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The Fermi GBM Gamma-Ray Burst Spectral Catalog: The First Two Years 2 Adam Goldstein1, J. Michael Burgess1, Robert D. Preece1, Michael S. Briggs1, Sylvain 1 Guiriec1, Alexander J. van der Horst2, Valerie Connaughton1, Colleen A. Wilson-Hodge3, 0 William S. Paciesas1, Charles A. Meegan2, Andreas von Kienlin4, P. N. Bhat1, 2 Elisabetta Bissaldi4, Vandiver Chaplin1, Roland Diehl4, Gerald J. Fishman3, n a Gerard Fitzpatrick5, Suzanne Foley4, Melissa Gibby6, Misty Giles6, Jochen Greiner4, J David Gruber4, R. Marc Kippen7, Chryssa Kouveliotou3, Sheila McBreen5, 4 Sineád McGlynn8,4 Arne Rau4, and Dave Tierney5 1 ] E H ABSTRACT . h p We present systematic spectral analyses of GRBs detected by the Fermi Gamma-Ray Burst - Monitor (GBM) during its first two years of operation. This catalog contains two types of o spectra extracted from 487 GRBs, and by fitting four different spectral models, this results in a r t compendiumofover3800spectra. Themodelswereselectedbasedontheirempiricalimportance s a to the spectral shape of many GRBs, and the analysis performed was devised to be as thorough [ and objective as possible. We describe in detail our procedure and criteria for the analyses, 1 and present the bulk results in the form of parameter distributions. This catalog should be v considered an official product from the Fermi GBM Science Team, and the data files containing 1 the complete results are available from the High-Energy Astrophysics Science Archive Research 8 Center (HEASARC). 9 2 Subject headings: gamma rays: bursts— methods: data analysis . 1 0 1. Introduction sible, so that useful inferences can be drawn from 2 the assembled data. Here we have followed in a 1 Compendia of physicalobservationsofan enig- line of successful GRB Catalogs from the Burst : matic phenomenon such as Gamma-Ray Bursts v And Transient Source Experiment (BATSE) to i (GRBs)shouldbeascompleteanduniformaspos- present the community with representative spec- X tral fits for a complete sample of Fermi Gamma- ar 1University of Alabama in Huntsville, 320 Sparkman Ray Burst Monitor (GBM) bursts, observed dur- Drive,Huntsville,AL35805, USA ing the first two years of operation (July 14, 2008 2Universities Space Research Association, 320 Spark- to July 13, 2010). The methodology of producing manDrive,Huntsville,AL35805, USA 3Space Science Office, VP62, NASA/Marshall Space this catalog strives to balance completeness, uni- FlightCenter,Huntsville,AL35812, USA formity,andaccuracy. Theselectioncriteria,tech- 4Max-Planck-Institut fu¨r extraterrestrische Physik niques, spectral models used for fitting, etc., all (Giessenbachstrasse 1,85748Garching,Germany) derive from a previous work, based upon BATSE 5School ofPhysics,UniversityCollegeDublin,Belfield, data(Mallozzi et al.1995), thatis beingprepared StillorganRoad,Dublin4,Ireland for publication as a complete sample from that 6Jacobs Technology earlier mission. It is our hope that the two data 7Los Alamos National Laboratory, PO Box 1663, Los sets, the current GBM sample and the complete Alamos,NM87545,USA 8Exzellenzcluster Universe, Technische Universität BATSE sample, canserveas a whole for compari- Mu¨nchen,Boltzmannstrasse2,85748Garching,Germany sonandcontrast. Further,wewillcontinuetoadd 1 tothisseriesasmoreobservationsareaccumulated 4. In Section 5, we present the spectral analysis by GBM. methodsandresults. AdescriptionoftheCatalog Many correlative studies in the field of GRB file format can be found in the Appendix. global properties studies rely on only two very distinctrepresentativespectra(Amati et al.2002; 2. GBM Detectors and Calibration Ghirlanda et al.2004;Yonetoku et al.2004). These GBM is one of two instruments on-board the are the time-integrated and peak flux spectra, rep- Fermi Gamma-Ray Space Telescope, which was resenting (respectively) the average emission and launched and placed into orbit on June 11, 2008. the most luminous. Defining these uniformly is GBM is a 14–detector instrument designed to nottrivialandtrade-offsinevitablymustbemade. study the gamma-ray sky in the energy band of We have chosen to accumulate every spectrum ∼8 keV–40 MeV. Twelve of the detectors are that meets a minimum flux significance into our sodiumiodide(NaI)scintillationdetectors,placed average spectrum, which leaves out quiescent pe- in groups of three on the side edges of the space- riods that will dilute the signal. For the peak flux craftandpointedatvariousanglesfromtheFermi spectra we have chosen a slice of the burst repre- LargeAreaTelescope(LAT)boresight. Thepoint- senting the peak flux on a particular time scale. ing angles were optimized through simulations to Because of the large dynamic range of burst du- adequatelysurveytheentireunoccultedskyatany rations (ms to thousands of s) we have chosen time during the orbit, while also biasing cover- a smaller accumulation interval for those bursts agetowardtheLATpointingdirection. Theother withdurationsshorterthan2scomparedtothose twodetectorsareeachcomposedofabismuthger- longer than 2 s. In this way, we can still make a manate (BGO) crystal and are placed on either distinction between the fluence and the peak flux side of the spacecraft pointing at right angles to spectra for the traditionally