Transfer of Radiation in Stochastic Media
Abstract
Radiative-transfer equations are derived for a medium with small stochastically defined opacity and energy fluctuations. These equations provide relations between the correlation functions connecting these fluctuations and the induced fluctuations in the radiation field. The theory is shown to provide a description of the solar atmosphere, which has statistically defined inhomogeneities due to an underlying convection zone. A simple inhomogeneous solar model atmosphere is defined by giving the statistical distribution of energy sources in the atmosphere. The assumptions of local thermodynamic equilibrium and a depth independent gray opacity are made. It is shown how the solutions to the stochastic transfer equations in this case may be conveniently organized through the use of certain Green's functions. Useful analytic approximations for these Green's functions are obtained by use of the invariance results of Sobolev, transform techniques, and the kernel approximation. In particular, it is shown that the spatial autocorrelation function of the emergent intensity may be related to the autocorrelation function of the energy fluctuations.
- Publication:
-
SAO Special Report
- Pub Date:
- June 1965
- Bibcode:
- 1965SAOSR.180.....R