We have found a system listed in the Kepler Binary Catalog ( P _ { orb } = 3.273 days ; 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 M _ { \odot } .
In this work we designate the object , KIC 10657664 , simply as “ KHWD3 ” ( “ Kepler Hot White Dwarf 3 ” ) .
We use the transit depth of \sim 0.66 % , the eclipse depth of \sim 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 ( “ ELV ” ) and illumination ( “ ILL ” ) effects , and the newly utilized Doppler boosting ( “ DB ” ) 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 0.26 \pm 0.04 M _ { \odot } or 0.37 \pm 0.08 M _ { \odot } ) .
All of the other system parameters are determined fairly robustly .
In particular , we show that the white dwarf has a radius of 0.15 \pm 0.01 R _ { \odot } which is extremely bloated over the radius it would have as a fully degenerate object , and an effective temperature T _ { eff } \simeq 14 , 500 K. Binary evolution scenarios and models for this system are discussed .
We suggest that the progenitor binary was comprised of a primary of mass \sim 2.2 M _ { \odot } ( the progenitor of the current hot white dwarf ) and a secondary of mass \sim 1.4 M _ { \odot } ( 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 the inner Regulus binary ) .