The Swift short gamma-ray burst rate density implications for detecting 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 {it Swift} to detect SGRBs. We account for the dominant biases to calculate a realistic SGRB rate density out to $z = 0.5$ using the {it 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.