short-class GRBs. the LAT boresight. Each BGO crystal is coupled The set of functions for fitting spectra was to two photomultiplier tubes, which collect the chosen for uniformity with the existing set of scintillation photons and convert them into elec- BATSEGRBSpectralCatalogs(Band et al.1993; tronic signals. The NaI detectors cover an energy Kaneko et al. 2006; Goldstein et al. in prep.), as rangefrom8 keV–1MeV, andthe BGO detectors well as with the (forthcoming) GBM Time Re- cover a range of 200 keV–40 MeV. Because of the solved Spectroscopy Catalog of Bright Bursts. In all-skycoverageofthe NaI detectors, andthe fact most cases where the statistics of the spectra are that the diameter of each NaI crystal (12.7 cm) sufficient, the data can support a number of free is ten times its thickness, the approximate loca- parametersthatisrarelygreaterthanfour. Hence, tion of a burst can be determined by comparing wehaveselectedspectralfunctionsthatsimplyex- the relative count rates in the detectors that ob- hibit two, three, and four free parameters. Our served the bursts. The source location is then choiceofthebestmodelforeachGRB,basedupon calculated in spacecraft coordinates and used in thefitstatistics,willbe discussedbelow;however, the production of the detector response matrices for many cases it is clear when a simple model (DRMs). The DRMs are mathematical models of fails to fit the data, or when the fit does not sig- the detectors’ response used to map the observed nificantlyimprovewithamorecomplicatedmodel. counts into photons of known energy. Each de- We start with a brief description of the GBM tector’s response is dependent on incident photon detectors and calibration in Section 2 and refer energy, the measured detector output energy, and to Meegan et al. (2009) and Bissaldi et al. (2009) the detector–source angle and the earth–source– for a more thorough and complete description of spacecraft geometry. the instrument and calibration respectively. This A key issue for accurate spectroscopy is the is followed, in Section 3, by a description of the fidelity of the detector calibration model, which methodology used in the production of this cata- matches detector pulse height analyzer (PHA) log, including detector selection, data types used, channels to physical energies. The individual energy selection and background fitting, and the GBM detectors were extensively calibrated be- source selection. We then offer a description of fore launch using several nuclear line sources thespectralmodelsusedinthiscataloginSection 2 (Bissaldi et al. 2009). In addition to line sources, tion work. As an example of non-linearity of the the BESSY accelerator in Berlin, Germany was response, see Figure 1, which is the spectrum of used to determine the low-energy light output of the bright GRB 081009using two NaI detectors. four of the flight-qualified NaI detectors. Finally, Solar flares provide anadditional means of cal- a source survey calibration was performed on the ibration of the GBM detectors, particularly the entire assembled Fermi Observatory, just prior to high-energy BGO detectors . For example, the observatory-level thermal vacuum testing. This positronannihilationline (511keV), neutroncap- last calibration consisted of several radioactive ture line (2.2 MeV), and various nuclear lines sources being individually placed at various an- (e.g., 4.4 and 6.1 MeV) were observed with BGO gles relative to the observatory in order to verify detector0inthesolarflareof2010June12(Abdo and validate the spacecraft and instrument scat- et al. in prep.), demonstrating the calibration of tering models, used in the DRMs (Hoover et al. that detector. In that flare there was a small gain 2008). shift (1%), showing limitations of the gainadjust- Giventhat the lowestenergy of the radioactive ment software and the 511 keV line had an addi- sources was 14.4 keV and that most of the detec- tional small offset (1%), possibly showing limita- tors were not calibrated with a continuum energy tions of the energy calibration of the BGO detec- source such as BESSY, it is useful to validate the tors. GBM calibration using on-orbit observations of In addition to persistent, known sources, cal- knownastrophysicalsources. Agoodspectroscopy ibration of GBM can be studied with other standardistheCrabNebula,whichhasbeenstud- transient events such as Soft Gamma Repeaters ied since the infancy of gamma-ray astronomy. (SGRs). SGR bursts are short, with typical dura- However,GBMisnotapointedinstrument,sowe tionsofseveraltenstoafewhundredmilliseconds. havemadeuseoftheEarthoccultationtechnique, Their νF energy spectra typically peak around ν as pioneered with BATSE (Harmon et al. 2002). 