Polarized Image Of Equatorial Emission In The Kerr Geometry

We develop a simple toy model for polarized images of synchrotron emission from an equatorial source around a Kerr black hole by using a semianalytic solution of the null geodesic equation and conservation of the Penrose-Walker constant. Our model is an extension of Narayan et al., which presented results for a Schwarzschild black hole, including a fully analytic approximation. Our model includes an arbitrary observer inclination, black hole spin, local boost, and local magnetic field configuration. We study the geometric effects of black hole spin on photon parallel transport and isolate these effects from the complicated combination of relativistic, gravitational, and electromagnetic processes in the emission region. Expanding in 1/r(s), we find an analytic approximation, consistent with previous work, for the geometric effect of spin on observed face-on polarization rotation in the direct image: Delta EVPA similar to -2a/r(s)(2), where a is the black hole spin and r(s) is the emission radius. We further show that spin introduces an order unity effect on face-on subimages: Delta EVPA similar to +/- a/root 27. We also use our toy model to analyze polarization "loops" observed during flares of orbiting hot spots. Our model provides insight into polarimetric simulations and observations of black holes such as those made by the EHT and GRAVITY.