A Gravitational Redshift Measurement of the White Dwarf Mass-Radius
  Relation
  The mass-radius relation of white dwarfs is largely determined by the
equation of state of degenerate electrons, which causes the stellar radius to
decrease as mass increases. Here we observationally measure this relation using
the gravitational redshift effect, a prediction of general relativity that
depends on the ratio between stellar mass and radius. Using observations of
over three thousand white dwarfs from the Sloan Digital Sky Survey and the Gaia
space observatory, we derive apparent radial velocities from absorption lines,
stellar radii from photometry and parallaxes, and surface gravities by fitting
atmospheric models to spectra. By averaging the apparent radial velocities of
white dwarfs with similar radii and, independently, surface gravities, we
cancel out random Doppler shifts and measure the underlying gravitational
redshift. Using these results, we empirically measure the white dwarf
mass-radius relation across a wide range of stellar masses. Our results are
consistent with leading theoretical models, and our methods could be used with
future observations to empirically constrain white dwarf core composition and
evolution.
