Issue 
A&A
Volume 530, June 2011



Article Number  A21  
Number of page(s)  25  
Section  Extragalactic astronomy  
DOI  https://doi.org/10.1051/00046361/201016270  
Published online  29 April 2011 
Spectral properties of 438 GRBs detected by Fermi/GBM^{⋆}
^{1}
SISSA, via Bonomea 265, 34136 Trieste, Italy
email: lara.nava@sissa.it
^{2}
Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy
Received: 6 December 2010
Accepted: 26 January 2011
We present the results of the spectral analysis of the public data of 438 gamma ray bursts (GRBs) detected by the Fermi Gamma ray Burst Monitor (GBM) up to March 2010. For 432 bursts we could fit the timeintegrated spectrum. In 318 cases we could reliably constrain the peak energy of their νF_{ν} spectrum by analyzing their timeintegrated spectrum between 8 keV and 35 MeV. Eighty percent of these spectra are fitted by a powerlaw with an exponential cutoff, and the remaining with the Band function. Among these 318 GRBs, 274 belong to the long GRB class and 44 to the short. Long GRBs have a typical peak energy ~ 160 keV and lowenergy spectral index α ~ − 0.92. Short GRBs have a harder peak energy ( ~ 490 keV) and a harder lowenergy spectral index (α ~ −0.50) than long bursts. For each Fermi GRB we also analyzed the spectrum corresponding to the peak flux of the burst. On average, the peak spectrum has a harder lowenergy spectral index than the corresponding timeintegrated spectrum for the same burst, but similar Ṫhe spectral parameters derived in our analysis of Fermi/GBM bursts are globally consistent with those reported in the GRB Cicular Network (GCN) archive after December 2008, while we found systematic differences in the lowenergy powerlaw index for earlier bursts.
Key words: radiation mechanisms: nonthermal / Gamma rays: general
Tables 2–5 are available in electronic form at http://www.aanda.org
© ESO, 2011
1. Introduction
Our current knowledge of the spectral properties of the prompt emission in GRBs mainly relies on the data collected in almost ten years by the Burst And Transient Source Experiment (BATSE) onboard the Compton GammaRay Observatory (CGRO).BATSE allowed characterization of the spectrum of the population of short and long GRBs over a wide energy range of 20 keV to 1–2 MeV. Analysis of such data revealed some important results about the spectral properties of these GRBs. The prompt spectra, integrated over the GRB duration (i.e. timeintegrated spectra), can typically be described well by a curved function showing a peak – in a νF_{ν} representation – at a typical energy of a few hundred keV, but its distribution spans nearly three orders of magnitude. Large dispersions also characterize the distributions of the low – and high – energy photon indices, whose characteristic values are α ~ − 1 and β ~ −2.3, respectively (Band et al. 1993; Ghirlanda et al. 2002; Kaneko et al. 2006). Similar results are obtained by considering the timeresolved spectral analysis of flux/fluence limited samples of brightBATSE bursts (Preece et al. 1998, 2000; Kaneko et al. 2006).
The BATSE data also suggest that there are two different classes of GRBs (long and short), based on both temporal and spectral features. Evidence of a spectral diversity between long and short bursts comes from their different hardnessratios (HR) (Kouveliotou et al. 1993). The higher HR of short bursts might be ascribed to a larger . Nava et al. (2008) and Ghirlanda et al. (2009 – G09 hereafter) showed that correlates both with the fluence and the peak flux. Although short and long bursts follow the very same peak flux relation, they obey different (parallel) fluence relations. This obviously implies that the distributions of the ratio /fluence is different for the two burst classes. Recently, Goldstein et al. (2010) have proposed this ratio as a discriminator between short and long GRBs. Owing to the relation between and the bolometric fluence and peak flux, a direct comparison between the distributions of the two different burst classes must take the different fluence/peak flux selection criteria into account. G09 analyzed and compared samples of short and long BATSE bursts selected with similar peak flux limits. They found that the peak energy distributions of the two classes are similar, while the most significant difference is in the lowenergy powerlaw indices, with short bursts typically having a harder α ~ − 0.4.
These global spectral properties of GRBs have also been confirmed by other satellites (BeppoSAX, HeteII and Swift) (Guidorzi et al. 2010; Sakamoto et al. 2005; Butler et al. 2007). However, the detectors onboard these satellites have different sensitivities thanBATSE and cover a narrower and different energy range. For instance, the relatively narrow energy range (15–150 keV) of Swift/BAT does not allow the spectral peak to be constrained for most of the detected bursts (Cabrera et al. 2007; Butler et al. 2007).