40 keVwith a very steepdecline in flux above the We have obtained excellent fits that are in good peak. Analysis of all the SGR bursts detected by agreement in every detector with the canonical GBM is currently underway (see Lin et al. 2011; CrabNebulaspectrum(for details,seeCase et al. van der Horst et al., in preparation; von Kien- 2011, Wilson-Hodge et al. in prep.). Notably, lin et al., in preparation). Typically the models therearenosystematicdeviationsintheresiduals andfitparametersareconsistentwiththosefound to the continuum fits that would indicate issues fromtheobservationsofotherinstruments(forre- with the calibration. The Earth occultation tech- views,seeWoods & Thompson(2006);Mereghetti nique uses 16 re-binned broad energy channels in (2008)). We fit the integrated count spectrum of the CSPEC data type (Meegan et al. 2009). one of the brightest bursts of SGR1550 − 5418 Whensomeverybrightsourceshavebeenfitted observedbyGBM.Thespectrumisbestfitwitha usingthe128energychannelCSPECdatatype,a modelthatagreeswithintheparameteruncertain- kinkinthespectrumat∼33keVcanbe observed. ties with the Israel et al. (2008) results obtained Thistakesa‘p-cygni’typeform,wheresomechan- for SGR1900+14 with Swift). This demonstrates nels (at lower energies) lie below the fitted model the ability of the low-energy calibration to fit the and others (at higher energies) lie above it. The overall spectrum well, except for the area around total extent in channel space is roughly 4–6 chan- the NaI K-edge where we notice that the cali- nels, while in energy space it is about 5–10 keV. bration is not adequate in removing instrumental Sincetheexcessresidualshaveequalweightbelow effects, as discussed above. and above the model fit and do not change the Concerning the calibration of GBM with re- fitted parameters appreciably when the affected spect to GRBs, a number of efforts have been channels are excluded, we have chosen to ignore pursued to compare the GRB spectra attained by thiseffectinthe currentwork. Itislikelythatthe GBM to spectra obtained by other instruments non-linear jump in the detector light output at observing the same bursts in approximately the the Na K-edge has not been modeled completely sameenergyband. OneofthefirstGRBsdetected (see the NaI K-edge discussion in Bissaldi et al. by GBM (GRB 080723B) was also observed by (2009)), which we will address in future calibra- two instruments onboard the INTEGRAL space- 3 craft. A study (von Kienlin et al. 2009) was per- theyaretooweaktodetermineiftheyhaveGRB- formed to compare GBM’s spectral analysis re- like spectra. sults with the ISGRI instrument (15 keV–1 MeV; Lebrun et al. 2003) and the SPI instrument (18 3.1. Detector Selection keV–8 MeV; Vedrenne et al. 2003). This burst GBM employs 14 detectors, situated at differ- wasselectedbecauseitwasbright,spectrallyhard, ent angles to promote monitoring of the full un- and seen in most GBM detectors. This analysis occultedsky: twelveNaIdetectorswithanenergy wasperformedbeforethe firstin-flightcalibration coverage of 8 keV to 1 MeV and two BGO de- was released, and before an accurate modeling of tectors with an energy coverage of 200 keV to 40 the spacecraft solar panels, which could block or MeV. For this catalog, we use the data produced attenuate the observationfromsome detectors. A by both NaI and BGO detectors. GBM was de- laterstudy(Tierney et al.2010)wasperformedon signed to observe the entire unocculted sky at all four other GRBs also detected by ISGRI, taking timesinordertoincreasethenumberofGRBsde- into accountblockeddetectors anda new in-flight tected. However, when GBM triggers on a GRB, calibration. These studies have confirmed that not all detectors have an optimal pointing for re- GRB spectra as measuredby GBM are consistent constructing the observedGRB spectrum. There- with other well-established and calibrated instru- fore,webeginwithall12NaI detectorsandselect ments. a subset of these detectors with optimum viewing angles. To ensure sufficient detector response, we 3. Method determined that using the detectors with viewing ◦ angles less than 60 from the location of a burst During the first two years of operation, GBM maximize the effective area and provide the best triggeredon491GRBs,487ofwhicharepresented signal for spectral analysis, since the detector an- inthiscatalog. Theremainingburstsareexcluded gleisstronglycorrelatedwiththecountrateinthe due to a low accumulation of counts or a lack of detector. Inaddition, we select the BGO detector spectral/temporal coverage. In order to provide that is closest to the NaI detectors in the subset. the most useful analysis to the community, we With this subset we run a program designed to haveattemptedtomakethemethodassystematic determine any spacecraft blockage that would in- and uniform as possible. When we deviate from terferewiththesignal. Inmostcasesthisprovides uniformity we indicate the circumstances clearly. a smaller subset of detectors that should be free Here we detail the detector and data selection as of any blockage. However, due to small inaccura- well as the process used to fit the data. Many cies in the detector mass model or locationuncer- of the criteria are adopted from the GBM Burst tainties, the blockage code does not alwaysreturn Catalog,(Paciesasetal.,inprep.) andwehaveat- a subset of detectors that is free from blockage. tempted to maintain this in all aspects. However, This is evident when the low-energy data deviate due to the nature of spectral analysis we demand strongly from the fit model, as depicted in Fig- stricter criteria to ensure that we have adequate ure 2. This can affect particular detectors when signal in all energy channels. This also effectively the burst is partially occulted by the spacecraft. reduces the GRB sample from that used in the When this occurs we remove these detectors from burst