Influence of the Atmospheric Model on Hanle Diagnostics

We clarify the uncertainty in the inferred magnetic field vector via the Hanle diagnostics of the hydrogen Lyman-α$\upalpha$ line when the stratification of the underlying atmosphere is unknown. We calculate the anisotropy of the radiation field with plane-parallel semi-empirical models under the nonlocal thermal equilibrium condition and derive linear polarization signals for all possible parameters of magnetic field vectors based on an analytical solution of the atomic polarization and Hanle effect. We find that the semi-empirical models of the inter-network region (FAL-A) and network region (FAL-F) show similar degrees of anisotropy in the radiation field, and this similarity results in an acceptable inversion error (e.g., ∼40G${\sim}\, 40~\mbox{G}$ instead of 50 G in field strength and ∼100∘${\sim}\,100^{\circ}$ instead of 90∘$90^{\circ}$ in inclination) when FAL-A and FAL-F are swapped. However, the semi-empirical models of FAL-C (averaged quiet-Sun model including both inter-network and network regions) and FAL-P (plage regions) yield an atomic polarization that deviates from all other models, which makes it difficult to precisely determine the magnetic field vector if the correct atmospheric model is not known (e.g., the inversion error is much larger than 40% of the field strength; >70G${>}\,70~\mbox{G}$ instead of 50G$50~\mbox{G}$). These results clearly demonstrate that the choice of model atmosphere is important for Hanle diagnostics. As is well known, one way to constrain the average atmospheric stratification is to measure the center-to-limb variation of the linear polarization signals. The dependence of the center-to-limb variations on the atmospheric model is also presented in this paper.