Spectral studies of the prompt emission of GRBs require a wide energy range, possibly extending from a few tens of keV to the MeV energy range. This allows a measure of the curvature of the GRB spectrum and constraining its peak energy, as well as its lowand highenergy spectral slopes.
The Fermi satellite, launched in June 2008, represents a powerful opportunity to shed light on the origin of the GRB prompt emission thanks to its two instruments: the Large Area Telescope (LAT) and the Gammaray Burst Monitor (GBM). LAT detected very highenergy emission ( > 100 MeV) from 19 GRBs in about two years. This emission component shares some common features with what has already been found in a few bursts by EGRET (Energetic GammaRay Experiment Telescope) onboard the CGRO satellite. In particular, highenergy ~GeV flux is still observed when the softer energy emission (in the subMeV domain) ceases, and often its onset lags the subMeV component (e.g. Ghisellini et al. 2010; Omodei et al. 2009).
The other instrument onboard Fermi is the GBM (Meegan et al. 2009), which is similar toBATSE and, despite its slightly worse sensitivity, allows study of the GRB spectrum over an unprecedentedly wide energy range, from 8 keV to 40 MeV. This is achieved by its twelve NaI detectors, giving a good spectral resolution between ~8 keV and ~1 MeV and two BGO detectors, which extend the energy range up to ~40 MeV. Similar toBATSE, the NaI detectors guarantee fullsky coverage, but their smaller geometric area (16 times lower than that of the LADs ofBATSE) implies a lower sensitivity. On the other hand, the presence of the BGO detectors allows the energy range to be extended for the first time for the study of the spectrum of the prompt emission to tens of MeV, thus accessing an energy range that is poorly explored with the CGRO instruments.
438 events, classified as GRBs^{1}, triggered the GBM until the end of March 2010. With this large sample of bursts we can perform the first robust statistical study of the spectral properties of Fermi/GBM bursts. The main aims of this paper are (a) to present the results of the spectral analysis of 438 Fermi bursts, (b) to show the distribution of their spectral parameters, (c) to compare the spectral properties of Fermi short and long GRBs, and (d) to compare the spectra integrated over the burst duration (timeintegrated spectra, hereafter) with the spectra of the most intense phase of the burst, i.e. its peak flux (peak spectra, hereafter).
Preliminary results of the spectral analysis of Fermi GRBs performed by the GBM team have been distributed to the community through the Galactic Coordinates Network (GCN) circulars. These amount to 228 GRBs (until March 2010), whereof 167 have a well constrained . Ongoing spectral calibrations of the GBM detectors mean that the results published in the GCN are “preliminary”, especially for the first bursts detected by the GBM. The GBM team continuously provides more updated detector response files, together with the public data of detected GRBs. A few months ago the software and the new response files were made public so that a systematic and reliable analysis of the spectra of Fermi/GBM bursts is now possible. We compare the results of our spectral analysis with those published in the GCN to search for possible systematic effects in the GCN results.
The paper is organized as follows. In Sects. 2 and 3 we describe the sample of Fermi GRBs and the procedure adopted to extract and analyze their spectral data. In Sect. 4 we present the spectral results and build their distributions, while considering short and long GRBs separately. In Sect. 4 we also compare the timeintegrated spectra and the peak spectra for the analyzed bursts. We summarize our results in Sect. 5.
2. The sample
The GBM detected 438 GRBs up to the end of March 2010. A list of the GRB trigger number and the position in the sky, computed by the GBM, is provided by the Fermi Science Support Center^{1}. The data of each GRB have been archived and made public since July 2008. Since the only information given in the public archive is the burst position, it was not possible to apply any selection in flux, fluence, or duration on the GBM online public archive, since a spectral catalog is not available. For this reason we started the systematic analysis of GBM bursts in order to determine the spectral parameters, fluence, and peak flux of all bursts detected by Fermi/GBM up to March 2010.
Preliminary spectral results of Fermi GRBs have been distributed by the GBM team through the GCN system. Starting on March 2010, the number of GCN of Fermi bursts substantially decreased, although the rate of detected bursts remained unchanged. We decided to limit our selection to March 2010, thus having a large sample of GCN results to compare with.
We collected all bursts with spectral information published in the GCN up to the end of March 2010 (228 objects). Among these, 148 long GRBs and 19 short have wellconstrained spectral parameters, in particular the peak energy of their νF_{ν}. In Sect. 4 we compare the GCN spectral parameters with those derived by us for the same bursts and search for possible systematic effects in the GCN results.
