Mean Escape Probabilities of Line Photons.

Abstract

view Abstract Citations (81) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Mean Escape Probabilities of Line Photons. Capriotti, Eugene R. Abstract Methods for solving the integral equation associated with the equation of radiative transfer are discussed for the cases of isotropic scattering and complete redistribution in frequency. The case of Doppler broadening is considered in detail for an infinite slab of large optical thickness and a homogeneous sphere of large optical thickness. In the first method, a minimal function is formed from the integral equation, and a variational technique is applied that yields a mean escape probability of high accuracy even when a low-order approximation is made. The second method entails the approximation of the integral equation by an nth-order differential equation where letting n = 2 usually effects a close approximation. The variational technique is also used to determine the effect caused by an albedo that differs significantly from unity. It is considered that, in the case of complete redistribution in frequency according to the Doppler mechanism in a medium of large optical thickness, photons diffuse only a short distance in space before acquiring a frequency shift large enough so that they escape the medium. Using the latter consideration, mean escape and absorption probabilities are computed for the case of a spherical gas containing impurities and for the case of a sphere expanding differentially with velocities that vary linearly with distance from the center of the sphere. Finally, a numerical method for handling the general case of incomplete redistribution in frequency, anisotropy of scattering, and a non-zero temperature gradient is considered. The differential equation of transfer is approximated by a system of linear differential equations and a solution found in terms of the matricants of the product calculus of Volterra. Publication: The Astrophysical Journal Pub Date: October 1965 DOI: 10.1086/148381 Bibcode: 1965ApJ...142.1101C full text sources ADS |