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Analytical Solution of the Hanle Effect in View of CLASP and Future Polarimetric Solar Studies

National Institute for Fusion Science, Toki 509-5292, Japan
Department of Fusion Science, SOKENDAI (The Graduate University for Advanced Studies), Toki 509-5292, Japan
National Astronomical Observatory of Japan, Mitaka 181-8588, Japan
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara 252-5210, Japan
Author to whom correspondence should be addressed.
Current address: Department of Science and Technology, Kwansei Gakuin University, Sanda 669-1337, Japan.
Current address: National Astronomical Observatory of Japan, Mitaka 181-8588, Japan.
Atoms 2019, 7(2), 55;
Received: 5 March 2019 / Revised: 28 May 2019 / Accepted: 29 May 2019 / Published: 4 June 2019
(This article belongs to the Special Issue Plasma Spectroscopy in the Presence of Magnetic Fields)
PDF [1366 KB, uploaded 4 June 2019]


We have solved a problem of the Hanle effect for the hydrogen Lyman- α line in an intuitive and straightforward way. The Stokes parameters amid an anisotropic radiation field and a magnetic field are derived as an analytical formula which enables us to conduct immediate analyses of observation data taken by spectro-polarimetry. The derived formula is, in particular, supposed to be used for the analysis of the data taken by CLASP (Chromospheric Lyman-Alpha Spectro-Polarimeter), which has aimed at measuring the linear polarization in the hydrogen Lyman- α line (121.6 nm) and then evaluating the magnetic field in the upper chromosphere and the transition region. The dependence of the Stokes parameters on the strength and direction of the magnetic field and on the observation angle is derived with our analytical model. The results show a satisfactory agreement with those of a more rigorous numerical calculation where the radiative transfer is taken into account and the consistency is assured between the anisotropic randiation field and the polarized atomic state. View Full-Text
Keywords: Hanle effect; polarization spectroscopy; solar atmosphere Hanle effect; polarization spectroscopy; solar atmosphere

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Goto, M.; Ishikawa, R.; Iida, Y.; Tsuneta, S. Analytical Solution of the Hanle Effect in View of CLASP and Future Polarimetric Solar Studies. Atoms 2019, 7, 55.

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