Peak energy of the prompt emission of long Gamma Ray Bursts vs their fluence and peak flux
Lara Nava, Giancarlo Ghirlanda, Gabriele Ghisellini, Claudio Firmani
aa r X i v : . [ a s t r o - ph ] J u l Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 31 October 2018 (MN L A TEX style file v2.2)
Peak energy of the prompt emission of long Gamma Ray Bursts vstheir fluence and peak flux
L. Nava , ⋆ , G. Ghirlanda , G. Ghisellini and C. Firmani , Osservatorio Astronomico di Brera, via E.Bianchi 46, I-23807 Merate, Italy Dipartimento di Fisica e Matematica, Universit´a degli Studi dell’Insubria, via Valleggio 11, I-22100 Como, Italy Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, A.P. 70-264, 04510, M´exico D.F., M´exico
Accepted 2008 July 23. Received 2008 June 22; in original form 2008 April 11
ABSTRACT
The spectral–energy (and luminosity) correlations in long Gamma Ray Bursts are being hotlydebated to establish, first of all, their reality against possible selection effects. These are beststudied in the observer planes, namely the peak energy E obspeak vs the fluence F or the peak flux P . In a recent paper (Ghirlanda et al. 2008) we started to attack this problem considering allbursts with known resdhift and spectral properties. Here we consider instead all bursts withknown E obspeak , irrespective of redshift, adding to those a sample of 100 faint BATSE burstsrepresentative of a larger population of 1000 objects. This allows us to construct a complete,fluence limited, sample, tailored to study the selection/instrumental effects we consider. Wefound that the fainter
BATSE bursts have smaller E obspeak than those of bright events. As aconsequence, the E obspeak of these bursts is correlated with the fluence, though with a slopeflatter than that defined by bursts with z . Selection effects, which are present, are shown notto be responsible for the existence of such a correlation. About 6% of these bursts are surelyoutliers of the E peak − E iso correlation (updated in this paper to include 83 bursts), sincethey are inconsistent with it for any redshift. E obspeak correlates also with the peak flux, with aslope similar to the E peak − L iso correlation. In this case there is only one sure outlier. Thescatter of the E obspeak – P correlation defined by the BATSE bursts of our sample is significantlysmaller than the E obspeak – F correlation of the same bursts, while for the bursts with knownredshift the E peak − E iso correlation is tighter than the E peak − L iso one. Once a very largenumber of bursts with E obspeak and redshift will be available, we thus expect that the E peak − L iso correlation will be similar to that currently found, whereas it is very likely that the E peak − E iso correlation will become flatter and with a larger scatter. Key words:
Gamma rays: bursts — Radiation mechanisms: non-thermal — X–rays: general
The correlation between the peak spectral energy E peak and thebolometric isotropic energy E iso emitted during the prompt (the socalled ”Amati” correlation, Amati et al. 2002) may be a key ingre-dient for our comprehension of the physics of Gamma Ray Bursts(GRBs). The proposed interpretations explain the E peak − E iso correlation as either due to geometric effects (Eichler & Levinson2004; Toma, Yamazaky & Nakamura 2005) or to the radiative pro-cess responsible for the burst prompt emission (Thompson 2006;Thompson, M´esz´aros & Rees 2007), though there is no unanimousconsensus. In addition, there is no agreement about the reality of thecorrelation itself. Indeed, Nakar & Piran (2005) and Band & Preece(2005) have pointed out the existence of outliers, while Ghirlanda ⋆ E–mail: [email protected] et al. (2005a) and Bosnjak et al. (2008), considering an updatedAmati relation, found no new outliers besides GRB 980425 andGRB 031203. More recently it has been argued that this correlationmight be the result of selection effects related to the detection ofGRBs (Butler et al. 2007 - hereafter B07).The existence of an E peak − E iso correlation was predicted(Lloyd, Petrosian & Mallozzi 2000) before the finding of Amatiet al. (2002). The prediction was based on the existence of a sig-nificant correlation in the observer frame between the peak en-ergy E obspeak and the bolometric fluence F of a sample of BATSE bursts. This finding has been recently confirmed by Sakamoto etal. (2008a) using a sample of bursts detected by
Swift , BATSE and
Hete–II . In particular, they note that X-Ray Flashes and X-Ray-Rich satisfy and extend this correlation to lower fluences. Amati etal. (2002) discovered the E peak − E iso correlation with a sample of12 bursts detected by Beppo
SAX with spectroscopically measured c (cid:13) Nava et al. redshifts. Later updates (e.g. Lamb, Donaghy & Graziani 2005;Amati et al. 2006; Ghirlanda et al. 2008 – hereafter G08) confirmedit with larger samples. In the most recent updates (76 bursts in G08and 83 in this paper) the GRBs with measured redshift and E obspeak define a correlation E peak ∝ E . , with only two outliers (GRB980425 and GRB 031203, but see Ghisellini et al. 2006). This lastsample contains bursts detected by different instruments/satellites,i.e. BATSE , Beppo
SAX,
Hete–II , Konus–Wind (all operative in theso–called pre–
Swift era) and, since 2005 (mostly) by
Swift . Theseinstruments have different detection capabilities and also differentoperative energy ranges.For these reasons is crucial to answer to the following ques-tion: is the E peak − E iso correlation real or is it an artifact of someselection/instrumental effect?To investigate this issue we should move to the observer frameplane corresponding to the Amati relation (i.e. the E obspeak – F plane)where the instrumental selection effects act. There, we can placethe “cuts” corresponding to the instrumental selection effects andsee if the distribution of the data points are affected by these cuts,or if, instead, they prefer to lie in specific regions of the plane, awayfrom these cuts.There are two main selection effects: first, a burst must have aminimum flux to be triggered by a given instrument. This minimumflux can be converted (albeit approximately) to a fluence by adopt-ing an average flux to fluence conversion ratio, as done in G08.This is the minimum fluence a burst should have to be detected.We call it “trigger threshold”, TT for short. Secondly, we need aminimum fluence also to find E obspeak and the spectral shape. In factwe can have bursts that, although detectable, have too few photonsaround E obspeak to reliably determine E obspeak itself. Consider also thatthe limited energy range of any detector inhibits the determinationof E obspeak outside that range. We call it “spectral threshold” – ST.While both selection effects are functions of E obspeak we foundthat the latter is dominant for all the detectors.In G08 we considered a sample of 76 GRBs with redshifts z (which we will call, for simplicity, z GRB sample). These bursts de-fine an Amati correlation in the form E peak ∝ E . ± . , consis-tent with what found by previous works. Moreover, G08 found thatthese bursts define a strong correlation also in the observer frame( E obspeak ∝ F . ± . ).We demonstrated that the ST truncation effect is biasing the z GRB sample of
Swift –bursts (i.e. bursts for which E obspeak has beendetermined from the fit of BAT spectra) while this is not the casefor the no– Swift z GRBs (i.e. bursts for which E obspeak has beendetermined from other instruments, namely Konus–Wind , BATSE , Beppo
SAX and
Hete–II ) . This leaves open two possibilities: (i)if those described above are all the possible conceivable selectioneffects, the no–
Swift z GRB sample represents an unbiased sampleand, therefore, the E obspeak – F correlation defined with these burstsis real; (ii) there are other selection effects biasing the sample of z GRBs. For instance, the optical afterglow luminosity might beproportional to the burst fluence, resulting in a bias in favour of γ –ray bright bursts. Another effect concerns the BATSE bursts,that had to be localized by the Wide Field Camera (WFC) of
Beppo
SAX. Although, formally, the TT for the WFC should notintroduce any relevant truncation, in G08 we have shown that allbursts detected by the WFC (with and without redshift or measur-able E obspeak ) had fluences much larger than its TT curve.To proceed further, in this paper we consider all bursts withmeasured E obspeak , irrespective of having or not a measured redshift.With this enlarged sample we study if the distribution of GRBsin the E obspeak – F plane is: (i) consistent or not with the correlation defined by the z GRBs; and (ii) if it is strongly biased or not by theconsidered selection effects.Besides using existing samples of bursts (from
Hete–II ,Sakamoto et al. 2005, from
Swift , B07, and from
BATSE , Kaneko etal. 2006, K06), we collected a
Konus–Wind sample from the GCNcirculars (Golenetskii et al., 2005, 2006, 2007, 2008) and we anal-ysed a new sample of
BATSE bursts reaching a fluence of − [ergcm − ]. This is the BATSE limiting fluence (ST) which allows to de-rive a reliable E obspeak from the spectral analysis. We therefore havea complete, fluence limited, sample of BATSE bursts. With this wecan study if there is any E obspeak – F correlation and if it is a result ofselection effects or not.By the same token, we can study the correlation between E peak and the peak luminosity L iso . This correlation was firstfound by Yonetoku et al. (2004), with a small number (16) of bursts,and was slightly tighter than the E peak − E iso correlation, and hadthe same slope. It will be interesting to see if this is still the caseconsidering our sample of 83 z GRBs. We can then investigate theinstrumental selection effects acting on this correlation by studyingit in the E obspeak – P plane, where P is the peak flux. E obspeak –FLUENCE PLANE The observer frame E obspeak – F correlation, found using z GRBs(filled symbols in Fig. 1), divides the plane in two regions corre-sponding to large fluence and low/moderate E obspeak (region–I) andlow fluence and large/moderate E obspeak (region–II). The absence ofbursts in region–I suggests that they are extremely rare because,otherwise, they would have been easily detected by present andpast GRB detectors. The absence of bursts in region–II could bedue to selection effects.In the following we will refer to GRBs with known z as z GRBs and we will indicate bursts without measured z as GRBs. z GRBs
Different detectors/satellites (
BATSE –CGRO,
Hete–II , Konus–Wind , Beppo
SAX,
Swift ) have been contributing the sample ofGRBs with measured z and E obspeak , possibly introducing differentinstrumental selection effects. G08, by considering the trigger ef-ficiency of these satellites (from Band 2003), excluded that this isaffecting the sample of 76 bursts defining the E obspeak – F correlation.However, a stronger selection effect was studied in G08: to add apoint in the E peak − E iso correlation, in addition to detect it, weneed to determine (through the spectral analysis) the peak energy E obspeak . This requires a minimum fluence. G08 simulated severalspectra of GRBs by assuming they are described by a Band func-tion. The values assumed for the low and high energy indeces arefixed to the typical values α = − and β = − . . By varying thepeak energy, the fluence and the duration G08 derived the “spectralanalysis thresholds” ST (shaded curves in Fig. 1) in the E obspeak – F plane for BATSE , Beppo
SAX and
Swift . Details of the simulationsare given in G08. These curves show that the limiting fluence F is a strong function of E obspeak . A burst on the right side of thesecurves has enough fluence to constrain its peak spectral energy. Asdiscussed in G08, Fig. 1 shows that the 27 Swift bursts (filled stars)with z and well constrained E obspeak (from C07) are affected by thisselection effect (dark and light grey areas labeled Swift in Fig. 1).Note that this is a small sub–sample of the bursts detected by
Swift .Indeed, in order to add a point to the E peak − E iso correlation, inaddition to z , also E obspeak is needed. C07, through the analysis of the c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux Figure 1.
