Hall-coupling of Slow and Alfvén Waves at Low Frequencies in the Lower Solar Atmosphere

The Hall effect due to weak ionization in the lower solar atmosphere is shown to produce significant coupling between slow magneto-acoustic and Alfvén waves, especially in highly inclined magnetic fields, and even at low frequencies (≈5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\approx }\, 5$\end{document} mHz and above). Based on the exact magneto-acoustic linear wave solutions in a 2D isothermal model atmosphere, a perturbation approach is used to calculate the coupling to Alfvén waves polarized in the third dimension. First, a fast wave is injected at the bottom and is partially and often strongly reflected/converted to a down-going slow wave at the Alfvén-acoustic equipartition height, depending on magnetic field inclination, frequency, and wave number. This slow wave then couples strongly to the down-going Alfvén wave via the Hall effect for realistic Hall parameters. The coupling is strongest for horizontal wavenumbers oriented opposite to the field inclination, and magnetic fields around 100 G, for which large values of the Hall parameter are co-spatial with the region where slow and Alfvén waves have almost identical wave forms. Second, a slow wave is injected at the bottom, and found to couple even more strongly to up-going Alfvén waves in certain regions of the wavenumber–frequency plane where acoustic-gravity waves are evanescent. These results contrast with those for Hall-mediated fast-Alfvén coupling, which occurs higher in the atmosphere and is evident only at much higher frequencies.