Investigating non-Keplerian motion in flare events with astrometric data

TL;DR

This work probes whether flares near Sgr A* exhibit non-Keplerian motion by performing Bayesian analyses of GRAVITY astrometric data under circular Keplerian and non-Keplerian hotspot scenarios, including planar geodesics, in Schwarzschild spacetime. It employs ray-traced centroids and EMCEE-based MCMC to compare averaged and individual flare data, estimating parameters such as the non-Keplerian ratio $\omega/\omega_K$ and a circularity metric $\gamma$. The main finding is that the data favor near-circular motion, with only marginal hints of super-Keplerian motion when the mass is fixed, and no robust evidence for non-Keplerian dynamics; importantly, inferred constraints are sensitive to correlations in the astrometric measurements. The study highlights that current precision and sampling limit definitive conclusions and emphasizes the need for improved astrometry to tightly constrain flare kinematics in the strong-field regime of Sgr A*.

Abstract

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 hotspot with either circular orbits parameterized by a non-Keplerian correction or planar geodesic orbits. It is confirmed that the astrometric data favor the circular orbits over non-circular ones, with the orbital circularity parameter of $γ= 0.99_{-0.10}^{+0.07}$. 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 $ω/ω_k = 1.45^{+0.35}_{-0.38}$, at approximately the 1$σ$ 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 non-uniform $u$-$v$ 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.

Figures (10)

• Figure 1: Schematic diagram for illustrating the parameters of hotspots in circular orbits (left panel) and planar geodesic orbits (right panel). The position $(r_0,\phi_0)$ is the initial position for the circular orbits, and is the innermost point for the planar geodesic orbits. The $\Delta T$ formulates the relative distance to the innermost point. The dashed circles represent the boundary of the positions in $(r,\phi)$ that we studied.
• Figure 2: Bottom-left panel: the posteriors of model parameters obtained from MCMC sampling for the circular orbit model in the equatorial plane. The red cross marks the globally best-fit parameters. Top-right panel: observed flare centroids (gray points) and the best-fit track (blue points) of a circularly orbiting hotspot in the equatorial plane. We have $\chi^2_\text{eff}=0.18$ for the best-fit parameters.
• Figure 3: Bottom-left panel: the posteriors of model parameters obtained from MCMC sampling for the circular orbit model. The red cross marks the globally best-fit parameters. Top-right panel: observed flare centroids (gray points) and the best-fit track (blue points) of a circularly orbiting hotspot in the equatorial plane. Here, the black hole mass $M$ is fixed at $4.3 \times 10^6 M_\odot$GRAVITY:2021xju. We have $\chi^2_\text{eff}=0.29$ for the best-fit parameters.
• Figure 4: Bottom-left panel: the posteriors of model parameters obtained from MCMC sampling for the circular orbit model. The red cross marks the globally best-fit parameters. Top-right panel: observed flare centroids (gray points) and the best-fit track (blue points) of a circularly orbiting hotspot. We use the Gaussian priors on the black hole mass $M=(4.297 \pm 0.012) \times 10^6M_\odot$ and distance $D=(8.277 \pm 0.009) \text{kpc}$ reported in Ref. GRAVITY:2021xju. The prior widths are set to $10\sigma$. We have $\chi^2_\text{eff}=0.35$ for the best-fit parameters.
• Figure 5: Bottom-left panels of (a)-(d): posteriors for the four individual flare events. The red cross marks the globally best-fit parameters. Top-right panels of (a)-(d): corresponding astrometry (gray points with error bars) and best-fit tracks (blue points) of a circularly orbiting hotspot for four individual flare events. Each panel corresponds to a flare event reported by the GRAVITY Collaboration. From panels (a) to (d), the corresponding values of $\chi^2_\text{eff}$ are 1.32, 0.90, 3.61 and 0.69, respectively.