Distribution in the E obspeak – F plane of the GRBs with measured redshift (filled symbols) and bursts without measured z published in the literature(open symbols). The bolometric fluence is obtained by integrating the spectrum in the range 1 keV–10 MeV. The bright BATSE sample (from K06) is shownby open circles (for well constrained E obspeak ) and up/down arrows (when only an upper/lower limit can be set on E obspeak from the spectral analysis of K06). Hete–II (Sakamoto et al. 2005) and
Swift bursts (B07 – but see text) without redshifts are shown with open triangles and stars, respectively. Shaded regionsrepresent the ST curves of minimum fluence, for different instruments (see G08 for more details), down to which it is possible to fit the spectrum and constrainthe spectral parameters.
BAT–
Swift spectra of bursts with known z , showed that, given thelimited energy range of this instrument (15–150 keV), the peak en-ergy could be determined only for a small fraction of bursts. There-fore, these 27 Swift bursts are all the GRBs (up to April 2008) forwhich both the z is known and E obspeak could be determined fromthe fit of the BAT– Swift spectrum. The fact that the
Swift sample,for which the spectral analysis of C07 yielded E obspeak , extends tothe estimated limiting ST is an independent confirmation of the re-liability of the method for simulating these curves. Note that a few Swift bursts are below these lines, but in these cases the peak energywas found using the combined
XRT–BAT spectrum (see G08).Instead, pre–
Swift z GRBs (partly detected by
BATSE and
Beppo
SAX – filled circles in Fig. 1) are not affected by the cor-responding ST curves. Note that only for
BATSE we could derivethe ST through our simulations. To this aim, the detector responseand background model is needed. For
Konus–Wind , Beppo
SAX and
Hete–II these informations are not public. However, for
Beppo
SAXwe can rescale the
BATSE thresholds (see G08 for details).The sample of z GRBs considered in this work contains 83objects, 76 from the sample collected in G08, plus 7 bursts re- cently detected (up to April 2008). For all these 7 bursts the spectralparameters come from fitting the
Konus–Wind spectra and are re-ported in the GCN circulars (see Tab. A3). With this updated sam-ple we find an Amati correlation with slope s = 0 . ± . and scatter σ = 0 . . The same sample defines also a corre-lation (Kendall’s τ = 0 . ) in the observer plane in the form E obspeak ∝ F . ± . .A way to investigate if the lack of GRBs in region–II of the E obspeak – F plane, i.e. between the distribution of bursts with z andthe ST curves defined in G08, is real or it is due to a still un-explained selection effect is to consider all GRBs with well con-strained E obspeak but without measured z . The scatter is found constructing the distribution of the logarithmic dis-tance orthogonal to the best fit correlation line, and fitting this distributionwith a Gaussian.c (cid:13) , 000–000
Nava et al. z We consider
Hete–II bursts (Sakamoto et al. 2005),
Swift bursts(from B07), the bright
BATSE sample (K06) and
Konus–Wind bursts (Golenetskii et al. 2005, 2006, 2007, 2008, GCN circulars).Through these samples we populate the E obspeak – F plane. We have considered the sample of 350
BATSE
GRBs published byK06. The selected bursts have either a peak photon flux (in the 50–300 keV energy range) larger than 10 [photon s − cm − ] or a flu-ence (integrated above 25 keV) larger than 2 × − [erg cm − ].We excluded the 17 events whose spectrum was accumulated forless than 2 sec as most likely representative of the short durationburst population. With the remaining GRBs, we constructed a firstsample selecting all bursts whose time integrated spectrum is fit-ted with a curved model (Band, cutoff power–law or smoothly–joined power law) providing an estimate of E obspeak . This samplecontains 279 GRBs. The remaining bursts form another sample pro-viding lower/upper limits on E obspeak : those GRBs fitted with a Bandor smoothly–joined power law with an high energy photon indexgreater than –2 provide a lower limit, as well as those fitted with asingle flat power law. On the contrary, bursts fitted by single steeppower laws (photon index < − ) provide an upper limit on E obspeak .Fig. 1 shows the K06 sample (open circles) in the E obspeak – F plane together with the 83 z GRBs. The
BATSE
ST curves are alsoshown. By comparing
BATSE
GRBs with z GRBs (filled symbolsin Fig. 1) we note that the two samples are consistent for E obspeak values in the 100 keV – 1 MeV range. However, note that in theK06 sample there are also a few bursts with considerably smallerfluence (but similar E obspeak ) with respect to z GRBs. In other words,there is an indication of the existence of bursts that lie betweenthe limiting
BATSE curves and the E obspeak – F correlation definedby z GRBs (region–II). From Fig. 1 it is clear that the sample ofbright
BATSE bursts is not strongly affected by the correspondingST. However, note that this sample is not appropriate to study thisissue because it is representative only of very bright
BATSE burstsand it is not complete in fluence.The K06 sample shows a weak E obspeak – F correlation with aKendall’s correlation coefficient τ = 0 . (3 σ significance). Other two samples of bursts with published spectral parameters arethat of
Hete–II and
Swift . The two references for the
Swift burstsare C07 and B07: the former focused on
Swift bursts with z and thelatter considered also bursts without redshifts. The C07 Swift burstswere included in the sample of the 83 z GRBs. For the
Swift burstswithout z we consider the analysis performed by B07 (but see alsoSakamoto et al. 2008b). They analysed GRB spectra with either thefrequentist method and through a Bayesian method. While the firstmethod allows to constrain the spectral E obspeak only if it lies in theenergy range where the spectral data are (15–150 keV for BAT– Swift ), the bayesian method infers the peak energy by assuming an E obspeak distribution as prior. For homogeneity with the analysis ofC07 and with the method used to find the ST, we consider only the Swift bursts of B07 without z which have their peak energy esti-mated through the frequentist method and for which this estimatehas a relative error < Swift bursts whichsatisfy these requirements. The
Hete–II group published some spectral catalogs of theirbursts (Barraud et al. 2003; Atteia et al. 2005; Sakamoto et al.2005). Sakamoto et al. (2005) performed the time integrated spec-tral analysis of 45 GRBs detected during the first 3 years of the
Hete–II mission. They performed spectral fits by combining thedata of the high energy detector (Fregate: 6–400 keV) and the lowenergy coded mask detector (WXM: 2–25 keV). We have consid-ered in this sample the 27 bursts without z (the remaining are al-ready included in the z GRB sample) and whose spectrum is fittedby a Band or cutoff power–law model which provides an estimateof E obspeak .Fig. 1 shows that Swift bursts (open stars) and
Hete–II bursts(open triangles) are both consistent with the correlation defined inthe E obspeak – F plane by the z GRB sample. Also the
Swift samplewithout z confirms the validity of the ST estimates. Note that theextension of Hete–II events at very low values of E obspeak is due tothe fit of their spectrum with the WXM instrument (see Sakamotoet al. 2005).Note that in the sample of 83 bursts with z there are also the Beppo
SAX and
Konus–Wind events. No spectral catalog of burstswithout redshifts has been published to date for these two satellites.
