Dynamical Inference from Polarized Light Curves of Sagittarius A*

Polarimetric light curves of Sagittarius A* (Sgr A*) sometimes exhibit loops in the Stokes $Q$ and $U$ plane over time, often interpreted as orbiting hotspot motion. In this work, we apply the differential geometry of planar curves to develop a new technique for estimating polarimetric rotation rates. Applying this technique to 230 GHz light curves of Sgr A*, we find evidence of clockwise motion not only during a post-flare period on 2017 April 11th, as previously discovered, but also during the quiescent days imaged by the Event Horizon Telescope (EHT). The data exhibit a clockwise fraction of $0.65 \pm 0.09$ and an overall $Q-U$ rotation rate of $-2.6 \pm 0.6 \ \mathrm{deg}\,t_g^{-1}$. We analyze a library of General Relativistic Magnetohydrodynamic (GRMHD) simulations and find that face-on, clockwise-rotating models with strong magnetic fields are most likely to be consistent with the observations. These results are consistent with EHT and GRAVITY Collaboration studies, and indirectly support an interpretation in which the polarized image of Sgr A* has been rotated by an external Faraday screen. This technique offers a novel probe of event horizon scale dynamics that complements dynamical reconstructions.