3. Spectral analysis
For the spectral analysis of Fermi/GBM bursts we used the recently released rmfit – v3.3pr7 software^{2}. For each GRB to be analyzed, the spectral analysis was done by combining together more than one detector. Following the criterion adopted in Guiriec et al. (2010) and Ghirlanda et al. (2010), we selected the most illuminated NaI detectors having an angle between the source and the detector normal lower than 80 degrees. We selected the BGO #0 or #1 if the selected NaI were all between #05 or #612, respectively. When the selected NaI were both between #05 and #612, both BGO detectors were used. However, if one of the two BGO had a zenith angle to the source larger than 100 degrees we excluded it from the analysis.
The very wide available energy range (from 8 keV to ~40 MeV) allows proper constraining of the peak energy of particularly hard GRBs (with larger than 1 MeV, i.e. the upper energy threshold of the NaI detectors) or the highenergy spectral power law, if present.
For the spectral analysis we used the CSPEC data (with time resolution of 1.024 s after the trigger time and 4.096 s before) for long GRBs and the TTE data (with time resolution of 0.064 s) for short GRBs. A first hint about the burst duration comes from the visual inspection of the lightcurves (at different temporal resolutions) stored in the quicklook directory provided with the data^{1}. We used this method to decide which type of data (CSPEC or TTE) is more suitable for spectral analysis. Both data types contain spectra with 128 energy channels. Following the prescription of the rmfit tutorial^{3} we considered the spectral data of the NaI detectors in the range 8 keV–900 keV and for the BGO detectors in the range 250 keV–35 MeV.
For each GRB we extracted the background spectrum by selecting a time interval before and after the burst that was as large as possible, but distant enough from the burst signal to avoid burst contamination. The spectra in these two time intervals were modeled in time with a polynomial of order between 0 and 4 to account for the possible time evolution of the background. Then, the spectral analysis software extrapolates the background to the time interval occupied by the burst. We used the most updated response files with extension rsp2, which allows rmfit to use a new response for each 5 deg of spacecraft slew, as explained in the rmfit tutorial.
Each spectrum was analyzed by adopting the Castor statistics (Cstat). Since we combined NaI and BGO detectors in the spectral analysis, we fitted the spectra by allowing for a calibration constant among the different detectors. The spectral results (Cstat and spectral parameters) obtained with the calibration constants free and fixed to 1 were compared. If no significant difference was found between the Cstat and the spectral parameters obtained in these two cases, the calibration constants were fixed to 1 (as also suggested in the rmfit manual). In nearly 30% of the cases, the Cstat significantly decreased by using free calibration constants. This is not directly related to the burst brightness (also for faint bursts the calibration constants can be required) even if, of course, the largest differences in Cstat values are found for bright bursts, since possible calibration offsets between instruments strongly affect the fit (in terms of Cstat) when data points have small errors.
Systematic residuals around the kedge of the NaI detectors are often visible, owing to calibration issues (Guiriec et al. 2010). For four bursts (for which this effect is particularly pronounced), we performed the spectral analysis both including and excluding a few channels between 30 keV and 40 keV (e.g. see Guiriec et al. 2010). While the spectral parameters and their errors are not sensitive to this choice, the value of the Cstat is quite different. For these four bursts we report the results of both the analyses (Table 2).
3.1. Spectral models
The spectral analysis performed by different authors (Preece et al. 2000; Sakamoto et al. 2005; Kaneko et al. 2006; Butler et al. 2007; Nava et al. 2008; Guidorzi et al. 2010) on data taken from different instruments revealed that GRB spectra are fitted by different models, the simplest ones being i) a single powerlaw model (PL), ii) a Band function (Band et al. 1993), which consists of two smoothly connected powerlaws and iii) a Comptonized model (CPL hereafter), i.e. a powerlaw with a highenergy exponential cutoff.
The timeresolved spectra of BATSE GRBs have been also fitted by combining thermal (blackbody) and nonthermal (powerlaw) models (e. g. Ryde et al. 2005; Ryde et al. 2009). Although these fits are intriguing for their possible physical implications (Pe’er et al. 2010), they are statistically equivalent to fits with the phenomenological models described above (Ghirlanda et al. 2007). Recently, Guiriec et al. (2010) have found evidence of a thermal black body component (summed to the standard Band function) in the spectrum of the Fermi GRB 100724B.
