Constraining ultralight bosonic dark matter with Keck observations of
  S2's orbit and kinematics
  Ultralight scalar dark matter is expected to be able to form a cloud
surrounding the supermassive black hole (SMBH) in the Galactic center. With
increasing precision of the observations of the stellar kinematics around the
SMBH, tiny effects from such a dark matter cloud, including its gravitational
perturbation and the direct coupling with ordinary matter may be detectable. In
this work, we search for possible evidence of the scalar cloud using accurate
orbital measurements of the S2 star around Sgr A*. We solve the first order
Post-Newtonian equation, considering simultaneously the extended mass
distribution of the scalar cloud and the additional coupling via Higgs-portal
or photon-portal interaction. We find that the astrometric and spectroscopic
data of the S2 star are well consistent with the scenario of point-like mass of
Sgr A*. We thus derive upper limits of the extended mass and the coupling of
the new interaction. The limits of the Higgs coupling and extended mass of the
scalar cloud are the most stringent ones for the scalar mass window between
$3.2\times 10^{-19}$ eV and $1.6\times 10^{-18}$ eV.
