TY - JOUR

T1 - The formation of polarized lines

T2 - Allowance for the Hanle effect

AU - Grachev, S. I.

N1 - Funding Information: I am grateful to V.V. Ivanov and D .G. Sidorin for useful discussions in the course of the work. This work was supported by the Russian Foundation for Basic Research (project no. 00-02-16870a), the Council for the Support of Leading Scientific Schools (project no. 00-15-96607), and the Federal Research and Technology Program “Astronomy.” Copyright: Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2001/12

Y1 - 2001/12

N2 - The paper formulates the standard theory for the transport of polarized radiation in the presence of resonance scattering in an atmosphere with a weak magnetic field, so that the Zeeman splitting is small compared to the Doppler line width. For an atmosphere with conservative scattering, this reduces to the Milne problem, which consists of computing a polarized radiation field in a medium with sources lying in infinitely deep layers. In the approximation of complete frequency redistribution, the problem reduces to solving a Wiener-Hopf integral equation for a (6 × 6)-matrix source function. Asymptotic and numerical solutions for the standard problem are obtained, including solutions for the Milne problem, for the case of a Doppler absorption profile. The line polarization profiles for the emergent flux at various angular distances from the disk center are derived, and the dependence of the limiting degree of polarization (at the line center at the disk edge) on the direction of the magnetic field is computed. For nearly conservative scattering with photon destruction probability ∈ ≪ 1, the limiting degree of polarization varies with ∈ in accordance with a simple empirical law similar to that found earlier for a medium with zero magnetic field.

AB - The paper formulates the standard theory for the transport of polarized radiation in the presence of resonance scattering in an atmosphere with a weak magnetic field, so that the Zeeman splitting is small compared to the Doppler line width. For an atmosphere with conservative scattering, this reduces to the Milne problem, which consists of computing a polarized radiation field in a medium with sources lying in infinitely deep layers. In the approximation of complete frequency redistribution, the problem reduces to solving a Wiener-Hopf integral equation for a (6 × 6)-matrix source function. Asymptotic and numerical solutions for the standard problem are obtained, including solutions for the Milne problem, for the case of a Doppler absorption profile. The line polarization profiles for the emergent flux at various angular distances from the disk center are derived, and the dependence of the limiting degree of polarization (at the line center at the disk edge) on the direction of the magnetic field is computed. For nearly conservative scattering with photon destruction probability ∈ ≪ 1, the limiting degree of polarization varies with ∈ in accordance with a simple empirical law similar to that found earlier for a medium with zero magnetic field.

UR - http://www.scopus.com/inward/record.url?scp=0035542006&partnerID=8YFLogxK

U2 - 10.1134/1.1426126

DO - 10.1134/1.1426126

M3 - Article

AN - SCOPUS:0035542006

VL - 45

SP - 960

EP - 966

JO - Astronomy Reports

JF - Astronomy Reports

SN - 1063-7729

IS - 12

ER -