Alkali lines at extreme densities and their impact on giant planet interior structure

Abstract

Alkali lines, in particular the sodium Na $D$ (5891$Å$, 5897$Å$) and potassium K $D$ (7667$Å$, 7701$Å$) resonance doublets, are dominant opacity sources in giant planets over a wide range of temperatures ($\gtrsim$1000K). Their strong pressure-broadened wings significantly influence the thermal structure of giant planets, especially at high pressures. Most detailed line-profile calculations have so far been limited to perturber densities up to $10^{21}$cm$^{-3}$. However, conditions in the deep atmospheres and interiors of giant planets can reach significantly higher densities, making the temperature gradients increasingly uncertain. We determined how physically consistent collisional broadening of the Na $D$ and K $D$ lines at extreme densities affects opacity calculations and consequently the inferred interior structure of giant planets. We computed detailed Na $D$ and K $D$ line profiles using unified line theory, extending to molecular hydrogen perturber densities of $n_{\rm H_2} = 5 \times 10^{22}$cm$^{-3}$, which translates to pressures up to $\sim$ 20kbar. The revised cross sections were incorporated into Rosseland mean opacity tables, which were then used to evaluate their effect on planetary thermal structures. At densities $n_{\rm H_2} > 10^{21}$cm$^{-3}$, the line profiles predicted by unified line theory exhibit significantly stronger wings than commonly used Voigt profiles, as well as density-dependent line shifts, which substantially increases Rosseland mean opacities. Consequently, the radiative-convective boundary of warm and hot giant planets can shift to lower pressures, producing warmer interior adiabats and increasing inferred core masses. We further find that Jupiter is unlikely to host a stable radiative layer at the present time or throughout most of its evolution, as the required Na and K abundances for this are well below observational constraints.