  Short, hard gamma-ray bursts (GRBs) are believed to originate from the
coalescence of two neutron stars (NSs) or a NS and a black hole (BH). If this
scenario is correct, then short GRBs will be accompanied by the emission of
strong gravitational waves (GWs), detectable by GW observatories such as LIGO,
Virgo, KAGRA, and LIGO-India. As compared with blind, all-sky, all-time GW
searches, externally triggered searches for GW counterparts to short GRBs have
the advantages of both significantly reduced detection threshold due to known
time and sky location and enhanced GW amplitude because of face-on orientation.
Based on the distribution of signal-to-noise ratios in candidate compact binary
coalescence events in the most recent joint LIGO-Virgo data, our analytic
estimates, and our Monte Carlo simulations, we find an effective sensitive
volume for GRB-triggered searches that is about 2 times greater than for an
all-sky, all-time search. For NS-NS systems, a jet angle of 20 degrees, a
gamma-ray satellite field of view of 10% of the sky, and priors with generally
precessing spin, this doubles the number of NS-NS short-GRB and NS-BH short-GRB
associations, to ~3-4% of all detections of NS-NSs and NS-BHs. We also
investigate the power of tests for statistical excesses in lists of
subthreshold events, and show that these are unlikely to reveal a subthreshold
population until finding GW associations to short GRBs is already routine.
Finally, we provide useful formulas for calculating the prior distribution of
GW amplitudes from a compact binary coalescence, for a given GW detector
network and given sky location.
