Machine- and deep-learning-driven angular momentum inference from Black Hole Explorer observations of the n=1 photon subring

The n=1 photon ring is an important probe of black hole (BH) properties and will be resolved by the Black Hole Explorer (BHEX) for the first time. However, how BH properties modify the n=1 photon ring is poorly understood. This understanding can be achieved by exploring n=1 subring simulations, as well as by performing feature extraction on these simulations to track changes in the geometry, which presents significant computational challenges. Here, we present a framework for the study of n=1 photon ring behavior and BH property measurement from BHEX images. We use KerrBAM to generate a grid of ~10⁶ images of subrings spanning the entire space of Kerr BHs. Intensity profiles are extracted from images using a novel feature extraction method developed specifically for BHEX. This extraction method is ~3000x faster than existing EHT tools. Additionally, we propose a novel, minimal set of geometric measurables for characterizing the behavior of the n=1 subring geometry. We apply these measurables to our simulations and test spin recovery on images using: (i) gradient boosting, a machine learning algorithm; and (ii) an extension of Deep Horizon, a deep learning framework. We find >90% correct recovery of BH properties using the machine/deep learning approaches, and characterize the space of resolution-dependent geometric degeneracies. Finally, we test both approaches on GRMHD simulations of black hole accretion flows, and report excellent recovery of spin at the expected inclination of M87*.