Radiative Transfer in Spherical Geometry with an Anisotropic Phase Function.

Details Radiative Transfer in Spherical Geometry with an Anisotropic Phase Function. Radiative Transfer in Spherical Geometry with an Anisotropic Phase Function.

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........23r&link_type=abstract

Thesis (PH.D.)--UNIVERSITY OF TORONTO (CANADA), 1982.Source: Dissertation Abstracts International, Volume: 43-03, Section: B, pa

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In spherical geometry the angular distribution of the intensity can become very anisotropic. This feature had been the focus of recent approximate solutions to the partial integro-differential equation of the transfer problem. We present a method of solution that treats the boundary conditions exactly and sets a standard of accuracy against which these approximations can be judged. The inward and outward intensities are represented by expansions in half-range or shifted Legendre polynomials. These provide moment theorems that close the set of equations for the half-range moments of the radiation field. This method of solution automatically allows an arbitrarily accurate description of an anisotropic phase function. In the case of strong forward peaking of the intensity the moment theorem can be modified to significantly accelerate the convergence of the solution. A Ricatti transformation makes possible a very accurate numerical integration of the moment equations. We compare these solutions to those of other methods for the Kosirev problems, the homogeneous sphere with a point source, and clouds with power-law opacities. For practical work, we have devised a very rapid solution based on a finite difference representation of the differential equations for the moments. This numerical method readily incorporates equations corresponding to other physical phenomena for a simultaneous solution. We apply our method to two problems of astronomical interest: circumstellar envelopes and interstellar clouds. The source of opacity is dust; the coherent scattering and temperature-independent opacity are convenient simplifications that leave unmasked the anisotropic phase function. We calculate the temperature distribution of the dust, the flux spectrum, extinction curve, visibility function, and surface brightness profile for a hypothetical envelope and cloud.

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