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.

The Amati and Yonetoku relations are two of the main energy and luminosity correlations that currently exist for gamma-ray bursts (GRBs). The Amati relation is a correlation between the intrinsic peak energy, E peak , in the F  spectrum of a burst and its equivalent isotropic energy, E iso . The Yonetoku relation is a correlation between E peak and the isotropic peak luminosity, L iso . In this paper, we use a recent data sample of 65 GRBs to investigate whether these two relations evolve with redshift, z. The z-correction and the k-correction are both taken into account. Our method consists of binning the data in redshift, z, then applying (for each bin) a fit of the form:the Amati relation, and of the form:for the Yonetoku relation, where E peak  is the mean value of the peak energy for the entire sample. The objective is to see whether the two fitting parameters, A and B, evolve systematically with z. Good least-squares fits were obtained with reasonable values for the linear regression coefficient, r. Our results indicate that the normalization, A, and the slope, B, do not evolve with redshift, and hence the Amati and Yonetoku relations seem to be redshift independent.

The lag-luminosity relation for gamma-ray bursts (GRBs) is an anti-correlation between the time lag, ?lag, which represents the delay between the arrival of hard and soft photons, and the isotropic peak luminosity, L. In this paper, we use a sample of 43 Swift bursts, which was taken from Ukwatta et al., to investigate whether this relation depends on redshift. Both the z-correction and the k-correction are taken into account. Our analysis consists of binning the data in redshift, z, then applying a fit of the form: for each bin, where ?lag0 is the time-lag in the burst’s source frame, and is the corresponding mean value for the entire sample. The goal is to see whether the two fitting parameters, A and B, evolve in a systematic way with z. Our results indicate that both the normalization, A, and the slope, B, seem to vary in a systematic way with redshift. We note that although good best-fits were obtained, with reasonable values for both the linear regression coefficient, r, and the reduced chi-squared, the data showed large scatter. Also, the number of GRBs in the sample studied is not large, and thus our conclusions are only tentative at this point. A flat universe with M = 0.27, ?? = 0.73, and a Hubble constant, H0 = 70 km.s^-1.Mpc^-1 is assumed

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