Two white dwarfs in ultrashort binaries with detached, eclipsing, likely sub-stellar companions detected by K2

Using data from the extended Kepler mission in K2 Campaign 10, we identify two eclipsing binaries containing white dwarfs with cool companions that have extremely short orbital periods of only 71.2 min (SDSS J1205-0242, a. k. a. EPIC 201283111) and 72.5 min (SDSS J1231+ 0041, a. k. a. EPIC 248368963). Despite their short periods, both systems are detached with small, low-mass companions, in one case a brown dwarf and in the other case either a brown dwarf or a low-mass star. We present follow-up photometry and spectroscopy of both binaries, as well as phase-resolved spectroscopy of the brighter system, and use these data to place preliminary estimates on the physical and binary parameters. SDSS J1205-0242 is composed of a 0.39 +/- 0.02M(circle dot) helium-core white dwarf that is totally eclipsed by a 0.049 +/- 0.006M(circle dot) (51 +/- 6M(J)) brown-dwarf companion, while SDSS J1231+ 0041 is composed of a 0.56 +/- 0.07M(circle dot) white dwarf that is partially eclipsed by a companion of mass +/- 0.095 M-circle dot. In the case of SDSS J1205-0242, we look at the combined constraints from common-envelope evolution and brown-dwarf models; the system is compatible with similar constraints from other post-common-envelope binaries, given the current parameter uncertainties, but has potential for future refinement.