Radiative transfer with finite elements

A finite element method for solving the resonance line transfer problem in moving media is presented. The algorithm works in three spatial dimensions on unstructured grids which are adaptively refined by means of an a posteriori error indicator. Frequency discretization is implemented via a first-order Euler scheme. We discuss the resulting matrix structure for coherent isotropic scattering and complete redistribution. The solution is performed using an iterative procedure, where monochromatic radiative transfer problems are successively solved. The present implementation is applicable for arbitrary model configurations with an optical depth up to 103-4. Results of Lyα line transfer calculations for a spherically symmetric model, a disk-like configuration, and a halo containing three source regions are discussed. We find the characteristic double-peaked Lyα line profile for all models with an optical depth $\ga$1. In general, the blue peak of the profile is enhanced for models with infall motion and the red peak for models with outflow motion. Both velocity fields produce a triangular shape in the two-dimensional Lyα spectra, whereas rotation creates a shear pattern. Frequency-resolved Lyα images may help to find the number and position of multiple Lyα sources located in a single halo. A qualitative comparison with observations of extended Lyα halos associated with high redshift galaxies shows that even models with lower hydrogen column densities than required from profile fitting yield results which reproduce many features in the observed line profiles and two-dimensional spectra