A simple PL function clearly indicates that no break/peak energy is detected within the energy range of the instrument. Furthermore, it is also statistically the best choice when the signaltonoise ratio of the analyzed spectra is very low because this model has the lowest number of free parameters. This was shown, for instance, by the analysis of the Swift/BAT spectral data (e.g. Cabrera et al. 2007).
The Band model (Band et al. 1993) has four free parameters to describe the low and high power law behaviors, the spectral break and the flux normalization. Typically, the lowenergy photon index α > − 2 [N(E) ∝ E^{α}] and the highenergy photon index β < − 2 [N(E) ∝ E^{β}], so that a peak in νF_{ν} can be defined. When there is no evidence of a highenergy photon tail or is near the highenergy boundary of the instrument sensitivity (and β is poorly constrained), a CPL model is preferred due to the lower number of parameters. Also in this case a peak energy can be defined when α > − 2. In the Band model the spectral curvature is fixed by α, β, and .
We fitted all these nested models to each GRB spectrum. The addition of one free parameter requires an improvement in Cstat of 9 for a 3σ confidence in this improvement. We chose this criterion to select the bestfit model. In addition, we also required that all the spectral parameters are well determined (i.e. no upper or lower limits).
3.2. Time integrated and peak flux spectra
As anticipated we analyzed, for each burst, (1) the spectrum integrated over its whole duration and (2) the spectrum corresponding to the peak of the burst. For the peak spectrum, this could be selected from the rawcount light curve as the temporal bin with the highest count rate. However, it may happen that bins with a similar count rate have very different spectra, and their flux can be considerably different. Therefore, a more physical approach for identifying the peak of the burst is to build its flux light curve (i.e. calculating the flux in physical units). In practice, we performed a timeresolved spectral analysis of each burst and built its flux light curve, where the flux is integrated over the 8 keV–35 MeV energy range, i.e. the same spectral range where the spectral analysis is performed). Then we identified the time bin corresponding to the largest flux and analyzed this spectrum to extract the peak spectrum parameters. As timescale for the timeresolved spectral analysis, we chose 1.024 and 0.064 seconds for the long and short GRBs, respectively. We adopt this procedure for all GRBs, i.e. even those having a timeintegrated spectrum better described by a simple powerlaw.
4. Results
The spectral parameters obtained from analysis of the timeintegrated spectra of the 438 Fermi/GBM bursts are reported in Tables 2 and 3. In particular, in Table 2 we list all the 323 bursts whose spectrum could be fitted with either the Band or CPL model (Col. 3). In five cases, the highenergy powerlaw index β is > − 2, and this reduces the number of bursts with welldefined peak energy to 318. In Table 3 we report all the 109 cases where a single powerlaw is the best fit to the data and the 6 cases where spectral analysis was impossible for lack of data.
In both tables we give the time interval over which the timeintegrated spectrum was accumulated and the bestfit model (Cols. 2, 3), the normalization constant (Col. 4) in units of photons cm^{2} s^{1} (computed at 100 keV for all models), and the spectral index α (Col. 5) of the lowenergy powerlaw. The peak energy of the νF_{ν} spectrum and (for the spectra fitted with the Band model) the highenergy spectral index β are listed in Cols. 6 and 7 of Table 2, respectively. We also report in both tables the value of the Cstat resulting from the fit and the associated degrees of freedom (d.o.f.). The last column in Table 2 gives the fluence obtained by integrating the bestfit model over the 8 keV–35 MeV energy range. For the spectra fitted with the PL model, we give the fluence (last column in Table 3) computed over a narrower energy range, 8 keV–1 MeV, because we could not identify where the peak energy is. For four bursts (GRB 081009140, GRB 090618353, GRB 090626189, and GRB 090926181), we performed the spectral analysis both including and excluding a few channels around the kedge. In these cases, we report both the results in the tables. In 19 cases we found that the fit with a Band model returns well constrained parameters, but it is not statistically preferred to the Comp model (the Cstat improvement is lower than 9). In these cases we list the parameters of both models in the tables.
In Table 4 we report the results of the peak spectra analysis. In particular, we list the initial (t_{1}) and final (t_{2}) times of the selected temporal bin, the bestfit model, its spectral parameters, Cstat, and degrees of freedom. The last column lists the peak flux estimated in the 8 keV–35 MeV energy range. Finally, in Table 5, we list the spectral properties and the fluence collected from the GCN Circulars. For each burst we also report the redshift (when available) and the GCN number.
