Volume 501, Number 1, July I 2009
|Page(s)||335 - 348|
|Published online||29 April 2009|
The Hanle effect in a random magnetic field
Dependence of the polarization on statistical properties of the magnetic field
Université de Nice, Observatoire de la Côte d'Azur, CNRS, Laboratoire Cassiopée, BP 4229, 06304 Nice Cedex 4, France e-mail: firstname.lastname@example.org
2 Indian Institute of Astrophysics, Koramangala, Bangalore 560 034, India
Accepted: 18 March 2009
Context. The Hanle effect is used to determine weak turbulent magnetic fields in the solar atmosphere, usually assuming that the angular distribution is isotropic, the magnetic field strength constant, and that micro-turbulence holds, i.e. that the magnetic field correlation length is much less than a photon mean free path.
Aims. To examine the sensitivity of turbulent magnetic field measurements to these assumptions, we study the dependence of Hanle effect on the magnetic field correlation length, its angular, and strength distributions.
Methods. We introduce a fairly general random magnetic field model characterized by a correlation length and a magnetic field vector distribution. Micro-turbulence is recovered when the correlation length goes to zero and macro-turbulence when it goes to infinity. Radiative transfer equations are established for the calculation of the mean Stokes parameters and they are solved numerically by a polarized approximate lambda iteration method.
Results. We show that optically thin spectral lines and optically very thick ones are insensitive to the correlation length of the magnetic field, while spectral lines with intermediate optical depths (around 10–100) show some sensitivity to this parameter. The result is interpreted in terms of the mean number of scattering events needed to create the surface polarization. It is shown that the single-scattering approximation holds good for thin and thick lines but may fail for lines with intermediate thickness. The dependence of the polarization on the magnetic field vector probability density function (PDF) is examined in the micro-turbulent limit. A few PDFs with different angular and strength distributions, but equal mean value of the magnetic field, are considered. It is found that the polarization is in general quite sensitive to the shape of the magnetic field strength PDF and somewhat to the angular distribution.
Conclusions. The mean field derived from Hanle effect analysis of polarimetric data strongly depends on the choice of the field strength distribution used in the analysis. It is shown that micro-turbulence is in general a safe approximation.
Key words: line: formation / polarization / magnetic fields / radiative transfer
© ESO, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.