THE FERMI GBM GAMMA-RAY BURST SPECTRAL CATALOG: FOUR YEARS OF DATA

The detector selection is consistent with Goldstein et al. (2012), i.e., a maximum of three Na i detectors together with one BGO detector were used for the spectral analysis. Since the effective area (i.e., detection efficiency) of the Na i detectors decreases rapidly for high incidence angles (Bissaldi et al. 2009) only detectors with source angles ⩽60° are used for the spectral analysis. In addition, it has been verified that the detectors were neither obstructed by the spacecraft nor by the solar panels of Fermi. However, due to small inaccuracies in the spacecraft mass model or location uncertainties, the blockage code does not always return a subset of detectors that is free from blockage. This is evident when the low-energy data deviate strongly from the fit model (Goldstein et al. 2012). When this occurs we remove these detectors from the selected sample. If more than three Na i detectors are qualified for the spectral fitting, the Na i detectors with the smallest source angles were used to avoid a fitting bias toward lower energies.

GBM persistently records two different types of science data, called CTIME (fine time resolution, coarse spectral resolution of 8 energy channels) and CSPEC (coarse time resolution, full spectral resolution of 128 energy channels). CTIME (CSPEC) data have a nominal time resolution of 0.256 s (4.096 s) which is increased to 64 ms (1.024 s) whenever GBM triggers on an event. After 600 s in triggered mode, both data types return to their non-triggered time resolution. The third and primary data type used in this catalog is the "time tagged events" (TTEs) which consist of individual events, each tagged with arrival time (2 μs precision), energy (128 channels) and detector number. The TTE data are generated and stored on-board in a continuously recycling buffer. When GBM enters trigger mode, the buffered pre-trigger TTE are transmitted as science data along with ∼300 s of post-trigger TTE.

For the purpose of this catalog, we choose a standard time binning of 1024 ms for bursts longer than 2 s in duration as defined by the burst T₉₀ (Kouveliotou et al. 1993) presented in von Kienlin et al. (2014) and 64 ms for bursts of duration 2 s and shorter. The time history of TTE typically starts at ∼30 s before trigger and extends to ∼300 s after trigger. This TTE data time span is adequate for the analysis of most GRBs. For GRBs that have evident precursors or emissions that last more than 300 s after trigger, we use the CSPEC data, which extend ∼4000 s before and after the burst for triggered events. CSPEC data were used for 76 GRBs in this catalog.

With the optimum subset of detectors selected, the best time and energy selections are chosen to fit the data. The available and reliable energy channels in the Na i detectors lie between ∼8 keV and ∼1 MeV. This selection excludes the overflow channel at high energies and those channels <8 keV where the transmission of gamma-rays is poor due to the silicone pad in front of the Na i crystal and the multi layer insulation around the detectors (Bissaldi et al. 2009). We perform a similar selection to the BGO detector for each burst, selecting channels between ∼300 keV and ∼38 MeV. We select enough pre- and post-burst data to sufficiently model the background and fit a single energy dependent polynomial (choosing up to fourth order) to the background. For each detector the time selection and polynomial order are varied until the χ² statistic map over all energy channels is minimized, resulting in an adequate background fit. This approach is rather subjective in that it is dependent on the observer's choice of the background intervals. In the future, it may be advantageous to implement more objective background selection methods such as the "direction dependent background fitting" method presented in Szécsi et al. (2013).

Knowing the background model, the background-subtracted count rates are summed over all Na i detectors for a given burst to produce a single GRB count light curve. Using this light curve, only time bins (1.024 s for long burst and 64 ms for short bursts) with an S/N greater or equal to 3.5 were selected, in agreement with Goldstein et al. (2012). This time selection is then applied to all detectors for a given burst.

This criterion ensures that there is adequate signal to successfully perform a spectral fit and constrain the parameters of the fit. This does however eliminate some faint bursts from the catalog sample (i.e., those with no time bins with signal above 3.5σ). While the possibility remains that not all signal from the GRB was selected, this method nevertheless provides the most objective way to obtain a selection of intrinsic GRB counts as including less significant bins would only increase the uncertainty in the measurements.

This selection is what we refer to as the F selection, since it is a time-integrated selection and the derived photon and energy fluences are representative of but not equal to the fluence over the total duration of the burst. We draw attention to the fact that time bins with an S/N less than 3.5, which were not included in the fitting process, also contribute to the photon and energy fluence. For more than 80% of the GRBs in the catalogue the ratio of count fluence (without the intervals with S/N < 3.5) versus the total counts (with the intervals with S/N < 3.5) is larger than 0.8. So while there are some bursts for which the fluence can be considerably underestimated, the other option would be to overestimate the fluence of those bursts by including background that contaminates the spectral fits.

The other selection performed is a 1.024 s peak photon flux selection for long bursts (T₉₀ > 2 s) and 64 ms peak count rate flux selection for short bursts (T₉₀ ⩽ 2 s). This selection is made by adding the count rates in the Na i detectors again and selecting the single bin of signal with the highest background-subtracted count rate. This selection is a snapshot of the energetics at the most intense part of the burst and is depicted as the P selection.

