TY - JOUR

T1 - Asymptotic theory of the transfer of polarized radiation with resonance scattering in the doppler core of the line

AU - Grachev, S. I.

N1 - Funding Information: This work was supported by grant P39300 from the Russian Fund for Fundamental Research (RFFR) and the International Science Fund, as well as RFFR grant 96-15-96622 (Program for the Support of Leading Scientific Schools). Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - In the first of the series of papers by Ivanov et al. it was shown that the model problem of the transfer of polarized radiation as a result of resonance scattering from two-level atoms in a homogeneous plane atmosphere in the absence of LTE comes down, in the approximation of complete frequency redistribution, to the solution of an integral matrix equation of the Wiener-Hopf type for a (2 × 2) matrix source function S(τ). In the second paper in this series, devoted to the vector Milne problem, complete asymptotic expansions of the matrix I(z) [which is essentially a Laplace transform of the matrix S(τ)] for the case of a Doppler profile of the coefficient of absorption, and the coefficients of asymptotic expansions of S(τ) (τ ≫ 1) are expressed in terms of coefficients of the expansions of I(z). We show that asymptotic expansions of S(τ) can be found directly from an integral matrix equation of the Wiener-Hopf type for S(τ). We give new recursive equations for the coefficients of these expansions, as well as a new derivation of asymptotic expansions of the matrix I, including its second column, which was considered only briefly by Ivanov et al.

AB - In the first of the series of papers by Ivanov et al. it was shown that the model problem of the transfer of polarized radiation as a result of resonance scattering from two-level atoms in a homogeneous plane atmosphere in the absence of LTE comes down, in the approximation of complete frequency redistribution, to the solution of an integral matrix equation of the Wiener-Hopf type for a (2 × 2) matrix source function S(τ). In the second paper in this series, devoted to the vector Milne problem, complete asymptotic expansions of the matrix I(z) [which is essentially a Laplace transform of the matrix S(τ)] for the case of a Doppler profile of the coefficient of absorption, and the coefficients of asymptotic expansions of S(τ) (τ ≫ 1) are expressed in terms of coefficients of the expansions of I(z). We show that asymptotic expansions of S(τ) can be found directly from an integral matrix equation of the Wiener-Hopf type for S(τ). We give new recursive equations for the coefficients of these expansions, as well as a new derivation of asymptotic expansions of the matrix I, including its second column, which was considered only briefly by Ivanov et al.

UR - http://www.scopus.com/inward/record.url?scp=52849138838&partnerID=8YFLogxK

U2 - 10.1007/BF02683950

DO - 10.1007/BF02683950

M3 - Article

AN - SCOPUS:52849138838

VL - 43

SP - 70

EP - 86

JO - Astrophysics

JF - Astrophysics

SN - 0571-7256

IS - 1

ER -