Multi-Frequency Models of Black Hole Photon Rings from Low-Luminosity Accretion Disks

Images of black holes encode both astrophysical and gravitational properties. Detecting highly-lensed features in images can differentiate between these two effects. We present an accretion disk emission model coupled to the Adaptive Analytical Ray Tracing (AART) code that allows a fast parameter space exploration of black hole photon ring images produced from synchrotron emission from 10 to 670 GHz. As an application, we systematically study several disk models and compute their total flux, photon ring radii, and optical depth. The model parameters are chosen around fiducial values calibrated to general relativistic magnetohydrodynamic (GRMHD) simulations and observations of M87*. For the parameter space studied, we characterize the transition between optically thin and thick regimes and the frequency at which the first photon ring is observable. Our results highlight the need for careful definitions of photon ring radius in the image domain, as in certain models, the highly lensed photon ring is dimmer than the direct emission at certain angles. We find that at low frequencies, the ring radii are set by the electron temperature, while at higher frequencies, the magnetic field strength plays a more significant role, demonstrating how multi-frequency analysis can also be used to infer plasma parameters. Lastly, we show how our implementation can qualitatively reproduce multifrequency black hole images from GRMHD simulations when adding time-variability to our disk model through Gaussian random fields. This approach provides a new method for simulating observations from the Event Horizon Telescope (EHT) and the proposed Black Hole Explorer (BHEX) space mission.