  Binary neutron star (NS) mergers are among the most promising astrophysical
sources of gravitational wave emission for Advanced LIGO and Advanced Virgo,
expected to be operational in 2015. Finding electromagnetic counterparts to
these signals will be essential to placing them in an astronomical context. The
Swift satellite carries a sensitive X-ray telescope (XRT), and can respond to
target-of-opportunity requests within 1-2 hours, and so is uniquely poised to
find the X-ray counterparts to LIGO/Virgo triggers. Assuming NS mergers are the
progenitors of short gamma-ray bursts (GRBs), some percentage of LIGO/Virgo
triggers will be accompanied by X-ray band afterglows that are brighter than
10^-12 erg/s/cm^2 in the XRT band one day after the trigger time. We find that
a soft X-ray transient of this flux is bright enough to be extremely rare, and
so could be confidently associated with even a moderately localized GW signal.
We examine two possible search strategies with the Swift XRT to find bright
transients in LIGO/Virgo error boxes. In the first strategy, XRT could search a
volume of space with a ~100 Mpc radius by observing ~30 galaxies over the
course of a day, with sufficient depth to observe the expected X-ray afterglow.
For an extended LIGO/Virgo horizon distance, the XRT could employ 100 s
exposures to cover an area of ~ 35 square degrees in about a day, remain
sensitive enough to image GW discovered GRB afterglows. These strategies
demonstrate that discovery of X-ray band counterparts to GW triggers will be
possible.
