The Swift short gamma-ray burst rate density: Implications for binary neutron star merger rates

Short gamma-ray bursts (SGRBs) observed by Swift potentially reveal the first insight into cataclysmic compact object mergers. To ultimately acquire a fundamental understanding of these events requires pan-spectral observations and knowledge of their spatial distribution to differentiate between proposed progenitor populations. Up to 2012 April, there are only some 30 per cent of SGRBs with reasonably firm redshifts, and this sample is highly biased by the limited sensitivity of Swift to detect SGRBs. We account for the dominant biases to calculate a realistic SGRB rate density out to z ≈ 0.5 using the Swift sample of peak fluxes, redshifts and those SGRBs with a beaming angle constraint from X-ray/optical observations. We find an SGRB lower rate density of 8_-3⁺⁵ Gpc^-3 yr^-1 (assuming isotropic emission) and a beaming corrected upper limit of 1100_-470⁺⁷⁰⁰ Gpc^-3 yr^-1. Assuming a significant fraction of binary neutron star mergers produce SGRBs, we calculate lower and upper detection rate limits of (1-180) yr^-1 by an Advanced LIGO (aLIGO) and Virgo coincidence search. Our detection rate is similar to the lower and realistic rates inferred from extrapolations using Galactic pulsar observations and population synthesis.