Second-order escape probability approximations in radiative transfer

Mathematics – Probability

Scientific paper

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Line Spectra, Photons, Probability Theory, Radiative Transfer, Stellar Atmospheres, Stellar Radiation, Approximation, Escape, Optical Thickness

Scientific paper

Second-order escape probability approximations make some allowance for the transfer of radiation between the point where a photon is created and that where it escapes or is absorbed. An approximation of this kind has recently been formulated by Puetter et al. (1982) for planar atmospheres of finite thickness, in the form of a first-order differential equation relating the integrated mean intensity to the source function. Two alternative normalizations to the one proposed by these authors are given, the first of these enforces global conservation of photons in each transition, and the second gives reasonably accurate results with much less computational effort than the first. These results, along with the first-order approximation and a second-order result of Ivanov (1972), are compared with accurate numerical results for static isothermal planar atmospheres. The maximum error for the photon-conserving approximation is less than 25 percent for Doppler and 7 percent for Lorentz broadening.

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