R-matrix methods for the computation of Brown Dwarf spectral line shapes

Abstract

Accurate profiles of alkali spectral lines pressure broadened by collisions with molecular hydrogen and atomic helium perturbers are of crucial importance for the modeling of atmospheres of brown dwarfs. Calculations of these Lorentzian profiles are computationally demanding as they involve the integration of coupled second-order differential equations describing the colliding atoms out to large radial separations, where the solutions can be matched to a combination of the solutions for non-interacting atoms. This process must be repeated for a wide range of energies and relative angular momenta of the perturbers. We report on the use of two R-matrix packages, RPROP2 and FARM to solve these equations for collisions of atomic helium with Na and K, which are the dominant alkalies in brown dwarf spectra. The RPROP2 routine is extremely slow in todays terms but is simple to use and to modify where necessary. Conversely the FARM routine is extremely fast but considerably less transparent, incorporating a less computationally intensive potential--following propagator at intermediate radial separations where the potential is more slowly varying and an analytical, asymptotic solution fitting routine for large radial separations.