Line shapes of the Na/K resonance line profiles perturbed by H_2 at extreme density

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 H_2 perturber densities reach several 10^19 cm^-3 in hot (T_ ̊m eff ≳ 1500 K) Jupiter-mass planets, and up to almost 10^21cm^-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 H_2 perturber densities may exceed 10^25 cm^-3. While Na/K-He/H_2 opacity tables have been constructed for the resonance lines that are valid to n_ H 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 H_2 in the unified theory at H_2 densities larger than 10^21 cm^-3 and compare to the corresponding Lorentzian profiles. 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 $ to $2 $ cm^-3. 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. 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.