TY - JOUR

T1 - Chandrasekhar's H-function revisited

AU - Nagirner, Dmitrij I.

AU - Ivanov, Vsevolod V.

N1 - Funding Information: The authors are indebted to anonymous referee for helpful comments. DIN acknowledges support by Russian Foundation for Basic Research Grant N 18-52-52006 . Publisher Copyright: © 2020 Elsevier Ltd Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5

Y1 - 2020/5

N2 - The Chandrasekhar H-function plays an important role in a wide class of problems of analytical radiative transfer theory. The H-function is the solution of well-known integral equations, both non-linear and linear. The physics of a particular problem under consideration determines the form of the so-called characteristic and dispersion functions, Ψ(μ) and T(μ), respectively. They appear in H-equations and determine their solutions. We show that Ψ(μ) and T(μ) can be restructured in such a way that the solutions of H-equations transforms from H(μ) to Hn(μ),n=2,3,4,… provided Ψ(μ) and T(μ) are replaced with Ψn(μ) and Tn(μ). The structure of the non-linear and linear H-equations does not change under this transformation. The basis of this restructuring is a recursion relation that gives Ψn(μ) and Tn(μ) in terms of Ψ(μ) and T(μ).

AB - The Chandrasekhar H-function plays an important role in a wide class of problems of analytical radiative transfer theory. The H-function is the solution of well-known integral equations, both non-linear and linear. The physics of a particular problem under consideration determines the form of the so-called characteristic and dispersion functions, Ψ(μ) and T(μ), respectively. They appear in H-equations and determine their solutions. We show that Ψ(μ) and T(μ) can be restructured in such a way that the solutions of H-equations transforms from H(μ) to Hn(μ),n=2,3,4,… provided Ψ(μ) and T(μ) are replaced with Ψn(μ) and Tn(μ). The structure of the non-linear and linear H-equations does not change under this transformation. The basis of this restructuring is a recursion relation that gives Ψn(μ) and Tn(μ) in terms of Ψ(μ) and T(μ).

KW - Analytical theory

KW - Multiple scattering

KW - Radiative transfer

KW - SCATTERING

UR - http://www.scopus.com/inward/record.url?scp=85081022179&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/a6ce4a6d-2e31-3c98-970b-3a1534fc8f83/

U2 - 10.1016/j.jqsrt.2020.106914

DO - 10.1016/j.jqsrt.2020.106914

M3 - Article

AN - SCOPUS:85081022179

VL - 246

JO - Journal of Quantitative Spectroscopy and Radiative Transfer

JF - Journal of Quantitative Spectroscopy and Radiative Transfer

SN - 0022-4073

M1 - 106914

ER -