Improving constraints on the extended mass distribution in the Galactic Center with stellar orbits

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*.