Wu 3
Particle Astrophysics Laboratory,Institute of High Energy Physics,Chinese Academy of Sciences,
Beijing 100039,The People’s Republic of China
Jin-Lu Qu 3,Shu-Mei Jia 1and Xue-Juan Yang 1
ABSTRACT
Using the data acquired in the Time To Spill (TTS)mode for long gamma-ray bursts (GRBs)collected by the Burst and Transient Source Experiment on board the Compton Gamma Ray Observatory (BATSE/CGRO ),we have carefully measured spectral lags in time between the low (25?55keV)and high (110?320keV)energy bands of individual pulses contained in 64multi-peak GRBs.We ?nd that the temporal lead by higher-energy γ?ray photons (i.e.,positive lags)is the norm in this selected sample set of long GRBs.While relatively few in number,some pulses of several long GRBs do show negative lags.This distribution of spectral lags in long GRBs is in contrast to that in short GRBs.This apparent di?erence poses challenges and constraints on the physical mechanism(s)of producing long and short GRBs.The relation between the pulse peak count rates and the spectral lags is also examined.Observationally,there seems to be no clear evidence for systematic spectral lag-luminosity connection for pulses within a given long GRB.
Subject headings:Gamma-rays:bursts —gamma-rays:observations —plasmas —radiation mechanism:general —methods:data analysis —shock waves
1.Introduction
Temporal delays in the arrival of low-energy photons relative to that of high-energy photons are well known in the spectra of gamma-ray bursts(GRBs).Link,Epstein&Priedhorsky(1993)used the autocorrelation analysis to investigate temporal properties of GRBs in di?erent energy bands. Cheng,Ma,Cheng,Lu&Zhou(1995)?rst quanti?ed the time delay of GRBs in the soft energy band.Fenimore&Zand(1995)found that the average autocorrelation of GRB temporal histories is a universal function that can measure the timescale as a function of energy.The dependence is a power law in energy with an index of～0.4.This is the?rst quantitative relationship between temporal and spectral structures in GRBs.Band(1997)performed a cross-correlation analysis on a sample of229strongest BATSE GRBs to demonstrate that the hard-to-soft spectral evolution is generic in most bursts.Norris,Marani&Bonnell(2000)estimated spectral lags between the light curves of6GRBs with known redshifts z in the energy ranges of the BATSE channel3 (100?300keV)and channel1(25?50keV),concluding that the pulse peak luminosity and the spectral lagτlag in time anticorrelate with each other and may well be?t with a power law L53≈1.3(τlag/0.01s)?1.15where L53is the GRB luminosity in unit of1053erg s?1.This appears to be the?rst valuable although preliminary information for GRB luminosity based on spectral and temporal properties of gamma-ray observations alone.Another tentative GRB luminosity indicator is the empirical relation between luminosity and variability?rst proposed by Fenimore& Ramirez-Ruiz(2000),indicating a correlation between spectral lags and V(variability)parameter. This correlation was further demonstrated by Schaefer,Deng&Band(2001)by systematically examining the available BATSE data ofτlag and of V for112GRBs.By extrapolating the lag-luminosity relation of GRBs(Ioka&Nakamura2001),Murakami,Yonetoku,Izawa&Ioka(2003) further inferred the star-formation history in the universe out to redshift z～4.