Figure 1 shows the distribution of accumulation times used for the fitting process based on the signal-to-noise selection criteria. The distribution of accumulation times reported is similar to the observed emission time of the burst, excluding quiescent periods, (e.g., Mitrofanov et al. 1999) and peaks at 0.26 s and ∼15 s for short and long GRBs, respectively. The dividing duration time scale between the two classes of GRBs is ∼1.27 s and is, as expected from the employed source selection methodology, somewhat smaller than the canonical 2 s (Kouveliotou et al. 1993). Figure 1 also includes the comparisons of the model photon fluence and model photon flux compared to the accumulation time. In both cases two specific regions are visible for long and short GRBs. In addition, Figures 1(b) and 1(c) show a clear correlation between the photon fluence (flux) and accumulation time, indicating the existence of two different burst groups, similar to the ones delineated by the hardness–duration relationship found by Kouveliotou et al. (1993).

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The single power law with two free parameters is defined as

$$\begin{equation} f_{ \rm {PL} }(E) = A \left(\frac{ E }{ E_{{\rm piv}} } \right)^{ \lambda }, \end{equation} \tag{ 1 }$$

where A is the amplitude and λ is the spectral index. The pivot energy (E_piv) normalizes the model to the energy range under consideration and helps reduce cross-correlation of other parameters. In all cases, E_piv is held fixed at 100 keV. While most GRBs exhibit a spectral break in the GBM passband, some GRBs are too weak to adequately constrain this break in the fits. These bursts are well fit by the single power law.

Band's GRB function (Band et al. 1993) has become the standard for fitting GRB spectra, and therefore we include it in our analysis:

$$\begin{eqnarray} f_{\rm { BAND} }(E) &=& A \left\lbrace \begin{array}{@{}l@{}}\left(\frac{E}{100 \ \rm keV }\right)^{\alpha } \exp \left [- \frac{ (\alpha +2) E}{ E_{\rm peak} } \right ], \ E < \frac{ (\alpha - \beta) \ E_{\rm peak} }{ \alpha +2} \\ \left(\frac{E}{ 100 \ \rm keV } \right)^{ \beta } \exp (\beta -\alpha) \left [ \frac{(\alpha -\beta) E_{\rm peak}}{100 \ \rm keV \ (\alpha +2)} \right ]^{\alpha -\beta }. \\ E \ge \frac{(\alpha -\beta) \ E_{\rm peak}}{\alpha +2} \end{array}\right.\nonumber\\ \end{eqnarray} \tag{ 2 }$$

The four free parameters are the amplitude, A, the low- and high-energy spectral indices, α and β, respectively, and the νF_ν peak energy, E_peak. This function is essentially a smoothly broken power law with a curvature defined by its spectral indices. The low-energy index spectrum is a power-law only asymptotically.

The Comptonized model is an exponentially cutoff power law, which is a subset of the Band function in the limit that β → −∞:

$$\begin{equation} f_{\rm {\scriptsize {COMP}}}(E) = A \ \left(\frac{E}{E_{{\rm piv}}}\right) ^{\alpha } \exp \left [ -\frac{(\alpha +2) \ E}{E_{\rm peak}} \right ] \end{equation} \tag{ 3 }$$

The three free parameters are the amplitude A, the low-energy spectral index α and E_peak. E_piv is again fixed to 100 keV, as for the power-law model.

The final model that we consider in this catalog is a broken power law characterized by one break with flexible curvature and is able to fit spectra with sharp or smooth transitions between the low- and high-energy power laws. This model, first published in Ryde (1999), where the logarithmic derivative of the photon flux is a continuous hyperbolic tangent, has been re-parameterized (Kaneko et al. 2006) as given below:

$$\begin{equation} f_{\rm {\scriptsize {SBPL}}}(E)=A \left (\frac{E}{E_{{\rm piv}}} \right)^b \ 10^{(a - a_{{\rm piv}})}, \end{equation} \tag{ 4 }$$

where

$$\begin{eqnarray} a&=&m\Delta \ln \left(\frac{e^q+e^{-q}}{2}\right), \nonumber \\ a_{{\rm piv}}&=&m\Delta \ln \left(\frac{e^{q_{{\rm piv}}}+e^{-q_{{\rm piv}}}}{2} \right), \nonumber \\ q&=&\frac{\log (E/E_b)}{\Delta }, \quad q_{{\rm piv}}=\frac{\log (E_{{\rm piv}}/E_b)}{\Delta },\nonumber \\ m&=&\frac{\lambda _2-\lambda _1}{2}, \quad b=\frac{\lambda _1+\lambda _2}{2}. \end{eqnarray} \tag{ 5 }$$

In the above relations, the low- and high-energy power-law indices are λ₁ and λ₂, respectively, E_b is the break energy in keV, and Δ is the break scale in decades of energy. The break scale is independent and not coupled to the power-law indices as for the Band function, and represents an additional degree of freedom. However, Kaneko et al. (2006) found that an appropriate value for Δ for GRB spectra is 0.3; therefore, we fix Δ at this value. In addition, we tested the behavior of Δ for some bright GRBs by letting it vary during the fit process. The results of this study are presented in Section 6.

