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 ( 17 ) 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 \propto 1 / t would be also compatible .
The current event rate of these non-Collapsar sGRBs with L _ { iso } > 5 \times 10 ^ { 49 } erg / s is 4.1 _ { -1.9 } ^ { +2.3 } Gpc ^ { -3 } yr ^ { -1 } .
The rate was significantly larger around z \sim 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 } 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 ( \approx 60 \% - 80 \% of Swift sGRBs ) with the above rate and time delay and a second group ( \approx 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 ( 17 ) .
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 _ { 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 .