Probing a Lorentz-violating parameter from orbital precession of the S2 star around the galactic centre supermassive black hole

TL;DR

This work tests Lorentz symmetry in the strong-gravity regime by constraining the Lorentz-violating parameter $\ell$ in a Schwarzschild-like black hole of bumblebee gravity using the S2 star orbit around Sgr A*. The authors derive the leading-order pericentre precession in the modified metric, develop a forward model for S2’s astrometric and spectroscopic signals, and perform a 14-dimensional Markov Chain Monte Carlo analysis with two priors to jointly fit the data. They obtain constraints $\ell = -8.01\times 10^{-5}{}^{+2.11\times10^{-4}}_{-2.09\times10^{-4}}$ (uniform) and $\ell = -1.00\times 10^{-5}{}^{+2.11\times10^{-4}}_{-2.09\times10^{-4}}$ (Gaussian) at 1$\sigma$, both consistent with GR and about three orders tighter than analogous EHT bounds for the SMBH-scale model. The results demonstrate that Galactic Center stellar dynamics provide a powerful, independent probe of Lorentz-violating gravity in the strong-field regime and chart a path for substantial improvements with future high-precision astrometric/spectroscopic data.

Abstract

Testing Lorentz symmetry in strong gravitational fields provides a promising probe of extensions to general relativity. The supermassive black hole Sgr~A* and the orbit of the S-stars offer a laboratory for such tests in a regime beyond weak field limit. We analyze the S2 orbital data focusing on the Schwarzschild-like black hole within bumblebee gravity, where deviations from general relativity are encoded in a single Lorentz-violating parameter $\ell$. Using a full 14-dimensional Markov Chain Monte Carlo analysis under uniform and Gaussian priors, we obtain $\ell = {-8.01 \times 10^{-5}}^{+2.77 \times 10^{-4}}_{-2.09 \times 10^{-4}} $ and $\ell = {1.00 \times 10^{-5}}^{+2.90 \times 10^{-4}}_{-2.91 \times 10^{-4}} $ at $1σ$ confidence level, respectively. These constraints are about three orders of magnitude tighter than those from Event Horizon Telescope imaging of Sgr~A*.

Figures (5)

• Figure 1: This figure shows the orbit of the S-star and its orbital elements. The solid ellipse represents the trajectory of the S-star, where $a$ is the semi-major axis, $e$ is the eccentricity, $\psi$ is the eccentric anomaly, $\phi$ is the true anomaly, and $r$ is the distance between the S-star and the SMBH Sgr A*.
• Figure 2: Left: The theoretically calculated orbit and the observational data points of astrometric positions of the S2 star. The black dashed curve shows the orbit predicted in the Schwarzschild black hole. The orange solid curve corresponds to the prediction obtained in the Schwarzschild-like black hole. The green circulars represent the observed astrometric positions. Sgr A* is located at the coordinate origin. Right: The variation of the radial velocity of the S2 star over time. The black dashed curve represents the prediction of the Schwarzschild black hole while the solid orange curve shows the result obtained from the Schwarzschild-like case. The red squares represent the observed radial velocities.
• Figure 3: The relationship between the orbital plane of the S-star and the observer's plane, along with the relevant Keplerian orbital elements. Here, the $Z$-axis coincides with the observer's line of sight, $\Omega$ is the longitude of ascending node, $\omega$ is the argument of pericentre (i.e., the angle from the ascending node to the pericentre measured in the orbital plane), the pentagram is the position of the S-star, and $\iota$ (the inclination) is the angle between the observer's plane and the orbital plane.
• Figure 4: The posterior distributions of the 14 parameters under uniform priors listed in Table \ref{['tab:table01']}. The dashed lines mark values of the best fit and $1\sigma$ confidence levels, which are also collected in Table \ref{['tab:table02']}.
• Figure 5: The posterior distributions of 14 parameters under Gaussian priors listed in Table \ref{['tab:table01']}. The dashed lines mark values of the best fit and $1\sigma$ confidence levels, which are also collected in Table \ref{['tab:table02']}.