We choose to fit these four different functions because the measurable spectrum of GRBs is dependent on intensity. Less intense bursts (in the observer frame) provide less data to support a large number of parameters. This may appear obvious, but it allows us to determine why in many situations a particular empirical function provides a poor fit, while in other cases it provides an accurate fit. For example, the energy spectra of GRBs are normally well fit by two smoothly joined power laws. For particularly bright GRBs, the Band and Sbpl functions are typically an accurate description of the spectrum, while for weaker bursts the Comp function is most appropriate. Bursts that have signal significance on the order of the background fluctuations do not have a detectable distinctive break in their spectrum and so the power law is the most appropriate function.

We classify fitted burst models as GOOD if the parameter error of all model parameters is within certain limits. This is a more conservative approach compared to Kaneko et al. (2006) and Goldstein et al. (2012) who only required the error of the parameter of interest to be within given limits. The motivation behind this new approach is to show parameter values of models which are globally well-constrained, rather than basing interpretations on constrained parameters of overall poorly constrained models. We simultaneously require for the low-energy power law an error less than 0.4, for high-energy power-law indices an error less than 1.0 and for all other parameters we require a relative error of 0.4 or less. These criteria are an arbitrary choice but are in line with other GRB catalogs (Kaneko et al. 2006; Goldstein et al. 2012). Applying these criteria, the number of bursts that classify as GOOD for each employed model can be seen in Table 2. We draw the reader's attention to the fact that for many GRBs there can be several models which qualify as GOOD.

In addition, we define a BEST sample in order to determine which of the GOOD models is the best representation of the burst emission. Besides the necessity of having constrained parameters—already required for the GOOD sample—we compare the difference in C-Stat (ΔC-Stat) per degree of freedom between the various models. In order to assess if a statistically more complex model, i.e., a model with more free fit parameters (hypothesis H1) is preferred over a simpler model (null hypothesis H0) according to its difference in C-Stat, we created a set of 5 × 10⁴ synthetic GRB spectra using the fit parameters of H0, obtained from the fit to the real data, as source counts. Similarly, the background counts of the synthesized spectra are estimated from the real data. The input source counts are then folded through the DRM. Finally, Poisson noise was added to the sum of the source and background counts. The synthetic spectra were then fitted with both models, adding Poisson fluctuations to each energy channel of the background spectrum during the fit process.

Integrating the ΔC-Stat distribution from 0% to 99.73% (i.e., a 3σ confidence interval) we identified a critical ΔC-Stat_crit. If the ΔC-Stat observed in the real data exceeds this critical value, then the null hypothesis is rejected and the statistically more complex model is preferred.

As the full GRB sample contains nearly 1000 GRBs doing the aforementioned analysis for all bursts is not feasible. We used four typical bursts which are located in four energy fluence classes, separated by one order of magnitude. These bursts are GRB 120608.489, GRB 110227.240, GRB 120129.580 and GRB 120526.303 with an energy fluence [10 keV–1 MeV] of 5.2 × 10⁻⁷ erg cm⁻², 1.9 × 10⁻⁶ erg cm⁻², 5.8 × 10⁻⁵ erg cm⁻², 1.3 × ⁻⁴ erg cm⁻², respectively.

For each of the aforementioned GRBs, we created a Pl versus Comp and a Comp versus Band distribution and determined the ΔC-Stat_crit for each model comparison. To assess which of the four models qualifies for the BEST sample we used the critical values as a function of fluence. For the comparison between the Band and the Sbpl such simulations were not necessary, as both functions have the same number of degrees of freedom. Therefore, the model with the lower C-Stat value was used.

As there is no observable correlation between ΔC-Stat_crit and the energy fluence (see Table 1) we use the average ΔC-Stat_crit value, for the model selection of all bursts, i.e., for Pl versus Comp we use ΔC-Stat_crit = 8.58 and for Comp versus Band we use ΔC-Stat_crit = 11.83

The key idea for the BEST parameter sample is to obtain the best estimate of the observed properties of GRBs. By using model comparison, the preferred model is selected, and the parameters are reviewed for that model. The models contained herein and in most GRB spectral analyses are empirical models, based only on the data received; therefore the data from different GRBs tend to support different models. Perhaps it will be possible to determine the physics of the emission process by investigating the tendencies of the data to support a particular model over others. This is the motivation to provide a sample that contains the best picture of the global properties of the data, that prompts the investigation of the BEST sample.

Applying the BEST criteria we are left with 941 GRBs for the fluence spectra and 932 GRBs for the P spectra (see again Table 2). These numbers are smaller than the total number of GRBs in this catalog (943). This is due to the fact that for some bursts the spectral fit did not converge properly and these bursts have been excluded from the BEST sample.

