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

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 Bromberg2013 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 L_iso > 5*10^49 erg/s is 4.1(-1.9,+2.3)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(-0.4,+1.4) * 10^52~erg/s and power-law indices 0.95(-0.12,+0.12) and 2.0(-0.8,+1.0). When considering the whole Swift sGRB sample we find that it is composed of two populations: One group (~ 60%-80% of Swift sGRBs) with the above rate and time delay and a second group (~ 20%-40% 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 Bromberg2013. 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 * 10^5 (f_b^-1 / 30) mergers took place in the Milky Way. If $0.025 m_\odot$ were ejected in each event this would have been sufficient to produce all the heavy r-process material in the Galaxy.