The H$\alpha$ line as a probe of chromospheric magnetic fields

We explore the diagnostic potential of the H$\alpha$ line for probing the chromospheric magnetic field using a realistic 3D radiative magnetohydrodynamic (rMHD) model. The Stokes profiles of the H$\alpha$ line are synthesized through full 3D radiative transfer under the field-free approximation, alongside the Ca II 8542 {\AA} and Fe I 6173 {\AA} lines for comparison. The line-of-sight (LOS) magnetic fields are inferred using the weak field approximation (WFA) for theH$\alpha$ and Ca II 8542 {\AA} lines, while the Fe I 6173 {\AA} line is analyzed through Milne-Eddington inversion techniques. The comparison between the inferred LOS magnetic field maps and the magnetic fields in the rMHD model revealed that the H$\alpha$ line core primarily probes the chromospheric magnetic field at log tau_500 = -5.7, which corresponds to higher layers than the Ca II 8542 {\AA} line core, which is most sensitive to conditions at log tau_500 = -5.1. On average, the Stokes V profiles of the H$\alpha$ line core form 500 km higher than those of the Ca II 8542 {\AA} line core. The H$\alpha$ polarization signals persist after adding noise, and with noise at the level of 10^-3 Ic, most simulated magnetic structures remain visible. These findings suggest that spectropolarimetric observations of the H$\alpha$ line can provide complementary insights into the stratification of the magnetic field at higher altitudes, especially when recorded simultaneously with widely used chromospheric diagnostics such as the Ca II 8542 {\AA} line.