The lag-luminosity relation or the variability-luminosity relation might make GRBs into stan-dard candles as cosmological distance indicator.This does not mean that all GRBs have the same luminosity.In this context,let us look at the cases of Cepheid variables and Type Ia supernovae (SNe Ia).The well-established period-luminosity relation of Cepheid variables allows us to know their intrinsic luminosities from periodicities in their light curves.Similarly,the decline rate of the light curve of a SN Ia may determine its peak luminosity after some corrections and adjustments (Phillips1993;see extensive references in Niemeyer&Truran2000).Now the lag/V-luminosity relation might o?er a possibility of estimating a GRB luminosity based on GRB observations alone. The cosmological signi?cance of this potential Cepheid-like relation is https://www.sodocs.net/doc/bb10225821.html,paring with SNe Ia as cosmological distance indicators,GRB cosmology has at least three apparent advantages (Norris2003;Dai,Liang&Xu2004):(1)much larger redshift z range;(2)much weaker e?ects of dust extinction;and(3)weaker possible luminosity evolution with redshift z.Fenimore&Ramirez-Ruiz(2000)take the lead in estimating the redshifts z for220bright,long duration BATSE GRBs by using V-luminosity relation.Norris(2002)used a two-branch lag-luminosity relationship to yield the number distribution of GRBs in luminosity,distance,and redshift z.It is further inferred that some GRBs are identi?ed to concentrate near the local galactic superplane,including GRB
980425which was known to associate with a supernova.Applying the lag-luminosity relation to 1218GRBs with positive lags,hardness ratios,peak?uxes and durations,Band,Norris&Bonnell (2003)compiled an extensive catalog for GRBs redshifts.Dai et al.(2004)attempted to constrain the mass density of the universe and the nature of dark energy with a sample of12GRBs with known redshifts,peak energies and break times of afterglow light curves.Their results are consis-tent with those from SNe Ia.Undoubtedly,a larger sample expected from the upcoming SWIFT satellite may provide further clues and constraints.
There have been several attempts to interpret the empirical relations for luminosity versus spectral lag or V in GRB observations.Salmonson(2000,2001)proposed that these correlations might be caused by the variety,among GRBs,of relativistic velocities at which emitting regions move toward the observer.He introduced the peak number luminosity N pk(i.e.,photons s?1) instead of the peak luminosity L pk.With this characterization,he not only reproduced the result of Norris et al.(2000),namely L pk∝τ?1.15
lag
but also obtained a better?t for the equivalent relation
N pk∝τ?0.98
lag .For a burst expanding with a Lorentz factorγ?1,he educed N pk∝τ?1
lag
.In terms
of the energy conservation when the radiative cooling dominates,Schaefer(2004)considered that the average cooling rate per particle in the emitting region of the jet should be either equal to the total luminosity L tot over the number of emitting particles(roughly～M jet/m proton)or the time derivative of the mean particle energy E pk,that is:˙E pk=?L tot/(M jet/m proton).Using the relation L tot=L pk?/(4π),where?≈πγ2is the solid angle into which the radiation is beamed at,and evaluating˙E pk by[E pk(T1)?E pk(T3)]/(T1?T3)∝τ?1
lag
,they derived the following relation L∝τ?1lag.On the other hand,Wu&Fenimore(2000)believed that the synchrotron cooling timescale in a magnetized jet is much shorter than the lag timescale.According to the internal shock model of GRBs(Rees&M′e szaros1994),there are three possible sources of time variation structure in GRB pulses:cooling,hydrodynamics,and geometric angular e?ects.Wu&Fenimore argued that cooling is much too fast to account for the observed lags and angular e?ects should be energy independent.Thus,only hydrodynamical processes are responsible for these lags.To be more precise,as magnetic?elds and relativistic?ows are likely to be involved in various ways, relativisitic magnetohydrodynamic(RMHD)processes(e.g.,Lou1992,1993a,1993b,1994,1996, 1998)might be relevant to the understanding these lags.Ioka&Nakamura(2001)argued that the pulse peak luminosity-variability relation might be caused by the variation in viewing angle of the source jet.The correlation between pulse lag or luminosity and jet-break time was noticed by Salmonson&Galama(2002),?rst revealing a connection between a feature of the GRB phase and the afterglow phase.The correlation may be qualitatively understood from models in which the Lorentzγfactor of an RMHD jet decreases as a function of angle away from the jet axis.Kocevski &Liang(2003)established empirically the connection between the GRB spectral evolution rate and spectral lag.They suspected that this may eventually reveal the underlying physical mechanism(s) for the spectral lag-luminosity correlation.
