The Complete BATSE Spectral Catalog of Bright Gamma-Ray Burs

a r X i v :a s t r o -p h /0605427v 1 17 M a y 2006The Complete Spectral Catalog of Bright BATSE Gamma-Ray Bursts Yuki Kaneko 1,Robert D.Preece 2,Michael S.Briggs 2,William S.Paciesas 2,Charles A.Meegan 3,David L.Band 4ABSTRACT We present a systematic spectral analysis of 350bright Gamma-Ray Bursts (GRBs)observed with the Burst and Transient Source Experiment (BATSE;～30keV –2MeV)with high temporal and spectral resolution.Our sample was selected from the complete set of 2704BATSE GRBs based on their energy ?u-ence or peak photon ?ux values to assure good statistics,and included 17short GRBs.To obtain well-constrained spectral parameters,several photon models were used to ?t each spectrum.We compared spectral parameters resulting from the ?ts using di?erent models,and the spectral parameters that best represent each spectrum were statistically determined,taking into account the parameter-ization di?erences among the models.A thorough analysis was performed on 350time-integrated and 8459time-resolved burst spectra,and the e?ects of in-tegration times in determining the spectral parameters were 0062af21bcd126fff7050bf5ing the results,we studied correlations among spectral parameters and their evolution pattern within each burst.The resulting spectral catalog is the most compre-hensive study of spectral properties of GRB prompt emission to date,and is available electronically from the High-Energy Astrophysics Science Archive Re-search Center (HEASARC).The catalog provides reliable constraints on particle acceleration and emission mechanisms in GRBs.

Subject headings:Catalog –gamma-rays:bursts

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1.Introduction

In recent years,multi-wavelength observations of afterglow emission of Gamma-Ray Bursts(GRBs)have provided great advancement in our knowledge of GRB progenitor,af-terglow emission mechanism,and their environment.Nonetheless,the physical mechanism that creates the prompt gamma-ray emission with extremely short variability is still not re-solved,thus understanding GRB prompt emission spectra remains crucial to revealing their true nature.GRB spectral analysis attempts to empirically characterize the spectra,which are generally well described,in the energy range of～10keV to a few MeV,by two power laws joined smoothly at certain energies(Band et al.1993).The spectral parameters(the power-law indices and the peak energy in the power density spectrum)are then used to infer the GRB emission and particle acceleration mechanisms.

Currently,the most favored GRB emission mechanism is the simple emission scenario of optically-thin synchrotron radiation by shock-accelerated electrons(“synchrotron shock model”;Tavani1996).This simple theoretical model,however,has previously been chal-lenged by the observations in the context of GRB prompt emission(Preece et al.1998a,b, 2000;Ghirlanda et al.2002;Lloyd-Ronning&Petrosian2002).While the synchrotron shock model can account for many of the observed spectra,a considerable number of spectra ex-hibit behavior inconsistent with this theoretical model.Meanwhile,it is also true that many observed spectra could be?tted with various photon models statistically as well as each other,due to the limited spectral resolution of available data and detector sensitivity.Since the photon models usually used in GRB spectral analysis are parameterized di?erently,the resulting spectral parameters are found to be highly dependent on photon model choices (Preece et al.2002;Ghirlanda et al.2002).Additionally,to deduce the emission mecha-nism from observations,spectra with?ne time resolution are necessary because of the short timescales involved in typical emission processes(i.e.,the radiative cooling time,dynamical time,or acceleration time).This is also indicated by the extremely short variability observed in GRB lightcurves(e.g.,Bhat et al.1992),although the detectors’?nest time resolution is still longer than the shortest physical timescales involved to produce GRBs.The inte-gration times of spectra certainly depend on the capabilities of the detector systems as well as the brightness of events and photon?ux evolution.GRB spectral analyses,therefore, have been performed on various timescales,yet a comprehensive study of the relations be-tween time-averaged and time-resolved spectra,and the e?ects of various integration times on spectral properties has not been done.Thus,in order for the spectral parameters to meaningfully constrain the physical mechanisms,a comprehensive spectral study with?nest possible spectral and temporal resolution,using various photon models,should be carried out with a su?ciently large database.

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Among all the gamma-ray experiments that have detected GRBs,the Burst and Tran-sient Source Experiment(BATSE;Fishman et al.1989),aboard the Compton Gamma-Ray Observatory(CGRO;Gehrels,Chipman,&Kni?en1994),provided the largest GRB database from a single experiment,consisting of observational data for2704GRBs(M.S. Briggs in preparation).For many of the BATSE GRBs,high time and energy resolution data are available.BATSE also provided wider energy coverage than current GRB missions such as HETE-2and Swift.The BATSE data,therefore,are the most suitable for detailed spec-tral studies of GRB prompt emission,both in quantity and quality.The previous BATSE GRB spectral catalog(Preece et al.2000,SP1hereafter)consisted of5500time-resolved spectra from156bright GRBs that occurred before October1998.The SP1burst sample was selected from a set of1771GRBs(from the BATSE4B catalog(Paciesas et al.1999) and the“current”catalog available online1),nearly1000bursts less than what is currently available in the complete database.The sample was also limited to the bursts that pro-vided more than eight spectra and therefore,excluded relatively shorter and weaker bursts. In addition,a combination of the Large Area Detector(LAD)and Spectroscopy Detector (SD)data was used,no time-integrated spectral?t(i.e.,spectrum with integration time of the burst duration)results were presented,and only one photon model was?tted to each spectrum.Finally,the mathematical di?erences in parameterization of each model were not taken into account to obtain corrected overall statistics of the analysis results.

