Polarimetry and astrometry of flares as dynamical probes for the mass of Sgr A*

Orbiting hot gas around the supermassive black hole Sgr A* in the Galactic Center is an excellent probe for the mass of the black hole and the physics in its environment. Using the GRAVITY interferometer at the VLTI, the positional change of Sgr A*'s near-infrared emission during bright states, called flares, can be measured with unique precision. Since 2018, we have observed 4 astrometric and 6 polarimetric flares, two of them are well-covered in both domains. All astrometric flares show clockwise motion on the sky with a period of around an hour, and we observe one polarization loop per astrometric loop. Due to the striking similarities between the flares, we combine them and present a common fit, taking into account the absence of strong Doppler boosting peaks in the light curves and the EHT-measured geometry. We find a flare radius of around 9 gravitational radii, and our results are consistent with Keplerian orbital motion of hot spots close to the ISCO in a predominantly poloidal (vertical) magnetic field configuration. Further, the average flare motion allows us to constrain the inclination and angular momentum vector direction. We show that the accretion flow geometry is consistent with the angular momentum of the inner clockwise disk of young stars and that the mass of Sgr A* of 4 million solar masses is within a small radius.