THE THIRD FERMI GBM GAMMA-RAY BURST CATALOG: THE FIRST SIX YEARS

Since the first γ-ray burst (GRB) was observed by the Vela satellite (Klebesadel et al. 1973), the number of flashes of high-energy radiation that have been detected has increased dramatically, especially since the 1991 launch of the Compton Gamma Ray Observatory and its γ-ray burst instrument, the Burst and Transient Source Experiment (BATSE; Meegan et al. 1992). The Gamma-ray Burst Monitor (GBM) technique of detecting and locating GRBs is largely based on BATSE (Fishman et al. 1989), which operated from 1991 to 2000. Both instruments employ multiple sodium iodide [Nai[Tl)] detectors to achieve a full sky field of view, they both have on board burst triggering capability, and both use the relative count rates to obtain the approximate directions to bursts. GBM also includes two bismuth germanate (BGO) detectors that are better suited for the detection of higher-energy γ-ray photons. BATSE, with significantly larger (20'' in diameter 1'' thick) [Nai[Tl)] detectors, had better sensitivity, while GBM has a broader energy range and higher data rate.

Fermi was launched on 2008 June 11 and has now been operating successfully in space for more than seven years. GBM's main task is to augment the mission's ability to detect and locate GRBs as well as to provide broadband spectral information. GBM extends the energy range of the main instrument, the Large Area Telescope (LAT: 30 MeV–300 GeV), down to the soft γ-ray and X-ray energy range (8 keV–40 MeV). This allows for observations over more than seven decades in energy.

In the six years of operation since triggering was enabled on 2008 July 12, GBM has triggered 3350 times on a variety of transient events: 1405 of these are classified as GRBs (in two cases the same GRB triggered GBM twice), 198 as bursts from soft γ repeaters (SGRs), 469 as terrestrial γ-ray flashes (TGFs), 794 as solar flares (SFs), 305 as charged particle (CP) events, and 179 as other events (Galactic sources, accidental statistical fluctuations, or too weak to classify). Table 1 shows a breakdown of the observed event numbers sorted by the time periods covered by the first GBM burst catalog (2008 July 12 to 2010 July 11; Paciesas et al. 2012), the second GBM catalog (2010 July 12 to 2012 July 11; von Kienlin et al. 2014), and the additional two years included in the current catalog (2012 July 12 to 2014 July 11), which are again separated according to event type. In addition, the number of Autonomous Repoint Requests (ARRs, described in Section 2.2 below) and GRBs detected by LAT observed with high confidence above 100 MeV (and 20 MeV) are given (Ackermann et al. 2013). The preliminary results of the GBM team analyses for bright bursts and those bursts simultaneously detected by other satellite instruments are reported in the Gamma-ray Coordinates Network (GCN) circulars¹⁹ , which is a very effective way of informing the GRB research community of the initial properties of GRBs. Here, we present the final results after a careful analysis of the full set of burst data using detector response functions for the best-available burst location. This catalog lists for each GRB the location and the main characteristics of the prompt emission, the duration, peak flux, and fluence. In addition, the distributions of these derived quantities for the entire six year period are also presented.

The upcoming GBM spectral catalog²⁰ provides information on the systematic spectral analysis of nearly all of the GRBs listed in the current catalog, including the time-integrated fluence and peak flux spectra. A new catalog of time-resolved spectral analysis of bright GRBs of the first four years has also been compiled (Yu et al. 2015).

In Sections 2.1 and 2.2, we briefly describe the GBM detectors and the GBM GRB localization technique together with a description of the on board triggering algorithms and the path of trigger information dissemination. Furthermore, a brief description of the GBM data products is presented. In Section 2.3, we report the GRB trigger statistics of the first six years, comparing them with the triggers on other event classes. Major changes in operational conditions occurring during years 5 and 6 are also mentioned. We provide a summary of the major steps of the catalog analysis in Section 3. The catalog results are presented in Section 4 and are discussed in Section 5. Finally, in Section 6, we conclude with a summary.

