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

TL;DR

Gaia DR3 reveals a mass underestimation problem for cool hydrogen-atmosphere white dwarfs with $T_{ m eff}<6000\,\rm K$. The authors integrate state-of-the-art WD atmospheres with quantum-mechanical calculations to reexamine hydrogen chemistry, emphasizing $H_3^+$ formation and related charge carriers in chemical equilibrium. They find that suppressing $H_3^+$ formation yields a cooling sequence consistent with Gaia data, implying that the free-electron pool is then set by $H$ ionization and that $H^-$ opacity is reduced. The work suggests that the partition function of $H_3^+$ may be overestimated or that missing anionic species (e.g., $H_2^-$ or $H_3^-$) or other mechanisms maintain charge balance, and calls for revisiting chemical-equilibrium treatments in cool WD atmospheres with targeted quantum calculations for hydrogen complexes.

Abstract

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.

Figures (7)

• Figure 1: The Hertzsprung-Russell (H-R) diagram for the 100 pc sample of white dwarfs: Gaia DR3 data (filled black dots, JTR22), pure hydrogen atmosphere cooling sequence of $log\,g=8$ with (red dots and solid line) and without (green dots and solid line) $\rm H_3^+$ species considered in the chemical equilibrium. Dots represent the effective temperature sequence from $8000\rm\,\rm K$ to $3000\rm\,\rm K$, from top to bottom, with an interval of $500\,\rm K$.
• Figure 2: The photospheric (at the Rosseland mean optical depth, $\tau_R=2/3$) abundance of species in the atmosphere of hydrogen white dwarf of $log\,g=8$ as a function of the effective temperature. Different colors and lines represent different species as indicated in the legend insert. The panels show results with (left) and without (middle) $\rm H_3^+$ species considered. The right panel shows the result obtained by assuming formation of a hypothetical anionic species (represented by $\rm H_2^-$ with the decreased formation energy).
• Figure 3: The photospheric (at the Rosseland mean optical depth, $\tau_R=2/3$) density (left panel) and refractive index at $\tau_R=2/3$ and $100$ (right panel), as a function of the effective temperature.
• Figure 4: The Hertzsprung-Russell (H-R) diagram for the sample of white dwarfs with PAN-STARRS nad BVK photometry (filled black dots, DBC17), pure hydrogen atmosphere cooling sequence of $log\,g=8$ with (red dots and solid line) and without (green dots and solid line) $\rm H_3^+$ species considered in the chemical equilibrium. Dots represent the effective temperature sequence from $8000\rm\,\rm K$ to $3000\rm\,\rm K$, from top to bottom, with an interval of $500\,\rm K$.
• Figure 5: The Hertzsprung-Russell (H-R) diagram. Data and models as in Fig. \ref{['F1']}.. The blue line and filled dots represent the cooling sequence computed assuming $\rm H_3^+$ partition function of RT11.