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

Large Gaia data set shows substantial misfit between models and observation for cool white dwarfs with $T_{\rm eff}<6000\,\rm K$, resulting in severe underestimation of masses of these stars. We aim to understand the underlying modelling issues. State of the art atmosphere models have been applied to analyse the Gaia DR3 sample of white dwarfs as well as quantum mechanical calculations to quantify formation and stability of different hydrogen species in the atmospheres of these stars. We reconcile the models and observations when we artificially suppress formation of $\rm H_3^+$ species, a process which substantially alters the chemical equilibrium at $T_{\rm eff}<6000\,\rm K$, resulting in an overabundance of free electrons and $\rm H^-$, and strengthening of $\rm H^-$ bound-free absorption. Removing the $\rm H_3^+$ species from chemical equilibrium consideration makes ionization of hydrogen atoms the main source of free electrons, with the resulting models reproducing well the Gaia white dwarfs cooling branch. Because $\rm H_3^+$ must form under the considered conditions, likely it is the overestimation of its partition function and resulting abundance or the formation of $\rm H_3^-$ or another anionic species that suppresses the formation of $\rm H^-$ as a countercharge for $\rm H_3^+$ in current models. Chemical equilibrium in cool, hydrogen atmospheres white dwarfs must be reconsidered in respect to the abundance of $\rm H_3^+$ species and presence of unaccounted charge species.