The white dwarf mass-radius relation and its dependence on the hydrogen envelope

Abstract

We present a study of the dependence of the mass-radius relation for DA white dwarf stars on the hydrogen envelope mass and the impact on the value of log g, and thus the determination of the stellar mass. We employ a set of full evolutionary carbon-oxygen core white dwarf sequences with white dwarf mass between 0.493 and 1.05 M☉. Computations of the pre-white-dwarf evolution uncovers an intrinsic dependence of the maximum mass of the hydrogen envelope on the stellar mass; i.e. it decreases when the total mass increases. We find that a reduction of the hydrogen envelope mass can lead to a reduction in the radius of the model of up to ∼12 per cent. This translates directly to an increase in log g for a fixed stellar mass, which can reach up to 0.11 dex, mainly overestimating the determinations of stellar mass from atmospheric parameters. Finally, we find a good agreement between the results from the theoretical mass-radius relation and observations from white dwarfs in binary systems. In particular, we find a thin hydrogen mass of M H ∼ 2 × 10 −8 M☉ for 40 Eridani B, in agreement with previous determinations. For Sirius B, the spectroscopic mass is 4.3 per cent lower than the dynamical mass. However, the values of mass and radius from gravitational redshift observations are compatible with the theoretical mass-radius relation for a thick hydrogen envelope of M H = 2 × 10 −6 M☉.