We present in this paper the high-energy resolution spectral analysis of350bright BATSE GRBs with?ne time resolution.The main objective of this work is to obtain con-sistent spectral properties of GRB prompt emission with su?ciently good statistics.This is done by a systematic analysis of the large sample of GRB spectra,using a set of pho-ton models,all?tted to each spectrum.Our spectral sample includes both time-resolved and time-integrated spectra for each burst:the time-resolved spectra within each burst has the best possible time resolution for the high-energy resolution data types used,and the time-integrated spectra are the sum of the resolved spectra within the bursts,covering entire duration of the bursts.We obtain well-constrained spectral properties by studying characteristics of each photon model,taking into account the parameterization di?erences, and statistically determining the best-?t model for each spectrum.The analysis performed here is much more comprehensive and consistent than that of SP1in the sense that(i)only LAD data are used,(ii)the burst sample selections are more objective,(iii)?ve di?erent photon models are?tted to each spectrum,both time-integrated and time-resolved,and(iv) the best-?t parameters of each spectrum are statistically determined.The use of various models allows us to compare the behavior of di?erent models as well as to obtain unbiased

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statistics for the spectral parameters.We also note that the BATSE data and the Detector Response Matrices(DRMs)used here have been regenerated since the publication of SP1, with a re?ned detector calibration database.This provided more precise LAD energy edges, thus assuring the improved accuracy of the spectral analysis.

Since our sample only includes bright bursts,there may be some bias in our analysis results.As reported previously in literature,there is a tendency of bright bursts being spectrally harder than dimmer bursts(e.g.,Nemiro?et al.1994;Mallozzi et al.1995;Dezalay et al.1997).Therefore,it is likely that our sample of bright bursts belongs to the harder side of the overall BATSE GRB sample,on average(e.g.,Lloyd,Petrosian&Mallozzi2000). It is particularly important to keep this in mind when studying global correlations with our spectral analysis results.Our selection criteria also excludes many bright short bursts with duration much less than a second.As a result,only～5%of our sample are short bursts (duration<2s)while short bursts comprises～19%of the entire BATSE GRB sample.

The paper is organized in the following manner.We?rst describe the burst sample and analysis interval selection methodology in§2.The details of the spectral analysis methods are then discussed in§3,including descriptions of the photon models used.We also discuss our simulation results in§4,which were performed to assist us in interpreting the analysis results correctly.Finally,the analysis results are presented in§5and summarized in§6. We note that there are two ways of identifying a BATSE burst;by the GRB name(“GRB yymmdd”)and by the BATSE trigger number.We use both the names and trigger numbers to refer to inpidual GRBs throughout this paper2.

2.Selection Methodology

During its nine-year lifetime that ended in June2000,BATSE triggered on a total of8021gamma-ray transient events,of which2704events were identi?ed as GRBs.The BATSE detectors were sensitive enough to detect relatively weak GRBs down to a peak photon?ux in256ms of～0.3s?1cm?2(50–300keV)and a total energy?uence in25–2000keV of～10?8ergs cm?2.Unfortunately,many dim bursts do not provide enough signal above background for high energy resolution spectral analysis,particularly for time-resolved spectroscopy.Therefore,we need to select and limit our analysis to GRBs with

lookup

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su?cient signal.In addition,the available data types and data ranges vary for each burst. In this section,we describe the methodology employed for the burst selection,the data type selection,and time and energy interval selections.

2.1.Burst Sample Selection

The primary selection was made based on the peak photon?ux and the total energy ?uence in the BATSE4B catalog(Paciesas et al.1999),as well as the current BATSE GRB catalog1for the post-4B bursts.The catalogs list a total of2702GRBs,of which two were later identi?ed as non-GRBs(trigger numbers5458and7523).Additionally,there are four triggered events that were later identi?ed as GRBs(trigger numbers1505,2580,3452,and 3934),bringing the total number of BATSE GRBs to2704.The number is consistent with the?nal BATSE5B catalog(M.S.Briggs et al.in preparation).Our sample was selected from these2704bursts.The burst selection criteria are a peak photon?ux in256ms(50–300keV)greater than10photons s?1cm?2or a total energy?uence in the summed energy range(～20–2000keV)larger than2.0×10?5ergs s?1.Having the criteria in either the peak photon?ux or total energy?uence allows inclusion of short bright bursts as well as long bursts with low peak?ux.The peak photon?ux criterion remains the same as SP1, although it was misstated in SP1as a1024-ms integration time.The energy?uence criterion has been lowered from the value used in SP1so as to include more bursts,while still securing su?ciently good statistics.A total of298GRBs satis?ed these criteria.

In addition,573GRBs out of2704do not have?ux/?uence values published in any BATSE GRB catalog,mainly due to gaps in the four-channel discriminator data that were used to obtain the?ux/?uence values.Nonetheless,for many of these bursts,?ner energy-resolution data are still available for spectral analysis,and some are bright enough to be included in this work.Therefore,we estimated the photon?ux and the energy?uence values for the bursts with no published?ux/?uence values,using available data.To estimate the peak photon?ux and energy?uence for such bursts,we used16-channel MER data(see§2.3 below for the description of the data type)binned to a256-ms integration time and?tted with a smoothly-broken power-law model(described later in§3.2.5).The peak photon?ux values(in256ms,～50–300keV)and the total energy?uence values(in～30–1900keV) were calculated from the?tted spectra.We note that using other photon models barely changed the outcome.There were some cases where MER data were not available but either HERB or CONT data existed.Most of these cases,however,turned out to be noticeably very weak,or else all of the available data were not complete,and therefore did not qualify for inclusion.In this way,55GRBs yielded peak photon?ux or total energy?uence values

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well above our threshold criteria,and were therefore included in this work.

