Temperature and density dependence of line profiles of sodium perturbed by helium^★

¹ GEPI, Observatoire de Paris, PSL Research University, UMR 8111, CNRS, Sorbonne Paris Cité, 61, Avenue de l’Observatoire, 75014 Paris, France
e-mail: nicole.allard@obspm.fr
² Institut d’Astrophysique de Paris, UMR7095, CNRS, Université Paris VI, 98bis Boulevard Arago, 75014 Paris, France
³ U.S. Army DEVCOM, Aviation and Missile Center, Charles M. Bowden Laboratory, Redstone Arsenal, AL 35898, USA
⁴ Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR6303, CNRS, Université de Bourgogne-Franche-Comté, 9, Avenue Alain Savary, 21078 Dijon Cedex, France

Received: 22 February 2023
Accepted: 16 April 2023

Abstract

Context. Ultracool stellar atmospheres and hot exoplanets show absorption by alkali resonance lines severely broadened by collisions with neutral perturbers. In the coolest and densest atmospheres, such as those of T dwarfs, Na I and K I broadened by molecular hydrogen and helium can come to dominate the entire optical spectrum. The effects of Na–He collision broadening are also central to understanding the opacity of cool DZ white dwarf stars.

Aims. In order to be able to construct synthetic spectra of brown dwarfs and cool DZ white dwarfs, where helium density can reach several 10²¹ cm⁻³, Na–He line profiles of the resonance lines have been computed over a wide range of densities and temperatures.

Methods. Unified line profiles that are valid from the core to the far wings at high densities are calculated in the semiclassical approach using up-to-date molecular data including electronic spin-orbit coupling from the sodium atom. Far wings are extended to more than 4000 cm⁻¹ from the line center when the helium density can reach 10²¹ cm⁻³ at 5000 K.

Results. We present a comprehensive study of Na–He collisional profiles at high density, and temperatures from 5000 K, which is the temperature prevailing in the atmosphere of ultra-cool DZ white dwarf stars, down to 1 K, which is the temperature in liquid helium clusters. Collision broadening and shift parameters within the impact approximation obtained in the semiclassical and quantum theory using our new accurate molecular data are presented.