Modeling Differential Faraday Rotation in the Solar Corona

For decades, radio remote-sensing techniques have been used to probe the plasma structure of the solar corona at distances of 2 – 20R⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$20~\mathrm{R}_{\odot }$\end{document}. Measurement of Faraday rotation, the change in the polarization position angle of linearly polarized radiation as it propagates through a magnetized plasma, has proven to be one of the best methods for determining the coronal magnetic-field strength and structure. Faraday-rotation observations of spatially extended radio sources provide the unique opportunity to measure differential Faraday rotation [Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}RM] the difference in the Faraday-rotation measure between two closely spaced lines of sight (LOS) through the corona. Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}RM is proportional to the electric current within an Ampèrian loop formed, in part, by the two closely spaced LOS. We report the expected Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}RM for two sets of models for the corona: one set of models for the corona employs a spherically symmetric plasma density, while the other breaks this symmetry by assuming that the heliospheric current sheet (HCS) is a finite-width streamer-belt region containing a high-density plasma. For each plasma-density model, we evaluate the ΔRM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta \mathrm{RM}$\end{document} for three model coronal magnetic fields: a radial dipole and interplanetary magnetic field (DIMF), a dipole + current sheet (DCS), and a dipole + quadrupole + current sheet (DQCS). These models predict values of 0.01≲ΔRM≲120radm−2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0.01\lesssim \Delta \mathrm{RM}\lesssim 120~\mbox{rad}\,\mbox{m}^{-2}$\end{document} over the range of parameter space accessible by modern instruments such as the Karl G. Jansky Very Large Array. We conclude that the HCS contribution to Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}RM is not negligible at moderate heliocentric distances (<8R⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$<8~\mathrm{R}_{\odot }$\end{document}) and may account for ≲20%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lesssim 20\,\%$\end{document} of previous observations of Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Delta $\end{document}RM (e.g. made by Spangler, Astrophys. J.670, 841, 2007).