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- W2069514882 abstract "view Abstract Citations (18) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Complete Rayleigh-Scattered Field Within a Homogeneous Plane-Parallel Atmosphere Mullikin, T. W. Abstract A direct numerical solution of the equation of radiative transfer in any particular model atmosphere is a rather lengthy task. This is particularly true if polarization is accounted for in a relatively thick atmosphere. The work of Ambartsumian and of Chandrasekhar shows that it is not necessary to solve the transfer equation completely if one is interested only in steady-state intensities of radiation on the bounding faces of a plane-parallel atmosphere. By heuristic principles of invariance they derived various non4inear equations which these special values of the intensity must satisfy. For a homogeneous atmosphere these equations can be considerably simplified, so that, even for the Rayleigh polarization scattering model, Chandrasekhar shows that reflection and transmission functions are simply expressed in terms of certain scalar functions, the X- and V-functions. In this paper we extend our previous work on scalar transfer equations to the Rayleigh polarization equations in a homogeneous atmosphere. We show that Chandrasekhar's results for scattering and reflection functions are merely the specialization to the boundary of formulae which hold within an atmosphere. This expresses the solution to this problem at any optical depth in an atmosphere of any optical thickness in terms of scalar functions for which there already exists an efficient and accurate computer program. We also obtain from this solution various asymptotic formulae of a relatively simple form. We work principally with linear integral equations. The non-linear equations which express the heuristic principles of invariance, which we have previously shown to be an incomplete set of equations, follow rigorously from the transfer equation by Laplace transform methods. Solutions to these nonlinear equations are obtained and give intensities within an atmosphere expressed as non-linear combinations of solutions to the linear integral equations. Publication: The Astrophysical Journal Pub Date: September 1966 DOI: 10.1086/148832 Bibcode: 1966ApJ...145..886M full text sources ADS |" @default.
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- W2069514882 title "The Complete Rayleigh-Scattered Field Within a Homogeneous Plane-Parallel Atmosphere" @default.
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