Numerical methods for solution of spectral line formation problems in the stellar atmospheres

Abstract

The theory of radiative transfer (RT) in the stellar atmospheres is one of the most important and most complex parts of the modern astrophysics. The observed spectra of the stars are the only source of information of their structural and dynamical properties. All RT problems in spectral lines are characterized by the non-local coupling of the radiation field and the state of matter. Additionally, the problem of spectral line formation by multi-level atoms is non-linear due to the strong non-linear coupling of the atomic level populations (i.e. the source functions) and the radiation field intensities in the corresponding line transitions. For its solution iterative procedure must be applied. The ever increasing complexity of RT problems (e.g. the treatment of time-dependent processes and multi-dimensional phenomena) requires fast and efficient numerical methods. Although there is a great progress in the field in the last decades the development of new approaches and algorithms that will cost small computational time and memory still deserves special attention. In this paper we describe two fast methods, the Iteration Factors Method (IFM) and Forth-and-Back Implicit Lambda Iteration (FBILI) that both use iteration factors to converge to the exact solution of multi-level problem of spectral line formation.