Polarized Image of Equatorial Emission in the Kerr Geometry

TL;DR

This paper presents a semi-analytic model for polarized images of synchrotron emission around Kerr black holes, highlighting the effects of black hole spin on observed polarization patterns and providing insights relevant to observations by EHT and GRAVITY.

Contribution

The authors extend previous models to include arbitrary observer inclination, black hole spin, and magnetic field configurations, offering an analytic approximation for spin-induced polarization effects.

Findings

Spin causes a face-on polarization rotation of approximately -2a/r_s^2.

Spin introduces an order unity effect on face-on subimages, ΔEVPA ~ ±a/√27.

The model helps interpret polarization loops during hotspot flares.

Abstract

We develop a simple toy model for polarized images of synchrotron emission from an equatorial source around a Kerr black hole by using a semi-analytic solution of the null geodesic equation and conservation of the Penrose-Walker constant. Our model is an extension of Narayan et al. (2021), 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. We find an analytic approximation, consistent with previous work, for the subleading geometric effect of spin on observed face-on polarization rotation in the direct image: $\Delta {\rm EVPA} \sim -2a/r_{\rm s}^2$, where $a$ is the black hole spin and $r_{\rm s}$ is the emission radius. We further show that spin introduces an order unity effect on face-on subimages: $\Delta {\rm EVPA} \sim \pm a/\sqrt{27}$. We also use our toy model to analyze polarization "loops" observed during flares of orbiting hotspots. Our model provides insight into polarimetric simulations and observations of black holes such as those made by the EHT and GRAVITY.