Testing the mass-radius relation of white dwarfs in common proper-motion pairs

Context. White dwarf masses are among the most important properties used to constrain their past and future evolution. Direct estimates of white dwarf masses are crucial for assessing the validity of theoretical evolutionary models and methods of analysis. Aims. The main goal of this work was to measure the masses and radii of white dwarfs that belong to widely separated, common proper-motion binaries with non-degenerate companions. These can be assessed, independently from theoretical mass-radius relations, through measurements of gravitational redshifts and photometric radii. Methods. We studied 50 white dwarfs with hydrogen-dominated atmospheres, performing a detailed analysis of high-resolution ( R ≈ 18 500) spectra via state-of-the-art grids of synthetic models and specialized software. We measured accurate radial velocities from the H α and H β line cores to obtain the white dwarf gravitational redshifts. Jointly with a photometric analysis, formalized by a Bayesian inference method, we measured precise radii for the white dwarfs in our sample, which allowed us to directly measure the white dwarf masses from their gravitational redshifts. Results. The distributions of measured masses and radii agree within 6% (at the 1- σ level) from the theoretical mass-radius relation, thus delivering a much smaller scatter in comparison with previous analyses that used gravitational redshift measurements from low-resolution spectra. Our comparison against model-dependent spectroscopic estimates produces a larger scatter of 15% on the mass determinations. We find an agreement within ≈10% from previous model-based, photometric mass estimates from the literature. Conclusions. Combining gravitational redshift measurements and photometric analysis of white dwarfs delivers precise and accurate empirical estimates of their masses and radii. This work confirms the reliability of the theoretical mass-radius relation from the lightest to the heaviest white dwarfs in our sample (≈0.38–1.3 M ⊙ ).