In Table 2 we present the composition of models for the BEST samples. From this table, it is apparent that the F spectral fits strongly favors the Comp model over the others in over half of all GRBs. The Band and Sbpl are favored by only few GRBs in the catalog. It should be noted that the number of GRBs best fit by Pl increases in the P selection mainly due to the fact that the smaller statistics from the short integration time are unable to support a model more complex than the Pl.

In addition to the BEST sample, we form a sample of GRBs with known redshift¹⁵ (determined either spectroscopically or photometrically) to investigate the rest-frame properties of the GRBs (see, e.g., Gruber et al. 2011a). The redshift distribution of the GBM GRBs with known redshift to date is shown in Figure 2. The redshift sample contains 45 triggered GRBs with an additional 3 untriggered GRBs (Gruber et al. 2012) for the F spectral fits. As apparent from Figure 2, the sample of GBM GRBs with measured redshift is compatible with the full sample of GRBs with redshift and therefore it can be concluded that the GBM observations do not introduce a new bias for bursts with measured redshift. This is also confirmed by an K-S test which yields a probability of 98% that the two distributions are drawn from the same population.

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At all times the cosmological parameters obtained from the Planck mission (Planck Collaboration 2005) with H₀ = 67.3 km s⁻¹ Mpc⁻¹, Ω_m = 0.315 (Ade et al. 2013) were used for this analysis.

The time-integrated spectral distributions depict the overall emission properties and do not take into account any spectral evolution. The low-energy indices, as shown in Figure 3, are distributed about a −1.1 power law typical of most GRBs. Up to 17% of the BEST low-energy indices exceed α > −2/3, violating the synchrotron "line-of-death" (Preece et al. 1998a), while an additional 18% of the indices are α < −3/2, violating the synchrotron cooling limit. The high-energy indices in Figure 4 peak at a slope of about −2.1 and have a long tail toward steeper indices. Note that very steep high-energy indices in the distribution of all high-energy index values indicate that the spectrum of these GRBs mimics closely a Comp model, which is equivalent to a Band function with a high-energy index of −∞. A significant fraction of Band model fits results in a high-energy power-law index β > −2 which would indicate a divergent energy flux at high energies. However, it was pointed out by Ackermann et al. (2012b) that the inclusion of Fermi/LAT upper limits in the fitting process results in considerably steeper (softer) high-energy power-law indices. The median value decreased from β ∼ −2.2 from the GBM-only fits to β ∼ −2.5 for the GBM and LAT joint spectral fits. Indeed, not a single case of their sample had a high-energy power-law index > − 2 after LAT data had been included. Ackermann et al. (2012b) conclude that intrinsic spectral breaks and/or softer-than-measured high-energy spectra must be fairly common in the GRB population in order to explain the lack of LAT-detected GRBs.

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The comparison of the single power-law index to the low- and high-energy indices makes evident that the simple power-law index is averaged over the break energy, resulting in an index that is on average steeper than the low-energy index, yet shallower than the high-energy index. In addition, the lack of power-law indices steeper than −2 suggest that GBM does not detect a population of GRBs with low E_peak. If a burst had a Band spectrum with E_peak near or below the GBM energy threshold a single power-law fit should have an index smaller than −2.

We also show in Figure 5 the difference between the time-integrated low- and high-energy spectral indices, ΔS = (α − β). This quantity is useful since the synchrotron shock model (SSM) makes predictions of this value in a number of cases (Preece et al. 2002) and the power-law index, p, of the electron distribution can be inferred from ΔS. The distributions of ΔS obtained from the GOOD and BEST F spectral fits are consistent with the time-resolved results in Preece et al. (2002), as well as the time-integrated results in Kaneko et al. (2006), peaking at ΔS ∼ 1 with a median value of 1.25.

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In Figures 6 and 7, we show the distributions for the break energy, E_b and the peak of the power density spectrum, E_peak, respectively. E_b is the energy at which the low- and high-energy power laws are joined, which is not necessarily representative of the E_peak. However, one can easily derive E_b from the Band E_peak values following Kaneko et al. (2006). The E_b for the GOOD Sbpl and Band fits has a clustering about 120 keV spanning roughly two orders of magnitude. The E_b distribution for the BEST sample is skewed to slightly smaller values than the GOOD sample implying that the Sbpl is more likely to be statistically preferred if E_b is low. The GOOD and BEST E_peak distributions all generally peak around 150–200 keV and cover just over two orders of magnitude, which is consistent with previous findings (Mallozzi et al. 1995; Lloyd et al. 2000) from BATSE. As discussed in Kaneko et al. (2006), although the Sbpl is parameterized with E_b, the E_peak can be derived from the functional form. We have calculated the E_peak for all bursts with low-energy index shallower than −2 and high-energy index steeper than −2.

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The overall distribution of E_peak is similar to that found using the BATSE Large Area Detectors, which had a much smaller bandwidth and larger collecting area. This would seem to indicate that it is unlikely a hidden population to be undiscovered within the 10 keV–40 MeV range which is in line with the results by Harris & Share (1998).