2.1. GBM Detectors

2.2. Triggering and Post-trigger Operations

2.3. Trigger Statistics

The GBM instrument, which is primarily designed to detect cosmic GRBs, additionally detects bursts originating from other cosmic sources, such as SFs and SGRs, as well as extremely short but spectrally hard TGFs observed from Earth's atmosphere, which have been associated with lightning events in thunderstorms. Table 1 summarizes the numbers of triggers assigned to these additional event classes, showing that their total number is of the same order as the total number of triggered GRBs. Approximately 10% of the triggers are mostly due to cosmic rays or trapped particles; the latter typically occur in the entry or exit regions of the SAA or at high geomagnetic latitude. In rare cases, outbursts from known Galactic sources have caused triggers. Finally, ∼6% of the GBM triggers are generated accidentally by statistical fluctuations or are too weak to be confidently classified. The quarterly trigger statistics over the six years of the mission are graphically represented in Figure 1. The rate of GRBs is slightly lower in the second two years because, at the beginning of 2011 July, triggers were disabled during those times when the spacecraft was at high geomagnetic latitudes. The McIlwainL parameter, which is used by the FSW as a threshold for disabling triggering, has been raised from 1.58 to 1.9 since year 5, while the McIlwainL threshold for disabling ARR has been retained at 1.58.

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It is evident from Figure 1 that the major bursting activity from SGR sources took place in the beginning of the mission, mainly in 2008 and 2009. In addition to the emission from previously known SGR sources (Lin et al. 2011; van der Horst et al. 2012; von Kienlin et al. 2012), GBM also detected a new SGR source (van der Horst et al. 2010). It is also obvious from the figure that the rate of monthly detected triggers on TGF events increased by a factor of ∼8 to about two per week after the upload of the new FSW version (V2.6) on 2009 November 10 (Briggs et al. 2013). This version includes additional trigger algorithms that monitor the BGO detector count rates in the 2–40 Mev energy range (see Table 2). This has two advantages: first, the TGF bursts show very hard spectra up to 40 MeV, and hence BGO detectors have a better sensitivity for TGFs, and second the deadtime in the [Nai[Tl)] detectors is much larger for γ-rays of energy²¹ ≥1 MeV (Briggs et al. 2013).

Table 3 summarizes the first trigger algorithm which triggered on bursts or flares from the different object classes. Once a trigger has occurred, the FSW continues to check the other trigger algorithms and ultimately sends back the information in TRIGDAT data as a list of trigger times for all of the algorithms that were satisfied. This detailed information was used in Paciesas et al. (2012) to investigate the apparent improvement in trigger sensitivity relative to BATSE. It was found that GBM's additional longer timescale triggers (>1.024 s) in the 50–300 keV energy range were mainly able to detect GRB events which would not have triggered the BATSE experiment. These observations are confirmed by analyzing the current full six year data set.

Table 3.  Trigger Algorithm Statistics

Algorithm	Time ms	Energy keV	GRBs	SGRs	TGFs	SFs	CPs	Other	Commenta
1–5	16–64	50–300	235	73	8	6	9	17	GRB
6–11	128–512	50–300	509	8	⋯	41	12	37	GRB
12–17	1024–4096	50–300	639	1	⋯	167	230	30	GRB
18–21	8192–16384	50–300	3	⋯	⋯	⋯	⋯	⋯	D
22–26	16–64	25–50	7	113	⋯	577	11	7	SF
27–32	128–512	25–50	2	3	⋯	1	2	⋯	D
33–38	1024–4096	25–50	8	⋯	⋯	2	11	3	D
39–42	8192–16384	25–50	1	⋯	⋯	⋯	8	3	D
43	16	>300	⋯	⋯	43	⋯	1	1	TGF
44–49	32–128	>300	⋯	⋯	⋯	⋯	⋯	5	D
50	16	>100	⋯	⋯	9	⋯	4	⋯	TGF
51–66	32–4096	>100	1	⋯	⋯	⋯	⋯	⋯	D
116–119	16	BGO	⋯	⋯	409	⋯	16	76	TGF

Note.

^a"GRB," "SF," and "TGF" indicate the source classes that are most likely to trigger the corresponding algorithm; "D" indicates that the algorithm was finally disabled at the end of year 4.

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Furthermore, we ascribe the improved trigger sensitivity of GBM to the lower trigger threshold of 4.5σ–5.0σ (see Table 2) compared to the BATSE setting of 5.5σ (see Table 1 in Paciesas et al. 1999). The longest timescale trigger algorithms in the 50–300 keV energy range, running at ∼16 s (20, 21) and ∼8 s (18, 19), were disabled at the beginning of the mission (see Table 2) since no event triggered algorithms 20 and 21 and only three GRBs triggered on algorithms 18 and 19. The algorithms running on energy channel 2 (25–50 keV) with timescales higher than 128 ms were disabled because they were mostly triggered by non-GRB (and non SGR) events. The short-timescale algorithms in the 25–50 keV energy range (22–26) were retained, mainly for the detection of SGR bursts, which are short and have soft energy spectra. Even these triggers were disabled during periods of high Solar activity (see Table 4). The new algorithms above 100 keV did not increase the GRB detection rate. They were disabled with the exception of the shortest timescale algorithms running at 16 ms, which is particularly suitable for the detection of TGFs. Table 2 clearly shows the capabilities of the newly introduced "BGO"-trigger algorithms 116–119 for TGF detection.