Preliminary results arising from the fit of
Konus–Wind spectra canbe found in the GCN circulars. We collected a sample of 29 GRBs(empty squares in Fig. 1) for which an estimate of E obspeak and thespectral shape is available and which are not already included inthe Hete–II or Swift samples considered above. For each burst weestimate the bolometric (1–10 keV) fluence and the bolometricpeak flux. The results are listed in Tab. A1 in the Appendix. Since Konus–Wind covers an energy range from 20 keV to a few MeV, agood spectral analysis of very hard bursts can be performed. Any-way, the determination of its TT and ST is not possible, as the back-ground model and the detector response are not public. Therefore,with respect to the distribution of these GRBs in the E obspeak – F plane(Fig 1), we can only note that it seems to be very similar to that ofbright BATSE bursts (empty circles).
BATSE
BURSTS
Among the above sample, the bright
BATSE bursts of K06 is thelargest and, given the spectral range of
BATSE , covers a wide rangein E obspeak . However, this sample was selected according to a min-imum peak flux or fluence threshold and it is not complete eitherin peak flux and fluence. Furthermore it extends down to a fluencelarger than the the minimum fluence required to derive E obspeak .Samples reaching smaller fluences indeed exist: Yonetoku etal. (2004) performed the spectral analysis of 745 GRBs from the BATSE catalog with flux larger than × − [erg cm − s − ].However, they exclude 56 GRBs for which they find a pseudo red-shift greater then 12 or no solution using the E peak − L iso rela-tion as a distance indicator. Thus the final sample is biased by thischoice as it most likely excludes the bursts with low fluence andintermediate/high peak energy and therefore is not representativeof the whole sample of BATSE bursts with fluences greater than thespectral threshold.It is clear from Fig. 1 that for
BATSE bursts “there is room” toextend the K06 sample to smaller fluences: if the ST for
BATSE arecorrect, we should be able to analyze bursts with fluence smaller c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux Figure 2.
The E obspeak – F plane for the sample of BATSE bursts. The fluence reported in this plot is the bolometric fluence (1–10 keV). The open circlesare GRBs of the K06 sample with catalog fluence larger than 2 × − erg cm − and the filled circles are the 100 GRBs analyzed in this paper. The arrowscorrespond to those bursts for which we can only estimate a lower/upper limit to E obspeak . The shaded region represents the minimum fluence requested toconstrain E obspeak from the spectral analysis. The left and right boundaries of this region are calculated for a burst lasting 5 and 20 seconds respectively (seeG08 for more details). The dotted line represents the best fit to the combined sample: E obspeak ∝ F . ± . . than 2 × − [erg cm − ]. Therefore, in order to increase the statis-tics and test the density of bursts in region–II we extend the BATSE sample to the limiting fluence of 10 − [erg cm − ]. To this aim weselected a representative sample of 100 BATSE bursts with a flu-ence F above 25 keV (which is a good proxy for the bolometricfluence), within the range − < F < × − [erg cm − ].The number of extracted GRBs per fluence bin follows the Log N –Log F distribution and therefore this sub–sample is representativeof the BATSE burst population in this fluence range (which corre-sponds to ∼ events).For all these bursts we analysed the BATSE
Large Area De-tector (LAD) spectral data which consist of several spectra accu-mulated in consecutive time bins before, during and after the burst.The spectral analysis has been performed with the software
SOAR v3.0 (Spectroscopic Oriented Analysis Routines), which we imple-mented for our purposes. For each burst we analysed the
BATSE spectrum accumulated over its total duration (which in most casescorresponds to the T parameter reported in the BATSE catalog). In order to account for the possible time variability of the back-ground we modeled it as a function of time (see e.g. K06).In most cases we could fit either the Band model (Band etal. 1993) or a cutoff power law model. To be consistent with themethod used to derive the spectral threshold curves of Fig. 1, weconsider that E obspeak is reliably determined if its relative error is lessthan 100%. If the relative error is greater or if the best fit model isa simple power law we derive the corresponding lower/upper limit.In these cases the burst is reported on the plot as an up/down arrow.In Tab. A2 in the appendix we list the bursts of our sampletogether with the results of the spectral fitting. BATSE bursts
In order to construct a complete sample of
BATSE bursts, we cutthe K06 sample at a fluence F (as reported in the BATSE catalog)greater than × − [erg cm − ] (213 GRBs). This complete sub–sample is representative of bright BATSE bursts. To this we addthe 100 bursts of our representative sample of the 1000 GRBs with c (cid:13) , 000–000 Nava et al.
Figure 3.
Scatter distributions of the sample of
BATSE bursts with wellestimated E obspeak around their best fit correlation in the E obspeak – F plane(see Fig. 2). The shaded distribution is of the 213 GRBs of K06 and thehatched distributions is of the 88 GRBs of our analysis (we have excludedupper/lower limits). The fit with gaussian functions of the two distributionshave scatter σ = 0 . for the K06 sample and σ = 0 . for our sample.The insert shows the scatter of the combined sample ( σ = 0 . ) (solid line),once we take into account that the GRBs analyzed by us are representativeof 1000 bursts. fluences between − and 2 × − [erg cm − ]. Fig. 2 shows the E obspeak and bolometric fluence (computed in the range 1 keV – 10MeV) of the sub–sample of bursts from the K06 sample (open cir-cles) together with the 100 bursts of our sample (filled circles). Thiscombined sample extends the K06 fluence limit to F > − ergcm − . Note that in this figure we plot the bolometric (1-10 keV)fluence estimated accordingly with the best fit model. Its value canbe different from the fluence value reported in the BATSE catalog.The distribution of
BATSE
GRBs in Fig. 2 defines a corre-lation with a large scatter. The Kendall’s correlation coefficient is τ = 0 . (7 σ significant). Since the dimmer part of the burst distri-bution in the E obspeak – F plane is affected by the ST truncation effect,we analyzed the correlation also following the method proposed byLloyd et al. (2000). We obtain a Kendall’s correlation coefficient τ = 0 . (5.5 σ significant). By fitting with the least square method,without weighting for the errors and neglecting the upper/lowerlimits, we obtain E obspeak ∝ F . ± . (dotted line in Fig. 2).In Fig. 3 we show the distribution of the scatter of the twosamples around the best fit correlation in the E obspeak – F plane. Thesehave standard deviation of σ =0.18 for the K06 sample (solid his-togram) and σ =0.29 for our representative sample (hatched his-togram). The combined sample (solid line in the insert) has a scatterdistribution with σ =0.26. In order to describe the scatter distribu-tion of BATSE bursts down to the fluence limit of
F > − [ergcm − ], we have to consider that our sample of 100 bursts is repre-sentative of the entire burst population (a factor 10 larger in num-ber) in the fluence range − < F < × − [erg cm − ]. Wefitted the scatter distributions of our (dashed line) and K06 (solidline) sample with gaussian functions and combined these best fitdistributions by renormalizing that of our sample by a factor 10(corresponding to the ratio of the extracted bursts with respect to Figure 4.
