Images and photon ring signatures of thick disks around black holes

Context. High-frequency very-long-baseline interferometry (VLBI) observations can now resolve the event-horizon-scale emission from sources in the immediate vicinity of nearby supermassive black holes. Future space-VLBI observations will access highly lensed features of black hole images – photon rings – that will provide particularly sharp probes of strong-field gravity. Aims. Focusing on the particular case of the supermassive black hole M 87*, our goal is to explore a wide variety of accretion flows onto a Kerr black hole and to understand their corresponding images and visibilities. We are particularly interested in the visibility on baselines to space, which encodes the photon ring shape and whose measurement could provide a stringent test of the Kerr hypothesis. Methods. We developed a fully analytical model of stationary, axisymmetric accretion flows with a variable disk thickness and a matter four-velocity that can smoothly interpolate between purely azimuthal rotation and purely radial infall. To determine the observational appearance of such flows, we numerically integrated the general-relativistic radiative transfer equation in the Kerr spacetime, taking care to include the effects of thermal synchrotron emission and absorption. We then Fourier transformed the resulting images and analyzed their visibility amplitudes along the directions parallel and orthogonal to the black hole spin projected on the observer sky. Results. Our images generically display a wedding cake structure composed of discrete, narrow photon rings (n = 1, 2, …) stacked on top of broader primary emission that surrounds a central brightness depression of model-dependent size. At 230 GHz, the n = 1 ring is always visible, but the n = 2 ring is sometimes suppressed due to absorption. At 345 GHz, the medium is optically thinner and the n = 2 ring displays clear signatures in both the image and visibility domains. We also examine the thermal synchrotron emissivity in the equatorial plane and show that it exhibits an exponential dependence on the radius for the preferred M 87* parameters. Conclusions. The black hole shadow is a model-dependent phenomenon – even for diffuse, optically thin sources – and should not be regarded as a generic prediction of general relativity. Observations at 345 GHz are promising for future space-VLBI measurements of the photon ring shape, since at this frequency the signal of the n = 2 ring persists despite the disk thickness and nonzero absorption featured in our models. Future work is needed to investigate whether this conclusion holds in a larger variety of reasonable models