Collisional influence on the differential Hanle effect method applied to the second solar spectrum of the A$^\mathsf{{2}}\Pi$–X$^\mathsf{{2}}\Sigma^{+}$ (0, 0) band of MgH

Abstract

Methods. This analysis is performed as follows: a) the Hanle effect Γ H parameter is derived by applying the differential Hanle effect method between the two extreme pairs of lines. Assuming no depolarizing collisions, a magnetic field strength follows, which is found to be 9.2 Gauss, in agreement with previous observations of the same kind; b) this Γ H parameter is entered in a code solving the NLTE polarized radiative transfer equations, and the other depolarizing parameter, namely the depolarizing collision rate, is then derived by adjusting the computed polarization to the observed one. Thus an average value of the rate per colliding hydrogen atom α (2) = 1.20 × 10 −9 cm 3 s −1 is obtained for the upper levels of the 12 lines (standard deviation 0.21 × 10 −9 cm 3 s −1 ). The corresponding model-dependent depolarizing rate is D (2) = (4.2 ± 0.7) × 10 7 s −1 at h = 200 km; c) this depolarizing rate is now introduced in the conversion of the Γ H parameter in terms of magnetic field strength: an average turbulent field strength of 29 ± 12 Gauss is derived as the final value, at height h = 200 ± 80 km where the polarization is formed. The Hönl-London factors of the lines under interest have been recalculated, leading to detect an error of a factor 2 in the recent literature. Results. The derived value B = 29 ± 12 Gauss at h = 200 ± 80 km is in fairly good agreement with the previous determinations based on the interpretation of the Sr i 4607 Å limb polarization, which has led to fields in the range 35−60 Gauss. Conclusions. Given the error bars, it seems unnecessary to put forward different formation regions for the Sr i and MgH lines.

Modeling scattering polarization in molecular solar lines in spherical geometry

“…This leads to 0.02 for MgH and 0.08 for C 2 in the line-forming region (h ≈ 200 km). These values are somewhat higher than what is assumed in Bommier et al (2006), but as already pointed out in her paper, as long as the value of is significantly less then unity, they will lead to approximately the same degree of linear polarization. We also show (Fig.…”

“…We therefore stick to the two-level approximation and use the intrinsic line polarizabilities given in Berdyugina et al (2002). In this two-level model, for the weak lines we consider here, the lower level population is almost not affected by radiative transitions in the line, so that LTE population of the lower level may be safely used for computing the line optical depth (see also Bommier et al 2006). …”

“…The issue of inelastic collisions rates has been previously discussed by Asensio Ramos & Trujillo Bueno (2005) and Bommier et al (2006). In order to get order-of-magnitude values for the collisional rates we use the following approach.…”

“…This polarization is due to scattering processes and is further modified by magnetic field and depolarizing collisions. It is used as a tool for magnetic field diagnostic via the Hanle effect and differential Hanle effect on lines with different magnetic sensitivity (Faurobert & Arnaud 2003;Berdyugina & Fluri 2004;Bommier et al 2006;Shapiro et al 2011). Planeparallel geometry is sufficient to model outgoing radiation for observations made on the solar disk.…”

“…Before modeling the line in spherical geometry, we therefore first use disk observations reported in the Second Solar Spectrum Atlas by Gandorfer (2000) in several MgH and C 2 lines in order to estimate these collision cross-sections. We implement the differential Hanle effect method first applied by Bommier et al (2006) to MgH lines, to derive C 2 elastic collision cross-sections. In Sect.…”