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We present an analysis of the binary and physical parameters of a uniquepulsating white dwarf with a main-sequence companion, SDSS J1136+0409, observedfor more than 77 d during the first pointing of the extended Kepler mission: K2Campaign 1. Using new ground-based spectroscopy, we show that thispost-common-envelope binary has an orbital period of 6.89760103(60) hr, whichis also seen in the photometry as a result of Doppler beaming and ellipsoidalvariations of the secondary. We spectroscopically refine the temperature of thewhite dwarf to 12330(260) K and its mass to 0.601(36) Msun. We detect sevenindependent pulsation modes in the K2 light curve. A preliminary asteroseismicsolution is in reasonable agreement with the spectroscopic atmosphericparameters. Three of the pulsation modes are clearly rotationally splitmultiplets, which we use to demonstrate that the white dwarf is notsynchronously rotating with the orbital period but has a rotation period of2.49(53) hr. This is faster than any known isolated white dwarf, but slowerthan almost all white dwarfs measured in non-magnetic cataclysmic variables,the likely future state of this binary.

Insights into internal effects of common-envelope evolution using the extended Kepler mission