Table 4.  Trigger Modification History

Date	Year/DOY/UT	Operation
7/1/12	2012/183:22:14:20	Elevate LLT thresholds to 101 for dets. NaI0-5
	2012/183:22:14:32	Disable triggers
	2012/184:01:39:24	Enable triggers
7/2/12	2012/184:01:39:44	Restore LLT thresholds to 24 for dets. NaI0-5
7/11/12	2012/193:18:11:31	LLTs set to 59 for dets. NaI0-5
8/3/12	2012/216:18:57:10	Disable soft trigger algs. 22–26
	2012/216:18:57:15	McIlwain = 1.58
8/6/12	2012/219:13:30:05	Restore LLT thresholds to 24 for dets. NaI0-5
	2012/219:13:30:10	Re-enable soft trigger algs. 22–26
8/7/12	2012/220:16:01:37	LLTs set to 59 for dets. NaI0-5

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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2.4. GBM FSW Upgrade: Year Five and Six

2.5. Trigger Status Modifications during Years 5 and 6

The GBM GRB catalog analysis process is described in detail in the first and second catalog papers (see the appendix of Paciesas et al. 2012; von Kienlin et al. 2014). Here, we briefly summarize the major analysis steps.

3.1. Burst Localization and Detector Response Matrix (DRM)

3.2. GRB Duration, Peak Flux, and Fluence

The analysis of GBM data products is fundamentally a process of hypothesis testing wherein the trial source spectra and locations are converted to predicted detector count histograms, and these are statistically compared to the observed data. GBM uses a special burst spectroscopy software package called RMFIT.²⁴ Here, we report the duration, peak flux, and fluence of each burst using an automatic batch fit routine implemented within RMFIT. Burst durations T₅₀ (T₉₀) are determined from the interval between the times where the burst has reached 25% (5%) and 75% (95%) of its maximum fluence, as illustrated by the horizontal and vertical dashed lines in Figure 3. The burst durations T₅₀ and T₉₀ were computed in the 50–300 keV energy range. This is primarily due to the fact that GRBs have their maximum spectral density in this energy range. In addition, this energy range makes it easier to compare the present results with those of the predecessor BATSE. It may be noted that GRB durations have been shown to have a power-law dependence on energy (Qin et al. 2013). The fluence for each burst was computed in two energy ranges: 50–300 keV and 10–1000 keV. The peak fluxes for each burst were computed in the same energy ranges and for three different timescales: 64, 256, and 1024 ms. Since a relatively small number of bursts have detectable emission in the BGO detectors, only [Nai[Tl)] data were used for the catalog analysis.

For each burst, a set of [Nai[Tl)] detectors was chosen with low source angles (typically <60°) and no apparent blockage by any other GBM detector, by LAT, or by the LAT radiators. For the majority of bursts, the GBM CTIME data, which have 256 ms time resolution pre-trigger and 64 ms resolution post-trigger, were used. TTE data were used for bursts where at least one of the peak fluxes occurs at or before the trigger time, which happens for many short bursts and a few longer ones. For each selected detector illuminated by a burst, the source and background time intervals are then selected. The source interval covers the burst emission time plus approximately equal intervals of background before and after the burst (generally at least ∼20 s on either side for long GRBs while it is ∼5 s or shorter for short GRBs). Background intervals are selected before and after the burst, about twice as wide as the burst duration and having a good overlap with the selected source interval before and after the burst, as shown in Figure 2. Background regions before and after the burst are fit by a polynomial of up to fourth order separately for each detector. Depending on the background fluctuations, the lowest-order polynomial that gives a good fit is chosen. The background-subtracted counts spectrum of each time bin in the source interval is fit to a model incident photon spectrum by folding the photon spectrum with the DRM and minimizing the CSTAT.²⁵ For the T₉₀ analysis, the incident model spectrum is the "Comptonized" (COMP) photon model:

$$\begin{eqnarray*}&&{f}_{\mathrm{COMP}}(E)=A\ {\left(\displaystyle \frac{E}{{E}_{\mathrm{piv}}}\right)}^{\alpha }\mathrm{exp}\left[-\displaystyle \frac{(\alpha +2)\ E}{{E}_{\mathrm{peak}}}\right].\end{eqnarray*}$$

The best-fit parameters are: amplitude A, the low-energy spectral index α, and peak energy E_peak (the parameter E_piv is fixed to 100 keV).

