Does H$\alpha$ Stokes~$V$ profiles probe the chromospheric magnetic field? An observational perspective

We investigated the diagnostic potential of the Stokes $V$ profile of the H$\alpha$ line to probe the chromospheric line-of-sight (LOS) magnetic field ($B_{\mathrm{LOS}}$) by comparing the $B_{\mathrm{LOS}}$ inferred from the weak field approximation (WFA) with that of inferred from the multi-line inversions of the Ca II 8542 {\AA}, Si I 8536 {\AA} and Fe I 8538 {\AA} lines using the STiC inversion code. Simultaneous spectropolarimetric observations of a pore in the Ca II 8542 {\AA} and H$\alpha$ spectral lines obtained from the SPINOR at the Dunn Solar Telescope on the 4th of December, 2008 are used in this study. The WFA was applied on the Stokes $I$ and $V$ profiles of H$\alpha$ line over three wavelength ranges viz.: around line core ($\Delta\lambda=\pm0.35$ {\AA}), line wings ($\Delta\lambda=[-1.5, -0.6]$ and $[+0.6, +1.5]$ {\AA}) and full spectral range of the line ($\Delta\lambda=\pm1.5$ {\AA}) to derive the $B_{\mathrm{LOS}}$. We found the maximum $B_{\mathrm{LOS}}$ strengths of $\sim+800$ and $\sim+600$ G at $\log\tau_{\mathrm{500}}$ = $-$1 and $-$4.5, respectively in the pore. The morphological map of the $B_{\mathrm{LOS}}$ inferred from the H$\alpha$ line core is similar to the $B_{\mathrm{LOS}}$ map at $\log\tau_{\mathrm{500}}$ = $-$4.5 inferred from multi-line inversions. The $B_{\mathrm{LOS}}$ map inferred from the H$\alpha$ line wings and full spectral range have a similar morphological structure to the $B_{\mathrm{LOS}}$ map inferred at $\log\tau_{\mathrm{500}}$ = $-$1. The $B_{\mathrm{LOS}}$ estimated from H$\alpha$ using WFA is weaker by a factor of $\approx 0.53$ than that of inferred from the multi-line inversions.
Comment: Accepted to be published in the ApJ on 25th February, 2023