Out of these selected bright bursts,we found two cases(trigger numbers3366and7835) in which the published?ux/?uence values were incorrect and the actual?ux/?uence values were much lower than the criteria used here.Consequently,these two bursts were excluded. We also found one case(trigger number5614,peak photon?ux=182photons s?1cm?2)in which the burst was so bright that the indication of possible pulse pile-up was seen in the energy spectra of all available detectors and the data were not usable.Thus,this burst was also excluded from this work.The resulting total number of GRBs included in this spectral analysis was350.The GRBs are listed in Table1,along with the data types,time and energy intervals,and numbers of time-resolved spectra contained.

2.2.Detector Selection

BATSE was speci?cally designed to detect GRBs and to study their temporal and spec-tral characteristics in great resolution.In order to increase the GRB detection probability, BATSE consisted of eight modules that were located at the corners of the CGRO spacecraft, so as to cover the entire4πsteradian of sky.Each module comprised two types of detec-tors;LAD and SD.They were both NaI(Tl)scintillation detectors of di?erent dimensions designed to achieve di?erent scienti?c goals.The LADs were50.8cm in diameter and1.27 cm in thickness,and provided burst triggering and burst localizations with high sensitivity. They were gain-stabilized to cover the energy range of～30keV–2MeV.The SDs were 12.7cm in diameter and7.62cm in thickness,and provided a higher energy resolution in～10keV–10MeV,depending on the gain of each detector at the time of a burst trigger.

In this spectral analysis,only the LAD data are used,mainly to take advantage of its larger e?ective area(Fishman et al.1989).Another reason that only the LAD data are used is due to a problem recently identi?ed in the SD DRMs at energies above～3MeV(Kaneko 2005).These problems could give rise to uncertainties in the SD DRMs and make SD data unreliable for spectral analysis at high energies.Moreover,limiting to one type of detector eliminates systematic uncertainties arising from di?erent detector characteristics,and thus keeps the analysis more uniform.For each burst,the data from the LAD with the highest counts are used.

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2.3.Data Type Selection

The LADs provided various types of data products to be used for various purposes. The data were collected in either burst mode or non-burst mode.The burst mode data accumulation started when a burst was triggered,whereas the non-burst mode data were usually continuous,except for possible telemetry gaps.The burst mode data generally provided higher resolution either in energy or in time than the non-burst mode data.The three LAD data types used in this work,in order of priority,are High Energy Resolution Burst data(HERB),Medium Energy Resolution data(MER),and Continuous data(CONT). The characteristics of each data type are listed in Table2(see SP1for more complete list of BATSE burst data types).The HERB and MER data are burst-mode data,for which the acquisition began at the time of a burst trigger,whereas CONT was continuous,non-burst mode data.The accumulation time of the HERB data is rate dependent,with minimum time-to-spill of128ms with a64-ms increment.HERB provides the highest energy resolution consisting of～120usable energy channels in energy range of～30–2000keV with modest sub-second time resolution,and thus is used as the primary data type.For each burst, the HERB data for the brightest LAD provides the?nest time resolution,and was always selected for the analysis.The coarser-time resolution(～300s)High Energy Resolution data (HER)are used as background data for the HERB,covering several thousand seconds before the trigger and after the HERB accumulation is?nished.However,especially for long,bright bursts,the HERB data can often be incomplete since HERB had a?xed memory space that could?ll up before the burst was over.In this work,we consider the HERB data incomplete when the data do not cover the burst duration(T90)or when the data do not include the main peak episodes(this could occur if a burst data accumulation was triggered by weak precursor).In such cases,or if HERB was not available,16-energy-channel MER data were used instead.Although MER provides medium energy resolution,it has much?ner time resolution(16and64ms)than HERB,making it possible to re-create the time resolution of the missing HERB.In the MER data,the CONT data are used as background;therefore,the spectra accumulated before the trigger time and after163.8seconds(the MER accumulation time)are identical to those of CONT,with2.048-s integration times.The downside of using MER is that the data are summed over multiple sets of detectors(usually two to four), and therefore,systematic errors tend to dominate over statistic errors,especially for bright bursts.Systematic errors cannot be modeled into the analysis and can contribute to large χ2especially at lower energies due to the high counts.This systematic e?ects can also be visible in the single-detector data(HERB and CONT)but are much more often found in the MER data of bright bursts.Examples of HERB and MER spectra of the same bright burst(GRB910503,trigger number143)that show such systematic deviations are seen in Figure1.Possible contributions to the systematics include the uncertainties from the LAD

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calibration(Preece et al.1998a)and the DRM(Pendleton et al.1995;Harmon et al.2002).

Lastly,in the cases where neither HERB nor MER were available for the analysis,16-energy-channel CONT data with2.048-s time resolution from the brightest LAD were used. Despite the lack of sub-second time resolution,the advantage of CONT is that the data are from a single detector and continuous.Thus,signi?cant precursor activities may be included in the analysis using the CONT data.This was not possible for HERB,because the data accumulations always started at triggers,and the background data(HER)did not provide a su?cient time resolution for pre-trigger data.For each of350bursts,the data type used is listed in column4of Table1,and the total number of bursts using each data type is270 (HERB),52(MER),and28(CONT).

