  We recommend that the search for exoplanets around binary stars be extended
to include X-ray binaries in which the accretor is a white dwarf, neutron star,
or black hole. We present a novel idea for detecting planets bound to such mass
transfer binaries: we propose that the X-ray light curves of these binaries be
inspected for signatures of transiting planets. X-ray transits may be the only
way to detect planets around some systems, while providing a complementary
approach to optical and/or radio observations in others. Any planets associated
with X-ray binaries must be in stable orbits. We consider the range of
allowable separations and find that orbital periods can be hours or longer,
while transit durations extend upward from about a minute for Earth-radius
planets in very close orbits, to hours for Jupiter-radius planets in wider
orbits. The search for planets around mass transfer binaries could begin at
once with existing X-ray observations of these systems. If and when a planet is
detected around an X-ray binary, the size and mass of the planet may be readily
measured, and it may also be possible to study the transmission and absorption
of X-rays through its atmosphere. Finally, a noteworthy application of our
proposal is that the same technique could be used to search for signals from
extraterrestrial intelligence. If an advanced exocivilization placed a Dyson
sphere or similar structure in orbit around the accretor of an X-ray binary in
order to capture energy, such an artificial structure might cause detectable
transits in the X-ray light curve.
