The Shadow of a Spherically Accreting Black Hole

TL;DR

This paper models the shadow of a spherical, optically thin accretion flow around a Schwarzschild black hole, showing the shadow's size is determined by spacetime geometry and independent of accretion details, relevant for black hole imaging.

Contribution

It provides a simple analytical model demonstrating the black hole shadow's size and shape are dictated by spacetime geometry, not accretion specifics, aiding interpretation of black hole images.

Findings

The shadow is always present in the model.

The shadow's outer edge is at the photon ring radius.

The shadow size is independent of the inner accretion radius.

Abstract

We explore a simple spherical model of optically thin accretion on a Schwarzschild black hole, and study the properties of the image as seen by a distant observer. We show that a dark circular region in the center --- a shadow --- is always present. The outer edge of the shadow is located at the photon ring radius $b_{\rm ph} \equiv \sqrt{27}r_g$, where $r_g=GM/c^2$ is the gravitational radius of the accreting mass $M$. The location of the shadow edge is independent of the inner radius at which the accreting gas stops radiating. The size of the observed shadow is thus a signature of the spacetime geometry and it is hardly influenced by accretion details. We briefly discuss the relevance of these results for the Event Horizon Telescope image of the supermassive black hole in M87.