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Figure 2 shows the light curve as measured by a single [Nai[Tl)] detector of a relatively long burst consisting of multiple emission periods, with the selected source and background intervals highlighted. Figure 3 shows a plot of the integrated GRB fluence in the 50–300 keV energy range derived from the model fitting for all time bins within the source interval. Several of the short duration plateaus seen in Figure 3 are the time intervals where no burst emission is observed. This function is used to determine the T₅₀ (T₉₀) burst duration from the interval between the times where the burst has reached 25% (5%) and 75% (95%) of its total fluence, as illustrated by the horizontal dashed lines.

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Peak fluxes and fluences are obtained in the same analysis, using the same choices of detector subset, source, background intervals, and background model fits. The peak flux is computed for three different time intervals: 64 ms, 256 ms, and 1.024 s in the energy range 10–1000 keV and, for comparison with the results presented in the BATSE catalog (Meegan et al. 1998), in the 50–300 keV energy range. The burst fluence is also determined in the same two energy ranges. The RMFIT analysis results presented above are stored in a BCAT fits file: glg_bcat_all_bnyymmddttt_vxx.fit with specified wildcards for the year (yy), month (mm), day (dd), fraction of a day (ttt), and version number (xx).

The catalog results can be accessed electronically through the High-Energy Astrophysics Science Archive Research Center browser interface at http://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html. Here, we provide tables that summarize selected parameters.

Table 5 lists the 1405 triggers of the first six years that were classified as GRBs. The GBM Trigger ID is shown along with a conventional GRB name as defined by the GRB-observing community. Note that the entire table is consistent with the small change in the GRB naming convention that became effective on 2010 January 1 (Barthelmy et al. 2009): if for a given date no burst has been "published" previously, then the first burst of the day observed by GBM includes the "A" designation even if it is the only one for that day. For year 5 and 6, only GBM-triggered GRBs for which a Gamma-ray burst Coordinates Network (GCN) Circular was issued are assigned a GRB name. The criterion for issuing a GBM Circular is if a GRB was either detected by any other mission (as listed in the last column of Table 5 ) or if it generated an ARR to the Fermi spacecraft or the count rate in the 50–300 keV energy range summed over the triggered detectors exceeded 1000 counts per second above the background. The third column lists the trigger time in universal time (UT). The next four columns of Table 5 list the sky location and associated statistical error,²⁶ along with the instrument that determined the location. The table also lists the GBM-derived location only if no higher-accuracy locations have been reported by any other instrument. If a higher-accuracy location is available, then its source is listed under the column "Location Source," which lists only the name of the mission rather than the specific instrument on board that mission (e.g., Swift implies the locations are either from Swift-BAT or Swift-XRT or Swift-UVOT). The errors on the GRB locations determined by other instruments are not necessarily 1σ values. For the GBM analysis, a location accuracy better than a few tenths of a degree provides no added benefit because of significant systematic errors in GBM location (Connaughton et al. 2015). Table 5 also shows which algorithm was triggered along with its timescale and energy range. Note that the listed algorithm is the first one to exceed its threshold but it may not be the only one. The table also lists other instruments that detected the same GRB.²⁷ Finally, we identify the GBM GRBs for which an ARR was issued by the GBM FSW in the last column of Table 5. We have a total of 93 GRBs (6.6% of the total) followed by ARRs during the first six years of Fermi, although the spacecraft might not have slewed in every case for technical reasons, such as Earth limb constraints. The majority of these ARRs were due to high peak fluxes. In addition, there were 26 ARRs that were issued for non-GRB triggers because of the misclassification by the GBM FSW.

