Radiative transfer in the broad emission line regions of quasi-stellar objects

Abstract

Most of the photoionization models used to account for the broad emission lines from quasi-stellar objects have adopted escape-probability approximations to avoid solving the equations of radiative transfer. The few published models based on transfer solutions have used the approximation of complete frequency redistribution for the hydrogen resonance lines. We show that both of these approximations lead to errors of at least factors of 2 in the calculated line ratios and to qualitative changes in the calculated atmospheric parameters. Here we solve the radiative transfer, statistical equilibrium, and energy-balance equations for an illuminated, plane-parallel cloud having a prescribed optical thickness and constant gas pressure. The cloud composition is assumed to be either pure hydrogen or H and He in the ratio 1 to 0.1. In addition, heavier elements are presumed to provide radiative cooling and heating and to absorb X-rays. Six energy-balance models are presented, all having the same illuminating radiation, optical thickness, and pressure. The first is a pure hydrogen model considered earlier by Hubbard and Puetter. Model 2 includes the effects of radiative cooling by heavy elements. In model 3 we add helium and X-ray opacity. Model 4 includes X-ray heating. In model 5 we replace the "on-the-spot" approximation by a solution of the Lyman continuum transfer equation. In model 6, line escape probabilities are replaced by solutions of the line transfer equations, including Lyα partial frequency redistribution. The largest changes in the calculated results are due to heavy-element cooling and to the transfer effects with partial frequency redistribution.