Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...158..191f&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 158, no. 1-2, April 1986, p. 191-199.
Astronomy and Astrophysics
Astrophysics
3
Approximation, Optical Thickness, Quasars, Radiation Distribution, Resonance Lines, Lyman Alpha Radiation, Transfer Functions
Scientific paper
This paper concerns approximation procedures which can replace the full transfer equation with RII partial frequency redistribution. Existing asymptotic analyses of the formation of optically thick resonance lines in dilute media show that the interior radiation field (away from boundaries) can be approximated by the solution of a space and frequency diffusion equation and provide an expression of the emergent radiation field, away from line center, in terms of the interior solution. Here an approximation for the angle-averaged intensity, to be used at all optical depths, is constructed by adding the solution of the interior diffusion equation to the surface value of the angle-averaged intensity. The validity of this approximation is tested by comparison with the solution of the full transfer equation, in the case where the probability of collisional deexcitation and the Doppler width of the line are uniform. The diffusion equation has then an analytical solution. The tests are performed first for a two-level atom, considering a wide range of optical thicknesses and densities, and also for the Lyα line under physical conditions typical of the quasar broad emission line regions. In the latter case, the validity of a mean escape probability approximation has also been examined.
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