The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits

The stars orbiting the compact radio source Sgr A* in the Galactic Centre are precision probes of the gravitational field around the closest massive black hole (candidate). In addition to adaptive optics assisted astrometry (with NACO@VLT) and spectroscopy (with SINFONI@VLT, NIRC2@Keck and GNIRS@Gemini) over almost three decades, since 2016/2017 we have obtained 50-100 μas astrometry with the four-telescope interferometric beam combiner instrument GRAVITY@VLT. In this paper we combine the astrometry and spectroscopy of four stars currently going through their pericentre passages, for a high precision determination of the gravitational potential around Sgr A*. The data are in excellent agreement with general relativity orbits around a single central point mass, M• = 4.30 × 106 M with a precision of about ±0.25%. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we improve the significance of our detection of the Schwarzschild precession in the S2 orbit to 7σ, fSP = 1.00 ± 0.14. An extended mass inside S2’s apocentre (≈ 0.23′′ or 2.4 × 10RS) must be . 3000M (1σ), or < 0.1% of M•. Adding the enclosed mass determinations from 13 stars orbiting Sgr A* at larger radii, the innermost radius at which the enclosed mass tentatively starts to exceed the mass of Sgr A* is at ≈ 2.5′′ ≥ 10 times the apocentre of S2. The excess is at a level of 0.3% of M•, or ≈ 104 M ). These limits and detections are in excellent agreement with the stellar mass distribution (including stellar mass black holes) obtained from the spatially resolved stellar luminosity function.