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. In addition to adaptive optics assisted astrometry (with NACO / VLT) and
spectroscopy (with SINFONI / VLT, NIRC2 / Keck and GNIRS / Gemini) over three
decades, since 2016/2017 we have obtained 30-100 mu-as astrometry with the
four-telescope interferometric beam combiner GRAVITY / VLTI reaching a
sensitivity of mK = 20 when combining data from one night. We present the
simultaneous detection of several stars within the diffraction limit of a
single telescope, illustrating the power of interferometry. The new data for
the stars S2, S29, S38 and S55 yield significant accelerations between March
and July 2021, as these stars pass the pericenters of their orbits between 2018
and 2023. This allows for a high-precision determination of the gravitational
potential around Sgr A*. Our data are in excellent agreement with general
relativity orbits around a single central point mass, M = 4.30 x 10^6 M_sun
with a precision of about +-0.25%. We improve the significance of our detection
of the Schwarzschild precession in the S2 orbit to 7 sigma. Assuming plausible
density profiles, an extended mass component inside S2's apocentre (= 0.23" or
2.4 x 10^4 R_S) must be 3000 M_sun (1 sigma), 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 excess mass beyond Sgr A* tentatively is seen is
r = 2.5" >= 10x the apocentre of S2. This is in full harmony with the stellar
mass distribution (including stellar-mass black holes) obtained from the
spatially resolved luminosity function.
