The Hermitian Solution of the Radiative Transfer Equation for Non-LTE Problems

Abstract

We present a new integrator of the polarized radiative transfer equation (RTE) which is directly applicable to the non-polarized (scalar) RTE. We suggest that this Hermitian algorithm is suitable for treating non-LTE problems, and derive the approximate ⋀-operator required to solve the equations of statistical equilibrium by means of preconditioning or linearization techniques. The performance of the new method in the scalar case is investigated by comparing its results with those obtained with other formal solvers of the RTE. It turns out that the Hermitian algorithm requires significantly coarser grids to attain the same accuracy in the specific and mean intensities. This should substantially accelerate the solution of non-LTE problems because the computational cost of determining self-consistent values of the atomic level populations with the currently-used operator splitting methods scales as N ², N being the number of spatial grid points.