Photon Ring Astrometry. I. A Simple Spin Measurement Technique for High-resolution Images of M87*

Abstract The supermassive black hole M87* is a target for future horizon-scale imaging that will resolve the first lensed ( n = 1) subimage of the photon ring. In this work, we identify a concrete observable—the displacement between the centers of the n = 1 photon ring subimage and the direct image. Assuming that the observed large-scale jet of M87 is aligned with the black hole spin axis, we separate the relative position of the photon ring into components parallel and transverse to the projected spin axis. We show that the parallel shift is primarily determined by inclination and emission radius, while the transverse shift is tightly correlated with inclination and spin. We demonstrate these effects both in a simple geometric model (to explain the underlying physics) and in general-relativistic magnetohydrodynamics simulations with magnetically arrested disks (to provide realistic instantiations). We find that a relative astrometric resolution of ≲ 0.1 μ as, achievable by the proposed Black Hole Explorer mission, is sufficient to constrain the spin to better than 9% if the accretion flow is prograde, 25% if the flow is retrograde, or 24% if the direction of the flow is undetermined. More generally, this identifies photon ring astrometry as a promising method to constrain the underlying spacetime geometry without relying on geometric modeling of the observed emission.