As has been suspected,the spectral lags of GRBs and their evolution are vital to probe the physics of GRB.We do want to know whether the lag-luminosity relation remains to be a
universal feature for GRBs.In fact,Sazonv,Lutovinov&Sunyaev(2004)have found that the peak luminosities of GRBs031203and980425measured from the given cosmological parameter and redshift z are much lower than ones expected with lag-luminosity relation.Perhaps,only a certain kind of GRBs(e.g.,those not associated with SNe)?t in the lag-luminosity relation.We would also like to know whether there are cases of negative lags in long GRBs.Previous observations of spectral lags were usually based on the data with a relatively low time resolution,such as the data acquired in the Discriminator Counts(DISCSC)mode of BATSE,with a time resolution of64ms.As most spectral lags in time are fairly small,typically≤100ms,an analysis of spectral lag properties using 64ms time bin data would appear somewhat coarse and insu?cient.In contrast,the TTS mode data of BATSE provides an opportunity to determine more precise temporal structures of GRB spectral lags.To resolve more?ne spectral lag information from TTS mode data(https://www.sodocs.net/doc/bb10225821.html,gs less than64ms)and especially to examine the distribution and evolution of the spectral lags are the major tasks we would like to pursue in this research work.
This paper is structured as follows.Observations and data analyses are described in§2.The results are presented in§3.In§4,we summarize the conclusions and provide discussions.
2.Database
The BATSE data acquired at both the TTS mode and the DISCSC mode were taken in the following four photon energy bands:25?55keV,55?110keV,110?320keV and>320keV.The two data acquisition modes of operation are fundamentally di?erent:The TTS mode records the time interval for every64γ-ray photons,while the DISCSC modes provides the number ofγ-ray photons in every64ms time interval.
As we would like to infer and estimate spectral lags with a time resolution less than64ms for individual pulses of a GRB,we interpolate the light curves obtained in the TTS mode with a temporal subinterval of8ms resolution under the key assumption that these64photons distribute more or less evenly within each time interval of TTS mode of operation.The empirical reason of binning data into8ms is that the resulting light curve with such a bin size is?ne enough to achieve a reasonable level of signal-to-noise(S/N)ratio.In order to empirically justify the validity of such a temporal interpolation scheme,we have?rst determined the spectral lags of a dozen GRBs based on the data of both TTS and DISCSC modes for comparison with time lags longer than150ms. The results are mutually consistent within estimated error bars.
The procedure of estimating spectral lags of GRBs using a cross-correlation function(CCF) has been widely adopted(e.g.,Link et al.1993;Fenimore et al.1995;Norris et al.2000).The CCF of x1(t)and x2(t)for the time duration of each pulse of GRBs,where x1(t)and x2(t)are respective light curves in two di?erentγ?ray photon energy bands(namely,energy band I:25?55
keV and energy band II:110?320keV),is simply de?ned by
<ν1(t+τ)ν2(t)>
CCF(τ:ν1,ν2)=
?(t?t max)
σr ?exp
exp ?(t?t max)2
w(π/2)1/2
a statistical weight of w i=1/y i,we?t the TTS data for GRBs,taking the pulse width measured
0.1σabove the background(y0or a+bt+ct2)(see Fig.1).For those GRB pulses of irregular shapes, we determine their pulse widths by direct visual examinations.
3.Results of Data Analysis
3.1.Distribution of Spectral Lags in Time
Several thousands of GRBs have been observed by BATSE/CGRO.As we plan to analyze the evolution of pulse spectral lags of long GRBs,we chose those GRBs with well separated multi-pulse pro?les and good S/N ratios.A sample of64multi-peak long GRBs have been carefully selected from the TTS data.We calculate the spectral lags in time for every individual pulse of the selected sample.From the left to right columns in order,Table1lists the GRB trigger number according to the‘BATSE Catalog’,the numeral identi?cation of individual pulse in each GRB event,the pulse peak time(or position)of the low-energy band25?55keV,the peak count rate of the low-energy band25?55keV,the pulse peak time(or position)of the high-energy band110?320keV,the peak count rate of the high-energy band110?320keV,and the inferred spectral lags in time, where the peak count rate is determined by the average of three bins around the maximum.Due to the presence of a Poisson background variation in the light curve,we note that the sign of a lag does not necessarily always accord with that of the di?erence between the peak times of high and low energy bands.
