arXiv2025
The orbit of the S2 star around Sagittarius A* provides a unique opportunity to test general relativity and study dynamical processes near a supermassive black hole. Observations have shown that the orbit of S2 is consistent with a Schwarzschild orbit at a 10$σ$ confidence level, constraining the amount of extended mass within its orbit to less than 1200 M$_\odot$, under the assumption of a smooth, spherically symmetric mass distribution. In this work we investigate the effects on the S2 orbit of granularity in the mass distribution, assuming it consists of a cluster of equal-mass objects surrounding Sagittarius A*. Using a fast dynamical approach validated by full N-body simulations, we perform a large set of simulations of the motion of S2 with different realizations of the cluster objects distribution. We find that granularity can induce significant deviations from the orbit in case of a smooth potential, causing precession of the orbital plane and a variation of the in-plane precession. Interactions with the cluster objects also induce a sort of "Brownian motion" of Sagittarius A*. Mock data analysis reveals that these effects could produce observable deviations in the trajectory of S2 from a Schwarzschild orbit, especially near apocenter. During the next apocenter passage of S2 in 2026, astrometric residuals in Declination may exceed the astrometric accuracy threshold of GRAVITY of about 30 $μas$, as it happens in 35 to 60% of simulations for black holes of 20 to 100 M$_\odot$. This presents a unique opportunity to detect, for the first time, scattering effects on the orbit of S2 caused by stellar-mass black holes, thanks to the remarkable precision achievable with GRAVITY. We also demonstrate that any attempt to constrain the extended mass enclosed within the orbit of S2 must explicitly account for granularity in the stellar-mass black hole population.