2.4.Time Interval Selection

We binned the data in time until each spectrum has a large enough signal-to-noise ratio (S/N)in the entire LAD energy band to ensure acceptable statistics for the time-resolved spectral analysis.The S/N is calculated based upon the background model of each burst. The background model is determined by?tting(each energy channel separately)a low-order (≤4)polynomial function to spectra that cover time intervals before and after each burst, for at least a few hundred seconds.In cases where the background data are not available for a su?ciently long period,the longest available time intervals were used,and the background model was checked against those determined using other LAD data available for the same burst.The burst start time is usually the trigger time.In the cases where CONT or MER were used,bright pre-trigger activity(containing signi?cant amount of emission)was also included in the analysis,and thus the start time can be negative relative to the trigger time.

In SP1,a minimum S/N of45was used for the time binning of spectra regardless of the data types used.The S/N level was chosen so that each spectral resolution element(non-overlapping full-width at half-maximum resolution elements,of which there are about16–20in the LAD energy range)has approximately10σof the signal on average,assuming a?at spectrum.The noise(orσ)de?ned here is the Poisson error of the observed total counts, including the background counts.Binning by a constant S/N,however,usually yields on average a few times larger number of time-resolved spectra when MER data are used,than the HERB and CONT cases.This is because the MER data are summed over two to four detectors,while HERB and CONT are single-detector data,and thus the MER data have higher S/N to begin with,on top of having a?ner time resolution.As a result,bursts with MER data were overrepresented in the time-resolved spectral sample of SP1due to the choice of data type,which in turn slightly biased the spectral parameter and model statistics

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presented there.The MER bursts do provide more time-resolved spectra on average since we use the MER data for long,bright GRBs;however,this is caused by the nature of the bursts and should not be caused by the choice of data type.To minimize the over-representation caused by the data type selection,we investigated which S/N value for MER would yield comparable numbers of time-resolved spectra compared with HERB binned by S/N≥45, for the same bursts.Since the MER data are mainly used for bright,long bursts,and also the oversampling problems are more likely to occur when the photon?ux is high,we selected 15bursts with high peak photon?ux( 50photons s?1cm?2in128ms,～30–2000keV, determined using HERB data),for which both MER and HERB data were available.We re-binned the HERB data with minimum S/N of45,and reproduced the same number of spectra for the same time intervals with MER data,by increasing the minimum S/N in steps. We found that a minimum S/N of45per detector could roughly accomplish this,regardless of the brightness,as shown in Figure2.Therefore,the minimum S/N used for the time binning is45×number of detectors,with the exception of10MER bursts.These10bursts were mostly with three or four detectors and the minimum S/N was found to be too high, for various reasons,when compared with the available portion of single-detector data(i.e., HERB or CONT)for the same burst.Consequently,for these bursts,the minimum S/N was reduced by steps of45until the binning comparable to that of HERB was achieved.

After time-binning by the minimum S/N,the last time interval,with a S/N less than the minimum value,was dropped.Although the last time bin may constitute a signi?cant tail portion of the burst,we found that this exclusion of the last time bin does not greatly a?ect the time-integrated spectral?ts.This is true even when the resulting time interval that is ?tted is much shorter than the T90of the burst(e.g.,a burst with a very long tail).Unlike for SP1where bursts with less than eight spectra were dropped,no bursts that satisfy the burst selection criteria described above are excluded,regardless of the resulting number of spectra after binning in each burst.This allowed the inclusion of17short GRBs(T90<2.0 s)as well as several dimmer bursts in this work.Note that a set of time-resolved spectra comprises the time-integrated spectrum of each burst;therefore,the time interval of the integrated spectrum is the sum of the intervals of all the resolved spectra within the burst. Most integrated spectra cover the T90duration.Columns6and7of Table1list the time intervals used for each burst.There are11bursts(BATSE trigger numbers298,444,1525, 2514,2679,3087,3736,6240,6293,7457,7610)that provided only one spectrum as a result of the time binning.In addition,there are six weak bursts(2112,3044,3410,3412,3917, and6668)for which the detection of the entire event was<45σ:they provided only one spectrum of28σ,15σ,26σ,28σ,40σ,and28σ,respectively.These six spectra were still included in the sample for completeness.Four of these six bursts are short GRBs.For these bursts that provided only one spectrum,the same spectra are considered as both the time-

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integrated and time-resolved spectra,and they are indicated by the pre?x“W”in column 1of Table1.It must also be noted that there are eight bursts(indicated by the pre?x“C”in column1of Table1)whose time-integrated spectra were used for calibration of the eight LADs(Preece et al.1998a).Since the?ts to a two-component empirical GRB model(§3.2, Equation2)was used for the calibration,the time-integrated spectra of these calibration bursts are,by default,expected to give smallχ2values when?tted with a two-component model(Equations2&4),although the time intervals used for the calibration and for this work are di?erent.

2.5.Energy Interval Selection

All LADs were gain-stabilized;therefore,the usable energy range for spectral analyses is～30keV–2MeV for all bursts.The lowest seven channels of HERB and two channels of MER and CONT are usually below the electronic lower-energy cuto?and were excluded. Likewise,the highest few channels of HERB and normally the very highest channel of MER and CONT are unbounded energy over?ow channels and also not usable.The actual energy range used in the analysis for each burst is shown in columns8and9of Table1.

