An accurate mass and radius measurement for an ultracool white dwarf

Studies of cool white dwarfs in the solar neighbourhood have placed a limit on the age of the Galactic disk of 8-9 billion years. However, determining their cooling ages requires the knowledge of their effective temperatures, masses, radii, and atmospheric composition. So far, these parameters could only be inferred for a small number of ultracool white dwarfs for which an accurate distance is known, by fitting their spectral energy distributions (SEDs) in conjunction with a theoretical mass-radius relation. However, the mass-radius relation remains largely untested, and the derived cooling ages are hence model-dependent. Here we report direct measurements of the mass and radius of an ultracool white dwarf in the double-lined eclipsing binary SDSS J013851.54-001621.6. We find M(WD)=0.529+/-0.010Msol and R(WD)=0.0131+/-0.0003Rsol. Our measurements are consistent with the mass-radius relation and we determine a robust cooling age of 9.5 billion years for the 3570K white dwarf. We find that the mass and radius of the low mass companion star, M(sec)=0.132+/-0.003Msol and R(sec)=0.165+/-0.001Rsol, are in agreement with evolutionary models. We also find evidence that this >9.5 Gyr old M5 star is still active, far beyond the activity lifetime for a star of its spectral type. This is likely caused by the high tidally-enforced rotation rate of the star. The companion star is close to filling its Roche lobe and the system will evolve into a cataclysmic variable in only 70 Myr. Our direct measurements demonstrate that this system can be used to calibrate ultracool white dwarf atmospheric models.