Orbital motion near Sagittarius A*

We report on the polarized light curves of the Galactic Center supermassive black hole Sagittarius A*, obtained at millimeter wavelength with the Atacama Large Millimeter/submillimeter Array (ALMA). The observations took place as a part of the Event Horizon Telescope campaign. We compare the observations taken during the low variability source state on 2017 Apr. 6 and 7 with those taken immediately after the X-ray flare on 2017 Apr. 11. For the latter case, we observe rotation of the electric vector position angle with a timescale of similar to 70 min. We interpret this rotation as a signature of the equatorial clockwise orbital motion of a hot spot embedded in a magnetic field dominated by a dynamically important vertical component, observed at a low inclination similar to 20 degrees. The hot spot radiates strongly polarized synchrotron emission, briefly dominating the linear polarization measured by ALMA in the unresolved source. Our simple emission model captures the overall features of the polarized light curves remarkably well. Assuming a Keplerian orbit, we find the hot spot orbital radius to be similar to 5 Schwarzschild radii. We observe hints of a positive black hole spin, that is, a prograde hot spot motion. Accounting for the rapidly varying rotation measure, we estimate the projected on-sky axis of the angular momentum of the hot spot to be similar to 60 degrees east of north, with a 180 degrees ambiguity. These results suggest that the accretion structure in Sgr A* is a magnetically arrested disk rotating clockwise.