3.Spectral Analysis

Our sample consisted of350GRBs,providing350time-integrated spectra and8459 time-resolved spectra.We analyzed both time-integrated and time-resolved spectra,each ?tted by a set of photon models that are commonly used to?t GRB spectra.Each of the photon models used consists of a di?erent number of free parameters and thus,provides di?erent degrees-of-freedom(dof)for each?t.This allows statistical comparisons among the model?ts.The?tting procedures and the photon models are discussed in this section.

3.1.Spectral Fitting Software

For the spectral analysis presented herein,we used the spectral analysis software RM-FIT,which was speci?cally developed for burst data analysis by the BATSE team(Mallozzi, Preece&Briggs2005).It incorporates a?tting algorithm MFIT that employs the forward-folding method(Briggs1996),and the goodness of?t is determined byχ2minimization.One advantage of MFIT is that it utilizes model variances instead of data variances,which enables

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more accurate?tting even for low-count data(Ford et al.1995).We analyzed both time-integrated and time-resolved spectra for each burst,using a set of photon models described below.

3.2.Photon Models

We have selected?ve spectral models of interest to?t the BATSE GRB spectra,three of which(BAND,COMP,and SBPL)were also employed in SP1.Having a variety of models in?tting each spectrum eliminates the need for manipulating one model,such as the“constrained”Band function introduced by Sakamoto et al.(2004),which requires some presumptions of the form for the original photon spectrum.GRB spectra are usually well-represented by a broken power law in the BATSE energy band.However,it is possible that the break energy lies outside the energy range,or that the spectrum is very soft or dim and the high-energy component is not detected.Therefore,we use a single power-law and a power-law with exponential cuto?model that may accommodate such spectra,in addition to the more commonly-?t broken power-law models.We review each model used in the analysis below.All models are functions of energy E,measured in keV.

3.2.1.Power Law Model(PWRL)

The?rst model is a single power law with two free parameters,

f PWRL(E)=A E

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3.2.2.The GRB Model(BAND)

The next model is the empirical model most widely used to?t GRB spectra(Band et al. 1993):

f BAND(E)=A E E peak if E

f BAND(E)=A (α?β)E peak100 βif E≥E c,

where

E peak

E c=(α?β)

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p～2.2?2.3that is constant in time(Gallant2002).Therefore,if p remains constant throughout a burst,βshould also remain constant in the context of the synchrotron shock model.In fact,it has been found with a smaller sample that the majority of GRBs do not exhibit strong evolution inβ(Preece et al.1998a),so we examine this here with a larger sample.

3.2.

0062af21bcd126fff7050bf5ptonized Model(COMP)

The next model considered is a low-energy power law with an exponential high-energy cuto?.It is equivalent to the BAND model without a high energy power law,namely β→?∞,and has the form

f COMP(E)=A E E peak .(3) Like the PWRL case,E piv was always?xed at100keV in this work;therefore,the model consists of three parameters:A,α,and E peak.There are many BATSE GRB spectra that lack high-energy photons(Pendleton et al.1997),and these no-high-energy spectra are usually ?tted well with this model.Another case where this model would be a good?t is when the e-foldin

g energy(E0≡E peak/(2+α))approaches～1MeV,and the high-energy index of the BAND model cannot be determined by the data.The model is so named because in the special case ofα=?1,it represents the Comptonized spectrum from a thermal medium; however,αis kept as a free parameter here.Note that whenα

3.2.5.Smoothly-Broken Power Law(SBPL)

The last model we have selected is a broken power law with?exible curvature at the break energy,and thus the model can accommodate spectra with very sharp breaks,as well as ones with very smooth curvature.This SBPL model is expressed by

f SBPL(E)=A E

2 ,a piv=mΛln e q piv+e?q piv

Λ,q piv=

log(E piv/E b)

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m=λ2?λ1

2

.

The parameters are the amplitude A in photons s?1cm?2keV?1,a lower power-law index λ1,a break energy E b in keV,a break scaleΛ,in decades of energy,and an upper power-law indexλ2.The amplitude A represents the photon?ux at E piv.The model introduces a break scaleΛas the?fth parameter;this is thus a?ve-parameter model.Like the PWRL and COMP models above,the pivot energy E piv is always?xed at100keV here.The amplitude A is determined at this E piv,and it represents a convenient overall energy scale.This model was originally created to be implemented into MFIT,and the full derivation is found in Appendix A.The basic idea in deriving this model was to have the derivative of the photon ?ux(in logarithmic scale)to be a continuous function of the hyperbolic tangent(Preece et al.1994;Ryde1999,SP1).The main di?erence between this model and the BAND model is that the break scale is not coupled to the power laws,and it approaches the asymptotic low-energy power law much quicker than the BAND model case.Therefore,the low-energy spectral indexλ1could characterize values that are closer to the true power law indices indicated by the actual data points,than is possible withαof the BAND model.Note also that asΛ→0,the model reduces to a sharply-broken power law.