4.1. Timeintegrated spectra
Out of the 432 bursts for which it was possible to perform the spectral analysis, 359 are long and 73 short. In the case of long (short) bursts, 274 (44) events have a welldefined peak energy, while 4 (1) are best fitted with a Band model with β > − 2. Most of the spectra are adequately fitted by the CPL model. This is true for both the long and short subgroups. Among the 109 spectra fitted with a simple powerlaw model, there are 81 and 28 long and short events.
In our analysis we integrated the spectrum over a time interval (ΔT) where the signal of the burst (for all NaI detectors combined) is stronger than the average background. Therefore, we adopt this integration time to separate short and long GRBs (i.e. Δt < 2 s and Δt > 2 s, respectively). The distribution of Δt is bimodal and short and long GBM bursts are separated into two log normal distributions with central value (standard deviation) ⟨ Log(Δt) ⟩ = 1.42 (σ = 0.39) and ⟨ Log(Δt) ⟩ = −0.33 (σ = 0.38) for long and short GRBs, respectively.
Fluence distribution – In Fig. 1 we show the LogN − LogF distributions of the Fermi GRBs analyzed. To show the fluence distribution of all the 432 GRBs that we could successfully fit, we computed the fluence in the 8 keV–1 MeV for the 323 GRBs fitted with either the Band or CPL model and for the 109 GRBs fitted with a powerlaw. We show separately the LogN − LogF for long (359 events) and short (73 events) GRBs. At large fluences the distribution of long and short has a very similar slope to the euclidean one (–3/2), which is shown for comparison. In Fig. 2 we show the LogN − LogF distribution by dividing our sample according to the bestfit model.
E_{peak}distribution – In Fig. 3 we show the peak energy distribution of the 318 GRBs (both long and short) and the fit with a Gaussian. Also, in Fig. 3 short and long events are shown separately and the KolmogorovSmirnov test gives a probability P_{KS} = 3.4 × 10^{15} that the two distributions of for long and short GRBs are drawn from the same parent distribution.
Spectral index distributions – In Fig. 4 we show the distribution of the lowenergy spectral index α for all the 318 GRBs and for short and long GRBs separately (having a P_{KS} = 7.3 × 10^{12}). Finally, in Fig. 5 we show the distribution of the highenergy spectral index β for the 60 timeintegrated spectra that are fitted with the Band model (see Table 2).
All the parameters distributions shown in Figs. 3 and 4 are fitted by Gaussian functions whose parameters are reported in Table 1.
Fig. 1 LogN − LogF of the 432 GRBs analyzed in this work (Tables 2 and 3). Short GRBs (73 events) and long GRBs (359 events) are shown with (red) triangles and (blue) circles, respectively. The black histogram refers to the entire sample. The dashed and dotdashed lines are two powerlaws with slope –3/2. The fluence F in erg/cm^{2} is obtained by integrating the bestfit model in the 8 keV–1 MeV energy range. 
Fig. 2 LogN − LogF distributions of all the GRBs fitted with the CPL or Band model and wellconstrained (pink circles) and of the 109 GRBs fitted with a single PL model (green triangles). For reference a power law with slope –3/2 is shown (dashed and dotdashed line). The fluence F in erg/cm^{2} is obtained by integrating the bestfit model in the 8 keV–1 MeV energy range. 
Fig. 3 Distribution of the peak energy for the GRBs listed in Table 2 fitted with either the Band or CPL model and with determined (318 GRBs). The solid line shows the fit with a Gaussian. Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dotdashed and dashed lines for long and short events, respectively). 
Fig. 4 Distribution of the lowenergy photon index for the 318 GRBs listed in Table 2 fitted with either the Band or CPL model and with determined . The solid (black) line shows the fit with a Gaussian. Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dotdashed and dashed line for long and short events, respectively). 
Fig. 5 Distribution of the highenergy photon index for 60 GRBs whose timeintegrated spectrum is best fit with the Band model. 
Parameters of the Gaussian fits of the distributions of the spectral parameters of Fermi/GBM bursts analyzed in this work.
Fig. 6 Comparison of timeintegrated and peakflux spectral parameters for the 227 GRBs whose peak spectrum could be fitted with the Band or CPL model (reported in Table 4 and present also in Table 2). Top panel: peak energy. Bottom panel: lowenergy spectral index (α). Empty (filled) symbols are GRBs for which the timeintegrated and the peak flux spectra have same (different) best fit model. Squares refer to short events and circles to long events. 