catalog. In addition, this catalog includes the selected sample. Finally, in the event that 4 GRBs not included in the GBM Burst Cata- more than 3 NaI detectors exist in our subsample log. GBM trigger number 081007.224contains an observation of a GRB triggered by Swift (GRB for a particular burst, we discardallbut the 3 de- tectorswiththesmallestsourceangles. Thishelps 081007A;Baumgartner et al.2009)at∼121safter to prevent a fitting bias toward lower energies for GBM.Theotherthree(GBMtriggers091013.989, bursts with more than 3 sufficient detectors,since 091022.752,&091208.623)whereoriginallyclassi- the high significance of data in the NaI detectors fied as unknowntriggersand werenot included in will influence the spectral fitting procedure more the Burst Catalog,however their spectra are con- than the lesseramountof data in the BGO detec- sistent with the GRB spectra observed by GBM. tors. With this final detector set for each burst, Twoothertriggerswereclassifiedasunknown,and we have an adequate and reliable dataset for per- the spectral analysis of those triggers reveal that 4 forming spectral analysis. channels is minimized, resulting in an adequate background fit. 3.2. Data Types 3.4. Source Selection Theprimarydatatypeusedinthis catalogwas the time-tagged event (TTE) data, which provide Once the background count rates are deter- absolute time resolution to 2 µs based on GPS, mined for each detector for a givenburst, we sum and high energy resolution of 128 channels. For the count rates and background models over all the purpose of this catalog, we choose a standard NaI detectors to produce a single lightcurve from time binning of 1024 ms for bursts greater than 2 whichwe makeobjectivetime selections. We sub- s in duration as defined by the burst t90 (see Pa- tractthe background,convertthe ratesto counts, ciesasetal. 2011)and64msforburstsofduration and calculate the signal-to-noise ratio (SNR) for 2sandshorter. ThetimehistoryofTTEtypically each time history bin. Only the time bins that startsat∼30sbeforetriggerandextendsto∼300 have a SNR greater or equal to 3.5 sigma are se- s after trigger. This timespan is adequate for the lected as signal. The time selections produced analysis of most GRBs. For GRBs that have ev- from this criterion are then applied to all detec- ident precursors or emissions that last more than tors for a given burst. This criterion ensures that 300saftertrigger,weusetheCSPECdata,which there is adequate signal to successfully perform a extend ∼4000 s before and after the burst. This spectral fit and constrain the parameters of the datatypealsohasacontinuous128channelenergy fit. This does howevereliminate some faintbursts resolutionwhichisnormallyaccumulatedat4.096 from the catalog sample (i.e., those with no time stemporalresolutionthatchangesto1.024sreso- bins with signal above 3.5 sigma). While this lutionfor∼600sstartingattriggertime. CSPEC strict cut was performed to provide an objective data was used for 22 GRBs in this catalog. catalog, it is possible that not all signal from a burst was selected. However, most of the signal 3.3. Energy Selection and Background below 3.5 sigma is likely indiscernible from the Fitting backgroundfluctuations,so aspectralanalysisin- cluding those bins would likely only increase the Withtheoptimumsubsetofdetectorsselected, uncertaintyinthemeasurements. Thisselectionis the best time and energy selections are chosen to what we refer to as the “fluence” selection, since fit the data. The available reliable energy chan- it is a time-integrated selection, and the fluence nels in the NaI detectors lie between ∼8 keV and derived is representative of the fluence over the ∼1MeV.Thisselectionexcludesoverflowchannels total duration of the burst. The other selection andthosechannelswheretheinstrumentresponse performed is a 1.024 ms peak photon flux selec- is poor and the background is high. Since the is- tion for long bursts and 64 ms peak count rate suewiththesodiumK-edgenoticeablyaffectsonly flux selection for short bursts as defined by their thebrightestGBMbursts,whichcompriseasmall t duration (Paciesas et al. in prep.). This se- percentageofthis catalog,wehavechosento keep 90 lection is made by adding the count rates in the thechannelsaffectedbytheK-edgeintheanalysis NaI detectors again and selecting the single bin ofallGRBs. Thefitparametersforburststhatare of signal with the highest background-subtracted affectedbynon-linearityaroundtheK-edgedonot count rate. This selection is a snapshot of the noticeably change; the only evident change in the energetics at the most intense part of the burst. resultsisthefitstatisticsandhencethe goodness- Figure 3 shows the distribution of accumulation of-fit. We perform a similar selection to the BGO timebasedonthesignal-to-noiseselectioncriteria. detectorforeachburst,selectingchannelsbetween The accumulation time reported is similar to the ∼300 keV and ∼38 MeV. With the resulting time observedemissiontimeoftheburst,excludingqui- series we select enough pre- and post-burst back- escent periods, (e.g. Mitrofanov et al. 1999). Fig- ground to sufficiently model the background and ure 3 also includes the comparisons of the model fitasingleenergydependentpolynomial(choosing up to 4th order) to the background. For each de- photon