The results of the duration analysis are shown in Tables 6–8. The values of T₅₀ and T₉₀ in the 50–300 keV energy range are listed in Table 6 along with their respective 1σ error estimates (Koshut et al. 1996) and start times relative to the trigger time. For a few GRBs, the duration analysis could not be performed either because the event was too weak or due to technical problems with the input data. Also, it may be noted that the duration estimates are only valid for the portion of the burst that is visible in GBM light curves summed over those [Nai[Tl)] detectors whose normals make less than 60° to the source. If the burst was partially occulted by Earth or had significant emission while GBM detectors were turned off in the SAA region, then the "true" durations may be underestimated or overestimated, depending on the intensity and variability of the undetected burst emission. GRBs which triggered while Fermi was close to SAA or the trigger is unusual in any other way, are indicated in Table 5 by a footnote. For technical reasons, it was not possible to perform a single analysis of the unusually long GRB091024A (Gruber et al. 2011) and GRB130925A, and so the analysis was carried out separately for the two triggered episodes. Similarly, GRB130925A (Evans et al. 2014; Greiner et al. 2014) also had three emission episodes well separated in time, for which GBM triggered on the first two episodes. These cases are also noted in the Table 5. The reader may note that for most GRBs, the present analysis used data binned no finer than 64 ms, and so the duration estimates (but not the errors) are quantized in units of 64 ms. However, for a few extremely short events, TTE/CTTE data were binned with widths of 32 ms or even 16 ms in a few cases. As a part of the duration analysis, peak fluxes and fluences were computed in two different energy ranges. Table 7 shows the values in 10–1000 keV and Table 8 shows the values in 50–300 keV. The analysis results for low fluence events are subject to large systematic errors primarily because they use 8-channel spectral data and should be used with caution. The fluence measurements in the spectroscopy catalog (Gruber et al. 2014), which uses the 128-channel CSPEC or TTE data, are more reliable for such weak events.

Figure 4 shows the sky distribution of GBM-triggered GRBs in Galactic coordinates. Crosses indicate long GRBs (T₉₀ > 2 s) and asterisks indicate short GRBs. Both the long and short GRB locations do not show any obvious anisotropy, which is consistent with an isotropic distribution of GRB arrival directions. Also shown are the locations of GRBs that triggered Swift-BAT in coincidence with GBM. Many of these Swift coincident GRBs also have redshifts estimated by detecting the optical afterglows with ground-based telescopes.

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The histograms of the logarithms of GBM-triggered GRB durations (T₅₀ and T₉₀) are shown in Figure 5. Using the conventional division between the short and long GRB classes (T₉₀ ≤ 2 s and T₉₀ > 2 s, respectively), we find that during the first 6 years there were 229 short GRBs and 1175 long GRBs. The short and long GRBs, as defined by their T₉₀ in 50–300 keV, may belong to two different classes (Kouveliotou et al. 1993). However, from the T₉₀ distribution shown in Figure 5, the distinction seems to be less than obvious. There are also several claims in the literature concerning the existence of three types of GRBs based on multiple GRB parameters like duration, fluence, spectrum, spectral lag, peak-count rate, etc., from the BATSE sample (Mukherjee et al. 1998; Horváth et al. 2006), Swift sample (Veres et al. 2010), and RHESSI sample (R̆ipa et al. 2012). The three groups are the familiar short-hard GRBs, long-soft GRBs, and soft-intermediate duration GRBs bridging the other two groups. Hence, we decided to independently assess the number of groups in the GRB durations (T₉₀ and T₅₀) as well as the duration-hardness distributions using a model-based clustering method with lognormal model components ("mclust"; Fraley & Raftery 2000). This method uses a binning-independent maximum likelihood function with correction for the degrees of freedom, refered to as the Bayesian Information Criterion (BIC). We find that both the log T₅₀ and log T₉₀ distributions are best described by two components with equal variance (see Figure 6). The difference in the BIC values between two and three components is 12 for T₅₀ and ∼15 for T₉₀ (see Figure 6), both suggesting a strong preference for two groups of GRBs in the present sample. Figure 5 also shows separately the lognormal fits to long and short GRBs. The variances of the lognormal components are constrained to be equal for each group. The goodness of fit is estimated using Kolmogorov-Smirnov test that yields probabilities of 0.745 and 0.796 in favor of the null hypothesis (data and model are drawn from the same distribution) for the T₉₀ and T₅₀ distributions, respectively.

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In addition, to quantify the extent to which two groups are statistically preferred compared to three populations, we have carried out Monte Carlo simulations. First, we simulated 10⁵ instances of T₉₀ and T₅₀ with the best two-group solution. We found that in 16 (p = 1.6 × 10⁻⁴) and 24 (p = 2.4 × 10⁻⁴) cases, respectively, the three-group solution was preferred. To gauge the significance of the three-group solutions, we have simulated 10⁴ instances with the best three-group solution for both T₉₀ and T₅₀. We found that a three-group solution was only preferred in 3 and 41 cases, respectively. This indicates that in the three-group solution, the third group is not clearly distinguished.

