Investigating non-Keplerian motion in flare events with astrometric data

The GRAVITY interferometer has achieved microarcsecond precision in near-infrared interferometry, enabling the tracking of flare centroid motion in the strong gravitational field near the Sgr A*. It might be promising to serve as a unique laboratory for exploring the accretion matter near black holes or testing Einstein's gravity. Recent studies debated whether there is a non-Keplerian motion of the flares in the GRAVITY dataset. This motivates us to present a comprehensive analysis based on error estimation under the Bayesian framework. This study uses astrometric flare data to investigate the possibility that the flares exhibit deviations from the circular Keplerian motion. We analyze both averaged and individual flare data, modeling the hot spot with either circular orbits parametrized by a non-Keplerian correction or planar geodesic orbits. It is confirmed that the astrometric data favor the circular orbits over noncircular ones, with the orbital circularity parameter of $\ensuremath{\gamma}=0.9{9}_{\ensuremath{-}0.10}^{+0.07}$. Our results show that the joint posteriors for black hole mass and non-Keplerian parameter are negatively correlated. Fixing the mass to be its established value yields a non-Keplerian parameter of $\ensuremath{\omega}/{\ensuremath{\omega}}_{k}=1.4{5}_{\ensuremath{-}0.38}^{+0.35}$, at approximately the $1\ensuremath{\sigma}$ level. The statistical significance is insufficiently high, and the conclusion is found to be sensitive to the presence of correlations in the astrometric data, which might originate from the nonuniform $u\ensuremath{-}v$ coverage in interferometer measurements. In this sense, the current data might be insufficient to draw a definitive conclusion regarding the presence of non-Keplerian motion. Future improvements in astrometry precision might enable stronger constraints on the kinematical behavior of the flares.