The E obspeak distributions for the K06 GRB sample (213 GRBs –shaded histogram) and for the sample that we have analyzed (88 GRBs withwell determined E obspeak over 100 bursts randomly extracted from the BATSE
Log N –Log F distribution in the range − < F < × − [erg cm − ]– hatched histogram). The solid and dashed lines are the gaussian fits to thetwo distributions. The K–S test (see text) confirms that the shift of E obspeak to lower values for dimmer bursts is statistically significant. In the insert arereported these two gaussian fits and their sum (solid line) which has beenobtained by multiplying the distribution of the 100 GRBs by 10 (dot–dashedline) in order to account for the total number of bursts in this fluence range. the total number of BATSE bursts in the same fluence bin). The re-sult is shown in the insert of Fig. 3 (solid line). The combined sam-ple (solid line in the insert) has a scatter distribution with σ =0.26.Fig. 2 shows that there are bursts with low fluence and high E obspeak and that the dispersion in E obspeak at low fluence is larger thenthe dispersion at high fluence. However, Fig. 2 also shows that, onaverage, the error on the E obspeak value increases for smaller fluences.This could imply that the larger scatter for smaller fluences is in partdue to larger errors on E obspeak . A simple way to determine the con-tributions to the total observed scatter σ tot , calculated orthogonallyto the fitting line, is: σ = σ E cos θ + σ (1)where σ E is the average relative error on E obspeak , θ is the angle de-fined by the slope of the correlation (whose angular coefficient isequal to tan θ = 0 . ) and σ c is the intrinsic scatter of the distribu-tion. For fluences greater than 2 × − [erg cm − ] (K06 sample) σ tot ∼ σ c = 0 . since the errors on E obspeak are small. On the otherhand, for fluences smaller than 2 × − [erg cm − ] (our sample), σ E = 0 . and σ tot = 0 . , leading to σ c = 0 . , to be comparedto σ c = 0 . for fluences greater than 2 × − [erg cm − ]. Thisleads us to conclude that the intrinsic scatter around the best fit lineincreases for smaller fluences. A caveat is in order: the scatter σ c does not take into account lower/upper limits, which also do notenter in the derivation of the best fit line. Thus σ c could be larger,but only slightly, since the number of upper/lower limits is verylimited.Through our BATSE sample we can also study the E obspeak dis-tribution. In Fig. 4 we show the E obspeak distribution of our BATSE c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux sample (hatched histogram) and that of bright BATSE bursts of K06(solid filled histogram – cut at 2 × − [erg cm − ]).The shift of the E obspeak distribution to lower values for smallerfluence selection is statistically significant: the K–S test gives aprobability P = 5 . × − that the two distributions belong tothe same population. Similarly to what has been done for the scat-ter distribution, we combine the two distributions by accounting forthe fact that our sample is representative of a larger population ofbursts in the − – 2 × − [erg cm − ] fluence range. The resultis shown in the insert of Fig. 4 (solid line). This total sample dis-tribution has a peak at E obspeak ∼
160 keV, i.e. smaller than the 260keV of bright bursts of K06, and a standard deviation σ =0.28. Al-though the widths of the distributions of E obspeak can be affected bythe measurement errors, the central values are not. E peak − E iso CORRELATION
In Fig. 5 we combine, in the E obspeak – F plane, our sample of BATSE bursts with the z GRBs (solid filled squares) and with the
Swift , Hete–II and
Konus–Wind samples of GRBs without redshifts.We note that bursts with known redshift (filled squares) areonly representative of the large fluence (for any E obspeak ) part of theplane. In particular, Fig. 5 shows the existence of bursts with lowfluence (between F − and F ∼ − [erg cm − ]) but E obspeak larger than 200 keV. These events are not present in the z GRB sam-ple. Their absence in the z GRB sample suggests the existence of aselection effect.However, z GRBs are those defining the Amati correlation (asin G08). We do not know if all the other bursts (without redshifts)represented in Fig. 5 satisfy this correlation.If these GRBs have a similar redshift distribution of those withmeasured z , then it is likely that they would define a rest frame E peak − E iso correlation with different properties (slope, normal-ization and scatter), since some of them stay apart from the E obspeak – F correlation defined by the z GRB sample. On the other hand,GRB 980425 and GRB 031203 do have a peak energy and fluenceconsistent with the z GRB sample, but it is their small redshift tomake them outliers with respect to the E peak − E iso correlation.The possibility that there is a considerable number of outliersof the E peak − E iso correlation in the BATSE sample has been dis-cussed in the literature (e.g. Nakar & Piran 2005; Band & Preece2005; K06 – but see also Ghirlanda et al. 2005; Bosnjak et al. 2007).We can test if a burst is consistent or not with the E peak − E iso correlation even if we do not know its redshift. Simply, we as-sign to the burst any redshift, checking if there is at least one z making it consistent with the correlation. By “consistent” we meanthe the burst must fall within the 3 σ scatter (assumed gaussian)of the correlation. This test was first proposed for the short bursts(Ghirlanda et al. 2004a) and then applied to BATSE long GRBs.More quantitatively, following Nakar & Piran (2005), we can writethe E peak − E iso correlation as E obspeak (1 + z ) = k (cid:18) πd F z (cid:19) a → E obspeak = kF a f ( z ); f ( z ) = (4 πd ) a (1 + z ) a (2)where F is the bolometric fluence. The function f ( z ) has a max-imum ( f max ) at some redshift and therefore all bursts for which E obspeak / ( kF a ) > f max are outliers. We can impose that the con-stant k accounts for the scatter of the best fit E peak − E iso corre-lation, and then find outliers at some pre–assigned number of σ . It correlation sample scatter K s E peak − L iso z GRB 0.28 –18.6 0.40 ± z GRB (only
Swift ) –11.4 0.26 ± z GRB (not
Swift ) –20.5 0.44 ± E peak − E iso z GRB 0.23 –22.7 0.48 ± z GRB (only
Swift ) –16.7 0.36 ± z GRB (not
Swift ) –24.4 0.51 ± E obspeak – P z
GRB 0.26 4.41 0.39 ± BATSE ± E obspeak – F z
GRB 0.23 4.00 0.40 ± BATSE a ± Table 1.
Results of the correlation analysis. For each correlation in the restframe and observed plane we give the values of the scatter, normalizationand slope. The correlations are in the form y = Kx s , where y is the loga-rithmic observed/rest frame peak energy in units of keV and x is the loga-rithm of the luminosity (energy) in erg s − (erg) or the peak flux (fluence)in erg cm − s − (erg cm − ). a : this is the value once depurated of thecontribution to the scatter of the measurement errors (see text). is worth to recall that this method assumes that the dispersion ofpoints, around the E peak − E iso correlation under test, is describedby a Gaussian function. With this assumption we can state that agiven GRB is Nσ inconsistent with the correlation, and quantifythe probability of having a certain number of outliers lying – say –more than 3 σ away. Since the Amati correlation, as discussed be-low, surely incorporates an extra–Poissonian dispersion term (Am-ati, 2006), the scatter distribution may not be a Gaussian, but it maycorrespond to the distribution function of this extra term. In otherwords: the scatter of the points around the Amati correlation is not due to the errors of our measurements, but reveals the presence ofan extra–observable not considered in the Amati relation. With thiscaveat, we nevertheless use this assumption (i.e. Gaussianity) forsimplicity.In Fig. 5 the grey area identifies, in the E obspeak – F plane, the“region of outliers”. Considering only BATSE bursts we can statethat the 6% of the complete sample considered in this paper is con-stituted by bursts which are surely outliers of the E peak − E iso relation. We can test if these outliers have different spectral proper-ties with respect to other bursts (that instead pass the above consis-tency test). By comparing their spectral parameters we find that theoutliers of the E peak − E iso correlation have a larger peak energythan the total sample of bursts (K–S probability P = 8 . × − )and a slightly harder low energy spectral index α (K–S probability P = 10 − ). From Fig. 5 we also note that there is no outlier forthe E peak - E γ correlation. E peak − L iso CORRELATION
Yonetoku et al. (2004, Y04), with a sample of 16 GRBs of known z , found that E peak ∝ L . , where L iso is the isotropic luminosityat the peak of the prompt light curve, but calculated using the timeaveraged spectrum (i.e. E peak and spectral indices), and not thespectral properties at the peak flux.This correlation appeared to be tighter (but with similar slope)than the E peak − E iso correlation, as originally found by Amati etal. (2002). Since then this correlation has been updated only once(Ghirlanda et al., 2005b).It is interesting to test if the same conclusions that can be c (cid:13) , 000–000 Nava et al.
Figure 5.
