Rotation in Event Horizon Telescope Movies

The Event Horizon Telescope (EHT) has produced images of M87* and Sagittarius A*, and will soon produce time sequences of images, or movies. In anticipation of this, we describe a technique to measure the rotation rate, or pattern speed $\Omega_p$, from movies using an autocorrelation technique. We validate the technique on Gaussian random field models with a known rotation rate and apply it to a library of synthetic images of Sgr A* based on general relativistic magnetohydrodynamics simulations. We predict that EHT movies will have $\Omega_p \approx 1^\circ$ per $GMc^{-3}$, which is of order $15\%$ of the Keplerian orbital frequency in the emitting region. We can plausibly attribute the slow rotation seen in our models to the pattern speed of inward-propagating spiral shocks. We also find that $\Omega_p$ depends strongly on inclination. Application of this technique will enable us to compare future EHT movies with the clockwise rotation of Sgr A* seen in near-infrared flares by GRAVITY. Pattern speed analysis of future EHT observations of M87* and Sgr A* may also provide novel constraints on black hole inclination and spin, as well as an independent measurement of black hole mass.