Hanle diagnostics of weak solar magnetic fields:

Inversion of scattering polarization in C₂ and MgH molecular lines

¹ Lagrange Laboratory, UMR 9273, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Campus Valrose, 06108 Nice, France
e-mail: marianne.faurobert@unice.fr
² Astronomical observatory Belgrade, Volgina 7, 11060 Belgrade, Serbia
e-mail: milic@aob.rs

Received: 1 June 2012
Accepted: 4 September 2012

Abstract

Context. The quiet Sun magnetism has been intensively investigated in recent years by various observational techniques. But several issues, such as the question of the isotropy and of the energy density spectrum of the mixed polarity turbulent magnetic fields, are still under debate.

Aims. Here we present an inversion method that allows us to constrain the depth-dependence of the magnetic field strength. We use the center-to-limb variations of linear scattering polarization measured in molecular lines of C₂ and MgH molecules with different sensitivities to the Hanle effect. We consider six C₂-triplets and one MgH line in the spectral range between 515.7 nm and 516.1 nm observed with the THEMIS Telescope.

Methods. One of the delicate problems with Hanle diagnostics is to disentangle the effects of elastic depolarizing collisions from the depolarization due to the Hanle effect of the magnetic field. By making use of the different sensitivities of the molecular lines in our spectral range to microturbulent magnetic fields and, by using a non-LTE radiative transfer modeling of the line formation, we are able to determine both the depolarizing collision cross-section and the magnetic strength. We use a standard 1D quiet Sun atmospheric model and we invert the full set of center-to-limb polarization rates measured at line centers, with a depth-dependent magnetic field described by three free parameters. The depolarizing collision cross-section is also treated as a free parameter. A downhill simplex method is used to find the best-fitting values for the collisional and magnetic strength parameters.

Results. For the elastic depolarizing collisions cross-section for the C₂ lines we obtain α⁽²⁾ = 1.6 ± 0.4 × 10^-9   cm³   s^-1, which is within an order of magnitude of the value previously obtained for MgH lines from a differential Hanle effect analysis. The observational constraints provided by the MgH and C₂ line polarization give access to the altitude range between z = 200 km and z = 400 km above the base of the photosphere. We find that the turbulent magnetic field strength decreases from 95 Gauss at the altitude z = 200 km to 5 Gauss at z = 400 km.

Conclusions. The turbulent magnetic field strength that we derive from the Hanle effect shows a strong vertical gradient in the upper photosphere. We point out that this behavior may explain why very different turbulent magnetic field strengths have been inferred from the interpretation of Hanle depolarization when using different lines formed at different altitudes. We notice that the presence of a strong depth gradient is not compatible with the assumption of isotropy of the turbulent field.