Full non-LTE multi-level radiative transfer

Context . The standard nonlocal thermodynamic equilibrium (non-LTE) multi-level radiative transfer problem only takes into account the deviation of the radiation field and atomic populations from their equilibrium distribution. Aims . We aim to show how to solve for the full non-LTE (FNLTE) multi-level radiative transfer problem, also accounting for deviation of the velocity distribution of the massive particles from Maxwellian. We considered, as a first step, a three-level atom with zero natural broadening. Methods . In this work, we present a new numerical scheme. Its initialisation relies on the classic, multi-level approximate Λ-iteration (MALI) method for the standard non-LTE problem. The radiative transfer equations, the kinetic equilibrium equations for atomic populations, and the Boltzmann equations for the velocity distribution functions were simultaneously iterated in order to obtain self-consistent particle distributions. During the process, the observer’s frame absorption and emission profiles were re-computed at every iterative step by convolving the atomic frame quantities with the relevant velocity distribution function. Results . We validate our numerical strategy by comparing our results with the standard non-LTE solutions in the limit of a two-level atom with Hummer’s partial redistribution in frequency, and with a three-level atom with complete redistribution. In this work, we considered the so-called cross-redistribution problem. We then show new FNLTE results for a simple three-level atom while evaluating the assumptions made for the emission and absorption profiles of the standard non-LTE problem with partial and cross-redistribution.