On the bimodal distribution of gamma-ray bursts

Kouveliotou et al. recently confirmed that gamma-ray bursts are bimodal in duration. In this paper we compute the statistical properties of the short (less than or = 2 s) and long (greater than 2 s) bursts using a method of analysis that makes no assumption regarding the location of the bursts, whether in the Galaxy or at a cosmological distance. We find the 64 ms channel on Burst and Transient Source Experiment (BATSE) to be more sensitive to short bursts and the 1024 ms channel to be more sensitive to long bursts. We show that all the currently available data are consistent with the simple hypothesis that both short and long bursts have the same spatial distribution and that within each population the sources are standard candles. The rate of short bursts per unit volume is about 40% of the rate of long bursts. Although the durations of short and long gamma-ray bursts span several orders of magnitude and the total energy of a typical short burst is smaller than that of a typical long burst by a factor of about 20, surprisingly the peak luminosities of the two kinds of bursts are equal to within a factor of about 2.