The Swift short gamma-ray burst rate density: Prospects for detecting binary neutron star mergers by aLIGO

Presently only 30% of short gamma ray bursts (SGRBs) have accurate 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. Assuming a significant fraction of binary neutron star mergers produce SGRBs, we calculate lower and upper detection rate limits of (1-180) per Yr by an advanced LIGO and Virgo coincidence search. Our detection rate is compatible with extrapolations using Galactic pulsar observations and population synthesis.