Source vector in Rayleigh-Cabannes scattering atmosphere - The nonconservative Milne problem

Details Source vector in Rayleigh-Cabannes scattering atmosphere - The nonconservative Milne problem Source vector in Rayleigh-Cabannes scattering atmosphere - The nonconservative Milne problem

Feb 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ap%26ss.200..129v&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 200, no. 1, p. 129-143.

Mathematics

3

Atmospheric Radiation, Atmospheric Scattering, Planetary Atmospheres, Rayleigh Scattering, Cauchy Problem, Radiative Transfer, Superposition (Mathematics), Vectors (Mathematics)

Scientific paper

We consider the radiative transfer in a nonconservative homogeneous plane-parallel semiinfinite planetary atmosphere where the scattering processes are described by the Rayleigh-Cabannes phase matrix and where the primary sources are in infinitely deep layers. If we use the superposition principle we derive the Cauchy problem for the source vector. As a by-product the external field of radiation for the problem described is obtained using the principle of invariance by Chandrasekhar (1960). The respective formulas for the radiation field in the deep layers and for the extrapolation distance are given. It is shown that the Rubenson degree of polarization even in the case of near-conservative atmospheres reaches the asymptotic regime at rather small values of the optical depth. The lambda-plane reliefs of the characteristic equation, extrapolation distance, and the normalized components of the source vector at the boundary are given along with a sample of zeros of the characteristic equation.

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