4.2. Peak spectra
For each burst we also extracted and analyzed the spectrum corresponding to its peak flux. To this aim, we performed a timeresolved spectral analysis of each burst. In the flux light curve, we then selected the time bin with the largest flux. The timescale is given by the resolution of the data, i.e. typically 1.024 s and 0.064 s for long and short GRBs, respectively. We also verified that in most cases the peak of the count rate coincides with the peak of the flux.
Out of the 432 analyzed GRBs, the peak spectrum could be extracted and fitted with a Band or CPL model in 235 cases. As before, the bestfit model is defined by requiring an improvement in the Cstat value of 9 (between a given model and a more complex one with one parameter more) and wellconstrained spectral parameters. In 27 cases (26 long and 1 short) the bestfit model of the peak spectrum is different from that of the timeintegrated spectrum. The spectral parameters of the peak spectra fitted with these two models are reported in Table 4.
In Fig. 6 we compare the peak energy and the low spectral index α at the peak flux with the values of the timeintegrated spectrum for bursts having all this information (227 events.). Empty (filled) symbols refer to GRBs for which the timeintegrated and the peak spectra are described by the same (a different) bestfit model. On average, the timeintegrated and peak spectrum values of are very similar, while the lowenergy spectral index, at the peak, is harder.
4.3. Comparison with GCN results
Since August 2008, the Fermi GBM team is providing preliminary results of the spectral analysis of a large number of the detected GRBs through the GCN Circulars. For each burst, the GCN circular reports the burst’s duration, spectral parameters, fluence, and photon peak flux (all with their associated errors). GCN circulars are promptly released when a burst occurs and are not updated after their first release. On the other hand, the GBM team is continuously providing, through the online archive, new versions of the detector response files, improved with respect to the first version used to perform their preliminary analysis. Our analysis benefits from the most updated response files. A meaningful comparison between our results and those preliminarily reported by the GBM team must account for this difference.
It is likely that the calibration of the different detectors has changed and been improved from the earliest to the latest circular, along with the software and tools used by the Fermi team. If this is the case, spectral parameters of the first bursts detected by Fermi and reported in the GCN could be affected by systematic biases, hopefully not present in our analysis. To verify this possibility, we plotted the spectral parameters (α and ) as a function of the date (in MJD) of the GRB detection, to point out any possible systematic trend of their values and/or associated uncertainties. The spectral parameters (from our sample and from the GCN sample) are plotted in the upper panels of Fig. 7.
In the GCN sample, long bursts (Fig. 7) detected at the beginning of the mission have a slightly harder α with respect to the following bursts and also to the same bursts analyzed by us. This trend is not present in the short burst sample. In this case, however, the sample is small, and short bursts are only present in the GCN sample starting from December 2008.
Fig. 7 Comparison of GCN preliminary results and our analysis. Upper panel: crosses and squares show (for long and short events respectively) the time trend of the spectral properties (α on the left and on the right) for GBM bursts whose preliminary spectral analysis has been reported in the GCN circulars. Circles and stars show the same for the sample of long and short bursts analyzed by us. We show only those bursts for which the same spectral models were used in our analysis and in the analysis reported in the GCN circulars. Time on the xaxis is in MJD units. Middle panels: central values and 1σ width for the α (left) and (right) distributions (long bursts only) for the GCN sample (crosses) and our sample (circles) as a function of time. Bottom panels show the average α and for two different periods of time, up to and after December 2008. 
A possible bias on the α values can be better quantified by probing how the α distribution for long bursts evolves in time. After having sorted GRBs according to their increasing date of detection, we consider the distribution of the spectral parameter up to a certain date and we fit it with a Gaussian function by deriving its central value and the standard deviation. This corresponds to showing how the cumulative distributions change by increasing the time span. Since a systematic difference in α between our analysis and what is reported in the GCNs might also be ascribed to a systematic difference in the choice of the bestfit model, we use only those bursts for which the bestfit model is the same in both analyses.
Our test starts on November 2008, when we start to have enough bursts for a reliable Gaussian fit. The middle left panel in Fig. 7 shows our results. The yaxis shows the central value of the Gaussian fit and the error bar correspond to its 1σ width. In the GCN sample a trend is clearly visible. Although at the 1σ level we see that all the central values are consistent, the mean of α (~−0.5 at the beginning) systematically evolves from harder to softer values, and then it levels off at about –0.85. This result rules out the possibility that the bias is due to a different choice in the bestfit model and suggests that another nonphysical effect could be biasing the lowenergy powerlaw indices towards harder values in the first months of the GCN data analysis. This trend is not present in our sample (Fig. 7, middle left panel), for which the α distribution does not evolve in time.