Because the GRB groups have less overlap if we consider more than one dimension, we consider the hardness in addition to the duration (discussed later in this section). We use only those bursts which have hardness errors less than the hardness value. We end up with a sample size of 1222. Using the BIC analysis again, we find that, similar to the one-dimensional distribution of durations, the duration-hardness data are also best described by two groups (see Figure 7). In Figure 7, the ellipses mark the 1σ contours of the two-dimensional Gaussians. They encompass ≈ 0.39 of the volume of the individual components (this is analogous to the 0.68 fraction marking the 1σ region in the one-dimensional Gaussian case). We find that 40.1% and 39.8% GRBs are contained within the ellipses for the short and long cases, respectively, which is consistent with the expectations. The difference between the best 2 and 3 group solutions is 4.6 and 8.9 for the T₉₀–HR (bottom) and T₅₀–HR (top) distributions, respectively. In the parlance of the BIC values, these constitute strong evidence for the two-group solution. In order to obtain a more quantitative assessment, we have again simulated distributions with the best two-group solution and found no cases in 10³ trials (p < 10⁻³) and 3 (p = 3 × 10⁻³) cases where the 3 three-group solution was preferred in the T₉₀–HR and T₅₀–HR distributions, respectively. In the case of the T₉₀–HR distribution, the best model has ellipsoidal components with equal volumes and shapes, but their orientation is free to vary (Figure 8 black solid line). For the T₅₀–HR distribution, the best model also has ellipsoidal components while their volumes, shapes, and orientations are constrained to be equal (Figure 8 black solid line). In short, the model-based clustering method applied to the hardness ratios and durations unveils only two clusters as the best solution: classical short/hard and long/soft groups consistent with a similar analysis carried out on the RHESSI data (R̆ipa et al. 2012).

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Using an entirely independent approach to estimate the number of populations that can exist in the observer-frame T₉₀ distribution, we employ a Bayesian Dirichlet mixture model composed of Gaussians (see Gershman & Blei 2012). This enables us to ask the question of how many sub-populations exist rather than asking whether three populations fit the data better than two populations. We use an approach similar to that followed by Chattopadhyay et al. (2007), except that we adopt a hierarchical Bayesian approach which allows us to leave the concentration as a free parameter in the model. The model returns posterior distributions of the probability for each sub-population that is found. We find that there are two significant Gaussian sub-populations with 95% highest density intervals for their existence covering p = 0.77–0.84 and p = 0.15–0.23 corresponding to Gaussian means of 27.5 and 0.79 s, respectively, for long and short bursts. Since the entire Dirichlet must sum to p = 1, this leaves little room for a third sub-population. In fact, the next-highest probability for an additional subpopulation is 0.001. Additionally, we checked this using Student-t distributions to model the sub-populations, i.e., seeing if non-normality or outliers changed the distributions. We found similar results with the Student-t distributions converging to Gaussians. We can therefore conclude that there exist only two sub-populations in the T₉₀ distribution of GBM-detected GRBs.

For a comparison with the BATSE distribution of GRB durations, we have performed the same classification on the current BATSE catalog of 2041 GRBs consisting of 500 short and 1541 long GRBs.²⁸ For the GBM GRB sample, the best-fitting model is two components with equal variances, while for the BATSE sample it is the two component with unequal variances. To compare similar quantities, we forced the unequal variance model for GBM (which gives only a marginally worse fit) and compared it to the BATSE models. The mean T₉₀ for the short bursts for BATSE versus GBM are ${T}_{{\rm{mean,short}}}^{{\rm{BATSE}}}=0.85\;{\rm{s}}$ and ${T}_{{\rm{mean,short}}}^{{\rm{GBM}}}=0.82\;{\rm{s}}$ for the long, similarly BATSE versus GBM ${T}_{{\rm{mean,long}}}^{{\rm{BATSE}}}=35.6\;{\rm{s}}$ and  ${T}_{{\rm{mean,long}}}^{{\rm{GBM}}}=28.3\;{\rm{s}}$. The mean durations of the short and long GRBs are consistent with those estimated above by the Bayesian analysis. It may be noted that the mean durations of the GBM-detected long GRBs is smaller than those of the BATSE-detected long GRBs. This could be an indication of the well-known tip-of-the-iceberg effect resulting from the higher sensitivity of BATSE detectors, which are 16 times larger than the GBM detectors.

