Modeling Differential Faraday Rotation in the Solar Corona

Abstract

For decades, radio remote-sensing techniques have been used to probe the plasma structure of the solar corona at distances of 2 – $20~\mathrm{R}_{\odot }$ . 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 [ $\Delta $ RM] the difference in the Faraday-rotation measure between two closely spaced lines of sight (LOS) through the corona. $\Delta $ RM is proportional to the electric current within an Amperian loop formed, in part, by the two closely spaced LOS. We report the expected $\Delta $ 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 $\Delta \mathrm{RM}$ 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 $0.01\lesssim \Delta \mathrm{RM}\lesssim 120~\mbox{rad}\,\mbox{m}^{-2}$ 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 $\Delta $ RM is not negligible at moderate heliocentric distances ( $<8~\mathrm{R}_{\odot }$ ) and may account for $\lesssim 20\,\%$ of previous observations of $\Delta $ RM (e.g. made by Spangler, Astrophys. J. 670, 841, 2007).