The Rate of Short-Duration Gamma-Ray Bursts in the Local Universe

Following the faint gamma-ray burst, GRB 170817A, coincident with a gravitational wave-detected binary neutron star merger at $d\sim40$ Mpc, we consider the constraints on a local population of faint short duration GRBs (defined here broadly as $T_{90}<4$ s). We review proposed low-redshift short-GRBs and consider statistical limits on a $d\lessapprox200$ Mpc population using Swift/Burst Alert Telescope (BAT), Fermi/Gamma-ray Burst Monitor (GBM), and Compton Gamma-Ray Observatory (CGRO) Burst and Transient Source Experiment (BATSE) GRBs. Swift/BAT short-GRBs give an upper limit for the all-sky rate of $<4$ y$^{-1}$ at $d<200$ Mpc, corresponding to $<5$% of SGRBs. Cross-correlation of selected CGRO/BATSE and Fermi/GBM GRBs with $d<100$ Mpc galaxy positions returns a weaker constraint of $\lessapprox12\ {\rm y^{-1}}$. A separate search for correlations due to SGR giant flares in nearby ($d<11$ Mpc) galaxies finds an upper limit of $<3\ {\rm y^{-1}}$. Our analysis suggests that GRB 170817A-like events are likely to be rare in existing SGRB catalogues. The best candidate for an analogue remains GRB 050906, where the Swift/BAT location was consistent with the galaxy IC0327 at $d\approx132$ Mpc. If binary neutron star merger rates are at the high end of current estimates, then our results imply that at most a few percent will be accompanied by detectable gamma-ray flashes in the forthcoming LIGO/Virgo science runs.