The value of E_peak can strongly affect the measurement of the low-energy index of the spectrum, as shown in Figure 8. A general trend appears to show that spectra with smaller E_peak values also have smaller values of the low-energy power-law index. This is due to the fact that when E_peak is close to the instrument's lower energy sensitivity limit, α has not yet reached its asymptotical value and is thus, on average, softer than it is in reality. In addition, smaller E_peak values tend to increase the uncertainty in the measurement of the low-energy index, mostly due to the fact that a spectrum with a low E_peak will exhibit most of its curvature near the lower end of the instrument bandpass.

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It is of interest to study the difference in the value of E_peak between the Band and Comp functions since they are the two main functions used to study GRB spectra, and Comp is a special case of Band. To study the relative deviation between the two values we calculate a statistic based on the difference between the values and taking into account their 1σ errors. This statistic can be calculated by

$$\begin{equation} \Delta E_{\rm peak}=\frac{\left|E_{\rm peak}^{C}-E_{\rm peak}^{B}\right|}{\sigma _{E_{\rm peak}}^{C}+\sigma _{E_{\rm peak}}^{B}}, \end{equation} \tag{ 6 }$$

where C and B indicate the Comp and Band values respectively. This statistic has a value of unity when the deviation between the E_peak values exactly matches the sum of the 1σ errors. A value less than one indicates the E_peak values are within errors, and a value greater than one indicates that the E_peak values are not within 1σ errors of each other. Figure 9 depicts the distribution of the statistic. Roughly 46% of the Band and Comp E_peak values are found to be outside the combined errors. This indicates that, although Comp is a special case of Band, a significant fraction of the E_peak values can vary by more than 1σ based on which model is chosen. If the allowed error range is extended to 3σ then only 14% of the E_peak values are not consistent.

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The distributions for the time-averaged energy flux and photon flux are shown in Figures 10 and 11, respectively. The photon and energy fluxes of the BEST sample have a median value of around 2.4 photons cm⁻² s⁻¹, and 3 × 10⁻⁷ erg cm⁻² s⁻¹, respectively in the 10–1000 keV band. When integrating over the full GBM spectral band, 10 keV–40 MeV, the BEST energy flux distribution broadens significantly, approximating a top hat function with a small high-flux tail spanning about two orders of magnitude. Note that the low-flux cutoff is due to both the sensitivity of the instrument and the clear deviation from a three-dimensional Euclidean distribution that is observed in a typical log N–log S plot (von Kienlin et al. 2014). In any case, the flux measurements with a more sensitive instrument will likely position the peak of the flux distribution at a lower flux value (see also Gruber et al. 2012). Similarly in Figures 12 and 13, the distributions for the BEST photon fluence and BEST energy fluence are depicted. The plots for the photon fluence appear to contain evidence of the duration bimodality of GRBs. While there is a discriminant peak at ∼30 photons cm⁻² there is also a deviation from a log-normal distribution at smaller photon fluence values. Fitting the photon fluence distribution in the 10–1000 keV band with a sum of two log-normal functions, we find peak values of $31_{-23}^{+91}$ and $1.1_{-0.6}^{+1.1}\ {\rm photons\ cm^{-2}}$, respectively. Similarly, the distribution of the energy fluence in the 10–1000 keV band can also be fit by the sum of two log-normal functions which result in peak values of $(3.2_{-2.5}^{+11.3})\times 10^{-6}$ and $(1.5_{-0.4}^{+0.6}) \times 10^{-7} \ {\rm erg\ cm^{-2}}$, respectively. It is interesting to note that while the Comp model is largely unaffected by the change in energy band due to the exponential cutoff, the Pl model shifts to one order of magnitude higher energy fluence values, as it overestimates the flux at higher energies (see Figure 12(d)). The brightest GRB contained in this catalog based on time-averaged photon flux is GRB 120323.507 (Guiriec et al. 2013) with a flux of ∼115 photons s⁻¹ cm⁻² and the burst with the largest average energy flux is GRB 111222.619 with an energy flux of ∼1.5 × 10⁻⁵ erg s⁻¹ cm⁻². The burst with the highest energy fluence is GRB 090902.462 (Abdo et al. 2009) with an energy fluence of ∼2.8 × 10⁻⁴ erg cm⁻² while the burst with the highest photon fluence is GRB 090618.353 with a photon fluence of >2300 photons cm⁻².

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In Figure 14 we present the BEST rest-frame spectral parameters for E_peak, E_b, E_iso and L_iso where the latter two have been determined in the rest-frame energy band between 1/(1 + z) keV and 10/(1 + z) MeV. Both, $E_{\rm peak}^{\rm rest}$ and $E_{\rm break}^{\rm rest}$ peak at roughly 600 keV and, similarly to the distributions in the observer frame, cover just two orders of magnitude. The E_iso distribution peaks at ∼10⁵³ erg and extends over more than three orders of magnitude. L_iso, on the other hand, has a median of ∼10⁵² erg s⁻¹ and covers three orders of magnitude.

