DIFFERENTIALLY MOVING MEDIA WITH MANY SPECTRAL LINES: STOCHASTIC APPROACH

• Published in: Journal of quantitative spectroscopy & radiative transfer 1998-12, Vol.60 (6), p.963-977
• Main Authors: WEHRSE, R., VON WALDENFELS, W., BASCHEK, B.
• Format: Article
• Language: English
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/S0022-4073(97)00188-X

Based upon the analytical solution of the radiative transfer equation for a given source function and a new approach to account for very many spectral lines contributing to the extinction, the connection between line properties and the emergent intensity is derived under the assumption that the wavelengths of the line centers follow a Poisson point process, whereas the other line parameters may have arbitrary distribution functions. A comparison with the widely used list of Kurucz shows that the Poisson distribution well describes deterministic “real” lines. The presentation by a Poisson point process requires only a modest number of parameters and is very flexible. It allows most operations to be carried out analytically and hence is very suitable to study the intricate influence of many lines on radiation fields in differentially moving media. We consider a simplified case of the solution of the radiative transfer equation in order to demonstrate the basic effects of the velocity field upon the emerging radiation field. Expressions for the expectation value of the intensity are derived, and examples are given for Lorentz line profiles and infinitely sharp lines, in particular as functions of the velocity gradient and the mean line density.