First semi-empirical test of the white dwarf mass-radius relationship using a single white dwarf via astrometric microlensing

In November 2019 the nearby single, isolated DQ-type white dwarf LAWD 37 (LP 145-141) aligned closely with a distant background source and caused an astrometric microlensing event. Leveraging astrometry from Gaia and followup data from the Hubble Space Telescope we measure the astrometric deflection of the background source and obtain a gravitational mass for LAWD 37. The main challenge of this analysis is in extracting the lensing signal of the faint background source whilst it is buried in the wings of LAWD 37's point spread function. Removal of LAWD 37's point spread function induces a significant amount of correlated noise which we find can mimic the astrometric lensing signal. We find a deflection model including correlated noise caused by the removal of LAWD 37's point spread function best explains the data and yields a mass for LAWD 37 of $0.56\pm0.08 M_{\odot}$. This mass is in agreement with the theoretical mass-radius relationship and cooling tracks expected for CO core white dwarfs. Furthermore, the mass is consistent with no or trace amounts of hydrogen that is expected for objects with helium-rich atmospheres like LAWD 37. We conclude that further astrometric followup data on the source is likely to improve the inference on LAWD 37's mass at the $\approx3$ percent level and definitively rule out purely correlated noise explanations of the data. This work provides the first semi-empirical test of the white dwarf mass-radius relationship using a single, isolated white dwarf and supports current model atmospheres of DQ white dwarfs and white dwarf evolutionary theory.