fluence and photon flux compared to the accumulation time. Note that both comparisons tectorthetimeselectionandpolynomialorderare varied until the χ2 statistic map over all energy contain two distinct regions associated with short 5 andlong GRBs. While there appearsto be a very clear correlation between the photon fluence and f (E)= the accumulation time, there is little correlation BAND α between the burst-averaged photon flux and the E exp −(α+2)E , E ≥ (α−β) Epeak accumulation time. However, the latter depicts a 100 keV Epeak α+2 rtieolantsihoinpshexipplsoimreidlairntoKtohuevehlaiortdonuesest–daul.r(a1t9io9n3)r.ela- A(cid:18)100EkeV(cid:19)βexp((cid:20)β−α) 10(cid:21)(0α−keβV)E(pαe+ak2) α−β, E(cid:18) < (α−β(cid:19)) Epeak (cid:20) (cid:21) 4. Models  α+2 (2) We chose four spectral models to fit the spec- Thefourfreeparametersaretheamplitude,A,the tra of GRBs in our selection sample. These mod- low and high energy spectral indices, α and β re- els include a single power law (PL), Band’s GRB spectively, and the νF peak energy, E . This function (BAND), an exponential cut-off power- ν peak function is essentially a smoothly broken power law (COMP), and smoothly broken power law law with a curvature defined by its spectral in- (SBPL).Allmodelsareformulatedinunitsofpho- dices. The low-energy index spectrum is a power tonfluxwithenergy(E)inkeVandmultipliedby anormalizationconstantA(phs−1 cm−2 keV−1). law only asymptotically. Below we detail each model and its features. 4.3. Comptonized Model 4.1. Power-Law Model This model considered for GRB spectra is an exponentially cutoff power-law, which is a subset Anobviousfirstmodelchoice,ubiquitousinas- of the Band function in the limit that β →−∞: trophysical spectra, is the single power law with two free parameters, E α (α+2) E f (E)=A exp − (3) E λ COMP Epiv " Epeak # f (E)=A (1) (cid:16) (cid:17) PL E (cid:18) piv(cid:19) The three free parameters are the amplitude A, where A is the amplitude and λ is the spectral the low energy spectral index α and Epeak. Epiv index. The pivot energy (E ) normalizes the is again fixed to 100 keV, as is the case for the piv model to the energy range under inspection and power law model. With the extended high-energy helpsreducecross-correlationofotherparameters. response of GBM compared to BATSE, we rarely Inallcasesinthiscatalog,E isheldfixedat100 sufferfromaninabilitytomeasurethehigh-energy piv keV. While most GRBs exhibit a spectral break spectraofmediumtostrongintensityGRBs;how- in the GBM passband, some weak GRBs are too ever,westillfindthattheComptonizedmodelad- weaktoadequatelyconstrainthisbreakinthefits equately describes many GRB spectra. and therefore we chose to fit these with the PL model. 4.4. Smoothly Broken Power-Law The final model that we consider in this cat- 4.2. Band’s GRB function alog is a broken power-law characterized by one Band’s GRB function (Band et al. 1993) has break with flexible curvature able to fit spectra becomethe standardforfitting GRB spectra,and with both sharp and smooth transitions between therefore we include it in our analysis: the low and high energy power laws. This model, first published in Ryde (1999), where the loga- rithmic derivative of the photon flux is a continu- ous hyperbolic tangent, has been re-parametrized (Kaneko et al. 2006) as such: b E fSBPL(E)=A 10(a−apiv) (4) E (cid:18) piv(cid:19) 6 where was determined throughextensive simulations using GRESS (Hoover et al. 2010) and validated by eq+e−q a=m∆ln , the source survey. The response matrices for all 2 (cid:18) (cid:19) GRBs in the catalog were made using GBMRSP v1.9oftheresponsegeneratorandversion2ofthe eqpiv +e−qpiv GBMDRMdatabase,andallresponsesemployat- apiv =m∆ln , mospheric response modeling to correct for possi- 2 (cid:18) (cid:19) bleatmosphericinterference. Inparticular,weuse (5) RSP2 files, which contain multiple DRMs based log(E/Eb) log(Epiv/E) on the amount of slew the spacecraft experiences q = , q = , ∆ piv ∆ duringtheburst. AnewDRMiscalculatedforev- ◦ ery 2 of slew, changing the effective area of each detector based on its angle to the source. These λ −λ λ +λ 2 1 1 2 m= , b= . DRMs are then all stored in a single RSP2 file 2 2 for eachdetector. During the fitting process,each In the above relations, the low- and high-energy DRM is weighted by the counts fluence through power law indices are λ1 and λ2 respectively, Eb the detector during each 2◦ slew segment. is the break energy in keV, and ∆ is the break The spectral analysis of all bursts was per- scale in decades of energy. The break scale is in- formed using RMfit, version 3.4rc1. RMfit em- dependent and not coupled to the power law in- ploys a modified, forward-folding Levenberg- dices as it is with the Band function, and as such Marquardt algorithm for spectral fitting. The represents an additional degree of freedom. How- Castor C-Statistic, which is a modified log likeli- ever,Kaneko et al.