Magnetic Field Measurements in the Solar Chromosphere Using the H$_β$ 4861Å~Line I: Forward Modeling Based on 1D Models

Abstract

The chromosphere is a complex solar atmosphere that hosts a variety of transients and transports significant free energy to heat the corona. However, due to the limited sensitivity of polarization measurement and the influence of spectral line broadening, the basic magnetic field configuration in the chromosphere has not yet been fully revealed to correspond to the observed phenomena. In this work, we investigated the validity and application of the magnetic field inversion method for the H$_β$~4861~Å spectral line with non-local thermodynamic equilibrium approximations. We generated synthetic spectra by incorporating magnetic fields into semi-empirical FAL models for quiet Sun and sunspots, and then performed inversions to obtain the magnetic fields, which were then compared with the magnetic fields in the models. In addition, we evaluated the accuracy of the magnetic fields obtained using the weak field approximations and the impact of using the WFA results as the initial guess model for non-LTE inversion on the final results. Our work validates the effectiveness of the inversion method for the measurement of line-of-sight magnetic field components, which significantly improved the accuracy in both weak field (0 -- 500~G) and strong field ($>$2000~G) regions, while maintaining accuracy in the intermediate field range of 500 -- 2000~G. This demonstrates that the inversion techniques we employed are capable of resolving Zeeman-sensitive spectral lines in the chromosphere, which can be applied to the H$_β$ observational data from the new generation Solar Full-disk Multi-layer Magnetograph at GanYu Solar Station to provide full disk chromospheric magnetic field information.

Figures (10)

• Figure 1: Contribution function (CF) of Stokes I (red curve) of synthetic in H$_\beta$ 4861.3 Å for FAL-C model atmosphere at wavelength $\Delta \lambda$ = [0, 3.6] Å from H$_\beta$ line center. The blue curve indicates optical depth $\mathrm{log}~\tau_{~500nm}$ = 1 in H$_\beta$ line.
• Figure 2: Grotrian diagram of hydrogen Balmer series including first two ordered lines. The blue lines indicate 7 allowed E1 transitions correspond to H$_\beta$. The y axis indicates relative level energies (term value in eV) of each state.
• Figure 3: Synthetic Stokes profiles with different magnetic field strengths. Panel (a) shows Stokes I profiles (yellow) in the range from 100 -- 4000 G and the fitting curves (blue dashed) with Voigt profile. Panel (b) shows Stokes V/I$\mathrm{_c}$, with green dots (as well as gray span in (a) and (b)) indicating wavelength range of [$-$0.26, 0.26] Å used for the inference of chromospheric magnetic fields using the WFA.
• Figure 4: Response function maps of Stokes profiles to the change of temperature and magnetic field strength. (a) and (b) show response functions of Stokes I to T and B, respectively, along optical depth. (c) and (d) show response functions of Stokes Q and V to B, respectively. The maps are scaled to arbitrary unit for RF to temperature and magnetic field, separately . The dashed horizontal lines indicates optical depths $\mathrm{log}~\tau_{~500nm}$= [0, $-$7] with even interval $\Delta$$\mathrm{log}~\tau_{~500nm}$= $-$1.0.
• Figure 5: Magnetic field retrieved with WFA in the chromosphere at $\mathrm{log}~\tau_{~500nm}$= $-$5.0. Inferred LOS components, transverse components, and calculated total field are plotted as a function of the model field strength in panel (a), (b), and (c), respectively. The inset in the lower right shows inferred fields in the weak field range [0, 400] G using the same color scheme. The black dashed line indicates linear correlation expectation of 1.0 between inferred total (vertical/transverse) field with model field strengths.