The histogram of spectral lags for341pulses in64GRBs has a distinctly asymmetric sharp peak-like distribution as displayed in Figure2.Also seen from Figure2is the important fact that shorter lags are much more numerous than longer lags.A large majority of spectral lags clearly show earlier arrivals ofγ?ray photons in the high-energy band,with the maximum lag distribution atτ～30ms.In contrast,only some20long GRBs show negative lags for which the absolute values are greater than their errors.Among these cases,there are10and5lags reaching2σand 3σsigni?cant levels,respectively.While most spectral lags are positive,those negative spectral lags,if further con?rmed to be real,would become additional constraints on physical models for GRBs.We have carefully examined those negative lags greater than2σsigni?cant level one by one to make sure that such negative lags are not caused by pulse overlaps.There are two major situations where negative spectral lags may arise.One situation usually occurs at the beginning of a GRB,such as the two GRBs6333and7247,while the other situation happens as spectral lags vary gradually from positive to negative ones,such as the GRBs5773(see Fig.3),7277and7301. The GRB6672is an exception:it began with a positive spectral lag,then negative lags appeared, but returned to positive lags again in the end.Sometimes,the lag of the?rst pulse in a GRB cannot be well determined for the trigger time is not really at the beginning of the burst.
Gupta,Gupta&Bhat(2002)have studied spectral lags for GRBs of short durations.They observed in a sample of156BATSE GRBs with T90(i.e.,90%of the duration time of a GRB)less
than2s.Unlike GRBs of longer durations in our data analysis,they found the percentage of short GRBs with negativeτlag is～26%,which is much higher than our result–only10and5negative spectral lags reaching above2σand3σlevel respectively among341pulses.Meanwhile,over 70%of short GRBs in their data sample have positive spectral lags in pulses.These signi?cantly di?erent distributions in positive and negative pulse spectral lags imply that there might be entirely di?erent physical mechanisms responsible for long and short GRBs.It should be clearly noted that in estimating spectral time lags,there is an algebraic sign di?erence between our notation and that of Gupta et al.(2002)(i.e.,our positive lags are their negative lags and vice versa).
3.2.Temporal Evolution of Spectral Lags
We can hardly see any systematic evolution of spectral lags.In other words,GRB spectral lags di?er from each other in great varieties.The spectral lags of most GRBs do not change in the order of magnitude.However,a few of them varied signi?cantly(e.g.,GRBs5773and6672). Some GRBs show their spectral lags increase(e.g.,GRBs4350and5548)or decrease(e.g.,GRB 5773)regularly with increasing time.Considering the di?erent physical mechanisms for GRBs(e.g., Piran1999;M′e szaros2002),this dissimilarity in the evolution of GRB lags is not strange.
To give a graphic description,we present in Figure4spectral lags versus peak count rates for those long GRBs with more than9pulse peaks,where the count rates are the sum of those in the energy bands I and III.
As shown by Figure4,relations between the count rates and the spectral lags are diverse.For example,in the case of GRB7113,the spectral lags remain almost constant for di?erent count rates.On the other hand,the spectral lags in GRBs6124,6587,7277and7975increase with decreasing count rates.Counter examples of such trend of variation do exist:the spectral lags of GRBs7605and7954tend to increase with increasing count rates.There seems to be no apparent relation between spectral lags and luminosity in general for pulses within a given long GRB.