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In Figure 15 we show the evolution of the BEST spectral parameters, α, β and E_peak, with redshift. While both the high-energy index and E_peak do not show a clear dependence with redshift (see also Gruber et al. 2011a), the low-energy index of the long GRBs shows a trend to steeper, i.e., softer, values at higher redshifts (see also Geng & Huang 2013). However, a Spearman rank correlation analysis shows that this correlation is not significant (P = 0.15).

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6.1.1. The Break Scale Δ

In order to test the behavior of the break scale Δ of the Sbpl model, we re-fitted all GOOD Sbpl spectra obtained from the F spectral fits. Contrary to the initial fits, we vary the break scale, thus increasing the number of free model parameters. After the fit, we applied the same quality cuts to the resulting parameters as for the GOOD Sbpl sample with the additional requirement that σ_Δ/Δ ⩽ 0.4. Out of the initial 384 Sbpl fits only 36 fulfilled this newly added criterion, with the fit not able to constrain 5 free parameters for the bulk of the GOOD sample. As intuitively obvious, only the most fluent portion of the sample could be fitted with such a complex model (see Figure 16), but it should be noted that the GRBs for which the break scale could be constrained are not necessarily the GRBs for which this model was selected as BEST in Section 5.2. In Figure 17 we show the distribution of Δ. As can be seen Δ varies between 0.1 and 0.7 with an average value of 0.4 ± 0.2. It is instructive to investigate how the additional free fit parameter affects the results of the other model components. In Figure 18 we show the relations between fixed and varying E_b, low- and high-energy power-law indices. The low-energy power-law index seems to tend toward shallower values (particularly when the index is already shallow with the fixed Δ) when letting Δ vary freely. In fact, 13 (36%) low–energy power–law indices are not consistent within 1σ. The high-energy power-law index has a tendency to steepen and 11 (31%) indices are not consistent within the 1σ limit. With 8 (22%) 1σ outliers, the situation is similar for E_b. In general, E_b tends toward harder values when Δ is allowed to vary.

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Similarly to the F spectral fits, we are going to present the results of the P spectral fits in this section.

The P spectral distributions have been produced by fitting the GRB spectra over the 1024 ms and 64 ms peak-flux duration of long and short bursts respectively. Note that the results from both long and short bursts are included in the following figures. The low-energy indices from the P selections of the BEST sample, as shown in Figure 19(b), have a median value of about −1.3 and show a bimodal distribution. This is due to the fact that more GRBs of the P sample are best fit by the Pl because, due to less photon fluence accumulation, the S/N decreases. Twenty percent of the BEST low-energy indices show α > −2/3 and violate the synchrotron "line-of-death," while an additional 32% of the indices are α < −3/2 and violate the synchrotron cooling limit, both of which are significantly larger percentages than those from the F spectra. The high-energy indices in Figure 20 peak at about −2.2 and again have a long tail toward steeper indices. The number of unconstrained high-energy indices increases when compared to the F spectra, again likely due to the poorer statistics resulting from shorter integration times. As has been shown with the F spectral fits, the Pl index serves as an average between low- and high-energy indices for the Band and Sbpl functions.

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Shown in Figure 21 is the ΔS distribution for the P spectra. This distribution seems consistent with the BATSE results found previously (Preece et al. 2002; Kaneko et al. 2006), but suffers from a deficit in values compared to the F fits largely due to the inability of the data to sufficiently constrain the high-energy power-law index. The distribution peaks at ∼1.3 and has a median value of 1.64.

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In Figures 22 and 23, we show the distributions for E_b and E_peak, respectively. As was evident from the F spectra, the E_b from the Sbpl fits appears to peak at 100 keV. The E_peak distribution for the BEST sample peaks around 260 keV and covers just over two orders of magnitude, which is consistent with previous findings (Preece et al. 1998b; Kaneko et al. 2006). It should be noted that the data over the short timescales in the P spectra do not often favor either the Band or the Sbpl model, resulting in large parameter errors.

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Even though it is less obvious, Figure 24 shows a correlation between the E_peak and low-energy power-law index and its uncertainty which is similar to the F spectral fits.

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In addition, we calculate and show the ΔE_peak statistic in Figure 25 and, as was the case with the F spectra, ∼46% of the Band and Comp E_peak values are found to be outside the combined errors. If the allowed error range is extended to 3σ then only 8% of the E_peak values are not consistent.

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The distributions for the peak energy flux and photon flux are shown in Figures 26 and 27, respectively. The photon flux of the BEST sample peaks around 4.5 photons cm⁻² s⁻¹, and the energy flux of the BEST sample peaks at 6.4 × 10⁻⁷ erg cm⁻² s⁻¹ in the 10–1000 keV band. When integrating over the full GBM spectral band, 10 keV-40 MeV, the dispersion in the energy flux increases and approximates a top hat function with a small high-flux tail spanning about two orders of magnitude. The brightest short GRB in terms of peak photon flux is GRB 120323.507 at >580 photons s⁻¹ cm⁻² while the most energetic short GRB is GRB 090227.772 with an energy flux of ∼8.3 × 10⁻⁵ erg s⁻¹ cm⁻².

