Complex hydrogen chemical equilibrium and Gaia low mass problem in cool white dwarfs

¹ Institute of Energy Technologies - Theory and Computation of Energy Materials (IET-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
² Jülich Aachen Research Alliance JARA Energy & Center for Simulation and Data Science (CSD), 52428 Jülich, Germany

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 28 November 2025
Accepted: 4 February 2026

Abstract

Context. The extensive Gaia dataset reveals a substantial misfit between models and observation for cool white dwarfs with T_eff < 6000 K, resulting in severe underestimations of their masses.

Aims. We aim to understand the underlying modeling issues related to this misfit.

Methods. We applied state-of-the-art atmosphere models to analyze the Gaia DR3 sample of white dwarfs, along with quantum mechanical calculations to quantify the formation and stability of different hydrogen species in the atmospheres of these stars.

Results. We find that we are able to reconcile the models and observations when we artificially suppress the formation of H⁺₃ species, a process which substantially alters the chemical equilibrium at T_eff < 6000 K, resulting in an overabundance of free electrons and H⁻ and strengthening of H⁻ bound-free absorption. Removing the H⁺₃ species from chemical equilibrium considerations makes the ionization of hydrogen atoms the main source of free electrons, with the resulting models reproducing the Gaia white dwarfs cooling branch well. Because H⁺₃ must form under the considered conditions, it is likely the overestimation of its partition function and the resulting abundance or the formation of H⁻ (or another anionic species) that leads to the suppression of the H⁻ formation as a countercharge for H⁺₃ in current models.

Conclusions. The chemical equilibrium in hydrogen atmospheres of cool white dwarfs must be reconsidered with respect to the abundance of H⁺₃ species and the presence of unaccounted charge species.