Inferring Solar Magnetic fields From the Polarization of the Mg II h and k Lines

TL;DR

This work assesses how Mg II h and k line polarization enables diagnosing solar chromospheric magnetic fields. It synthesizes the physics behind Zeeman, Hanle, atomic polarization, J-state interference, magneto-optical effects, and partial redistribution, presenting NLTE forward modeling and 1D inversions (HanleRT-TIC) and their application to CLASP2 data. The study shows that, while weak-field approximations offer quick longitudinal-field estimates, full Stokes inversions require accounting for 3D radiative transfer and ad-hoc 3D-like contributions to capture horizontal inhomogeneities, anisotropy, and velocity gradients. The findings underscore the potential and current limitations of Mg II h/k as chromospheric magnetic diagnostics and emphasize the need for advanced 3D inversion frameworks and next-generation space missions to fully exploit these lines for solar magnetism.

Abstract

The polarization of the Mg II h and k lines holds significant diagnostic potential for measuring chromospheric magnetic fields, which are crucial for understanding the physical processes governing the energy transport and dissipation in the solar upper atmosphere, as well as the subsequent heating of the chromosphere and corona. The Chromospheric Layer Spectropolarimeter was launched twice in 2019 and 2021, successfully acquiring spectropolarimetric observations across the Mg II h and k lines. The analysis of these observations confirms the capability of these lines for inferring magnetic fields in the upper chromosphere. In this review, we briefly introduce the physical mechanisms behind the polarization of the Mg II h and k lines, including the joint action of the Zeeman and Hanle effects, the magneto-optical effect, partial frequency redistribution, and atomic level polarization. We also provide an overview of recent progress in the interpretation of the Stokes profiles of the Mg II h and k lines.

Figures (9)

• Figure 1: Left panel: Grotrian diagram of the Mg II atomic model, illustrating the transitions corresponding the Mg II h and k lines at 280.353 nm and 279.635 nm, respectively, as well as the subordinate lines at 279.160 nm, 279.875 nm, and 279.882 nm. Right panel: Intensity profiles of the Mg II h and k lines, as well as the subordinate lines observed in an active region by the IRIS satellite. The vertical dashed curves indicate the center of these lines. The subscripts 3, 2, and 1 denote the line cores, emission peaks, and near wings of the h and k lines, respectively.
• Figure 2: The two panels to the left illustrate the Zeeman splitting of the energy levels corresponding to a transition between atomic levels with $J_u=1$ and $J_l=0$. The top left panel shows the case of an evenly distributed population among the magnetic sublevels, while the bottom left panel shows an uneven distribution. The relative populations are indicated by the blue circles on the blue horizontal lines representing the magnetic sublevels. The quantization $\mathcal{Z}$--axis is taken along the magnetic field. The central and right columns show the calculated emission profiles for the Stokes $I$, $Q$, $U$, and $V$ parameters, respectively, assuming a Zeeman splitting of $\Delta\lambda_D/2$. The reference direction for positive Stokes $Q$ is defined by an azimuth $\chi$ with respect to the transverse component of the magnetic field. When $\chi= 0$, i.e. when the reference direction is parallel to the transverse component of the magnetic field, the Stokes U signal vanishes. The black solid and red dotted curves correspond to the emissivity with evenly and unevenly distributed populations, respectively. The Stokes $I$ profile in the evenly distributed population case is normalized to its integral over wavelength. In the unevenly distributed population case, the relative intensities of the $\pi$ and $\sigma$ components are adjusted according to the population ratios shown in the bottom left panel (i.e., the ratio of populations for the the magnetic sublevels M = -1, 0, and 1 is 2:1:2).
• Figure 3: Temporally and spatially averaged $Q/I$ profile at $\mu=0.1$ observed by CLASP2 (black dots), $Q/I$ profile resulting from the forward synthesis in the FAL-C semi-empirical model with a three-term Mg II atomic model in the absence of a magnetic field (red curve), and height where the optical depth at each wavelength is unity for $\mu=0.1$ (green dashed curve), corresponding to the scales on the right axis. The reference direction for positive Stokes $Q$ is the parallel to the nearest solar limb. The CLASP2 observational data are reproduced with permission from Rachmeler2022ApJ.
• Figure 4: Synthetic $Q/I$ (panel a), $U/I$ (panel b), and $V/I$ (panel c) Mg II h and k profiles in the FAL-C semi-empirical model for a los with $\mu=0.1$. The different color curves correspond to calculations with magnetic fields inclined 45$^\circ$ with respect to the local vertical toward the observer, with different strengths indicated by the color (see legend in panel a). The asymmetry in the $V/I$ profile at 279.88 nm arises because it actually consists of two blended spectral components. This figure is similiar to that in delPinoAleman2020ApJ, but with a magnetic field with a different direction and strength.
• Figure 5: $V/I$ profiles of the Mg II k (panel a) and h (panel b) lines in the FAL-C semi-empirical model for a los with $\mu=1.0$ and for a magnetic field of 100 G parallel to the los. The blue (red) curves correspond to the calculation including (neglecting) scattering polarization. This figure is similar to that in AlsinaBallester2016ApJL.