Theory of Radiative Transfer in Inhomogeneous Atmospheres. III. Extension of the Perturbation Method to Azimuth-Independent Terms

Abstract

view Abstract Citations (6) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Theory of Radiative Transfer in Inhomogeneous Atmospheres. III. Extension of the Perturbation Method to Azimuth-Independent Terms Abhyankar, K. D. ; Fymat, A. L. Abstract In the case where the phase matrix, corresponding to the azimuth-independent term of the radiation field scattered by an inhomogeneous plane-parallel atmosphere, is separable in the form P(0)( , `) = M ( ) Mt (M') (where the dagger stands for simple transposition), the simplified matrix equations of the problem are treated by the perturbation method of Fymat and Abhyankar. The nonlinear singular integral equations for the matrix functions K, L, K*, and L*, given by Sekera (1963), are solved by linearizing the equation for K. This linearized equation is written in an operator form, and its N-solution is given. After substitution of this solution in the equation for L, the resulting linear equation is also written in its operator form and its N-solution is obtained. The convergence of these series solutions is studied, and the regions of convergence in the case of a Rayleigh-scattering law are delimited when the solution for conservative Rayleigh scattering is taken as the reference. Publication: The Astrophysical Journal Pub Date: March 1970 DOI: 10.1086/150378 Bibcode: 1970ApJ...159.1009A full text sources ADS | Related Materials (2) Part 1: 1969ApJ...158..315F Part 2: 1969ApJ...158..325F