Hanle effect from a dipolar magnetic structure: the case of the solar corona and the case of a star

Context. The context is the magnetic field measurement in external solar or stellar layers by interpreting line polarization measurements and the Hanle effect. Aims. The aim is to model the Hanle effect depolarization by integrating upon a star on the one hand, and by integrating along a line-of-sight through the solar corona on the other hand. Methods. The formalism of the atomic density matrix is recalled. Particular attention was devoted to the four axis rotations necessary to transform the magnetic field reference frame into that of the line-of-sight. Results. In the stellar case, the discrepancy between the results by López Ariste et al. (2011, A&A, 527, A120) and the symmetry considerations by Ignace etal. (2011, A&A, 530, A82) is resolved. In the solar case, the computations of the hydrogen Lyα polarization by Derouich et al. (2010, A&A, 511, A7) are revisited, owing to symmetry considerations. Conclusions. In the stellar case, we confirm that the effect integrated on a star leads to a non-vanishing magnetic depolarization due to the high non-linearity of the Hanle effect. In the solar case, we find that the Hanle sensitivity of hydrogen Lyβ and Lyγ could be better adapted to the measurement of the coronal background magnetic field. They form a pair of lines of different and complementary sensitivity, which makes it possible to determine the full vector. Lyα would be instead adapted to the coronal loop magnetic field measurement, because this field is stronger and suited to the Lyα Hanle sensitivity