4.Conclusions
We have calculated the spectral lags in time in pulses of64long GRBs using the TTS data of the BATSE/CGRO in the twoγ?ray photon energy bands25?55keV and110?320keV.For the majority of pulses in GRBs,we see clear signals of earlier arrivals of high-energyγ?ray photons, with a spectral lag distribution peaked at a lag time ofτ～30ms.However,a few pulses do show negative lags,that is,lower-energyγ?ray photons arrived earlier than higher-energyγ?ray photons for pulses in a GRB event.While we cannot provide a rigorous statistical test for these negative lags as we do not know the actual distribution of spectral lags,the existence of such negative spectral lags in time for pulses in GRBs appears to be signi?cant enough.
The dependence of the peak count rates on spectral lags varies signi?cantly on the basis of individual GRB event.
Several GRBs show that their spectral lags either increase or decrease regularly with increasing time.Wu&Fenimore(2000)argued that time lags between di?erent energyγ?ray photons might be mainly determined by the relevant dynamical timescale.Such regular and systematic changes in a GRB may be caused by some special processes associated with the shell ejecta movement.Based on our data analysis,we note that there is no strong evidence for a general correlation between spectral lags and luminosities to hold for pulses within a given GRB event.Although only one case, Hakkila&Gilblin(2004)noted that the peak luminosity ratio between two peaks of GRB5478is not in agreement with the ratio predicted by the lag versus peak luminosity.
We are grateful to the anonymous referee for a careful reading of several versions of this manuscript and for encouragement,constructive criticisms,valuable suggestions and helpful com-ments to improve the manuscript.This work has been partially supported by the National Science Foundation of China(NSFC10273010)and by the State Basic Science Research Projects of China (TG20000776).Y.Q.L.has been supported in part by the ASCI Center for Astrophysical Ther-monuclear Flashes at the Univ.of Chicago under Department of Energy contract B341495,by the Special Funds for Major State Basic Science Research Projects of China,by the THCA,by the Collaborative Research Fund from the National Natural Science Foundation of China(NSFC)for Young Outstanding Overseas Chinese Scholars(NSFC10028306)at the NAOC,Chinese Academy of Sciences,by NSFC grant10373009at the Tsinghua Univ.,and by the Yangtze Endowment from the Ministry of Education at the Tsinghua Univ.A?liated institutions of Y.Q.L.share this contribution.
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Fig. 1.—Upper panel:Two light curves ofγ?ray photon energy bands I and III of GRB4350. Three pulses can be clearly identi?ed in this GRB event and the higher energyγ?ray photons lead the lower ones(i.e.,positive spectral lags).Lower panel:Each pulse may be well?t by Model I. The procedure of determining the width of a pulse is also shown here.
Fig. 2.—The histogram for spectral lags of all341pulses in64GRBs of BATSE/CGRO data acquired in the TTS mode.Positive spectral lags indicate earlier arrivals of higher-energyγ-ray photons.The two energy bands ofγ-ray photons are25?55keV and110?320keV,respectively.
Fig.3.—Two light curves ofγ?ray photons in energy bands I and III of GRB5773.Four pulses can be readily identi?ed in this GRB event.The spectral lags change from positive to negative as can be seen by a direct visual inspection.
Fig. 4.—Variations of count rates versus spectral lags in time for12multi-pulse GRBs of BATSE/CGRO in the TTS mode.The numeral marked at one appropriate corner in each panel is the trigger number of that GRB given by‘The BATSE Catalog Burst Name’.
