Thomson Scattering in the Lower Corona in the Presence of Sunspots

Polarized scattered light from low (few tens of megameter altitudes) coronal transients has been recently reported in Solar Dynamics Observatory/Helioseismic and Magnetic Image (HMI) observations. In a classic paper, Minnaert (1930) provided an analytic theory of polarization via electron scattering in the corona. His work assumed axisymmetric input from the photosphere with a single-parameter limb-darkening function. This diagnostic has recently been used to estimate the free-electron number and mass of HMI transients near the solar limb, but it applies equally well to any coronal material, at any height. Here we extend his work numerically to incorporate sunspots, which can strongly effect the polarization properties of the scattered light in the low corona. Sunspot effects are explored first for axisymmetric model cases, and then applied to the full description of two sunspot groups as observed by HMI. We find that (1) as previously reported by Minnaert, limb darkening has a strong influence, usually increasing the level of linear polarization tangential to the limb; (2) unsurprisingly, the effects of the sunspot generally increase at the lower scatterer altitudes, and increase the larger the sunspot is and the closer to their center the scatterer subpoint is; (3) assuming the Stokes Q > 0 basis to be tangential to the limb, sunspots typically decrease the Stokes Q/I polarization and the perceived electron densities below the spotless case, sometimes dramatically; and (4) typically, a sizeable non-zero Stokes U/I polarization component will appear when a sunspot’s influence becomes non-negligible. However, that is not true in rare cases of extreme symmetry (e.g., scattering mass at the center of an axisymmetric sunspot). The tools developed here are generally applicable to an arbitrary image input.