Title:The BATSE-Swift luminosity and redshift distributions of short-duration GRBs

Abstract: We compare the luminosity function and rate inferred from the BATSE short hard bursts (SHBs) peak flux distribution with the redshift and luminosity distributions of SHBs observed by Swift/HETE II. While the Swift/HETE II SHB sample is incompatible with SHB population that follows the star formation rate, it is compatible with a SHB rate that reflect a distribution of delay times after the SFR. This would be the case if SHBs are associated with binary neutron star mergers. The available data allows, however, different interpretations. For example, a population whose rate is independent of the redshift fits the data very well. The implied SHB rates that we find range from $\sim 8$ to $\sim 30h_{70}^3$Gpc$^{-3}$yr$^{-1}$. This is a much higher rate than what was previously estimated. A detailed (2 dimensional) look at the best fit models shows, however, some discrepancy between the four Swift/HETE II SHBs and the models based on BATSE SHBs. This could be a statistical fluke. It could also arise from wrong estimates of the triggering criteria or from selection effects. If real it may indicate the existence of two SHB populations with different luminosity functions and redshift distributions.