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

We compare the luminosity function and rate inferred from the BATSE peak flux distribution of short hard bursts (SHBs) with the redshift and luminosity distributions of SHBs observed by Swift/HETE II. While the Swift/HETE II SHB sample is incompatible with the SHB population that follows the star formation rate, it is compatible with an SHB rate that reflects a distribution of delay times after the SFR. This would be the case if SHBs were 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 ∼8 to ∼30 h₇₀³ Gpc^-3 yr^-1. This rate, which is comparable to the rate of neutron star mergers estimated from statistics of binary pulsars, is a much higher rate than what was previously estimated. We stress that our analysis, which is based on observed SHBs, is limited to bursts with luminosities above 10⁴⁹ erg/s. Weaker bursts may exist, but if so they are hardly detected by BATSE of Swift, so their rate is very weakly constrained by current observations.