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In Figure 28 we present the rest-frame spectral parameters for E_peak, E_b, E_iso and L_iso of the P spectral fits where the latter two have been determined in the rest-frame energy band between 1/(1 + z) keV and 10/(1 + z) MeV. Both, $E_{\rm peak}^{\rm rest}$ and $E_{\rm break}^{\rm rest}$ peak at roughly 600 keV and, similarly to the distributions in the observer frame, cover just two orders of magnitude. The E_iso distribution is narrower than the one obtained from the F spectral fits and has a median of ∼10⁵² erg. L_iso, on the other hand, has a median of ∼3 × 10⁵² erg s⁻¹ and covers ∼3 orders of magnitude.

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In Figure 29 we show the evolution of the BEST spectral parameters, α, β and E_peak, with redshift. None of the parameters shows a dependence with redshift.

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When studying the two types of spectra in this catalog, it is instructive to study the similarities and differences between the resulting parameters (see Table 3). Plotted in Figure 30 are the low-energy indices, high-energy indices, and E_peak energies of the P spectra as a function of the corresponding parameters from the F spectra. Most of the P spectral parameters correlate with the F spectral parameters on the order of unity. There are particular regions in each plot where outliers exist, and these areas indicate that either the GRB spectrum is poorly sampled or that significant spectral evolution exists in the F measurement of the spectrum that skews the time-integrated spectral values. Examples of the former case are when the low-energy index is ≳ − 1.2 or the high-energy index is steeper than average (≲ − 2).

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Table 3. The Median Parameter Values and the 68% CL of the Distributions of the GOOD Sample

Model	Low-energy	High-energy	Epeak	Ebreak	Photon Flux	Energy Flux	ΔS
	Index	Index	(keV)	(keV)	(photons s−1 cm−2)	(10−7 erg s−1 cm−2)
Fluence spectra
Pl	$-1.54_{-0.20}^{+0.17}$	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	$2.52_{-1.11}^{+3.91}$	$3.41_{-1.48}^{+7.11}$	⋅⋅⋅
Comp	$-0.96_{-0.30}^{+0.37}$	⋅⋅⋅	$211_{-109}^{+333}$	⋅⋅⋅	$2.53_{-1.10}^{+4.22}$	$3.19_{-1.66}^{+8.55}$	⋅⋅⋅
Sbpl	$-0.98_{-0.23}^{+0.28}$	$-2.35_{-0.52}^{+0.35}$	$166_{-82}^{+293}$	$112_{-55}^{+151}$	$3.29_{-1.54}^{+4.71}$	$4.54_{-2.40}^{+9.51}$	$1.38_{-0.37}^{+0.63}$
Band	$-0.86_{-0.25}^{+0.33}$	$-2.29_{-0.39}^{+0.30}$	$174_{-73}^{+286}$	$118_{-41}^{+168}$	$3.16_{-1.55}^{+4.85}$	$4.64_{-2.50}^{+7.96}$	$1.43_{-0.39}^{+0.53}$
BEST	$-1.08_{-0.44}^{+0.43}$	$-2.14_{-0.37}^{+0.27}$	$196_{-100}^{+336}$	$103_{-63}^{+129}$	$2.38_{-1.05}^{+3.68}$	$3.03_{-1.40}^{+7.41}$	$1.26_{-0.32}^{+0.50}$
Peak flux spectra
Pl	$-1.50_{-0.20}^{+0.16}$	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	$4.77_{-2.69}^{+9.55}$	$7.29_{-4.25}^{+16.25}$	⋅⋅⋅
Comp	$-0.75_{-0.28}^{+0.38}$	⋅⋅⋅	$270_{-138}^{+370}$	⋅⋅⋅	$8.49_{-4.57}^{+12.79}$	$13.19_{-7.39}^{+32.57}$	⋅⋅⋅
Sbpl	$-0.79_{-0.23}^{+0.27}$	$-2.49_{-0.64}^{+0.33}$	$202_{-105}^{+422}$	$141_{-63}^{+239}$	$14.46_{-7.74}^{+18.70}$	$24.44_{-13.77}^{+48.07}$	$1.76_{-0.46}^{+0.68}$
Band	$-0.64_{-0.28}^{+0.32}$	$-2.41_{-0.46}^{+0.33}$	$239_{-116}^{+327}$	$153_{-54}^{+240}$	$14.62_{-7.81}^{+18.40}$	$24.69_{-13.02}^{+45.58}$	$1.78_{-0.47}^{+0.57}$
BEST	$-1.32_{-0.33}^{+0.74}$	$-2.24_{-0.38}^{+0.26}$	$261_{-130}^{+364}$	$133_{-39}^{+349}$	$4.57_{-2.49}^{+8.82}$	$6.49_{-3.46}^{+17.52}$	$1.64_{-0.36}^{+0.59}$

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It is common belief that E_peak is significantly larger at the peak of the GRB, compared to the average E_peak. Figure 30(c), and similar results found in Goldstein et al. (2012) and Nava et al. (2011), seems to contradict this belief with marginal difference between E_peak measured at the peak of the photon flux and E_peak measured over the full duration of the burst.

