We report the discovery of four short-period eclipsing systems in the Kepler light curves , consisting of an A-star primary and a low-mass white dwarf ( WD ) secondary ( dA+WD ) —KIC 4169521 , KOI-3818 , KIC 2851474 , and KIC 9285587 .
The systems show BEaming , Ellipsoidal and Reflection ( BEER ) phase modulations together with primary and secondary eclipses .
These add to the 6 Kepler and 18 WASP short-period eclipsing dA+WD binaries that were previously known .
The light curves , together with follow-up spectroscopic observations , allow us to derive the masses , radii , and effective temperatures of the two components of the four systems .
The orbital periods , of 1.17 – 3.82 days , and WD masses , of 0.19 – 0.22 M _ { \odot } , are similar to those of the previously known systems .
The WD radii of KOI-3818 , KIC 2851474 , and KIC 9285587 are 0.026 , 0.035 , and 0.026 R _ { \odot } , respectively , the smallest WD radii derived so far for short-period eclipsing dA+WD binaries .
These three binaries extend the previously known population to older systems with cooler and smaller WD secondaries .
KOI-3818 displays evidence for a fast-rotating primary and a minute but significant eccentricity , \sim 1.5 \times 10 ^ { -3 } .
These features are probably the outcome of the mass-transfer process .