(2006)foundthatanappropri- hood statistic based on the Cash parametrization ate value for ∆ for GRB spectra is 0.3, therefore (Cash1979)isusedinthemodel-fittingprocessas we fix ∆ at this value. Studies on the behavior of a figure of merit to be minimized. This statistic ∆pertainingtoGBMGRBsmaybepossibleafter is preferable overthe more traditional χ2 statistic more bright bursts have been detected; therefore minimization because of the non-Gaussian count- this is left to possible future catalogs. ing statistics present when dividing the energy spectra of GBM GRBs into 128 channels. Al- 5. Data Analysis & Results though it is advantageous to perform the spectral fitting using C-Stat, this statistics provides no es- To study the spectra resulting from the GBM timation of the goodness-of-fit, since there exists detectors, a method must be established to as- nostandardprobabilitydistributionforlikelihood sociate the energy deposited in the detectors to statistics. For this reason, we also calculate χ2 the energy of the detected photons. This associa- for each spectral fit that was performed through tion is dependent on effective area and the angle minimizing C-Stat. This allows an estimation of of the detector to the incoming photons. To do the goodness-of-fit of a function to the data even this, detector response matrices (DRMs) are used though χ2 was not minimized. This also allows to convertthe photonenergiesinto detectorchan- for easy comparison between nested models. nel energies. The DRM is a mathematical model We fit the fourfunctions describedinSection4 ofthedepositionofphotonenergyinthecrystal— to the spectrum of each burst. The BAND and a photonthat interactsby the photoelectric effect COMP functions are parametrized with E , will deposit 100% of its energy, subject to resolu- peak the peak in the power density spectrum, while tion broadening, while a photon that interacts by the SBPL is parametrized with the break energy, a single Compton scatter may deposit only a por- E . We choose to fit these four different function ofits energy. The exceptionto this is whena break tions because the measurable spectrum of GRBs photon carrying the energy of the iodine K–shell is dependent on intensity, as is shown in Figure escapes the crystal. The energy calibration de- 4. Observablylessintenseburstsprovidelessdata termines the energy boundaries of the energy de- to support a large number of parameters. This position channels. The DRMs record this energy may appear obvious, but it allows us to deter- response of the detectors at various angles, which 7 mine why in many situations a particular empir- at least 6 since the probability for achieving this ical function provides a poor fit, while in other difference is ∼0.01. The parameter distributions cases it provides an accurate fit. For example, are then populated with the spectral parameters the energy spectra of GRBs are normally well fit from the BEST spectral fits. by two smoothly joined power laws. For particu- larlybrightGRBs,theBANDandSBPLfunctions 5.1. Fluence Spectra are typically an accurate description of the spec- The time-integrated fluence spectral distribu- trum,whileforweakerburststheCOMPfunction tions admit results that are averaged over the is most acceptable. Bursts that have signal sig- duration of the observed emission. It should be nificance on the order of the background fluctua- noted that the following distributions do not take tions donothavea detectabledistinctive breakin intoaccountanyspectralevolutionthatmayexist their spectrum and so the power law is the most withinbursts. Thelow-energyindices,asshownin acceptable function. Although for weaker GRBs Figure 5, distribute about a −1 power law typical a model with more parameters is not statistically of most GRBs. Up to 33% of the GOOD low- preferred, it is instructive to study the parame- energyindicesviolatethe−2/3synchrotron“line- ters of even the weaker bursts. In addition, the of-death”, while an additional 62% of the indices actual physical GRB processes can have an effect violate the −3/2 synchrotron cooling limit. The onthespectraanddifferentempiricalmodelsmay high-energy indices in Figure 6 peak at a slope fit certain bursts better than others. The spectral slightly steeper than −2 and have a long tail to- results, including the best fit spectral parameters ward steeper indices. Note that the large number andthephotonmodel,arestoredinfilesfollowing of unconstrained (or very steep) high-energy in- the FITS standard (see Appendix for file descrip- dices in the distribution of all high-energy index tion) and are hosted as a public data archive on values indicates that a large number of GRBs are HEASARC1. better fit by the COMP model, which is equiva- Wheninspectingthedistributionoftheparam- lenttoaBANDfunctionwithahigh-energyindex eters for the fitted models, we first define a data of −∞. The comparison of the simple power law cut based on the goodness-of-fit. We require the index to the low- and high-energy indices makes χ2 statisticforthefittobewithinthe3σexpected evident that the simple power law index is aver- regionfor the χ2 distribution of the given degrees aged over the break energy, resulting in a index offreedom, andwedefine a subsetofeachparam- that is on averagesteeper than the low-energyin- eter distribution of this data cut as GOOD if the dex yetshallowerthan the high-energyindex. We parameter error is within certain limits. Follow- alsoshowinFigure6(d)thedifferencebetweenthe ingKaneko et al.