However,introducing a?fth parameter can be a problem in?tting the LAD spectra. Although the HERB data provides126energy channels,the energy range encompasses only about20energy resolution elements,as mentioned earlier.Fitting a four-parameter model to the HERB data can already cause the covariance matrix between parameters[C]to be ill-determined,resulting in unconstrained parameters.This is indicated by a condition num-ber for[C]?1that is of the order of the reciprocal of the machine precision,meaning that the matrix is nearly singular(e.g.,Press et al.1992).Consequently,having an additional free parameter usually results in highly cross-correlated,unconstrained parameter determi-nations,and is not favored.For this reason,in SP1,Λwas?xed for each time-resolved spectral?t to the value determined by the time-integrated?t for the corresponding burst; however,there is no reason to presume thatΛremains constant throughout a burst,and also it could be problematic if the initial time-integrated break scale is unconstrained.On the other hand,we may not be able to constrainΛany better than a particular value,due to the ?nite energy resolution of the LADs,even if the?ve-parameter model?t can be done.To resolve this issue,we have simulated SBPL spectra with various parameters and?tted these spectra with the SBPL model for various values ofΛ.The simulation results are discussed in§4.2.

We emphasize that the break energy E b of the SBPL model should not be confused with E peak of the BAND and COMP models.The break energy is simply the energy at which the spectrum changes from the low-energy to high-energy power law,whereas E peak

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is the energy at which theνFνspectrum peaks.The break energy E b is also di?erent from the characteristic energy E c in the BAND model(Equation2),which is the energy where the low-energy power law with exponential cuto?ends and the pure high-energy power law starts.However,theνFνpeak energy of the SBPL spectra,as well as the spectral break energy of BAND,can be easily derived(see the Appendices B and C)for comparison among the various models,which we have done here for the?rst time.

4.Spectral Simulations

In order to interpret the quantitative analysis results correctly,we?rst need to under-stand the general characteristics and behavior of each photon model when applied to the BATSE LAD GRB spectra.Therefore,we have generated a large set of simulated burst spectra with various spectral shapes and signal strengths,and subjected them to our analy-sis regime.To create a set of simulated count spectra,a source photon model with speci?c parameters and a background count model of an actual(typical)LAD burst are folded through the corresponding LAD DRM,and Poisson noise is added.It should be noted that the simulated spectra do not include any sources of systematic e?ects that are present in the real spectra.There are two main objectives in simulating data for this study.One is to investigate the behavior of the BAND and COMP models in the limit of low S/N and the other is to explore the break scale determination of SBPL.

4.1.BAND 0062af21bcd126fff7050bf5P

The broken-power law nature of the GRB spectra indicates that there typically are considerably lower photon?uxes at higher energies.Because of this,there is a good chance that the LADs are not sensitive enough to detect the non-thermal high-energy power law component of spectra in fainter bursts.In such cases,even if the original source spectra have high-energy components,our data may not be able to identify this component and therefore, the no-high-energy COMP model may statistically?t as well as the BAND model.As an example,we show in Figure3a comparison between the BAND and the COMP photon spectra with the same A,α,and E peak values.In fact,Band et al.(1993)found that the simulated four-parameter BAND spectra with low S/N could be adequately?tted with the three-parameter COMP model,although there were some shifts in the COMP-?t parameters. In order to validate this for our dataset and using our analysis tool(RMFIT,§3.1),we have further explored these two models by creating sets of simulated burst spectra,based on the

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actual?t parameters of some of the observed GRB spectra that clearly have high-energy components.

To start with,we selected a sample of six bright GRB spectra(three each with HERB and CONT)to which the BAND model?ts substantially better than the COMP model, with well-constrained parameters,resulting in largeχ2improvements(?χ2>20)for the additional1dof.This assures that the observed spectra have a high-energy power law component that is statistically signi?cant.Based on the spectral parameters provided with the BAND?ts to the sample spectra(i.e.,spectra with high-energy component),sets of100 simulated spectra with various S/N were created.For the S/N variation,we used the actual ?tted amplitude value and the values decreased by a step of a factor of10until the S/N was a few.As a result,a total of19sets provided2 S/N 200in the entire LAD energy range,based on the typical LAD background count model that was taken as input for the simulation.

The sets of simulated spectra were then?tted with the BAND and the COMP models. Some example results are presented in Table3(upper two tables),where x indicates a median value of the parameter x and the standard deviation isσx=

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with the BAND model.The results are summarized in Table3(lower two tables).In the high E peak case,we found that the BAND?ts did not converge about a third of the time, regardless of the S/N.The?tting failure is caused by a very poorly-constrained parameter (βin this case).On the other hand,in the low E peak case,the number of failed?ts was signi?cantly smaller for the spectra with lower S/N.In both cases,the E peak and α values ?tted by the BAND model were consistent with the simulated COMP parameters,while β only gave upper limits in a range of～?2.5to～?4.The simulation results suggest that the BAND model fails to converge when a spectrum has su?cient high-energy photon?ux but lacks the high-energy power-law component with?nite spectral index.The spectrum in such a case essentially is the COMP model,which is the BAND model withβ→?∞(see §3.2.4).As an example,Figure4shows two COMP models that produced simulated spectra with S/N～80but with di?erent E peak values.As mentioned above,the BAND model fails to?t the high-E peak spectrum much more frequently than the low-E peak one.From Figure 4,it is evident that the high-E peak spectrum has much larger photon?ux at about1MeV although the overall signal strengths are similar.Therefore,it is very likely that the spectra that the BAND model fails to?t lack a high-energy power law component,yet this does not mean that these are the no-high-energy(NHE)spectra identi?ed by Pendleton et al.(1997), which show no counts above300keV.

