Detection of the Temperature Dependence of the White Dwarf Mass-Radius Relation with Gravitational Redshifts

TL;DR

This study uses a large catalog of white dwarfs to empirically confirm that their mass-radius relation depends on temperature, with hotter stars showing larger radii and lower surface gravities at fixed radius or gravity.

Contribution

The paper provides the first direct measurement of the temperature dependence of the white dwarf mass-radius relation using gravitational redshifts from a large survey dataset.

Findings

Warmer white dwarfs have larger radii than cooler ones at fixed surface gravity.

Gravitational redshift differences between warm and cool white dwarfs are statistically significant.

Results agree with theoretical predictions of temperature-dependent mass-radius relation.

Abstract

Models predict that the well-studied mass-radius relation of white dwarf stars depends on the temperature of the star, with hotter white dwarfs having larger masses at a given radius than cooler stars. In this paper, we use a catalog of 26,041 DA white dwarfs observed in Sloan Digital Sky Survey Data Releases 1-19. We measure the radial velocity, effective temperature, surface gravity, and radius for each object. By binning this catalog in radius or surface gravity, we average out the random motion component of the radial velocities for nearby white dwarfs to isolate the gravitational redshifts for these objects and use them to directly measure the mass-radius relation. For gravitational redshifts measured from binning in either radius or surface gravity, we find strong evidence for a temperature-dependent mass-radius relation, with warmer white dwarfs consistently having greater gravitational redshifts than cool objects at a fixed radius or surface gravity. For warm white dwarfs, we find that their mean radius is larger and mean surface gravity is smaller than those of cool white dwarfs at 5.2{\sigma} and 6.0{\sigma} significance, respectively. Selecting white dwarfs with similar radii or surface gravities, the significance of the difference in mean gravitational redshifts between the warm and cool samples is >6.1{\sigma} and >3.6{\sigma} for measurements binned in radius and surface gravity, respectively, in the direction predicted by theory. This is an improvement over previous implicit detections, and our technique can be expanded to precisely test the white dwarf mass-radius relation with future surveys.