Line shapes of the Na/K resonance line profiles perturbed by H₂ at extreme density

¹ LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Sorbonne Paris Cité, CNRS, 61 Avenue de l'Observatoire, 75014 Paris, France
² Institut d’Astrophysique de Paris, UMR7095, CNRS, Université Paris VI, 98bis Boulevard Arago, 75014 Paris, France
³ Department of Physics and Astronomy, University of Louisville, Louisville, Kentucky 40292, USA

^★ Corresponding author: nicole.allard@obspm.fr

Received: 21 August 2025
Accepted: 1 October 2025

Abstract

Context. Collision broadening by molecular hydrogen of sodium and potassium is one of the major broadening mechanisms in the atmospheres of brown dwarf stars and exoplanets at an effective temperature of about 1000 K. The relevant H₂ perturber densities reach several 10¹⁹ cm⁻³ in hot (T_eff ≳ 1500 K) Jupiter-mass planets, and up to almost 10²¹ cm⁻³ (≈30 bar) for more massive or cooler objects. The Juno Microwave Radiometer has enabled observations of Jupiter’s atmosphere down to previously inaccessible depths where pressures near 10⁶ bar have to be considered and the relevant H₂ perturber densities may exceed 10²⁵ cm⁻³.

Aims. While Na/K–He/H₂ opacity tables have been constructed for the resonance lines that are valid to n_H2 = 10²¹ cm⁻³, at higher density it is important to ensure accurate absorption cross-sections of these species in the models. We accurately determine the broadening of Na/K by H₂ in the unified theory at H₂ densities larger than 10²¹ cm⁻³ and compare to the corresponding Lorentzian profiles.

Methods. The theory of spectral line shapes, especially the unified approach we have developed, makes possible accurate models of stellar spectra that account both for the centers of spectral lines and their extreme wings in one consistent treatment. In this study, we examine the density dependence of the Na and K D2 (P_3/2) components, respectively, at 5889.95 Å and 7664.90 Å from 1 × 10²¹ to 2 × 10²² cm⁻³.

Results. Lorentzian profiles from impact broadening theory are only valid in the core of the line not farther than a few half-widths as long as there is no overlap between the core of the line and possible quasi-molecular features in the wings due to close collisions.

Conclusions. The accurate computation of line profiles from collision broadening at high density requires use of a Fourier transform of the autocorrelation function inside the model atmosphere code. We strongly warn that use of Lorentzian profiles at a high perturber density neglects radiation during close collisions and may lead to erroneous conclusions.