The rate, luminosity function and time delay of non-Collapsar short GRBs

Abstract

We estimate the rate and the luminosity function of short (hard) Gamma-Ray Bursts (sGRBs) that are non-Collapsars, using the peak fluxes and redshifts of BATSE, Swift and Fermi GRBs. Following Bromberg et al., we select a sub-sample of Swift bursts which are most likely non- Collapsars. We find that these sGRBs are delayed relative to the global star formation rate (SFR) with a typical delay time of a 3-4 Gyr (depending on the SFR model). However, if two or three sGRB at high redshifts have been missed because of selection effects, a distribution of delay times of ∝1/t would be also compatible. The current event rate of these non-Collapsar sGRBs with Liso > 5 x 1049 erg s-1 is 4.1+2.3-1.9 Gpc-3 yr-1. The rate was significantly larger around z ~ 1 and it declines since that time. The luminosity function we find is a broken power law with a break at 2.0+1.4-0.4 x 1052 erg s-1 and power-law indices 0.95+0.12-0.12 and 2.0+1.0-0.8. When considering the whole Swift sGRB sample we find that it is composed of two populations: one group (≈60-80 per cent of Swift sGRBs) with the above rate and time delay and a second group (≈20-40 per cent of Swift sGRBs) of potential 'impostors' that follow the SFR with no delay. These two populations are in very good agreement with the division of sGRBs to non-Collapsars and Collapsars suggested recently by Bromberg et al. If non-Collapsar sGRBs arise from neutron star merger this rate suggest a detection rate of 3-100 yr-1 by a future gravitational wave detectors (e.g. Advanced Ligo/Virgo with detection horizon on 300 Mpc), and a co-detection with Fermi (Swift) rate of 0.1-1 yr-1 (0.02-0.14 yr-1). We estimate that about 4 x 105(f -1b/30) mergers took place in the Milky Way. If 0.025M{bull's eye} were ejected in each event this would have been sufficient to produce all the heavy r-process material in the Galaxy.