A simple problem of radiative transfer by multilevel atoms

Abstract

We consider the problem of determining the radiation fields reflected and transmitted by a slab containing multilevel hydrogen atoms and illuminated on one side by a given radiation field. We treat the extreme non-LTE situation in which the populations of the different levels are determined by the radiative processes. We take into account the population and the transfer effects in a self-consistent way by solving the transfer equations in all the lines and continua together with the equations of statistical equilibrium for all levels. We limit ourselves to the idealistic case of rectangular profiles in the lines and continua and to a model of atoms with 4 levels and a continuum. Under conditions close to thermodynamic equilibrium we empirically derive a Schuster-like law for the continua with transmitted radiation fields varying as the inverse of the optical thickness. Turning to out-of-equilibrium conditions we emphasize the crucial role of the loss probability of the Lyα photons. Owing to the rapid decrease of the excitation/ionization degree in the medium and contrary to the conservative case the optical thicknesses of the subordinate transitions now remain finite even when the population of the fundamental level along the line-of-sight becomes infinite. As a result of this relative transparency the strong emission lines formed by recombination mechanisms can escape from the medium. Although the present problem remains largely academic because of the number of simplifications introduced we suggest some possible applications and developments.