Impact of a granular mass distribution on the orbit of S2 in the Galactic center

¹ Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 1, 85748 Garching, Germany
² Department of Physics, Sapienza, Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
³ Technion – Israel Institute of Technology Haifa, 3200003 Haifa, Israel
⁴ Astronomy Dept and Oden Institute, University of Texas at Austin, Austin, TX 78712, USA
⁵ Department of Physics, Technical University of Munich, 85748 Garching, Germany
⁶ Departments of Physics & Astronomy, Le Conte Hall, University of California, Berkeley, CA 94720, USA
⁷ Max-Planck-Institute für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁸ Centro Ricerche Enrico Fermi, Via Panisperna 89a, 00184 Rome, Italy
⁹ Istituto Nazionale Fisica Nucleare, Unitá Roma 1, Dipartimento di Fisica, Sapienza, Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
¹⁰ Istituto Nazionale di Astrofisica, Osservatorio astronomico di Roma, Monteporzio, Italy

^★ Corresponding author: mbordoni@mpe.mpg.de

Received: 21 February 2025
Accepted: 6 July 2025

Abstract

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 10σ confidence level. The amount of extended mass within its orbit has been constrained to below 1200 M_⊙, 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 performed a large set of simulations of the motion of S2 with different realizations of the cluster objects distribution. We found that granularity can induce significant deviations from the orbit in case of a smooth potential, causing a precession of the orbital plane and variations in the in-plane precession. Larger deviations were observed for higher masses of individual cluster objects and an increased total mass of the cluster. For a cluster mass of 1000 M_⊙ enclosed within the apocenter of S2, the average precession of the S2 orbital plane over a full orbit reaches up to 0.2 arcmin for 1 M_⊙ cluster objects and up to 1.5 arcmin for 100 M_⊙ objects. The in-plane precession deviates by up to 1.5 arcmin, corresponding to a fractional variation of 13%. Interactions with the cluster objects also induce a sort of Brownian motion of Sagittarius A*, with a mean displacement of up to 6 µas and velocity up to 238 m s^-1. Our mock data analysis revealed that these effects could produce observable deviations in the trajectory of S2 from a Schwarzschild orbit, especially near the apocenter. During the next apocenter passage of S2 in 2026, astrometric residuals in declination could exceed the astrometric accuracy threshold of GRAVITY (≈30 μas), as typically occurs in 35 to 60% of simulations for black holes of 20-100 M_⊙. 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 and its future upgraded version, 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.