Ring Position Angles and Spin in M87* and Sgr A*

Event Horizon Telescope (EHT) images of black holes appear as rings with a brightness asymmetry. Here, we expand on our previous study of the asymmetry magnitude \(a_1\) to study the position angle of the peak brightness asymmetry \(\mathrm{PA}_1\) in general relativistic magnetohydrodynamic (GRMHD) models. For larger spin magnitudes (\(a_{*}>0\) and \(a_{*}\lesssim-0.5\)), the mean \(\mathrm{PA}_1\) falls within \(1σ\) of the approaching limb of the black hole, regardless of viewing inclination, disk magnetization, or source. By comparing the \((a_1, \mathrm{PA}_1)\) distribution in M87* observations with models, we demonstrate that we can mildly disfavor low-magnitude spins and strongly disfavor all spin vectors that point toward Earth. The alignment of \(\mathrm{PA}_1\) relative to the large-scale jet axis may suggest that M87*'s disk does not have a large tilt. By combining \(\mathrm{PA}_1\) with the pattern speed measured in optimistic 2026 M87* video conditions, the EHT can constrain whether M87* is prograde or retrograde with \(\sim 84\%\) accuracy. In Sgr A*, we show that a detection of \((a_1, \mathrm{PA}_1)\) could constrain the magnitude and direction of the galactic center spin vector. Finally, if future EHT expansions increase the sample of horizon-scale sources, a simple set of observables (ring diameter, asymmetry magnitude, and asymmetry angle) could enable robust constraints on black hole mass, spin, and inclination.