The standard deviations of ${\mathrm{log}}_{10}({T}_{90}/{\rm{s}})$ for short bursts in the GBM sample is 0.51 while for BATSE it is 0.64. The same quantity for long GRBs in the GBM sample is 0.64 while for BATSE it is 0.42. The larger difference between the widths of long and short GRBs of the BATSE sample explains the preference for the model with unequal variances. However, the reason for unequal widths is not clear.

Since there are several changes and interruptions in the GBM triggers and trigger algorithms during this catalog period (see Table 4), it will not be strictly accurate to obtain the burst rate by dividing the number of bursts by the total duration of six years. Instead, we derived the average GRB rates by fitting the integral interval distributions of the burst trigger times to an exponential distribution function. The estimated daily rate of short GRBs is (0.137 ± 0.009) while that of long GRBs is 0.602 ± 0.018. The fraction of short GRBs is 0.207 ± 0.015. Selecting periods where all three BATSE trigger algorithms were set to the same value (e.g., a threshold of 5.5σ from 1992 September 14 to 1994 September 19 and from 1996 August 29 to the end of the mission), the observed fraction of short GRBs is 24% (Paciesas et al. 1999). The shortest and longest time intervals between consecutive short bursts are 1.34 hr and 59 days, respectively, while the average interval is 7.28 days. Similarly, the shortest and longest time intervals between consecutive long bursts are 631 s and 11.8 days (with no interruptions) while the average interval is 1.66 days. As already claimed in the first catalog, we ascribe the lower fraction of short GRBs observed with GBM (20.7%) compared to BATSE (24%) not to a deficit of short events, but rather to an excess of long events detected by GBM's longer timescale trigger algorithms (see Section 2.3). The average GBM GRB trigger rate of ∼242 ± 6.5 bursts year⁻¹ is comparable to the BATSE rate of  300 bursts year⁻¹, despite the large difference in area between the BATSE and GBM detectors. The BATSE detectors were a factor of 16 larger in area, as mentioned before, resulting in a difference of a factor of four in sensitivity. However, the log N–log P curve is much flatter near the BATSE threshold than the −3/2 power law seen at higher intensities. Also, the GBM trigger thresholds is set at 4.5σ above threshold, while for BATSE it was set at 5.5σ. The higher setting was needed to reject BATSE triggers due to fluctuations in the flux from Cygnus X-1. Although GBM employs 12 detectors compared to 8 for BATSE, the sky coverage is about the same due to obstructions by the LAT on Fermi, as opposed to clear views obtained on the Compton Gamma-ray Observatory (CGRO). Most significantly, GBM triggers on 5 timescales from 16 to 4096 ms, at two different phases, whereas BATSE triggered only on 3 timescales 64, 256, and 1024 ms. Pre-launch predictions of the GBM burst rate were approximately 200 bursts year⁻¹ based on scaling from BATSE and assuming the same trigger algorithms. This is, within statistics, the observed rate of GBM triggers that would have triggered on one of the BATSE timescales. The additional ∼ 42 bursts year⁻¹ arise mostly from the triggers on the new 4096 ms timescale.

Since the orbits of Fermi and GRO are similar, GBM and BATSE should have similar celestial sensitivity maps. However, sensitivity sky maps are not maintained for GBM since the isotropy of gamma-ray bursts is no longer controversial. Furthermore GBM slightly favors triggering on long GRBs, since the thresholds for the 64 ms timescales are higher (5.0σ, see Table 2) than for 256 and 1024 ms (both 4.5σ).²⁹

To characterize the dependence of burst spectral hardness on the duration, we computed the hardness of each GRB as the ratio of burst fluence during the T₅₀ or T₉₀ intervals in the energy band 50–300 keV to that in the 10–50 keV band. In this analysis, the hardness was derived from the time-resolved spectral fits for each GRB by using photon model fit parameters that are a by-product of the duration analysis. Figure 9 shows scatter plots of hardness versus T₅₀ and T₉₀ durations, showing that the GBM data also exhibit the anti-correlation of spectral hardness with duration as known from BATSE data (Kouveliotou et al. 1993). However, the individual data points are somewhat misleading, as the high hardness ratios tend to have large statistical errors, which are not plotted for the sake of clarity. Hence, we also computed the weighted mean hardness ratios for GRBs in equal bins of logarithmic durations.³⁰ These are shown in green with their corresponding weighted errors. The green points indicate a gradual hardening of the GRBs as the durations fall below T₉₀ = 2 s, which is in contrast to PHEBUS³¹ and BATSE observations, which showed a more discrete change in hardness at T₉₀ = 2 s (Dezalay et al. 1992; Paciesas et al. 1998). However, we do not see any positive correlation of hardness ratio with duration for long GRBs as reported previously (Dezalay et al. 1996). Instead, we see a weak anti-correlation (correlation coefficient of −0.17) of hardness ratio with duration of long GRBs in our six year sample.

