On the radiative equilibrium of a stellar atmosphere. IX.

Abstract

In this paper the problem of diffuse reflection by a semi-infinite plane-parallel atmosphere is considered along the lines of the earlier papers of this series. Explicit solutions are obtained for the cases when the scattering of radiation by the atmosphere takes place in accordance with the phase functions λ(1+ x cosθ), (0<λ≤1, -1≤x≤1), and (1 + cos²θ). It is shown how simple, closed expressions can be found for the angular distribution of the reflected radiation in a general nth approximation. Only certain simple algebraic equations need be solved for their "characteristic roots" to bring the solutions. to their numerical forms. Tables of certain constants and functions required for the practical use of the solutions are provided.