Event Horizon Telescope Pattern Speeds in the Visibility Domain

The Event Horizon Telescope is preparing to produce time sequences of black hole images, or movies. In anticipation, we developed an autocorrelation technique to measure apparent rotational motion using the image-domain pattern speed $\Omega_p$. Here, we extend this technique to the visibility domain and introduce the visibility amplitude pattern speed $\Omega_{\mathrm{VA}}$. We show that in the Illinois v3 library of EHT source models, $\Omega_{\mathrm{VA}}$ depends on the source inclination, black hole mass, black hole spin, accretion state (MAD or SANE), and baseline length, and then provide approximate fits for this dependence. We show that $\Omega_{\mathrm{VA}}$ is particularly sensitive to baseline length for MAD (strongly magnetized) models, and that the slope of this dependence can be used to constrain black hole spin. As with $\Omega_p$, models predict that $\Omega_{\mathrm{VA}}$ is well below the Keplerian frequency in the emission region for all model parameters. This is consistent with the idea that $\Omega_{\mathrm{VA}}$ measures an angular phase speed for waves propagating through the emission region. Finally, we identify the information that would be provided by space-based millimeter VLBI such as the proposed BHEX mission.