  To date GW170817, produced by a binary neutron star (BNS) merger, is the only
gravitational wave event with an electromagnetic (EM) counterpart. It was
associated with a prompt short gamma-ray burst (GRB), an optical kilonova, and
the afterglow of a structured, off-axis relativistic jet. We model the
prospects for future mergers discovered in gravitational waves to produce
detectable afterglows. Using a model fit to GW170817, we assume all BNS mergers
produce jets with the same parameters, and model the afterglow luminosity for a
full distribution of observer angles, ISM densities, and distances. We find
that in the LIGO/Virgo/KAGRA O4 run, 30% - 45% of BNS mergers with a
well-localized counterpart will have an afterglow detectable with current
instrumentation in the X-ray, radio and optical. Without a previously detected
counterpart, 10% - 15% will have an afterglow detectable by wide-area radio and
optical surveys, compared to only about 5% - 12% of events expected to have
bright (on-axis) gamma-ray emission. Most afterglows that are detected will be
from off-axis jets. Further in the future, in the A+ era (O5), 40% - 50% of
mergers will have afterglows detectable with next-generation X-ray and radio
instruments. Future wide-area radio survey instruments, particularly DSA-2000,
could detect 40% of afterglows, even without a kilonova counterpart. Finding
and monitoring these afterglows will provide valuable insight into the
structure and diversity of relativistic jets, the rate at which mergers produce
jets, and constrain the angle of the mergers relative to our line of sight.