Consistency test of the E peak − E iso correlation. The open symbols represent the bursts without redshifts detected by Hete–II (triangles),
BATSE (open and filled circles),
Swift (open stars) as described in the legend. The solid line is the E peak − E iso correlation transformed in the observer E obspeak – F plane. The long–dashed line is the 3 σ scatter of the E peak − E iso correlation. The “region of outliers” is the grey shaded. Bursts falling in this region are notconsistent with the E peak − E iso correlation for any redshift: they are outliers at more than σ (if the scatter distribution is Gaussian, see text). In the upperleft corned we also show the “region of outliers” of the E peak − E γ correlation (adapted from Ghirlanda et al. 2007) if bursts have a 90 ◦ jet opening angle.The dotted line is the fit to the z GRB sample (filled squares) and the dashed line is the fit to the complete sample of
BATSE bursts described in Sec.3.1 (seealso Tab.1) drawn for the E peak − E iso correlation (i.e. the presence of selec-tion effects and of outliers) can now be extended to the E peak − L iso correlation. To this aim we have considered the z GRB sample (seeTab. A3 in the Appendix) and we have calculated for all these burststheir isotropic equivalent luminosity L iso . This is computed by in-tegrating the time averaged spectrum after renormalizing it with thepeak flux. Note that, strictly speaking, this luminosity does not cor-respond to the peak luminosity (see Ghirlanda et al. 2005b), sinceit adopts the time averaged E obspeak .In Tab. A3 we report the sample of 83 GRBs with their peakflux, the energy range where it is computed, the references and L iso .To calculate L iso we adopted the same method used to compute E iso (see Ghirlanda et al. 2007 for more details).In Fig. 6 we show the E peak − L iso and the E peak − E iso corre-lations defined with the 83 GRBs of Tab. A3. The no– Swift bursts (empty symbols) and the
Swift bursts (filled squares) are shown.In both cases, the correlations are highly significant (rank corre-lation coefficient are respectively 0.83 with a chance probability . × − and 0.84 with a chance probability . × − ). Thesolid lines show the best fit with the least square method (with-out accounting for the measurement errors): we obtain E peak ∝ L . ± . and E peak ∝ E . ± . . The fits of the no– Swift burstsample (dotted line) and of the
Swift burst sample (dashed line) arealso shown. The results of these fits performed considering differ-ent samples are shown in Tab. 1.Our sample of 83 z GRBs confirms the finding of Yonetokuet al. (2004), even if we obtain a flatter slope. Fitting the scatterdistribution of the E peak − L iso correlation with a Gaussian wederive σ = 0 . . Comparing it with the corresponding scatter ofthe E peak − E iso correlation ( σ = 0 . ) we find that, contrary to c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux Figure 6. E peak − L iso and E peak − E iso correlations for 83 GRBs with measured redshift and spectral parameters. The best fit of the whole sample isshown with a solid line. Note that the fit performed on the Swift sample alone (filled squares) has in both cases a very flat slope (dashed line) with respect tothe slope derived for no–
Swift bursts (dotted line). The results of these different analysis are reported in Tab. 1. For an explaination of the flat slope found withthe
Swift sample see G08. what initially found by Yonetoku et al. (2004), the scatter of thiscorrelation is slightly larger.We can investigate if this correlation is affected by any of theselections effects that have been studied in G08 for the E peak − E iso correlation. In particular we show in Fig. 7 the observer frame E obspeak – P correlation where P is the bolometric peak flux. Note thatalso in this plane the z GRBs define a strong correlation (dotted line– with slope 0.39) and that the GRB samples without z consideredin this work are consistent with this correlation (differently to whathappens in the E obspeak – F plane). The dashed line represents the bestfit obtained considering only BATSE bursts. They define a flattercorrelation (slope 0.28) with respect to the z GRB sample. Note thatthis happens also in the E obspeak – F correlation and it is likely due tothe difficulty of the BATSE instrument to see very low E obspeak at lowfluence/peak flux.The peak flux P is the quantity on which the trigger condition(for most instruments) is determined. We plot in Fig. 7 the triggerlimiting curves (from G08) as a function of E obspeak . We note thatfor BATSE the TT curve is separated from the distribution of thecorresponding bursts (open and filled circles). This is because thedominant selection effect acting on our
BATSE complete sample isthe ST (see Fig. 2). In other words, the bursts that can be displayedin the E obspeak – P plane are not all the bursts that can be detectedby a given instrument, but only those with a sufficient number ofphotons to make possible the determination of E obspeak .The Hete–II bursts, instead (triangles), are very near to theirTT. For this instrument we are not able to determine the ST curves,but it is likely that the dominant selection effect acting on
Hete–II bursts is the need to trigger them.For
Swift bursts we have an intermediate case: their TT curveis not truncating their distribution, even if they lie closer (than
BATSE bursts) to it.Also for the E peak − L iso correlation we can test if there areoutliers. Ghirlanda et al. (2005b) tested this through a sample of 442 GRBs with redshifts derived by the lag–luminosity relation.They did not find evidence for outliers. In this work we test the E peak − L iso correlation with the same method described abovefor the E peak − E iso correlation. In Fig. 7 we show the “region ofoutliers” for the E peak − L iso correlation. Only one burst (of theK06 sample) is inconsistent with this correlation at more than 3 σ . To study the role of possible instrumental selection effects on theAmati relation we have focused our attention on the observational E obspeak – F plane. Here we can compare the distribution of differ-ent samples of GRB (for example, z GRBs and GRB with unknownredshift). To this aim we adopt the analysis performed by G08, re-ferring to two different instrumental biases: the trigger threshold(TT, the minimum fluence derived considering the minimum fluxrequired to trigger a burst) and the spectral analysis threshold (ST,the minimum fluence needed to constrain the GRB spectral prop-erties). These curves depends on E obspeak and define what part of theobservational plane is accessible.First we updated the sample of bursts with redshift, adding 7new recent GRBs, for a total of 83 objects. These GRBs definea E peak ∝ E iso0 . ± . correlation in the rest frame, very simi-lar to that obtained with previous (and smaller) samples. In theobserver plane, they define a slightly flatter correlation ( E obspeak ∝ F . ± . ). The scatter of these two correlations is the same (seeTab. 1). As G08 pointed out, the BATSE
ST curve is not biasing thedistribution of
BATSE bursts with redshift in the observer plane,while the
Swift
ST could, in the sense that the distribution of
Swift bursts (with redshift) is truncated by the
Swift
ST curve. Then whythe
BATSE bursts (with redshift) are not truncated by their corre-sponding ST? Is it because of a real, intrinsic correlation or is itdue to another, hidden, selection effect? One way to answer this c (cid:13) , 000–000 Nava et al.
Figure 7.
Consistency test of the E peak − L iso correlation. The filled squares are bursts with measured redshifts. The solid line is the E peak − L iso correlationtransformed in the observer E obspeak – P plane (here it is represented the bolometric peak flux). The long dashed line is the 3 σ scatter of the E peak − L iso correlation (as discussed in Sec. 5). The shaded triangle delimits the “region of outliers”. Bursts falling in this region are not consistent with the E peak − L iso correlation for any redshift: they are outliers at more than σ (if the scatter distribution is Gaussian, see text). The dotted and dashed lines show the best fitobtained by considering respectively the z GRB sample and the
BATSE complete sample. The curves represent the TT estimated for different instruments byassuming that the trigger is based on the peak flux criterion. crucial question is to analyze all GRBs with E obspeak , even withoutredshift. The BATSE sample of GRBs is the best suited for this aimbecause: i) it contains a large number of bursts; ii) large sample ofbright GRBs have been already analyzed, and iii) for
BATSE wealready know the ST curve. Then we pushed the spectral analysisto the limit, deriving the spectral parameters for a representativesample of 100
BATSE
GRBs with a (bolometric) fluence between − [erg cm − ] (corresponding to the ST limit) and × − [erg cm − ] (the limiting fluence of K06). These 100 GRBs repre-sent a large population of 1000 GRBs, in the same fluence range.Combining our and the K06 samples we have a homogeneous andcomplete sample, best suited to study how BATSE
GRBs populatethe E obspeak – F plane. Using this complete, fluence limited, samplewe find: • GRBs without redshifts, in this plane, are not spread in theregion free from instrumental selection effects, but define a corre- lation with a flat slope ( ∼ . ) and a scatter larger for smallerfluences (after accounting for the errors increasing for smaller flu-ences). Fig. 8 is a graphic illustration of this: different grey levelscorresponds to different density of points in the E obspeak – F plane,once we take out the effect of the overall increase in density goingto smaller fluences (for the Log N –Log S slope). The way we dothis is the following: we consider different fluence–bins and in eachof those we count the total number N f of objects. Then we dividethis fluence–bin into E obspeak –bins, counting the number of objectsin each small area, dividing it by N f . Each small area is then char-acterized by a number n i,f (between 0 and 1), which correspondsto a different level of grey. Note that the data points do not fill theentire accessible region of the plane but concentrate along a stripe.Note that the shape of this concentration of points is not determinedby the ST curve, reported in Fig. 8 for a typical burst lasting 20 s.The only effect of the ST curve to the found correlation is to cut itat the smallest fluences and E obspeak . The very flat slope could be due c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux Figure 8.
