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A Third Hot White Dwarf Companion Detected by Kepler

We have found a system listed in the Kepler Binary Catalog (3.273 day period; Prsa et al. 2010) that we have determined is comprised of a low-mass, thermally-bloated, hot white dwarf orbiting an A star of about 2.3 solar masses. In this work we designate the object, KIC 10657664, simply as KHWD3. We use the transit depth of ~0.66%, the eclipse depth of ~1.9%, and regular smooth periodic variations at the orbital frequency and twice the orbital frequency to analyze the system parameters. The smooth periodic variations are identified with the classical ellipsoidal light variation and illumination effects, and the newly utilized Doppler boosting effect. Given the measured values of R/a and inclination angle of the binary, both the ELV and DB effects are mostly sensitive to the mass ratio, q = M_2/M_1, of the binary. The two effects yield values of q which are somewhat inconsistent - presumably due to unidentified systematic effects - but which nonetheless provide a quite useful set of possibilities for the mass of the white dwarf (either 0.18 +/- 0.03 M_Sun or 0.37 +/- 0.08 M_Sun). All of the other system parameters are determined fairly robustly. In particular, we show that the white dwarf has a radius of 0.15 +/- 0.01 R_Sun which is extremely bloated over the radius it would have as a fully degenerate object, and an effective temperature T_eff = 14,100 +/- 350 K. Binary evolution scenarios and models for this system are discussed. We suggest that the progenitor binary was comprised of a primary of mass ~2.2 M_Sun (the progenitor of the current hot white dwarf) and a secondary of mass ~1.4 M_Sun (the progenitor of the current A star in the system). We compare this new system with three other white dwarfs in binaries that likely were formed via stable Roche-lobe overflow (KOI-74, KOI-81, and Regulus).