Mathematics – Probability
Scientific paper
Dec 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975azh....52.1252i&link_type=abstract
Astronomicheskii Zhurnal, vol. 52, Nov.-Dec. 1975, p. 1252-1262. In Russian.
Mathematics
Probability
Nongray Atmospheres, Radiative Transfer, Stellar Atmospheres, Thermodynamic Equilibrium, Absorptivity, Atmospheric Models, Atmospheric Temperature, Integral Equations, Linear Equations, Milne Method
Scientific paper
Radiative equilibrium of an atmosphere in which the departures from greyness are small-scale in frequency, although they may be arbitrarily strong is considered. It is shown that one may use a statistical approach to describe the small-scale dependence of the intensity on frequency, retaining at the same time all the information on large-scale variations of the intensity with frequency. This description is based on the use of a new concept introduced in the paper, namely, partial intensity of radiation. It is assumed that the opacity probability distribution function does not vary along the spectrum and is depth-independent. Under these assumptions the temperature profile is shown to satisfy a homogeneous integral equation with a symmetrical displacement kernel. This equation is a generalization of the Milne equation.
Ivanov Valentin
Kheinlo A. G.
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