Bayesian Evidence for Inspiraling Hotspot Motion in the Galactic Center

Abstract

During flaring episodes, polarimetric observations of the Galactic Center black hole Sagittarius A* (Sgr A*) reveal evolving, loop-like trajectories in the Stokes Q-U plane, the so-called Q-$U loops. Keplerian models of transiently energized orbiting features, hotspots, have been employed to reproduce these polarimetric signatures. In this work, we develop a Bayesian framework to infer the time-dependent kinematics of the hotspot from polarized light curves, using a general prescription for its motion. We model the emitting region's trajectory as a continuous, piecewise sequence of K kinematic segments, each described by radial and azimuthal velocity parameters. We perform analyses with K=1,2,3 and compare these models to millimeter-wavelength ALMA observations of Sgr A* from 2017 April 11 that include two subsequent Q-U loops, extending the observational constraints on the kinematics. We examine the effects of the local magnetic field geometry, spectral index, and kinematic profile of the hotspot's trajectory on the polarized signal. We find statistically significant evidence that the emitting region follows a non-geodesic inspiraling trajectory, and this preference over a strictly Keplerian orbit strengthens sharply when a longer data segment is modeled. The inspiraling non-Keplerian models are preferred to a purely Keplerian model based on both the Bayesian log-evidence comparison and the reduced chi-square statistic. Our results offer new insight into the nature of flaring events in the Galactic Center and the episodically produced hotspots associated with them.