Interferometric inference of black hole spin from photon ring size and brightness

The n=1 photon ring is a full image of the astrophysical source around a black hole, produced by photons that execute n1 half-orbit around the event horizon on their way to an observer. The Black Hole Explorer (BHEX) is a proposed extension of the Event Horizon Telescope to space that will target the n=1 photon rings of the supermassive black holes M87^ and Sgr\, A^. In this paper, we introduce a new interferometric observable that will be directly measurable on BHEX baselines and which admits a clear image-domain interpretation in terms of the photon ring brightness profile. Across a wide range of semi-analytic equatorial emission models, we find that the azimuthal intensity profile of the ring can change depending on the astrophysics of the source, but its width wb is weakly sensitive to these details -- much like the ring shape, which has previously been identified as a probe of the spacetime geometry. Our survey suggests that interferometric measurements of the photon ring diameter and wb can place constraints (to \!20\%) on the spin and inclination of a black hole with a known mass-to-distance ratio, such as Sgr\, A^. State-of-the-art numerical simulations support this finding, paving the way to a precise photon-ring-based spin measurement for Sgr\, A^ with BHEX.