Detecting circumbinary exoplanets and hierarchical stellar triples with the LISA gravitational radiation mission

We investigate the possibility of detecting planetary or stellar companions orbiting white dwarf binaries using the LISA gravitational radiation detector. Specifically, we consider the acceleration of the barycenter of the white dwarf binary due to the orbiting third body as well as the effect of changes in the tidal field across the binary due to the perturber's eccentric orbit. We find that the movement of the barycenter is detectable for both stellar and planetary mass objects. If circumbinary planets occur with frequencies similar to gas giant planets around isolated main sequence stars, then we expect to find of order 10 such planets in four years of LISA observations. For a longer, ten-year mission the accessible parameter space for planetary mass, orbital period, and binary orbital period grows and LISA's associated yield increases to ~100 expected detections.