Radiative Transfer with Many Spectral Lines

Abstract

The radiative transfer equation, a partial integro-differential equation, is of particular interest for astronomers since it links the spectral properties of the light received (e.g. on Earth) with the properties of the matter from the place of origin (e.g. a star) to the place of the observer.

One major difficulty in its solution is the strong variability of the extinction coefficient entering the equation (e.g. often by more than 6 dex in a small frequency interval). Furthermore, often contributions from more than 10⁸ narrow spectral lines have to be included. This has essentially inhibited up to now the accurate consideration of photon fluxes and pressures in radiation-hydrodynamic modelling.

In this contribution two new algorithms developed in collaboration with B. Baschek and W. v. Waldenfels are introduced that allow the efficient calculation of radiation fields with many lines whenever the detailed spectral information is not required. In the first one the extinction coefficient is represented by a ’generalized opacity distribution function’. In a second method the line positions, strengths and profiles are described by a Poisson point process.

The resulting expressions which are valid both in static and differentially moving media become particularly convenient inside a very optically thick medium (“diffusion limit”).