Exploring the role of accretion disk geometry in shaping black hole shadows

TL;DR

This paper investigates how the geometry and optical properties of accretion disks influence the appearance of black hole shadows, providing a unified framework for interpreting high-resolution black hole images.

Contribution

It introduces a novel method to analyze black hole images by decomposing accretion disks into luminous segments, linking disk geometry with observable image features across different optical regimes.

Findings

Lensing ring broadens with increased disk thickness in optically thin flows.

Photon ring position remains robust as the innermost edge of the lensing structure.

Critical absorption coefficient determines the transition from optically thin to thick appearance.

Abstract

We study black hole imaging in the context of geometrically thick accretion disks in Schwarzschild spacetime. By decomposing the emitting region into a set of one-dimensional luminous segments, each characterized by its inclination angle and inner radius, we construct transfer functions that capture key image features-namely, the direct image, lensing ring, and photon ring. This approach allows a unified treatment of disk geometry and viewing angle. We explore three regimes: optically thin, optically thick, and partially optically thick disks. For optically thin flows, increasing the disk thickness (characterized by the half-opening angle $\psi_0$) broadens the lensing ring, gradually bridging the photon ring and the direct image. The photon ring remains narrow, but its position robustly defines the innermost edge of the lensing structure. In the optically thick case, image features are primarily determined by the first intersection of traced light rays with the disk, and we provide analytical criteria for the presence of lensing and photon rings based on the critical deflection angles. For partially optically thick disks, we adopt a simplified radiative transport model and find a critical absorption coefficient $\chi \sim (6M\psi_0)^{-1}$ beyond which the image rapidly transitions from an optically thin- to thick-disk appearance. These results help clarify the respective roles of the photon and lensing rings across different disk configurations, and may offer a useful framework for interpreting future high-resolution black hole observations.