Theoretical quasar emission-line ratios. VI - A probabilistic radiative transfer equation for finite slab atmospheres

Details Theoretical quasar emission-line ratios. VI - A probabilistic radiative transfer equation for finite slab atmospheres Theoretical quasar emission-line ratios. VI - A probabilistic radiative transfer equation for finite slab atmospheres

Jul 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982apj...258...46p&link_type=abstract

Astrophysical Journal, Part 1, vol. 258, July 1, 1982, p. 46-52.

Mathematics

Probability

13

Emission Spectra, Line Spectra, Probability Theory, Quasars, Radiative Transfer, Astronomical Models, Atmospheric Models, Photoabsorption, Slabs, Stochastic Processes

Scientific paper

Previous papers in this series have been based on an approximation in which the line ratios were inferred from those computed for a semi-infinite cloud model. In this paper we present a superior method, which permits the treatment of the emission-line clouds as slab atmospheres of finite thickness. In common with our previous semi-infinite approach, it is based on photon escape probabilities, yet it recognizes the important distinction between the photon escape probability and the flux divergence. This distinction is neglected in all existing models of energy balance in QSO emission-line clouds. This neglect can lead to order of magnitude errors in the cooling rates, casting doubt on the results of past models.
The present method reduces to the previous one in the semi-infinite case. It not only produces the correct source function S∞ at the surface of a semi-infinite atmosphere S∞(τ-0) = ɛ1/2B for a constant Planck function B and photon destruction probability ɛ, but it derives the empirical relationship ST(τ=0) ≍ ɛ1/2S∞(τ=T) proposed by Avrett and Hummer relating the source function at the surface of a finite slab of optical thickness T to the source function at τ = T in a semi-infinite slab. We show that the method provides a solution that departs from the exact solution by at most a few tens of percent in cases of physical interest, while retaining all the advantages of the previous method.

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