The whole α distributions for the two different samples are somewhat different, with the GCN sample having slightly harder spectral indices ( ⟨ α ⟩ = −0.86 compared to ⟨ α ⟩ = −0.92 derived from our analysis), as shown by the last point in the middleleft panel of Fig. 7. We are interested in understanding whether this difference can be totally ascribed to the bias affecting the first bursts and, in this case, in determining the date from which GCN preliminary results are consistent with those obtained by our analysis with the most updated response files. The bottom panels of Fig. 7 show the average values of α and for two different periods of time: up to the end of December 2008 and from January 2009 to March 2010.
Figure 8 shows the difference Δα between the lowenergy spectral indices as reported in the GCN sample and as derived by us for bursts common to both samples. The upper panel shows bursts fitted with the same bestfit model in both analyses (i.e. the same subsample as used in Fig. 7). The bottom panel, instead, shows all bursts common to both samples. Approximately up to the end of December 2008, this difference is not randomly distributed around Δα = 0, but is systematically larger. This justifies our choice of considering these two time intervals for the bottom panels of Fig. 7, showing that bursts in the GCN sample up to the end of December 2008 have a mean α = −0.5, while the α distribution of the remaining bursts is peaked around α = −0.9, perfectly consistent with our results. The same separation has been applied to our sample, which does not show any difference in α when comparing bursts before and after December 2008 (bottom left panel in Fig. 7).
The values (right panels in Fig. 7) are untouched by this effect. The results from the two different samples are highly consistent. A weak trend is visible, but the central value of the distribution spans 130 keV to 150 keV, a very narrow range if compared to the width of the distribution and to the typical errors on this parameter.
5. Summary and conclusions
We analyzed the spectra of all GRBs detected by the Fermi/GBM between 14 July 2008 and 30 March 2010. There are 438 GRBs, and for 432 of them we have all the data needed to perform the spectral analysis. The timeintegrated spectrum is best fitted with a powerlaw model (110 spectrareported in Table 3) or a curved model (323 spectra – reported in Table 2), which is either the Band model (65 spectra) or a cutoffpowerlaw (CPL) model (258 spectra).
Among the 432 GRBs for which we could analyze the spectrum, we identify 73 short and 359 long bursts. Their LogN − LogF is similar (Fig. 1) and its highfluence tail is consistent with a power law with slope –3/2.
The 73% of the bursts detected by the GBM up to March 2010 could be fitted with a curved model (Band or CPL, with a prevalence of the latter model) and in the majority (318 out of 323) of these cases we could constrain the spectral parameters, in particular, the peak energy of the νF_{ν} spectrum. This is possible thanks to the wide energy range of the GBM spectra extending from 8 keV to ~35 MeV. This is the sample we considered for characterizing the spectral parameters of the timeintegrated spectra of Fermi GRBs. Within this sample there are 44 short and 274 long GRBs. The comparison of their spectral properties shows that short GRBs have higher than do long events (Fig. 3) and a slightly harder lowenergy spectral index α (Fig. 4).
Fig. 8 Difference between α values reported in the GCN Circulars and α values derived from our analysis. Top panel: bursts for which the spectrum is described by the same model both in our analysis and in the GCN analysis. Bottom panel: bursts common to both samples regardless of the spectral model chosen to describe the spectrum. 
The finding that short Fermi GRBs have harder peak energy than long events seems opposite to what has been found from the comparison of short and long GRBs detected by BATSE (Ghirlanda et al. 2009).
However, the Fermi short GRBs also have larger peak fluxes than long events. A more detailed comparison between long and short GRBs detected by Fermi/GBM and BATSE is presented in Nava et al. (2010).
A second major part of the present work was to characterize the spectra of the peak of each GRB. Through timeresolved spectroscopy, we isolated and analyzed the spectrum corresponding to the peak of the flux light curve of each burst. The results are reported in Table 4. By comparing the peak spectrum and the timeintegrated spectrum of individual GRBs, we find that the peak spectra have similar of the timeintegrated spectra but harder lowenergy spectral index α (Fig. 6).
Finally we compared the results of our spectral analysis with those reported in the GCN circulars. We found that the still not fully completed calibrations of the GBM detectors means that the GCN results of bursts comprised between July and December 2008 are affected by a systematic overestimate of the hardness of the GRB spectrum at low energies (i.e. the spectral parameter α). This systematic bias does not affect and is not present in our results, which were obtained with the most recent releases of the GBM response files.
