Characterizing the Cool KOIs. V. KOI-256: A Mutually Eclipsing Post-Common Envelope Binary

We report that Kepler Object of Interest 256 (KOI-256) is a mutually eclipsing post-common envelope binary (ePCEB), consisting of a cool white dwarf (M = 0.592 +/- 0.089 MSun, R = 0.01345 +/- 0.00091 RSun, Teff = 7100 +/- 700 K) and an active M3 dwarf (M = 0.51 +/- 0.16 MSun, R = 0.540 +/- 0.014 RSun, Teff = 3450 +/- 50 K) with an orbital period of 1.37865 +/- 0.00001 days. KOI-256 is listed as hosting a transiting planet-candidate by Borucki et al. and Batalha et al.; here we report that the planet-candidate transit signal is in fact the occultation of a white dwarf as it passes behind the M dwarf. We combine publicly-available long- and short-cadence Kepler light curves with ground-based measurements to robustly determine the system parameters. The occultation events are readily apparent in the Kepler light curve, as is spin-orbit synchronization of the M dwarf, and we detect the transit of the white dwarf in front of the M dwarf halfway between the occultation events. The size of the white dwarf with respect to the Einstein ring during transit (REin = 0.00473 +/- 0.00055 RSun) causes the transit depth to be shallower than expected from pure geometry due to gravitational lensing. KOI-256 is an old, long-period ePCEB and serves as a benchmark object for studying the evolution of binary star systems as well as white dwarfs themselves, thanks largely to the availability of near-continuous, ultra-precise Kepler photometry.