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

## TL;DR

This study investigates how the hydrogen envelope mass affects the mass-radius relation of DA white dwarfs, revealing that envelope variations can significantly impact mass and gravity estimates, with implications for observational data interpretation.

## Contribution

It provides a detailed analysis of the hydrogen envelope's influence on white dwarf mass-radius relation and compares theoretical predictions with observational data.

## Key findings

- Hydrogen envelope mass decreases with increasing stellar mass.
- Reducing hydrogen envelope mass can decrease radius by up to 12%.
- Theoretical models align with observations when considering thin hydrogen envelopes.

## 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 Msun. Computations of the pre-white dwarf evolution uncovers an intrinsic dependence of the maximum mass of the hydrogen envelope with 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%. This translates directly into an increase in log g for a fixed stellar mass, that 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 MH ~ 2 10^-8 Msun, for 40 Eridani B, in agreement with previous determinations. For Sirius B, the spectroscopic mass is 4.3% 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 MH = 2 10^-6 Msun.