Polarized Image of Equatorial Emission in the Kerr Geometry

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 [1], 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: ∆EVPA ∼ −2a/r 2 s , where a is the black hole spin and rs is the emission radius. We further show that spin introduces an order unity effect on face-on subimages: ∆EVPA ∼ ±a/ √ 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.

Polarized image of an equatorial emitting ring around a 4D Gauss-Bonnet black hole

“…As in refs. [24,25], we consider a thin accretion disk around a 4D Gauss-Bonnet black hole (2) and the disk is assumed to locate on the equatorial plane of the black hole. The distant observer lies in the face-on orientation with an angle θ tilted from the normal direction of the accretion disk as shown in Fig.…”

“…Following in refs. [24,25], we here assume that the fluid has only radial and tangential velocity components in the accretion disk plane, but no vertical velocity. The magnetic field is assumed to has radial, tangential and vertical components.…”

“…We here set photon energy measured by an observer at infinity is k t = −1. Thus, the corresponding orthogonal time component and orthogonal space component of photon at the location P in the the G-frame (the geodesic frame [24,25]) can be expressed as…”

“…In general, one must resort to numerical simulations to get an exact description of polarized images from emission around black holes, which is generally computationally expensive. Recently, a simple model of an equatorial ring of magnetized fluid orbiting has been used to investigate the polarized images of synchrotron emission around black holes [24,25]. It is shown that the polarization signatures of the image, including linear polarization angle, relative polarized intensity and the strokes Q − U loops, are dominated by black hole geometry together with the fluid velocity, magnetic field configuration, and observer inclination.…”

“…The paper is organized as follows: In Sec. II, we introduce briefly the 4D Gauss-Bonnet black hole [28] and reviews the calculation of the observed polarization image for the orbiting fluid model [24,25]. In Sec.…”