Semi-analytical Study on the Polarized Images of Black Hole due to Frame Dragging

TL;DR

This study analyzes how frame dragging affects the polarized images of black holes with retrograde accretion flows, revealing critical locations and their relations through semi-analytical methods.

Contribution

It provides a systematic investigation of the critical locations in polarized black hole images caused by frame dragging, including approximate analytic expressions for an on-axis observer.

Findings

Identified three critical locations in polarized images of black holes.

Derived approximate analytic expressions for these locations for on-axis observers.

Clarified the spatial hierarchy and discrepancies among the critical points.

Abstract

An initially retrograde accretion flow is transformed into a prograde configuration before plunging into the black hole, as a result of the frame-dragging effect induced by the black hole's rotation. The polarized image of a black hole shaped by such an accretion flow manifests three distinctive critical locations: the turning point of the flow's primary image, the polarization-flip location on the image plane, and the position of the primary image corresponding to the flow's actual turning point in spacetime. Due to the influences of gravitational lensing and gravitational Faraday rotation, these three positions generally do not coincide. In this work, we examine a thin equatorial accretion disk composed of initially retrograde, geodesically moving flows, and conduct a systematic investigation into the interrelations and discrepancies among these critical locations. We elucidate the spatial hierarchy among the three, and for an on-axis observer, we derive approximate analytic expressions characterizing their positions.