Graphic illustration of the E obspeak – F correlation. We considerdifferent fluence–bins and in each of those we count the total number N f of objects. Then we divide this fluence–bin into E obspeak –bins, counting thenumber of objects in each small area, dividing it by N f . Each small area isthen characterized by a number n i,f (between 0 and 1), which correspondsto a different level of grey. In this way the increasing number of bursts fordecreasing fluence (the “Log N –Log S ” effect) is accounted for, and it doesnot influence n i,f . Note that the data points do not fill the entire accessi-ble region of the plane (to the right of the ST curve shown in Fig. 2), butconcentrate along a stripe. to the difficulty of having BATSE
GRBs with E obspeak smaller than ∼ keV, whose existence is demonstrated by other instruments.However, the paucity of the derived upper limits on E obspeak suggeststhat this effect is marginal. • Formally, the scatter is not greater than the scatter of the E peak − E iso correlation (both have σ = 0 . once the contributionto the scatter of the measurement errors are taken into account).Despite that, the entire BATSE sample and the z GRB populationdefine two E obspeak – F correlations which have significantly differentslopes. If their redshift distribution is similar, then they will definetwo different correlations also in the E peak − E iso plane: consider-ing then the two samples together, we will define a correlation withintermediate slope and a scatter larger than the individual one. • If the above point holds (i.e. if the redshift distributions ofGRBs of unknown redshifts is the same of the z GRBs) then wecan conclude that there exists an E peak − E iso correlation, not de-termined by selection effects, even if its slope and scatter may bedifferent from what we know now. We should emphasize that by theterm ”correlation” we mean that GRBs will occupy a “stripe” in the E peak − E iso plane with a relatively large scatter (fitting it with χ method one would obtain a very large reduced χ r ). In other words,it is very likely that there is another (third) variable responsible forthe scatter. In fact one finds a tighter correlation considering, as athird variable, the jet break time (Ghirlanda, Ghisellini & Lazzati2004; Laing & Zhang 2005) or the time of enhanced prompt emis-sion (Firmani et al. 2005). Another cause for a large scatter is theviewing angle, if a significant number of bursts are seen slightlyoff–axis. • In the
BATSE sample there are a few bursts with small or inter-mediate fluences but large E obspeak , not present in the z GRB sample.Among them there are some surely outliers of the E peak − E iso correlation (as defined by the z GRB sample), i.e. bursts that lie atmore than 3 σ from it, for any redshift. The number of these sureoutliers is however very small, amounting to the 6 per cent of theentire population. • We have also investigated the E peak − L iso correlation, andits counterpart ( E obspeak – P ) in the observer plane. First, we partlyconfirm the original findings of Yonetoku et al. (2005, see also theupdate in Ghirlanda et al. 2005b): with the z GRB sample we finda strong E peak − L iso correlation, whose slope is flatter than orig-inally found ( s = 0 . instead of 0.5) and whose scatter is greaterthan the scatter of the E peak − E iso correlation. • In the observer plane, instead, the E obspeak – P correlation of ourcomplete sample of BATSE bursts is tighter than the the E obspeak – F correlation ( σ = 0 . instead of σ = 0 . ). Its slope is s = 0 . ,flatter than the E peak − L iso correlation ( s = 0 . ), but howeversteeper than the E obspeak – F slope ( s = 0 . ). There is only one sureoutlier. • Selection effects are in this case determined by the TT curves.These effects are present, being responsible for the cutting at lowpeak fluxes, but they do not influence the slope and scatter for peakfluxes larger than the what defined by the TT curves. • Considering the z GRB sample we have that the E peak − E iso correlation is tighter than the E peak − L iso one. Considering ourcomplete BATSE sample and moving to the observer plane, wehave just the opposite: the E obspeak – P correlation is tighter than the E obspeak – F one. • It is then conceivable that the E peak − L iso correlation, oncea large number of burst with redshift will be available, will bestronger than the E peak − E iso one.The general conclusion we can draw from our study is that,although selection effects are present, they do not determine thespectral–energy and spectral–luminosity correlations. These couldbe characterized by a slope and scatter different from what we havedetermined now using heterogeneous bursts samples with mea-sured redshift, but we found that E peak is indeed correlated withthe burst energetics or peak luminosity. Therefore it is worth to in-vestigate the physical reason for this relation. ACKNOWLEDGEMENTS
We thank M. Nardini for stimulating discussions. We thank par-tial funding by a 2008 PRIN–INAF grant and ASI I/088/06/0 forfunding.
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APPENDIX A: TABLES c (cid:13) , 000–000 Nava et al.
GRB α β E obspeak
F P T GCNkeV erg/cm erg/s/cm s050326 -0.74 ± . -2.49 ± . ± ± . ± +0 . − . +1600 − +0 . − . +178 − +0 . − . +73 − ± . +25 − +0 . − . +83 − +0 . − . +36 − +0 . − . -2.31 +0 . − . +40 − +0 . − . -2.57 +0 . − . ± ± . -2.27 +0 . − . +74 − +0 . − . +549 − +0 . − . +8 − +0 . − . -2.41 +0 . − . +59 − +0 . − . -2.02 +0 . − . +204 − ± . +173 − +0 . − . +52 − ± . +27 − +0 . − . -2.28 +0 . − . +19 − ± . ± ± . +19 − ± . +22 − +0 . − . +95 − +0 . − . +95 − ± . -3.10 +0 . − . ± +0 . − . -2.36 +0 . − . +43 − +0 . − . +469 − ± . +25 − +0 . − . +93 − Table A1.
Spectral and temporal properties of 29
Konus–Wind bursts without known redshift. The listed fluence and peak flux are estimated in the range 1–10 keV. It is also reported (when available) the estimated burst duration T. The references are: Golenetskii et al., 2005a, 2005b, 2005c, 2005d, 2005e; Golenetskiiet al., 2006a, 2006b, 2006c, 2006d, 2006e, 2006f, 2006g, 2006h, 2006i; Golenetskii et al., 2007a, 2007b, 2007c, 2007d, 2007e, 2007f, 2007g, 2007h, 2007i,2007j, 2007k; Golenetskii et al., 2008a, 2008b, 2008c, 2008d. The GCN circulars number is reported in the last column.c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux GRB α β E obspeak
Fluence GRB α β E obspeak
FluencekeV erg/cm keV erg/cm
469 -1.16 ± ±
95 (1.1 ± ± ±
29 (6.0 ± ± ±
56 (3.8 ± ±
68 (1.6 ± ± ±
66 (2.0 ± ± ± ± ± ±
29 (1.4 ± ± ±
91 (5.3 ± ± ±
46 (3.5 ± ± > ± (2.6 ± ± ± ±
74 (1.0 ± ± ± ±
229 (2.0 ± ± ±
94 (5.3 ± ±
142 (7.4 ± ± ±
15 (1.2 ± ±
63 (3.5 ± ± ± ±
24 (1.1 ± ± ±
16 (4.9 ± ± ± ±
84 (5.7 ± ± ±
58 (1.1 ± ± ± ±
28 (4.7 ± ± ±
63 (2.5 ± ± ±
31 (4.6 ± ± ± ±
29 (7.5 ± ± <
30 (1.1 ± ± ±
756 (8.9 ± ± ±
36 (7.0 ± ±
22 (1.1 ± ± ± ±
26 (5.9 ± ± ± ± ± ± ± ±
31 (6.4 ± ± ± ±
36 (2.1 ± <
30 (3.4 ± ± ± ±
22 (4.2 ± ± ±
11 (9.3 ± ± ±
19 (2.0 ± ± ±
156 (8.2 ± ± <
30 (1.1 ± ±
211 (4.7 ± ±
16 (1.4 ± ± >
107 (4.1 ± ± ±
205 (3.9 ± ± ± ±
183 (7.4 ± ± ± ±
60 (1.5 ± <
30 (3.4 ± ±
35 (2.2 ± <
30 (1.5 ± ±
80 (2.9 ± ± ± ±
35 (1.4 ± <
30 (1.6 ± ±
29 (1.9 ± ± ± ±
77 (6.8 ± ±
55 (3.4 ± <
30 (2.8 ± ± ± ±
99 (4.1 ± ±
156 (3.0 ± ± ± ±
62 (1.2 ± ±
93 (1.1 ± ± ± ±
26 (2.7 ± ± ±
28 (1.0 ± ± ± ±
52 (1.6 ± ± ± ±
21 (1.5 ± ± ± ±
38 (8.1 ± ± ±
141 (1.4 ± ±
19 (1.2 ± ± ± ±
220 (2.5 ± ±
225 (6.6 ± ± ±
582 (3.8 ± ± ± ±
21 (1.1 ± ± ±
81 (9.6 ± ± ± ±
55 (2.1 ± ± ± ±
142 (8.6 ± ±
151 (8.0 ± ± ± ±
69 (4.6 ± ± ±
100 (2.7 ± ± ± ±
43 (3.4 ± ±
53 (5.9 ± <
30 (1.5 ± ± ±
134 (1.1 ± ±
141 (1.4 ± ± ± ±
180 (9.4 ± ± ± ±
22 (4.1 ± ± <
30 (2.3 ± ± ± ±
47 (2.2 ± ± ±
114 (2.9 ± ± ±
257 (9.1 ± ±
53 (1.3 ± ±
14 (2.2 ± ± <
30 (1.1 ± ± ±
26 (1.2 ± ± ± ± ± ±
61 (2.1 ± ± ± ±
42 (1.1 ± ± ±
153 (3.6 ± ± ± ±
34 (3.2 ± ± ±
291 (4.9 ± ±
64 (3.5 ± ± ±
216 (3.7 ± ± ± ±
41 (1.5 ± ± ±
37 (3.2 ± Table A2.
Sample of
BATSE bursts analyzed in this work. The trigger number and the spectral parameters of the fit of the time integrated spectrum arereported. In the last column we report the bolometric fluence obtained by integrating the best fit spectrum. For those bursts whose spectrum allows only toset a lower/upper limit on E obspeak we report the BATSE catalogue fluence (i.e. >
25 keV). When is not possible to constrain the value of α we performed thespectral fit by fixing α to an appropriate value. These values are reported in table without errors.c (cid:13) , 000–000 Nava et al.
