Spherical accretion in alternative theories of gravity

The groundbreaking image of the black hole at the center of the M87 galaxy has raised questions at the intersection of observational astronomy and black hole physics. How well can the radius of a black hole shadow can be measured, and can this measurement be used to distinguish general relativity from other theories of gravity? We explore these questions using a simple spherical flow model in general relativity, scalar Gauss--Bonnet gravity, and the Rezzolla and Zhidenko parameterized metric. We assume an optically thin plasma with power-law emissivity in radius. Along the way we present a generalized Bondi flow as well as a piecewise-analytic model for the brightness profile of a cold inflow. We use the second moment of a synthetic image as a proxy for EHT observables and compute the ratio of the second moment to the radius of the black hole shadow. We show that corrections to this ratio from modifications to general relativity are subdominant compared to corrections to the critical impact parameter, and argue that this is generally true. We find that astrophysical model parameters are the dominant source of uncertainty in this calculation, emphasizing the importance of understanding the astrophysical model. Given a sufficiently accurate astrophysical model, however, it is possible using measurements of the black hole shadow to distinguish between general relativity and other theories of gravity.