(2006),forthelow-energypower time-integrated low- and high-energy spectral in- law indices, we consider GOODvalues to have er- dices, ∆S =(α−β). This quantity is useful since rors less than 0.4, and for high-energy power law the synchrotron shock model makes predictions indices we consider GOOD values to have errors of this value in a number of cases (Preece et al. lessthan1.0. Forallotherparametersweconsider 2002). The fluence spectra distribution of ∆S a GOOD value to have a relative error of 0.4 or bears resemblance to the time-resolved results in better. The motivation for this is to show well– Preece et al.(2002),aswellastime–integratedre- constrained parameter values, rather than basing sults in Kaneko et al. (2006). interpretationsonparametersthatarepoorlycon- In Figure 7, we show the distributions for the strained. break energy, E and the peak of the power break Inaddition,wedefineaBESTsamplewherewe density spectrum, E . E is the energy peak break compare the goodness-of-fit of all spectral models at which the low- and high-energy power laws foreachburstandselectthemostpreferredmodel are joined, which is not necessarily representative based on the difference in χ2 per degree of free- of the E . The E for the SBPL has a peak break dom. The criterion for accepting a model with a strong clustering about 100 keV, while the peak single additional parameter is a change in χ2 of for the BAND distribution is closer to 200 keV. The E distributions allgenerally peak around peak 1http://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html200 keV and cover just over two orders of mag- 8 nitude, which is consistent with previous find- combined errors. This indicates that, although ings (Mallozzi et al. 1995; Lloyd et al. 2000) from COMP is a special case of BAND, a significant BATSE. As discussed in Kaneko et al. (2006), al- fractionoftheE valuescanvarybymorethan peak thoughtheSBPLisparametrizedwithE ,the 1σ based on which model is chosen. break Epeak canbederivedfromthefunctionalform. We The distributions forthe time-averagedphoton have calculated the Epeak for all bursts with low- flux and energy flux are shown in Figure 10. The energy index shallower than -2 and high-energy photonfluxpeaksaround2photonscm−2s−1,and index steeper than -2, and we have used the co- the energyflux peaks at2.5×10−7 ergscm−2 s−1 variance matrix to formally propagate and calcu- in the 8-1000 keV band. When integrating over late the errors on the derived Epeak. The peak the full GBM spectral band, 8 keV - 40 MeV, the andoveralldistribution ofEpeak is similar to that energy flux broadens and for all but the simple foundbytheBATSELargeAreaDetectors,which power law model, approximates a top hat func- had a much smaller bandwidth and larger collect- tion with a small high-flux tail spanning about 2 ing area. This would seem to indicate that it is orders of magnitude. Note that the low-flux cut- unlikelyfortheretobeahiddenpopulationundis- off is due to the sensitivity ofthe instrument, and covered by either instrument within the 20 keV thereforethepeakofthedistributionsaredirectly - 2 MeV range. Additionally, the value of Epeak affected by the instrument sensitivity. A distri- can strongly affect the measurement of the low- bution of flux measurements with a more sensi- energy index of the spectrum, as shown in Figure tive instrument will likely position the peak at a 8. A general trend appears to show that lower lower flux. Similarly in Figure 11, the distribu- Epeak values tend to increase the uncertainty in tionsforthephotonfluenceandenergyfluenceare the measurement of the low-energy index, mostly depicted. The plots for the photonfluence appear due to the fact that a spectrum with a low Epeak to contain evidence of the duration bimodality of will exhibit most of its curvature near the lower GRBs, and have discriminant peaks at about 1 end of the instrument bandpass. In many cases, and 20 photons cm−2. The energy fluence in the if the low-energy index is found to be reasonably 8-1000keVbandpeaksatabout1×10−6ergcm−2, steep (.−1), the uncertainty ofthe index is min- while the peak in the 8 keV-40 MeV band shifts imized even if Epeak is low. nearly an order of magnitude to about 1×10−5 It is of interest to study the difference in the erg cm−2 for all except the COMP model. The value of E between the BAND and COMP COMP model is largely unaffected by the change peak functions since they are the two main functions inenergybanddueto theexponentialcutoff. The used to study GRB spectra, and COMP is a spe- brightest GRB contained in this catalog based on cial case of BAND. To study the relative devia- time-averaged photon flux is GRB 081009 with a tion between the two values we calculate a statis- flux of > 30 ph s−1 cm−2 and the burst with the tic basedonthe differencebetweenthe valuesand largest average energy flux is GRB 090227B with taking into account their 1σ errors. This statistic anenergyflux of∼1.3×10−5 ergss−1cm−2. The can be calculated by most fluent burst (although not the longest duration) in the catalog is GRB 090618with a photon |EpCeak −EpBeak| fluence of > 2600 ph cm−2 and an energy fluence ∆E = (6) peak σC +σB of >2.5×10−4 ergs cm−2. Epeak Epeak where C and B indicate the COMP and BAND 5.2. Peak Flux Spectra values respectively. This statistic has a value of unity when the deviation between the E val- The following peak flux spectral distributions peak ues exactly