GRB z α β
Peak Flux a Range L iso E peak RefkeV erg/s keV970228 0.695 -1.54 [ 0.08 ] -2.5 [ 0.4 ] 3.7e-6 [ 0.8e-6 ] 40-700 9.1e51 [ 2.18e51 ] 195 [ 64 ] 1970508 0.835 -1.71 [ 0.1 ] -2.2 [ 0.25 ] 7.4e-7 [ 0.7e-7 ] 50-300 9.4e51 [ 1.25e51 ] 145 [ 43 ] 3970828 0.958 -0.7 [ 0.08 ] -2.1 [ 0.4 ] 5.9e-6 [ 0.3e-6 ] 30-1.e4 2.51e52 [ 7.7e51 ] 583 [ 117 ] 1971214 3.42 -0.76 [ 0.1 ] -2.7 [ 1.1 ] 6.8e-7 [ 0.7e-7 ] 40-700 7.21e52 [ 1.33e52 ] 685 [ 133 ] 1980326 1.0 -1.23 [ 0.21 ] -2.48 [ 0.31 ] 2.45e-7 [ 0.15e-7 ] 40-700 3.47e51 [ 1.e51 ] 71 [ 36 ] 4980613 1.096 -1.43 [ 0.24 ] -2.7 [ 0.6 ] 1.6e-7 [ 0.4e-7 ] 40-700 2.e51 [ 6.7e50 ] 194 [ 89 ] 4980703 0.966 -1.31 [ 0.14 ] -2.39 [ 0.26 ] 1.6e-6 [ 0.2e-6 ] 50-300 2.09e52 [ 4.86e51 ] 499 [ 100 ] 1990123 1.600 -0.89 [ 0.08 ] -2.45 [ 0.97 ] 1.7e-5 [ 0.5e-5 ] 40-700 3.53e53 [ 1.23e53 ] 2031 [ 161 ] 1990506 1.307 -1.37 [ 0.15 ] -2.15 [ 0.38 ] 18.6 [ 0.1 ] 50-300 4.18e52 [ 1.33e52 ] 653 [ 130 ] 1990510 1.619 -1.23 [ 0.05 ] -2.7 [ 0.4 ] 2.5e-6 [ 0.2e-6 ] 40-700 6.12e52 [ 1.07e52 ] 423 [ 42 ] 1990705 0.843 -1.05 [ 0.21 ] -2.2 [ 0.1 ] 3.7e-6 [ 0.1e-6 ] 40-700 1.65e52 [ 2.77e51 ] 348 [ 28 ] 1990712 0.433 -1.88 [ 0.07 ] -2.48 [ 0.56 ] 4.1 [ 0.3 ] 40-700 7.46e50 [ 1.91e50 ] 93 [ 15 ] 1991208 0.706 1.85e-5 [ 0.06e-5 ] 20-1.e4 4.32e52 [ 0.38e52 ] 313 [ 31 ] 2991216 1.02 -1.23 [ 0.13 ] -2.18 [ 0.39 ] 67.5 [ 0.2 ] 50-300 1.13e53 [ 3.75e52 ] 642 [ 129 ] 1000131 4.50 -0.69 [ 0.08 ] -2.07 [ 0.37 ] 7.89 [ 0.08 ] 50-300 1.41e53 [ 5.59e52 ] 714 [ 142 ] 1000210 0.846 2.42e-5 [ 0.15e-5 ] 20-1.e4 8.78e52 [ 1.1e52 ] 753 [ 26 ] 2000418 1.12 2.8e-6 [ 0.4e-6 ] 20-1.e4 2.e51 [ 4.8e50 ] 284 [ 21 ] 2000911 1.06 -1.11 [ 0.12 ] -2.32 [ 0.41 ] 2.0e-5 [ 0.2e-5 ] 15-8000 1.65e53 [ 2.89e52 ] 1856 [ 371. ] 1000926 2.07 1.5e-6 [ 0.26e-6 ] 20-1.e4 4.73e52 [ 1.3e52 ] 310. [ 20. ] 2010222 1.48 5.7e-7 [ 0.32e-7 ] 20-1.e4 7.87e51 [ 4.51e50 ] 766 [ 30. ] 2010921 0.45 -1.6 [ 0.1 ] 9.2e-7 [ 1.4e-7 ] 20-1.e4 7.33e50 [ 1.33e50 ] 129. [ 26. ] 2011211 2.140 -0.84 [ 0.09 ] 5.0e-8 [ 1.e-8 ] 40-700 3.17e51 [ 0.32e51 ] 185 [ 25 ] 1020124 3.198 -0.87 [ 0.17 ] -2.6 [ 0.65 ] 9.4 [ 1.8 ] 2.-400 5.12e52 [ 2.03e52 ] 390 [ 113 ] 1020405 0.695 -0.0 [ 0.25 ] -1.87 [ 0.23 ] 5.e-6 [ 0.2e-6 ] 15-2000 1.38e52 [ 7.83e50 ] 617 [ 171 ] 5020813 1.255 -1.05 [ 0.11 ] 32.3 [ 2.1 ] 2-400 2.58e52 [ 2.4e51 ] 478 [ 95 ] 1020819B 0.41 -0.9 [ 0.15 ] -2.0 [ 0.35 ] 7.e-7 [ 0.7e-7 ] 25-100 1.49e51 [ 3.23e50 ] 70. [ 21. ] 7020903 0.25 -1.0 [ 0.0 ] 2.8 [ 0.7 ] 2-400 6.7e48 [ 0.26e48 ] 3.37 [ 1.79 ] 6021004 2.335 -1.0 [ 0.2 ] 2.7 [ 0.5 ] 2-400 4.6e51 [ 0.12e51 ] 267 [ 117 ] 6021211 1.01 -0.85 [ 0.09 ] -2.37 [ 0.42 ] 30 [ 2 ] 2-400 7.13e51 [ 9.9e50 ] 94 [ 19 ] 1030226 1.986 -0.9 [ 0.2 ] 2.7 [ 0.6 ] 2-400 8.52e51 [ 2.23e51 ] 290 [ 63 ] 1030328 1.520 -1.14 [ 0.03 ] -2.1 [ 0.3 ] 11.6 [ 0.9 ] 2-400 1.1e52 [ 1.55e51 ] 328 [ 35 ] 1030329 0.169 -1.32 [ 0.02 ] -2.44 [ 0.08 ] 451 [ 25 ] 2-400 1.91e51 [ 2.37e50 ] 79 [ 3 ] 1030429 2.656 -1.1 [ 0.3 ] 3.8 [ 0.8 ] 2-400 7.6e51 [ 1.47e51 ] 128 [ 37 ] 1040924 0.859 -1.17 [0.05] 2.6e-6 [ 0.3e-6 ] 20-500 6.1e51 [ 1.1e51 ] 102 [ 35. ] 1041006 0.716 -1.37 [ 0.14 ] 1.0e-6 [ 0.1e-6 ] 25-100 8.65e51 [ 1.36e51 ] 108 [ 22 ] 1050126 1.29 -0.75 [0.44 ] 0.698 [ 0.07 ] 15-150 1.12e51 [ 0.25e51 ] 263 [ 110 ] 8050223 0.5915 -1.5 [0.42 ] 0.7 [ 0.1 ] 15-150 1.43e50 [ 0.2e50 ] 110 [ 54 ] 8050318 1.44 -1.34 [0.32 ] 3.2 [ 0.3 ] 15-150 5.11e51 [ 0.8e51 ] 115 [ 27 ] 8050401 2.9 -1.0 [0.0 ] -2.45 [0.0 ] 2.45e-6 [ 0.12e-6 ] 20-2000 2.03e53 [ 0.1e53 ] 501 [ 117 ] 9050416A 0.653 -1.01 [0.0 ] -3.4 [0.0 ] 5.0 [ 0.5 ] 15-150 9.3e50 [ 0.9e50 ] 28.6 [ 8.3 ] 10050505 4.27 -0.95 [0.31 ] 2.2 [ 0.3 ] 15-350 5.65e52 [ 0.8e52 ] 661. [ 245 ] 11050525A 0.606 -0.01 [0.11 ] 47.7 [ 1.2 ] 15-350 9.53e51 [ 2.5e51 ] 127 [ 5.5 ] 12050603 2.821 -0.79 [0.06 ] -2.15 [0.09 ] 3.2e-5 [ 0.32e-5 ] 20-3000 2.13e54 [ 0.22e54 ] 1333 [ 107 ] 13050803 0.422 -0.99 [0.37 ] 1.5 [ 0.2 ] 15-350 1.31e50 [ 2.6e49 ] 138 [ 48 ] 14050814 5.3 -0.58 [0.56 ] 1.0 [ 0.3 ] 15-350 3.0e52 [ 5.6e51 ] 339 [ 47 ] 15050820A 2.612 -1.12 [0.14 ] 1.3e-6 [ 0.13e-6 ] 20-1000 9.1e52 [ 6.8e51 ] 1325 [ 277 ] 16050904 6.29 -1.11 [0.06 ] -2.2 [0.4 ] 0.8 [ 0.2 ] 15-150 1.1e53 [ 3.9e52 ] 3178 [ 1094.] 