Acknowledgments
This research has made use of the public Fermi/GBM data and software obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center. We acknowledge the GBM team for the public distribution of the spectral properties of Fermi/GBM bursts through the GCN network. We thank the referee for his/her useful comments. This work has been partly supported by ASI grant I/088/06/0. L.N. thanks the Osservatorio Astronomico di Brera for the kind hospitality for the completion of this work.
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Online material
Spectral parameters of the timeaveraged spectra of 323 Fermi/GBM GRBs fitted with a curved function.
Spectral parameters of the timeaveraged spectra of 109 Fermi/GBM GRBs fitted with a power law.
Spectral parameters of the peak spectra of 235 Fermi/GBM GRBs fitted with a curved function.
Spectral parameters of the Fermi/GBM GRBs collected from the GCN Circular Archive.
All Tables
Parameters of the Gaussian fits of the distributions of the spectral parameters of Fermi/GBM bursts analyzed in this work.
Spectral parameters of the timeaveraged spectra of 323 Fermi/GBM GRBs fitted with a curved function.
Spectral parameters of the timeaveraged spectra of 109 Fermi/GBM GRBs fitted with a power law.
Spectral parameters of the peak spectra of 235 Fermi/GBM GRBs fitted with a curved function.
Spectral parameters of the Fermi/GBM GRBs collected from the GCN Circular Archive.
All Figures
Fig. 1 LogN − LogF of the 432 GRBs analyzed in this work (Tables 2 and 3). Short GRBs (73 events) and long GRBs (359 events) are shown with (red) triangles and (blue) circles, respectively. The black histogram refers to the entire sample. The dashed and dotdashed lines are two powerlaws with slope –3/2. The fluence F in erg/cm^{2} is obtained by integrating the bestfit model in the 8 keV–1 MeV energy range. 

In the text 
Fig. 2 LogN − LogF distributions of all the GRBs fitted with the CPL or Band model and wellconstrained (pink circles) and of the 109 GRBs fitted with a single PL model (green triangles). For reference a power law with slope –3/2 is shown (dashed and dotdashed line). The fluence F in erg/cm^{2} is obtained by integrating the bestfit model in the 8 keV–1 MeV energy range. 

In the text 
Fig. 3 Distribution of the peak energy for the GRBs listed in Table 2 fitted with either the Band or CPL model and with determined (318 GRBs). The solid line shows the fit with a Gaussian. Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dotdashed and dashed lines for long and short events, respectively). 

In the text 
Fig. 4 Distribution of the lowenergy photon index for the 318 GRBs listed in Table 2 fitted with either the Band or CPL model and with determined . The solid (black) line shows the fit with a Gaussian. Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dotdashed and dashed line for long and short events, respectively). 

In the text 
Fig. 5 Distribution of the highenergy photon index for 60 GRBs whose timeintegrated spectrum is best fit with the Band model. 

In the text 
Fig. 6 Comparison of timeintegrated and peakflux spectral parameters for the 227 GRBs whose peak spectrum could be fitted with the Band or CPL model (reported in Table 4 and present also in Table 2). Top panel: peak energy. Bottom panel: lowenergy spectral index (α). Empty (filled) symbols are GRBs for which the timeintegrated and the peak flux spectra have same (different) best fit model. Squares refer to short events and circles to long events. 

In the text 
Fig. 7 Comparison of GCN preliminary results and our analysis. Upper panel: crosses and squares show (for long and short events respectively) the time trend of the spectral properties (α on the left and on the right) for GBM bursts whose preliminary spectral analysis has been reported in the GCN circulars. Circles and stars show the same for the sample of long and short bursts analyzed by us. We show only those bursts for which the same spectral models were used in our analysis and in the analysis reported in the GCN circulars. Time on the xaxis is in MJD units. Middle panels: central values and 1σ width for the α (left) and (right) distributions (long bursts only) for the GCN sample (crosses) and our sample (circles) as a function of time. Bottom panels show the average α and for two different periods of time, up to and after December 2008. 

In the text 
Fig. 8 Difference between α values reported in the GCN Circulars and α values derived from our analysis. Top panel: bursts for which the spectrum is described by the same model both in our analysis and in the GCN analysis. Bottom panel: bursts common to both samples regardless of the spectral model chosen to describe the spectrum. 

In the text 
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