Non–LTE treatment of molecules in the photospheres of cool stars

We present a technique to treat systems with very many levels, like molecules, in non–LTE. This method is based on a superlevel formalism coupled with rate operator splitting. Superlevels consist of many individual levels that are assumed to be in LTE relative to each other. The usage of superlevels reduces the dimensionality of the rate equations dramatically and, thereby, makes the problem computationally more easily treatable. Our superlevel formalism retains maximum accuracy by using direct opacity sampling (dOS) when calculating the radiative transitions and the opacities. We developed this method in order to treat molecules in cool dwarf model calculations in non–LTE. Cool dwarfs have low electron densities and a radiation field that is far from a black body radiation field, both properties may invalidate the conditions for the common LTE approximation. Therefore, the most important opacity sources, the molecules, need to be treated in non–LTE. As a case study we applied our method to carbon monoxide. We find that our method gives accurate results since the conditions for the superlevel method are very well met for molecules. Due to very high collisional cross sections with hydrogen, and the high densities of H2 the population of CO itself shows no significant deviation from LTE. Subject headings: molecular processes – methods: numerical – stars: atmospheres – stars: low-mass, brown dwarfs – radiative transfer – line: formation