Table1.Spectral Lags of GRBs of BATSE/CGRO in the TTS Mode GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms)
2191113.719427.04113.9813191.89448±54.4 2116.1720678.17115.7241205.2471.36±54.08
3119.9114846.08119.3521079.44478.4±15.6
4127.768229.48127.526275.81438.08±57.2
5131.937239.85132.045768.08424±16
6134.158348.71133.826385.35435.2±12.96 249115.314463.0614.2318077.1964.64±10.24 218.9827320.1919.0260113.95-5.76±8
321.9639382.0321.2693848.28107.52±8
425.0226597.925.0243470.9333.28±16.64
532.2413462.7632.113356.52120±12
641.489394.7142.688170.37252.8±8.8 67810.947418.090.8720105.5264.29±21.25
20.947418.090.8720105.5268±78
3 1.518440.53 1.4223727.880±8.13
4 4.727413.53 4.716477.24-7.87±11.81
5 6.047125.27 5.9913956.3325.4±8
6 6.657897.96 6.5316235.2515.75±8
77.557274.857.714807.7963.74±10.62
89.398316.69.3416141.5839.51±8
910.917915.5310.8216109.9272.8±8
1013.386987.7213.4710829.1742.05±14.02
1118.276483.8618.187221.3667.2±8 869116.954094.3117.985931.28142.53±16.77 296.15089.7394.956021.75117.6±19.6
3110.785478.87110.977979.88336±16.8
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 9731 3.028807.73 2.1812537.31651.2±10.4 223.417051.824.567036.9112±11.2
10851 3.913195.1 1.8329906.9474.24±74.24
2 6.524122.74 5.7541496.01752±46
37.619972.917.3920160.15172.8±44.8
120410.095554.460.129852.05-0.96±8
20.994407.614956.157.87±8
3 2.984298.2 2.93788.4578.91±11.9
54471 6.5910676.96 6.95087.8496±9.6 213.637045.2513.253737.58207.2±14.4 556810.755865.030.868639.7382.66±39.95
2 1.911073.6 1.8334474.0362.88±48.96
3 2.7512678.03 2.7432657.64-10.4±8
557510.311065.870.2315611.22144.64±13.44
2 6.686076.1
3 6.025046.1696±16
38.6810190.028.5811250.8444.35±8
49.2211655.859.259916.9272.11±8
59.9611351.29.9310029.780±20.8
56011 4.475476.04 2.375029.91563.6±96.6
27.47002.757.139498.09460.1±55.8
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 56281 6.917630.217.189852.22-6.4±43.2
27.78090.297.7111792.7540±8
39.038091.899.0110009-2.82±8
410.0610466.0510.215583.6121.7±8 57261 3.476173.52 3.384185.61112±14
2 5.386131.64 5.036228.2562.09±8
37.377520.29 6.987547.7936.48±8
5731114.256106.9714.036032.8589.86±8 234.316040.3334.127833.284±8
338.696479.9738.587496.6899.2±8 598910.3869045.970.27110138.3870.4±8
2 1.121951.07 1.038125.868.88±8
318.715184.6418.587545.0639.51±8
420.4828495.3320.3611093.8964.92±8
523.7830222.1823.547458.0178.72±8 61241 1.1814047.67 1.1432134.29139.2±8
2 6.1218155.54 6.142918.3418.05±8
37.3417233.617.083909920.4±8
48.2216553.998.6454925.3222.5±8
59.3421629.419.4266180.7119.76±8
610.0219731.3810.0272543.1711.25±8
711.316476.9811.2949369.3710.08±8
812.7721607.1112.7672135.5611.2±8
914.8615829.0814.7827685.8546.77±8
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 6168125.29263.2525.1115846.34144±16.8 227.5412669.2927.2730621.96108.99±41.92
63361 4.369241.58 4.4619402.6418.24±21.89
2 5.413560.22 5.1829018.18239.68±15.84
3 6.7111840.69 6.3812467.35-11.29±14.11
655410.625432.320.234483.81601.6±33.6
28.96558.739.023394.9114.02±8
6587110.139493.229.719390.7788±29.44 211.2511099.4910.9215888.32138.69±8