Integral distributions of the peak fluxes observed for GRBs in the first six years are shown in Figures 10–12 for the three different timescales and separately for short and long GRBs. In Euclidean space, if all of the long GRB progenitors are uniformly distributed, then they would be expected to follow a −3/2 power law. However, in Big Bang cosmology, the effects of the (unknown) GRB luminosity function, along with their distribution in redshift (which follows more or less the star formation rate up to z ∼ 4) and the threshold of the instrument are all convolved together to produce the observed distribution. The GRB peak flux distributions could, however, provide useful constraints in various astrophysical studies, such as in determining the true GRB rate for any jet model (Guetta et al. 2005). The integral fluence distributions for the two energy intervals are also shown in Figure 13. It may be noted that the integral fluence distributions show far more curvature than the integral peak flux distributions. Although the deficit at the highest fluence end may be due to small number statistics, the observed departure from the expected power law of slope −3/2 at low fluence may be due to the fact that these GRB fluence estimates suffer from relatively large systematic errors, primarily due to the limited spectral channels and rather narrow time bins with very few events which are used for spectral fitting. Moreover, GRB triggers on GRB peak flux and not on fluence, so that there is no clear, well-defined GBM fluence threshold.

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The third GBM catalog comprises a list of 1403 cosmic GRBs that triggered GBM between 2008 July 12 and 2014 July 11. The increased sample of GRBs in this catalog confirms the conclusions of the earlier two year and four year catalogs. The six year average GRB rate detected by GBM is (0.662 ± 0.018) per day. The shortest and longest time interval between consecutive GRB triggers is 10 minutes and 11.77 days (with no interruptions), respectively. The shortest time interval is close to the minimum time for GBM to re-trigger. The longest time interval is ∼8 times larger than the average value of 1.5 days. Assuming that the GRB triggers follow Poisson statistics, this implies that such a large time gap could occur once in ∼10 years. The average rate of burst detections per year is (∼242 ± 6.5 year⁻¹), which is only slightly smaller compared to the detection rate of the BATSE instrument of ∼300 year⁻¹ (Paciesas et al. 1999). One would have expected a larger difference due to the superior detection sensitivity of BATSE. This perhaps can be explained by GBM's additional range of trigger timescales (primarily the 2 and 4 s timescales), which are compensating for the higher burst detection threshold of GBM (∼ 0.7 versus ∼ 0.2 photons cm⁻² s⁻¹ for BATSE). The distribution of GBM durations is consistent with the well-known bimodal distribution measured previously (Kouveliotou et al. 1993).This is supported by two independent analyses. Assuming a T₉₀ value of 2 s to distinguish between short and long GRBs, the median durations of the two groups are 0.58 s and 26.62 s for the GBM sample, while they are 0.45 s and 30.75 s, respectively, for the BATSE sample. The median duration of GBM-detected long bursts is lower than that of BATSE-detected long GRBs. However, the fraction of short GRBs in the GBM sample is about 21%, which is not significantly different from that detected by BATSE, which is 24%.

Support for the German contribution to G.B.M. was provided by the Bundesministerium für Bildung und Forschung (BMBF) via the Deutsches Zentrum für Luft und Raumfahrt (DLR) under contract number 50 QV 0301. A.v.K. was supported by the Bundesministeriums für Wirtschaft und Technologie (BMWi) through DLR grant 50 OG 1101. S.M.B. and O.J.R. acknowledge support from Science Foundation Ireland under grant No. 12/IP/1288. H.F.Y. acknowledges support by the DFG cluster of excellence "Origin and Structure of the universe." A.G. is funded by the NASA Postdoctoral Program through Oak Ridge Associated Universities. The UAH co-authors gratefully acknowledge NASA funding from co-operative agreement NNM11AA01A. C.K. and C.A.W.H. gratefully acknowledge NASA funding through the Fermi GBM project.