Studies of BATSE bursts (Kouveliotou et al. 1993) have resulted in the widespread adoption of a two-group categorization: long bursts (those with durations ≥ 2 seconds) and short bursts (those with durations ≤ 2 seconds). This categorization, one must recall, used the observed T 90 time durations for bursts (during which 90% of a burst's fluence is measured).In this work, we have explored two ideas: 1) a statistical search for a possible third, intermediate category of bursts (between the "short" and the "long" ones) among 2041 BATSE GRBs and 757 Swift/BAT ones; 2) a study of bursts' intrinsic durations, where durations in the bursts' reference frames (instead of the observed durations) are considered; for this, 248 Swift/BAT bursts that have redshift measurements were statistically analyzed for the same categorization goal.We first use a Monte Carlo method to determine the proper binning of each GRB, considering that bursts come with different uncertainties on their durations. Then, using the method of minimization of chi-square χ 2 , we search for the best fit of the normalized frequency distributions 1 N0 dN d ln T of durations; this allows us to compare fits with two groups ("short" and "long") with fits with three groups ("short", "long", and "intermediate").Our results indicate that the distributions of observed durations are better fitted by three groups than two groups for Swift/BAT data; interestingly, the "intermediate" group appears rather clearly for both observed and intrinsic durations. For BATSE data, the statistical test does not prefer three groups over two.We discuss the results, their possible underlying causes, and reasonable interpretations.

We use a sample of Swift gamma-ray bursts (GRBs) to analyze the Amati and Yonetoku correlations. The first relation is between E p,i , the intrinsic peak energy of the prompt GRB emission, and E iso , the equivalent isotropic energy. The second relation is between E p,i and L iso , the isotropic peak luminosity. We select a sample of 71 Swift GRBs that have a measured redshift and whose observed E obs p is within the interval of energy 15-150 keV with a relative uncertainty of less than 70%. We seek to find correlation relations for long-duration GRBs (LGRBs) with a peak photon flux P ph ≥ 2.6 ph/cm 2 /s. Uncertainties (error bars) on the values of the calculated energy flux P, the energy E iso , and the peak isotropic luminosity L iso are estimated using a Monte Carlo approach. We find 27 Swift LGRBs that satisfy all our constraints. Results of our analyses of the sample of 71 GRBs and the selected subsample (27 GRBs) are in good agreement with published results. The plots of the two relations for all bursts show a large dispersion around the best straight lines in the sample of 71 LGRBs but not so much in the subsample of 27 GRBs.

Ever since the insightful analysis of the durations of gamma-ray bursts (GRBs) by Kouveliotou et al. (1993), GRBs have most often been classified into two populations: "short bursts" (shorter than 2.0 seconds) and "long bursts" (longer than 2.0 seconds). However, recent works have suggested the existence of an intermediate population in the bursts observed by the Swift satellite. Moreover, some researchers have questioned the universality of the 2.0-second dividing line between short and long bursts: some bursts may be short but actually result from collapsars, the physical mechanism behind normally long bursts, and some long ones may originate from mergers, the usual progenitors of short GRBs.In this work, we focus on GRBs detected by the Fermi satellite (which has a much higher detection rate than Swift and other burst-detecting satellites) and study the distribution of their durations measured in the observer's reference frame and, for those with known redshifts, in the bursts' reference frames. However, there are relatively few bursts with measured redshifts, and this makes an accurate study difficult. To overcome this problem, we follow Zhang and Wang (2018) and determine a "pseudo-redshift" from the correlation relation between the luminosity L p and the energy E p , both of which are calculated at the peak of the flux. Interestingly, we find that the uncertainties in the quantities observed and used in the determination of pseudo-redshifts, do affect the precision of the individual results significantly, but they keep the distribution of pseudo-redshifts very similar to that of the actual ones and thus allow us to use pseudo-redshifts for our statistical study. We briefly present the advantages and disadvantages of using pseudo-redshifts in this context.We use the reduced chi-square and the maximization of the log-likelihood to statistically analyze the distribution of Fermi GRB durations. Both methods show that the distribution of the observed (measured) and the intrinsic (source/rest frame) bursts durations are better represented by two groups/populations, rather than three.

We compute the expected luminosity function of gamma-ray bursts (GRBs) in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic powerĖ and contrast in Lorentz factor κ = max / min . We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist), then the luminosity function has two branches. At high luminosity it follows the distribution ofĖ while at low luminosity it is close to a power law of slope −0.5. We then examine if existing data can constrain the luminosity function. Using the log N-log P curve, the E p distribution of bright Burst and Transient Source Experiment (BATSE) bursts and the X-ray flash (XRF)/GRB ratio obtained by High Energy Transient Explorer 2 (HETE2), we show that single and broken power laws can provide equally good fits of these data. Present observations are therefore unable to favour one form or the other. However, when a broken power law is adopted they clearly indicate a low-luminosity slope −0.6 ± 0.2, compatible with the prediction of the internal shock model.Key words: methods: statistical -stars: luminosity function, mass function -gamma-rays: bursts. I N T RO D U C T I O NThe isotropic luminosity of long gamma-ray bursts (GRBs) is known to cover a wide range from underluminous, nearby bursts such as GRB 980425 or GRB 060218 (with L 10 47 erg s −1 ) to ultrabright objects like GRB 990123 (L 10 53 erg s −1 ). While it has been suggested that the weakest GRBs could simply be normal events seen off-axis (Yamazaki, Yonetoku & Nakamura 2003), this possibility has been recently discarded both from limits on afterglow brightness and for statistical reasons (Soderberg et al. 2004;Daigne & Mochkovitch 2007). The difference of six orders of magnitude between the brightest and weakest GRBs is therefore probably real. The parameters (stellar rotation, metallicity etc.) which are responsible for this diversity in radiated power are not known. However, in the restricted range 10 51 L 10 53 erg s −1 the value of the isotropic luminosity is possibly fixed by the opening angle of the jet which may always carry the same characteristic energy (Frail et al. 2001).The purpose of this paper is to see how basic theoretical ideas and existing data can be used to constrain the GRB luminosity function (LF) p(L). First, we should insist that p(L) here represents the 'apparent' LF which includes viewing angle effects and beaming E-mail: zitouni@iap.fr (HZ); daigne@iap.fr (FD); mochko@iap.fr (RM) statistics (i.e. bursts with narrow jets are more likely seen off-axis and therefore underrepresented in the distribution). It is therefore different from the 'intrinsic' LF p 0 (L) which would be obtained with all GRBs seen on-axis. In the lack of a complete, volume-limited sample of GRBs with known redshift, only indirect observational indicators such as the log N-log P plot can constrain the LF. These indic...