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 (WD 1142-645) aligned closely with a distant background source and caused an astrometric microlensing event. Leveraging astrometry from \Gaia{} and followup data from the \textit{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.