Hot-spots around Sagittarius A*: Joint fits to astrometry and polarimetry

Observations of Sagittarius A* (Sgr A*) in near-infrared (NIR) show irregular flaring activity. Flares coincide with astrometric rotation of brightness centroid and with looping patterns in fractional linear polarization. These signatures can be explained with a model of a bright hot-spot, transiently orbiting the black hole. We extend the capabilities of the existing algorithms to perform parameter estimation and model comparison in the Bayesian framework using NIR observations from the GRAVITY instrument, and simultaneously fitting to the astrometric and polarimetric data. Using the numerical radiative transfer code ipole, we defined several geometric models describing a hot-spot orbiting Sgr A*, threaded with magnetic field, and emitting synchrotron radiation. We then explored the posterior space of our models in the Bayesian framework with a nested sampling code dynesty. We have used 11 models to sharpen our understanding of the importance of various aspects of the orbital model, such as non-Keplerian motion, hot-spot size, and off-equatorial orbit. All considered models converge to realizations that fit the data well, but the equatorial super-Keplerian model is favored by the currently available NIR dataset. We have inferred an inclination of ~ 155 deg, which corroborates previous estimates, a preferred period of ~ 70 minutes, and an orbital radius of ~ 12 gravitational radii with the orbital velocity of ~ 1.3 times the Keplerian value. A hot-spot of a diameter smaller than 5 gravitational radii is favored. Black hole spin is not constrained well.