However, time-resolved spectral analyses in the past have shown (e.g., Kaneko et al. 2006; Lu et al. 2012 for BATSE and GBM GRBs, respectively) that two different E_peak-evolution patterns can (co-)exist in a single GRB:

• 1.  
  E_peak can evolve from hard-to-soft and/or
• 2.  
  E_peak shows a tracking behavior with respect to the photon flux.

If a GRB evolves from hard-to-soft, the peak of the photon flux does not necessarily correspond to the highest E_peak value (see also Crider et al. 1999). Only when E_peak tracks the intensity its highest value is indeed expected at the peak photon flux.

In addition, the time-averaged E_peak is also dependent on the ratio of the peak photon flux versus the average photon flux of the GRB. A larger ratio, i.e., a higher photon flux at the peak of the burst, skews the average E_peak toward the E_peak found at peak flux. Therefore, a marginal difference between E_peak of the F spectral fits and P spectral is expected.

In a forthcoming catalog (H. F. Yu et al., in preparation), the results of a time-resolved study of GBM GRBs will be presented.

To aid in the study of the systematics of the parameter estimation, as well as the effect of statistics on the fitting process, we investigate the behavior parameter values as a function of accumulation time and the photon fluence for the F BEST spectra and peak photon flux for the P BEST spectra, respectively. These distributions are shown in Figures 31–33, respectively. As the photon fluence is correlated with the duration of a burst (see again Figure 1(b)) any correlation of a spectral parameter with the accumulation time will also be correlated with photon fluence.

When fitting the time-integrated spectrum of a burst, we find the low- and high-energy indices trend toward steeper values for bursts with longer accumulation times. The simple Pl index trends from shallow values of ∼ − 1.3 to a steeper value of ∼ − 2. The low-energy index for a spectrum with curvature tends to exhibit an unusually shallow value of ∼ − 0.4 for short GRBs or extremely low fluence spectra, and steepens to ∼ − 1.5 for longer GRBs or higher fluence spectra. Similarly, the high-energy index trends from ∼ − 1.2 at short durations or low fluence to ∼ − 2.7 at long durations or high fluence, although this is complicated by unusually steep and poorly constrained indices that indicate that an exponential cutoff may result in a more reliable spectral fit. When inspecting the E_peak as a function of accumulation time the resulting plot is reminiscent of the hardness/duration correlation with two distinct regions for the long and short GRBs. As for the correlation between E_peak and photon fluence a trend is much less apparent. If a burst is assumed to have significant spectral evolution, then obviously the E_peak will change values through the time history of the burst, typically following the traditional hard-to-soft energy evolution. For this reason, spectra that integrate over increasingly more time will tend to suppress the highest energy of E_peak within the burst, so a general decrease in E_peak is expected with longer integration times. However, the photon fluence convolves the integration time with the photon flux. This means that an intense burst with a short duration and high E_peak may have on the order the same fluence as a much longer but less intense burst with a smaller E_peak. This causes significant broadening to the decreasing trend as shown in Figure 32(c).

The distribution of parameters as a function of the peak photon flux, however, is much less clear. The distributions shown in Figure 33 are more susceptible to uncertainty because of smaller statistics involved in the study of the P section of the GRB, except in some cases where the peak photon flux is on the order of the photon fluence. Ignoring the regions where the parameters are poorly constrained, another trend emerges from the low-energy indices; they appear to become slightly more shallow as the photon flux increases. The high-energy indices, however, appear to be unaffected by the photon flux, although a trend of steeper indices with higher photon fluxes seems apparent. Finally, no obvious trend is visible for E_peak as a function of the peak photon flux (Spearman rank correlation coefficient of −0.05 with a chance probability of P = 0.9). However, when inspecting E_peak as a function of peak energy flux, as shown in Figure 34, a correlation becomes apparent (Spearman rank correlation coefficient of ∼1 with P = 8 × 10⁻⁰⁸). The lack and existence of a correlation between E_peak and the photon and energy flux, respectively is expected because it is the energy of collected photons and not their number that drives the hardness (and thus E_peak) of a GRB.

The spectral results, including the best fit spectral parameters and the photon model, are stored in files following the FITS standard and will be hosted as a public data archive on High-Energy Astrophysics Science Archive Research Center (HEASARC).¹⁶ The values returned by default in a Browse search of the catalog are the most recent values, which will be the results presented here upon acceptance of this paper. However, the values and results obtained by Goldstein et al. (2012) will still be available by ftp. The keyword scatalog indicates which catalog a file belongs to. Both the differences between the methodologies and how to retrieve the older files will be fully documented at HEASARC.