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 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 × 1049 erg s−1 is |$4.1_{-1.9}^{+2.3}\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$|. 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 |$2.0_{-0.4}^{+1.4} \times 10^{52} \,\mathrm{erg\,s}^{-1}$| and power-law indices |$0.95_{-0.1 2}^{+0.12}$| 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 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 |$4 \times 10^5 (f_{\rm b}^{-1}/30)$| mergers took place in the Milky Way. If 0.025M⊙ were ejected in each event this would have been sufficient to produce all the heavy r-process material in the Galaxy.