Sobolev's Φ- Functions of Radiative Transfer in Planar and Spherical Scattering Media

Details Sobolev's Φ- Functions of Radiative Transfer in Planar and Spherical Scattering Media Sobolev's Φ- Functions of Radiative Transfer in Planar and Spherical Scattering Media

May 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974ap%26ss..28..233p&link_type=abstract

Astrophysics and Space Science, Volume 28, Issue 1, pp.233-244

Astronomy and Astrophysics

Astrophysics

2

Scientific paper

In recent years Sobolev's Φ-function of radiative transfer has been discussed in connection with the resolvent of Milne's integral equation such that it plays an important role in the determination of the radiation field in semi-infinite (or finite) atmospheres with internal sources (cf. Sobolev, 1963). In the present paper, the part of Sobolev's Φ-function in plane-parallel and spherical, isotropically scattering, atmospheres with internal source distribution is investigated from analytical and numerical aspects. With the aid of invariant imbedding (cf. Bellmanet al., 1968), we computed Sobolev's Φ-function of Milne's integral equation for the planar case by solving the Cauchy system for the auxiliary function and Chandrasekhar'sX- andY-functions. The corresponding Φ-function for the spherical case is readily obtained from the for the planar case.

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