The rate and luminosity function of Short 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. The Swift/HETE II SHB sample is incompatible with SHB population that follows the star formation rate. However, it is compatible with a distribution of delay times after the SFR. This would be the case if SHBs are associated with binary neutron star mergers. The implied SHB rates that we find range from \sim 8 to \sim 30h_{70}^3Gpc^{-3}yr^{-1}. This rate is a much higher than what was previously estimated and, when beaming is taken into account, it is comparable to the rate of neutron star mergers estimated from statistics of binary pulsars. If GRBs are produced in mergers the implied rate practically guarantees detection by LIGO II and possibly even by LIGO I, if we are lucky. Our analysis, which is based on observed short hard burst is limited to bursts with luminosities above 10^{49}erg/sec. Weaker bursts may exist but if so they are hardly detected by BATSE or Swift and hence their rate is very weakly constrained by current observations. Thus the rate of mergers that lead to a detection of a gravitational radiation signal might be even higher.