17050908 3.344 -1.26 [0.48 ] 0.7 [ 0.1 ] 15-150 8.29e51 [ 1.3e51 ] 195 [ 36 ] 18050922C 2.198 -0.83 [0.26 ] 4.5e-6 [ 0.7e-6 ] 20-2000 1.9e53 [ 2.3e51 ] 417 [ 118 ] 19051022 0.80 -1.176 [0.038] 1.e-5 [ 0.13e-5 ] 20-2000 3.57e52 [ 2.7e51 ] 918 [ 63 ] 20051109A 2.346 -1.25 [0.5 ] 5.8e-7 [ 2.e-7 ] 20-500 3.87e52 [ 3.8e51 ] 539 [ 381 ] 21060115 3.53 -1.13 [0.32 ] 0.9 [ 0.1 ] 15-150 1.24e52 [ 2.0e51 ] 288 [ 47 ] 22060124 2.297 -1.48 [0.02 ] 2.7e-6 [ 0.8e-6 ] 20-2000 1.42e53 [ 1.35e51 ] 636 [ 162 ] 23060206 4.048 -1.06 [0.34 ] 2.8 [ 0.2 ] 15-150 5.57e52 [ 9.0e51 ] 381 [ 98 ] 24060210 3.91 -1.12 [0.26 ] 2.7 [ 0.3 ] 15-150 5.95e52 [ 8.0e51 ] 575 [ 186 ] 25060218 0.0331 -1.622 [0.16 ] 1.e-8 [ 0.1e-8 ] 15-150 1.34e47 [ 0.3e47 ] 4.9 [ 0.3 ] 26060223A 4.41 -1.16 [0.35 ] 1.4 [ 0.2 ] 15-150 3.27e52 [ 5.5e51 ] 339 [ 63 ] 27060418 1.489 -1.5 [0.15 ] 6.7 [ 0.4 ] 15-150 1.89e52 [ 1.59e51 ] 572 [ 114 ] 28060510B 4.9 -1.53 [0.19 ] 0.6 [ 0.1 ] 15-150 2.26e52 [ 1.78e51 ] 575 [ 227 ] 29
Table A3. continue.... c (cid:13) , 000–000 obspeak vs Fluence and Peak Flux GRB z α β
Peak Flux a Range L iso E peak RefkeV erg/s keV060522 5.11 -0.7 [0.44 ] 0.6 [ 0.1 ] 15-150 2.0e53 [ 3.7e51 ] 427 [ 79 ] 30060526 3.21 -1.1 [0.4 ] -2.2 [0.4 ] 1.7 [ 0.1 ] 15-150 1.72e52 [ 3.1e51 ] 105.2[ 21.1 ] 31060605 3.78 -1.0 [0.44 ] 0.5 [ 0.1 ] 15-150 9.5e51 [ 1.5e51 ] 490 [ 251 ] 32060607A 3.082 -1.09 [0.19 ] 1.4 [ 0.1 ] 15-150 2.0e52 [ 2.7e51 ] 575 [ 200 ] 33060614 0.125 11.6 [ 0.7 ] 15-150 5.3e49 [ 1.4e49 ] 55 [ 45 ] 34060707 3.43 -0.73 [0.4 ] 1.1 [ 0.2 ] 15-150 1.4e52 [ 2.8e51 ] 302 [ 42 ] 35060714 2.711 -1.77 [0.24 ] 1.4 [ 0.1 ] 15-150 1.42e52 [ 1.e51 ] 234 [ 109 ] 36060814 0.84 -1.43 [0.16 ] 2.13e-6 [ 0.35e-6 ] 20-1000 1.e52 [ 1.e51 ] 473 [ 155 ] 37060904B 0.703 -1.07 [0.37 ] 2.5 [ 0.1 ] 15-150 7.38e50 [ 1.4e50 ] 135 [ 41 ] 38060906 3.686 -1.6 [0.31 ] 2.0 [ 0.3 ] 15-150 3.55e52 [ 3.9e51 ] 209 [ 43 ] 39060908 2.43 -0.9 [0.17 ] 3.2 [ 0.2 ] 15-150 2.6e52 [ 4.6e51 ] 479 [ 110 ] 40060927 5.6 -0.93 [0.38 ] 2.8 [ 0.2 ] 15-150 1.14e53 [ 2.0e52 ] 473 [ 116 ] 41061007 1.261 -0.7 [0.04 ] -2.61 [0.21 ] 1.95e-5 [ 0.28e-5 ] 20-1e4 1.74e53 [ 2.45e52 ] 902 [ 43 ] 42061121 1.314 -1.32 [0.05 ] 1.28e-5 [ 0.17e-5 ] 20-5000 1.41e53 [ 1.5e51 ] 1289 [ 153 ] 43061126 1.1588 -1.06 [0.07 ] 9.8 [ 0.4 ] 15-150 3.54e52 [ 3.0e51 ] 1337 [ 410 ] 44061222B 3.355 -1.3 [0.37 ] 1.5 [ 0.4 ] 15-150 1.82e52 [ 2.75e51 ] 200 [ 28 ] 45070125 1.547 -1.1 [0.1 ] -2.08 [0.13 ] 2.25e-5 [ 0.35e-5 ] 20-1.e4 3.24e53 [ 5.e52 ] 934 [ 148 ] 46070508 0.82 -0.81 [0.07 ] 8.3e-6 [ 1.1e-6 ] 20-1000 3.3e52 [ 3.9e51 ] 342 [ 15 ] 47071003 1.100 -0.97 [0.07 ] 1.22e-5 [ 0.2e-5 ] 20-4000 8.4e52 [ 1.5e51 ] 1678 [ 231 ] 48071010B 0.947 -1.25 [0.6 ] -2.65 [0.35 ] 8.92e-7 [ 3.7e-7 ] 20-1000 6.4e51 [ 5.3e49 ] 101 [ 23 ] 49071020 2.145 -0.65 [0.3 ] 6.04e-6 [ 2.1e-6 ] 20-2000 2.2e53 [ 9.6e51 ] 1013 [ 205 ] 50071117 1.331 -1.53 [0.15 ] 6.66e-6 [ 1.8e-6 ] 20-1000 1.e53 [ 7.e51 ] 648 [ 318 ] 51080319B 0.937 -0.82 [0.01 ] -3.87 [0.8 ] 2.17e-5 [ 0.21e-5 ] 20-7000 9.6e52 [ 2.3e51 ] 1261 [ 25 ] 52080319C 1.95 -1.2 [0.1 ] 3.35e-6 [ 0.74e-6 ] 20-4000 9.5e52 [ 1.2e51 ] 1752 [ 505 ] 53
Table A3. a Peak Fluxes are in erg/s/cm or photons/s/cm . Reference for the Peak Flux (or Luminosity): 1) Firmani et al. 2006; 2) Ulanov et al. 2005 ( L iso computed as [ P/F ][1+ z ] E iso ); 3) Jimenez et al. 2001; 4) Amati et al. 2002; 5) Price et al. 2003; 6) Sakamoto et al. 2005; 7) Hurley et al. GCN 1507; 8) GRBBAT on line table (http://swift.gsfc.nasa.gov/docs/swift/archive/grb table/); 9) Golenetskii et al. 2005f, GCN 3179; 10) Sakamoto et al. 2006a 11) Hullinger etal. 2005; 12) Blustin et al. 2006; 13) Golenetskii et al. 2005g; 14) Parson et al. 2005; 15) Tueller et al. 2005; 16) Cenko et al., 2006; 17) Sakamoto et al. 2005b;18) Sato et al. 2005; 19) Golenetskii et al. 2005h; 20) Golenetskii et al. 2005i; 21) Golenetskii et al. 2005j; 22) Barbier et al. 2006a; 23) Golenetskii et al.2006j; 24) Palmer et al. 2006a; 25) Sakamoto et al. 2006b; 26) Campana et al., 2006; 27) Cummings et al. 2006a; 28) Cummings et al. 2006b; 29) Barthelmyet al. 2006; 30) Krimm et al. 2006a; 31) Markwardt et al. 2006a; 32) Sato et al. 2006a; 33) Tueller et al. 2006; 34) Mangano et al. 2007; 35) Stamatikos etal. 2006a; 36) Krimm et al. 2006b; 37) Golenetskii et al. 2006k; 38) Markwardt et al. 2006b; 39) Sato et al. 2006b; 40) Palmer et al. 2006b; 41) Stamatikoset al. 2006b; 42) Golenetskii et al. 2006l; 43) Golenetskii et al. 2006m; 44) Krimm et al. 2006c; 45) Barbier et al. 2006b; 46) Golenetskii et al. 2007l; 47)Golenetskii et al. 2007m; 48) Golenetskii et al. 2007n; 49) Golenetskii et al. 2007o; 50) Golenetskii et al. 2007p; 51) Golenetskii et al. 2007q; 52) Golenetskiiet al. 2007r; 53) Golenetskii et al. 2007s.c (cid:13)000