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KOI-3278 is a self-lensing stellar binary consisting of a white-dwarfsecondary orbiting a Sun-like primary star. Kruse and Agol (2014) noticed smallperiodic brightenings every 88.18 days in the Kepler photometry and interpretedthese as the result of microlensing by a white dwarf with about 63$\%$ of themass of the Sun. We obtained two sets of spectra for the primary that allowedus to derive three sets of spectroscopic estimates for its effectivetemperature, surface gravity, and metallicity for the first time. We used thesevalues to update the Kruse and Agol (2014) Einsteinian microlensing model,resulting in a revised mass for the white dwarf of $0.539^{+0.022}_{-0.020} \,M_{\odot}$. The spectra also allowed us to determine radial velocities andderive orbital solutions, with good agreement between the two independent datasets. An independent Newtonian dynamical MCMC model of the combined velocitiesyielded a mass for the white dwarf of $0.5122^{+0.0057}_{-0.0058} \,M_{\odot}$. The nominal uncertainty for the Newtonian mass is about four timesbetter than for the Einsteinian, $\pm 1.1\%$ vs. $\pm 4.1\%$ and the differencebetween the two mass determinations is $5.2 \%$. We then present a jointEinsteinian microlensing and Newtonian radial velocity model for KOI-3278,which yielded a mass for the white dwarf of $0.5250^{+0.0082}_{-0.0089} \,M_{\odot}$. This joint model does not rely on any white dwarf evolutionarymodels or assumptions on the white dwarf mass-radius relation. We discuss thebenefits of a joint model of self-lensing binaries, and how future studies ofthese systems can provide insight into the mass-radius relation of whitedwarfs.

The Mass of the White Dwarf Companion in the Self-Lensing Binary KOI-3278: Einstein vs. Newton