Radiative Transfer in a Sphere Illuminated by a Parallel Beam: an Integral Equation Approach
Abstract
The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. The analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the interconnection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems as provided.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1986
 DOI:
 10.1086/163923
 Bibcode:
 1986ApJ...301..554S
 Keywords:

 Atmospheric Scattering;
 Planetary Atmospheres;
 Radiative Transfer;
 Albedo;
 Computational Astrophysics;
 Extinction;
 Integral Equations;
 Variational Principles;
 Lunar and Planetary Exploration;
 PLANETS: ATMOSPHERES;
 RADIATIVE TRANSFER