matches the sum of the 1σ errors. A have been produced by fitting the GRB spec- value less than one indicates the E values are tra over the 1024 ms and 64 ms peak flux dura- peak within errors, and a value greater than one indi- tion of long and short bursts respectively. Note cates that the E values are not within errors that the results from both long and short bursts peak of each other. Figure 9 depicts the distribution of are included in the following figures. The low- the statistic and roughly 25% of the BAND and energy indices from the peak flux selections, as COMP E values are found to be outside the shown in Figure 12, also distribute about the peak 9 typical −1 power law. 42% of the GOOD low- the simple power law model and approximates a energyindicesviolatethe−2/3synchrotron“line- top hat function with a small high-flux tail span- of-death”, while an additional 40% of the indices ningabout2ordersofmagnitude. TheGRB with violate the −3/2 synchrotron cooling limit, both the brightest peak photon flux is GRB 081009 at of which are significantly larger percentages than >130 ph s−1 cm−2. This GRB is also the bright- those from the fluence spectra. The high-energy est GRB in terms of time-averaged photon flux indicesinFigure13peakataslopesightlysteeper which makes it an excellent burst for calibration than−2andagainhavealongtailtowardsteeper studies. Similar to the time-averagedenergy flux, indices. Thenumberofunconstrainedhigh-energy the burst with highest peak energy flux is GRB indices increases when compared to the fluence 090227B at >8.0×10−5 ergs s−1 cm−2. spectra, likely due to the poorer statistics result- When studying the twotypes of spectra in this ing from shorter integration times. As shown catalog, it is instructive to study the similarities with the fluence spectra, the PL index serves as and differences between the resulting parameters. an average between low- and high-energy indices Plotted in Figure 17 are the low-energy indices, for the BAND and SBPL functions. Shown in high-energyindices,andE energiesofthepeak peak Figure 13(d) is the ∆S distribution for the peak fluxspectraasafunctionofthecorrespondingpa- flux spectra. This distribution is roughly con- rameters from the fluence spectra. Most of the sistent with the BATSE results found previously peak flux spectral parameters correlate with the (Preece et al. 2002; Kaneko et al. 2006), but suf- fluence spectral parameters on the order of unity. fers from a deficit in values due in large part to There are particular regions in each plot where the inability of the data to sufficiently constrain outliers exist, andthese areasare indications that the high-energy power law index. either the GRB spectrum is poorly sampled or In Figure 14, we show the distributions for there exists significant spectral evolution in the E and E . As was evident from the flu- fluence measurement of the spectrum that skews break peak ence spectra, the E from the SBPL fits ap- the fluence spectral values. Examples of the for- break pears to peak at 100 keV, meanwhile the E mer case are when the low-energy index is atypi- break fromBANDisharderandpeaksatabout200keV. cally shallow(&−0.5)or the high-energyindex is TheE distributionsforallmodelspeakaround steeper than average (. −3). An example where peak 150 keV and cover just over two orders of mag- spectral evolution may skew the correlation be- nitude, which is consistent with previous findings tween the two types of spectra is apparent in the (Preece et al.1998;Kaneko et al.2006). Itshould comparison of E . Here, it is likely that a flu- peak benotedthatthedataovertheshorttimescalesin ence spectrum covering significant spectral evolu- the peakflux spectradonotoftenfavorthe SBPL tionwillproducealowerenergyE thanismea- peak model, resulting in large parameter errors. Using sured when inspecting the peak flux spectrum. the propagation of errors scheme to calculate the E for SBPL therefore causes many of the val- 5.3. The BEST Sample peak uestobelargelyunconstrained. Thisresultsinthe TheBESTparametersampleproducesthebest much smaller E distribution for SBPL seen in peak estimate of the observed properties of GRBs. By Figure 14(b). In addition, we calculate and show using model comparison, the preferred model is the ∆E statistic in Figure 15 and, as was the peak selected, and the parameters are reviewed for casewiththe fluence spectra,∼25%oftheBAND that model. The models contained herein and in and COMP E values are found to be outside peak most GRB spectral analyses are empirical mod- the combined errors. els, based only on the data received;therefore the The distributions for the peak photon flux and datafromdifferentGRBstendtosupportdifferent energy flux are shown in Figure 16. The photon models. Perhaps it will be possible to determine flux peaks around 4 photons cm−2 s−1, and the the physics of the emission process by investigat- energy flux peaks at 7.4 × 10−7 ergs cm−2 s−1 ing the tendencies of the data to support a par- in the 8-1000 keV band. When integrating over ticular model over others. It is this motivation, the full GBM spectral band, 8 kev-40 MeV, the aswellasthe motivationtoprovideasamplethat dispersion in the energy flux increases for all but contains the best picture of the global properties 10