The Swift short gamma-ray burst rate density: implications for binary   neutron star merger rates
  Short gamma-ray bursts (SGRBs) observed by {\it Swift} are potentially revealing 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 April 2012 there are only some 30% of SGRBs with reasonably firm redshifts, and this sample is highly biased by the limited sensitivity of {\it Swift} to detect SGRBs. We account for the dominant biases to calculate a realistic SGRB rate density out to $z\approx0.5$ using the {\it 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 $8^{+5}_{-3}$ $\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$ (assuming isotropic emission), and a beaming corrected upper limit of $1100^{+700}_{-470} $ $\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$. 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 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. 
David Coward, Eric Howell, Tsvi Piran, Giulia Stratta, Marica   Branchesi, Omer Bromberg, Bruce Gendre, Ronald Burman and Da...
astro-ph.CO astro-ph.HE gr-qc