4.2.SBPL Break Scales

Another topic that needs to be addressed is the break scale(Λ)of the SBPL model,as mentioned in§3.2.5.The purpose of this simulation is to test the feasibility of performing the 5-parameter SBPL model?ts withΛas a free parameter,as well as to examine the capability of the determination ofΛby alternatively using a set of4-parameter SBPL models with?xed Λ.First,we created sets of100simulated SBPL spectra withΛvalues0.01and between0.1 and1.0with an increment of0.1(11total,in decades of energy),while keeping the other parameters?xed at typical?t values of E b=300keV,λ1=?1.0,andλ2=?2.5.Figure 5shows the11simulated spectra inνFν,with A=0.05.The upper limit ofΛ=1.0 (in decades of energy)is reasonable,considering that the LAD spectra span less than two decades of energy.The spectrum withΛ=0.01represents a sharply-broken power law.To provide variations in the signal strength,the amplitude A was set to a typical value of0.05 in one group,and was0.01in the other group,corresponding to the median S/N of～100 and～30per spectrum,respectively.Each of the simulated spectra was then?tted with the full5-parameter SBPL model allowingΛto vary,with a set of4-parameter SBPL models, each withΛ?xed to the11values mentioned above,as well as with the BAND and the COMP models for comparison.

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4.2.1.Finding the Break Scale

In Figure6,we show theΛvalues found by the5-parameter SBPL model?ts,withΛas a free parameter.For the high S/N case,the correctΛvalues were found up toΛ～0.6, with relatively small dispersions.For the low S/N case,only the very sharp break(Λ=0.01) was constrained by the5-parameter?ts.As for the other parameters associated with the ?ts,we found that even for the bright cases,the5-parameter?ts resulted in relatively large uncertainties in all parameters,which worsened asΛbecame larger.This was also indicated by the large cross-correlation coe?cients among all parameters,resulting from the?ts.This con?rms that?tting?ve free parameters at once does not determine the parameter with a good con?dence,regardless of the S/N of spectrum,and therefore,the full5-parameter?t is not favored.It is,however,worth noting that despite the large errors,Λfound by the 5-parameter?ts may still provide a rough estimate of the break scale even for faint spectra, as a last resort.

Alternatively,we could employ the grid-search method(Bevington&Robinson2003) using a subset of4-parameter SBPL?ts with various?xed values ofΛto determine the real Λ.Having such a set of4-parameter model?ts to each spectrum enables us to construct a one-dimensionalχ2map forΛ,showingχ2as a function ofΛ.From theχ2map,we can determine the most likely value ofΛ(where theχ2is minimum)as well as the con?dence interval,while having the other parameters still constrained.

The χ2 map obtained from a4-parameter model?tting of the bright(S/N～100) simulated spectra is shown in Figure7.We?nd from theχ2map that forΛ≤0.4the set of4-parameter?ts yields a minimum forχ2at the correctΛvalues with1σuncertainties less than0.01.However,forΛ≥0.5,theΛvalue could not be su?ciently constrained, especially at the upper ends,and the BAND model starts to give satisfactory?ts that are statistically comparable to the SBPL model?ts.This suggests that in the case ofΛ≥0.5 we can only determine the lower limit ofΛ=0.5with con?dence.Furthermore,forΛ>0.6, the uncertainties associated with other spectral parameters become large although they are still in agreement within the uncertainties with the simulated values.As for the faint spectra (S/N～30),we found that the total change inχ2for the entire set ofΛvalues was only about4,which is within the2σcon?dence interval for?dof=1;therefore,the correct value ofΛcannot be determined even with the use of4-parameter?ts,due to the low S/N.In such cases,however,we also found that theΛdetermined from the5-parameter SBPL?t can be used as an estimate.In other words,the?t using a4-parameter model withΛclosest to the Λfound from the5-parameter?t could yield parameters that are adequately constrained and still consistent with the actual simulated parameters.The simulation was done both with 128-energy channel data and16-energy channel data,in order to investigate the possible

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e?ects that might arise from the energy resolution issues.We found no di?erences between the128-channel data and the16-channel data in determining the break scales.

Based on these simulation results,we concluded that the4-parameter SBPL models withΛ>0.5do not contribute much additionally to our analysis;therefore,we decided to use a set of4-parameter SBPL models withΛ=0.01,0.1,0.2,0.3,0.4,and0.5,as well as 5-parameter SBPL model withΛvaried,andΛ?xed to the time-integrated?t value(for comparison with SP1).With regard to cross-correlations among the spectral parameters,E b andλ2are found to be always strongly anti-correlated in both4-parameter and5-parameter ?ts.Moreover,the4-parameter?ts whereΛis?xed tend to produce higher anti-correlation between E b andλ1than the5-parameter cases,which is expected for the?xed break scale cases.Not surprisingly,in the5-parameter?ts,theλ1(λ2)is more strongly correlated(anti-correlated)withΛ,asΛbecomes larger.There was no explicit di?erence found in these cross-correlations according to S/N,although in the faint case,the parameters were more di?cult to be constrained.

