Re-evaluating Lyman $α$ wing opacities and the low mass-problem in cool white dwarfs

TL;DR

This work revisits the Ly alpha wing opacity in cool hydrogen-atmosphere white dwarfs by employing angle-resolved ab initio H3 potential energy surfaces to better capture H–H2 collisions in a quasi-static framework. By comparing one- and multi-perturber approaches and applying the updated opacities to Gaia and multi-wavelength data, the study finds the revised opacity improves near-UV colors for cooler stars but still fails to reconcile optical colors and the Gaia-based low-mass trend. The analysis shows that modifying CIA opacity does not resolve the discrepancy, while decreasing bound-free H− opacity helps optical/IR colors but degrades UV fits, indicating that the low-mass problem cannot be solved by Ly alpha wing changes alone. The authors conclude that improved opacities and comprehensive multi-wavelength observations are essential, and until a physical solution emerges, ad hoc corrections to Gaia-based mass estimates remain a practical workaround.

Abstract

Gaia observations have reignited interest in the optical and ultraviolet (UV) opacity problems of cool white dwarfs ($T_{\rm eff} \leq 6000$ K), which were thought to be resolved nearly two decades ago through the inclusion of Lyman $α$ red wing opacity arising from H-H$_2$ collisions in atmospheric models. Recent studies have revealed that their masses derived from Gaia optical photometry are 0.1$-$0.2 M$_{\odot}$ lower than expected from single-star evolution. Since the Ly $α$ H-H$_2$ wing opacity significantly affects the blue end of their optical spectra, it may contribute to the mass discrepancy. To investigate this hypothesis, we revisited the Ly $α$ opacity calculations in the quasi-static single and multi-perturber approximations by explicitly using the ab initio potential energy data of H$_3$ while fully accounting for the H-H$_2$ collision angle. We find that the opacity is slightly smaller than the standard models at the shortest wavelengths ($\leq5000$ angstrom), but larger at longer wavelengths. Comparing synthetic magnitudes (GALEX, Gaia, WISE) to the observations of the 40 pc white dwarf sample, we note that the revised models tentatively reproduce the observed $NUV-G$ colours for stars cooler than 6000 K, but still fail to match $G_{\rm BP} - G_{\rm RP}$ colours, resulting in similarly low inferred masses ($\leq 0.5$ M$_{\odot}$) as obtained with the standard Ly $α$ opacity. Exploring other dominant opacity sources, we discover that decreasing the strength of the bound-free H$^-$ opacity in existing models better reproduces the optical and infrared colours, while collision-induced absorption (CIA) opacity is ineffective in resolving the low-mass problem. We highlight the need for improved opacities and multi-wavelength observations in future studies.

Figures (10)

• Figure 1: Geometry for the interaction of the H$_{2}$ molecule with the H atom where $\theta$ is the collision angle, $|\vec{r}_{{\rm H}_{2}}|=A$ is the internuclear separation between the two H atoms in H$_{2}$, $\vec{r}_{c}$ is the distance between the centre of mass of H$_{2}$ to H atom. The positions of the three H atoms as defined in the centre of mass reference frame boothroyd1996 are labelled in the figure.
• Figure 2: H$-$H$_{2}$ potential energy curves for the ground state (black) and first excited Rydberg state (red) at three different collision angles. The orange dots and blue pluses denote the ab initio data for the ground state and first excited state of the H$_{3}$ system boothroyd1996 where $\vec{r}_{{\rm H}_2}=1.40$ a.u. The solid black and red lines represent the polynomial fits to the ground and excited state energies, respectively. The potential energy curves used by KS06 for the collision angle of 90$^{\circ}$ are shown in solid cyan lines for comparison (right panel).
• Figure 3: The energy difference between the ground state ($E_1$) and the lowest Rydberg energy state ($E_3$) obtained from polynomial fits to the data for various collision angles. The potential energy difference from KS06 and Peng1995 for $D_{3h}$ geometry (equilateral triangle) is shown for comparison.
• Figure 4: Upper panel: Absorption cross-section of the Ly $\alpha$ red wing per unit perturber density where the pressure broadening is caused by collisions of the H atom with H$_{2}$ for $T_{\mathrm{eff}}$ values of 3000, 4000, 5000, and 6000 K. The dashed red lines are the values for $\theta$ between 75 to 90$^{\circ}$ while the solid red lines are for the case considering all H-H$_2$ collision angles. The opacity from KS06 kowalski2006 is shown in solid black lines for comparison. Lower panel: Variation of the wavelength as a function of H-H$_2$ separation $r_c$, corresponding to the energy difference $E_3-E_1$ considering different collision angles. The dashed grey lines denote the wavelength 4600 Å corresponding to a separation of 1.4 a.u. for collision angles 75-90$^{\circ}$.
• Figure 5: Absorption cross-section of the Ly $\alpha$ red wing per unit perturber density where the pressure broadening is caused by collisions of the H atom with H$_{2}$ for $T_{\mathrm{eff}}$ values of 3000, 4000, and 6000 K for different $n_{\rm H_2}$ number densities under the quasi-static multiple-perturber approximation. The opacity from KS06 kowalski2006 is shown in solid black lines for comparison.