Abstract
An overview of Analytical Radiative Transfer (ART) theory is presented. ART problems are classified in three logical trees and briefly discussed. The classifications are based on a) physics of interaction of radiation and matter; b) methods of solution; c) geometry of the medium.
Several representative examples of nontrivial results from ART are discussed. The connection between the well-known \(\sqrt \varepsilon \) law and scaling laws for finite slabs is elucidated. Three types of asymptotic results for the two-level frequency independent source function S are illustrated: 1) In spatial asymptotic regimes, where the optical thickness T and/or the optical depth ̄ is large; 2) the asymptotic expression for nearly conservative source function (ε « 1) in terms of the conservative one (ε = 0), where ε is the photon destruction probability per scattering; 3) the contribution of high-order scatterings to S.
ART problems of scattering polarization in spectral lines are discussed under the assumption of complete frequency redistribution. The \(\sqrt \varepsilon \) law is generalized to incorporate polarization. The limiting limb polarization in the line core is expressed in terms of the components of the vector source function S(̄) for ̄ = 0. For an isothermal atmosphere the largest possible core polarization at the limb for a Doppler broadened line is found.
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Ivanov, V.V. (1991). Analytical Methods of Line Formation Theory: Are they Still Alive?. In: Crivellari, L., Hubeny, I., Hummer, D.G. (eds) Stellar Atmospheres: Beyond Classical Models. NATO ASI Series, vol 341. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3554-2_9
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