0062af21bcd126fff7050bf5parison with BAND&COMP

The simulated SBPL spectra were also?tted with the BAND and COMP models.The results of the BAND and COMP?ts to the bright simulated SBPL spectra(i.e.,S/N～100)are summarized in Table4.As seen in the table(also in Figure7),the BAND model is not able to adequately?t the SBPL spectra with relatively sharp break scale (Λ 0.3)because of its rather in?exible,smooth curvature.The COMP model did not provide statistically acceptable?ts,regardless of theΛvalues,for this particular set of simulated spectra.Generally,for sharply broken spectra with smallΛ,the E peak andαof BAND(also COMP)are larger than the SBPL“E peak”andλ1,while the BANDβis smaller thanλ2.The opposite is true for smooth break spectra with largeΛ.The tendencies are clearly seen in the exampleνFνspectra in Figure8,in which the BAND and COMP?ts to the simulated SBPL spectra withΛ=0.01and0.5are shown.The BAND model seems to?t the SBPL spectra withΛ～0.4the best,at least for these given values of E b and λ1,2.The BAND?t to this spectrum,in fact,resulted in E peak consistent with the SBPL “E peak”andαlarger thanλ1,which agrees with what was found from the SBPL?ts to the simulated BAND spectra in an earlier section(§4.1).We also observe in Table4that the BAND?ts yielded much smaller E peak range(～390?460keV)than the simulated“E peak”(～300?670keV).Although the COMP?ts were signi?cantly worse,the COMP E peak was always higher andαwas always softer than the BAND case,consistent with what we found in§4.1.

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In terms ofχ2statistics,for the bright spectra with S/N～100,we?nd that the SBPL model can?t substantially better than the BAND model(at con?dence level>99.9%)to the simulated SBPL spectra withΛ≤0.3;however,for the higher values ofΛ,BAND begins to?t statistically as well as SBPL?ts.Also in the bright spectrum case,the COMP model gave worse?ts for all values ofΛ,due to the lack of a high-energy component,and thus the SBPL?ts were always better for this given set of the simulated spectral parameters.In the case of dim spectra with S/N～30,on the other hand,the SBPL?tted better than the BAND or the COMP model forΛ=0.01and0.1,but only at con?dence level of～90%. Also for the dim spectra withΛ>0.1,we found that the BAND and the COMP?ts are statistically as good as the SBPL?t.

5.Spectral Catalog and Analysis Results

We?tted the?ve photon models(PWRL,BAND,BETA,COMP,SBPL;see§3.2)as well as SBPL with?xed break scales(Λ=0.01,0.2,0.3,0.4,0.5,&time-integrated value) to each of the350time-integrated spectra and8459time-resolved spectra.The spectral catalog containing all?t results is available electronically as a part of the public data archive at the High-Energy Astrophysics Science Archive Research Center(HEASARC)3.All the ?t results are archived in the standard Flexible Image Transport System(FITS)format4. The results of the comprehensive spectral analysis performed herein constitute the richest resource of GRB prompt emission spectral properties.Therefore,careful examination of these results enables us to better constrain physical mechanisms for GRB prompt emission process.These results also allows us to explore systematics that are internal to the spectral models employed.

The overall performance of each model in?tting all spectra is summarized in Table5, in which the percentages of acceptable?ts yielded by each model are shown.The BETA model is excluded here because it is a special case of the BAND model and was used only to investigate the constant-βhypothesis in each burst.The BETA model?ts are explored in§5.5.Also,the SBPL used here is the set of4-parameter model?ts,with the break scale Λdetermined according to minimumχ2as described in§4.2.Therefore,we used the dof for 5-parameter?ts to determine goodness of?ts,since we are indeed allowing the break scale (the?fth parameter)to vary.From Table5,it is clear that many spectra are adequately

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?tted with various photon models.As determined solely by theχ2of the?ts,the SBPL model seems to be able to?t the data better than the other models,as seen in the Table 5,although the values are only slightly better than those obtained by the BAND model. The time-resolved spectra provide betterχ2values,partially due to the lower S/N compared with the time-integrated spectra.This is especially evident in the results for the COMP cases,possibly indicating the existence of NHE spectra within high-energy bursts(Pendleton et al.1997).As expected,the PWRL model resulted in poor?ts for most of the spectra. In the following sections,we look at the results of our spectral analysis in terms of the parameter distributions,the model statistics,the comparison between time-integrated and time-resolved spectra,correlations among the spectral parameters,evolution of high-energy power law index(β),and the comparison between short and long bursts.

5.1.Spectral Parameter Distributions

The spectral parameters can be compared by two di?erent aspects;namely,a com-parison among parameters yielded by di?erent models,and a comparison between time-integrated and time-resolved parameters.The comparison among the models reveals the internal characteristics of each model,whereas the comparison between the time-integrated and time-resolved parameters uncovers the di?erences internal to the spectra.

Before comparing the?tted parameters of various models,there are some issues to be discussed.As mentioned in§3.2,the parameterizations are di?erent in each model.For clarity,the free parameters in each model are summarized in Table6.The main concern here is the di?erence in the low-energy spectral indices:αof BAND and COMP andλ1 of SBPL,whereαis the asymptotic power-law index,whileλ1is the index of the actual power law?t to the data.The natural consequence of this is thatαtends to be harder thanλ1(i.e.,α>λ1),when?tted to the same data,which was con?rmed in the simulation study presented in§4(we note,however,α～λ1ifΛis large and/or E b is low).They are, therefore,not directly comparable.In order to minimize the discrepancies,an“e?ective”α(αe?)was introduced by Preece et al.(1998b).This is the tangential slope at25keV in a logarithmic scale,and is found to describe the data more accurately than the?tted asymptoticαvalue.The25keV is the lower energy bound of LAD and therefore,αe?is the index of the low-energy power law within the data energy range.Therefore,we employ theαe?instead of the?ttedαvalues for BAND and COMP?ts in the following parameter distribution comparisons.A detailed discussion ofαe?can be found in Appendix D.

Another issue in comparing and presenting the spectral parameter distributions is the uncertainty associated with each parameter.The parameter distribution in a large sample

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