Using Photon Ring Astrometry to Constrain Black Hole Spin and Mass

Future very long baseline interferometry (VLBI) arrays, such as the next generation Event Horizon Telescope (ngEHT) and the Black Hole Explorer (BHEX), will allow us to produce high-resolution images of the near-horizon region of supermassive black holes. A horizon-scale image of a black hole comprises a diffuse direct image of weakly lensed emission from the material near the black hole and a bright ring of strongly lensed emission that has circumnavigated the black hole, known as the photon ring. Modeling the most brightly emitting material as a thin ring in the equatorial plane, we show that comparing the sizes and positions of the direct image and the photon ring can be used to constrain the black hole's spin and mass-to-distance ratio.