We recommend that the search for exoplanets around binary stars be extended to include X-ray binaries (XRBs) 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, proposing 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 XRBs 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, to hours for Jupiter-radius planets. The search for planets around XRBs 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 XRB in order to capture energy, such an artificial structure might cause detectable transits in the X-ray light curve.
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