311.8711200.9311.711877.4394.08±72.24
413.8114157.6213.5830840.6263.36±8.45
514.9712111.715.0527281.214.11±8
616.8114243.1116.9435134.5261.6±11.2
721.515612.3220.6841642.40±11.23
822.6911547.7322.7336169.0610.9±8
923.2116687.8523.1842142.4-6.72±8.4
1024.7817749.8924.8246530.7122.4±8
1126.1113593.4726.3535845.339±12.37
1227.5318791.4226.9852804.52-0.8±8
1329.9915973.0729.9440879.1645.16±8.47
1431.1512667.7731.121965.711.29±8
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 71131 3.3714402.16 3.2828654.0465.09±8
2 6.5117721.437.4232685.9524.1±8
38.7817510.578.7431280.82 4.51±8
412.0319428.9510.2638888.7610.54±8
516.6923126.1816.7165265.06-0.64±8
619.757515.4519.7469960.8922.4±8.4
721.3730765.4521.3654300.8221.89±8
822.5523176.5722.9241652.650.8±8
923.3827241.7624.161314.25-12.2±14.6
1024.6526648.1324.5860490.65-13.54±8
1126.3435474.0926.3483907.049.54±8
1228.0623596.5928.1951085.72-22.46±8
1329.2228968.9829.2262544.488.47±8
1431.1137284.1133.857153.23 5.8±8
1535.3826963.7935.9859132.3425.0±8 724010.666143.530.6215187.18 5.85±8
2 3.029470.0
3 3.0222659.8739.04±8
72771 5.818330.56 5.627526.7578.62±11.23 212.069470.1511.918152.2335.33±11.78
313.1410034.3913.118292.9316.93±8.47
413.939891.2113.948363.95-28.16±24.64
515.569805.2315.5610040.36-28±8.4
616.9410139.8916.910283.65-8.38±8
723.5210585.9123.59677.311.9±11.9
824.3210334.1824.169153.41-10.09±8
925.7814267.5925.7312911.01-15.74±11.81
1027.9410905.5827.3810817.12-92.8±32
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 7343126.2313877.4825.3435294.7233.6±16.8 232.19970.7431.3918137.39235.87±8
338.7311990.9838.329087.97313.82±22.42
477.99681.4576.8811955.1588±36 728110.1819313.040.0835588.556.99±56.45
20.5624548.620.5629636.6817.92±8
3 1.3814841.3
4 1.3911134.64-5.71±8
7605116280.250.826372.4347.2±9.6
2 2.067473.61 2.045608.9579.03±8
3 2.846769.1 2.567014.72109.66±8
4 5.096219.777.335920.665.0±15.8
510.477038.210.456106.6725.34±8.45
612.556421.3212.496028.9467.07±8
713.917052.9714.354542.31-3.87±33.9
816.16217.2516.076229.8268.08±8
916.676533.5916.866651.8539.68±11.9 76511 2.636889.28 2.448383.71130.48±13.5
2 3.987423.85 3.5510129.1212.48±21.6
37.738513.087.498494.76118.88±8
427.587887.4927.426972.15202.24±23.04
528.269172.2928.2111805.6698.78±8
630.029383.2729.719821.42265.57±15.44
731.978674.5131.669437.04162.4±8.4
834.059159.4533.912863.55134.4±8.4 769510.019997.590.1434082.127.68±8
Table1—Continued
GRB Trigger Pulse Peak1Peak Rate1Peak2Peak Rate2Spectral Lag Number ID(i)Position(s)(counts/s)Position(s)(counts/s)in Time(ms) 7906117.2627293.0217.1352387.8154.18±8 220.5862602.420.52130010.5392.22±8.38
322.7162967.5322.62125032.3278.72±8
425.7229331.2925.6430459.1140±8
526.8228886.4826.7819976.0989.38±8
629.6849836.6229.6469791.9159.36±8
731.351076.8531.2563184.793.44±8 795410.8518555.320.836346.0648±8
2 1.2315929.81 1.2453627.1813.76±8
39.4530656.889.4268396.6960.48±8
410.1422981.4410.1253973.0741.92±8
510.7331529.5510.7386100.8337.76±8
61210284.521216411.95-2.25±8
712.8521002.6812.8432831.522.5±8
813.8918092.2513.8934841.6347.24±8
914.8718788.4214.8145039.0524.75±8