The Shadow of a Spherically Accreting Black Hole

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 ${b}_{\mathrm{ph}}\equiv \sqrt{27}{r}_{g}$, 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.