Integrals of the transfer equation. I - Quadratic integrals for monochromatic, isotropic scattering

Details Integrals of the transfer equation. I - Quadratic integrals for monochromatic, isotropic scattering Integrals of the transfer equation. I - Quadratic integrals for monochromatic, isotropic scattering

Apr 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...213..165r&link_type=abstract

Astrophysical Journal, Part 1, vol. 213, Apr. 1, 1977, p. 165-176.

Astronomy and Astrophysics

Astrophysics

18

Atmospheric Scattering, Entire Functions, Isotropic Media, Monochromatic Radiation, Radiative Transfer, Albedo, Atmospheric Radiation, Atmospheric Stratification, Boundary Value Problems, Half Spaces, Inhomogeneity, Quadratic Equations

Scientific paper

Quadratic integrals of the transfer equation are introduced for the case of monochromatic isotropic scattering in a plane-parallel atmosphere. These integrals are described as natural generalizations to all depths in the atmosphere of a certain class of results exemplified by the Hopf-Bronstein relation and the square-root law of Frisch and Frisch (1975). Two quadratic integrals (Q and R) are constructed on the basis of a fundamental equation, the Q-integral is used to derive and generalize the cited relation and law for the type of scattering considered, and the mean intensity is determined at the boundary of two half-spaces having different albedoes and source distributions. The R-integral, regarded as a generalization of the flux integral to nonconservative atmospheres, is applied to the case of an isotropic point source of radiation situated between two slabs. Some special inhomogeneous source distributions are also examined.

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