  Dark matter is undoubtedly one of the fundamental, albeit unknown, components
of the standard cosmological model. The failure to detect WIMPs, the most
promising candidate particle for cold dark matter, actually opens the way for
the exploration of viable alternatives, of which ultralight bosonic particles
with masses $\sim 10^{-21}$ eV represent one of the most encouraging. Numerical
simulations have shown that such particles form solitonic cores in the
innermost parts of virialized galactic halos that are supported by internal
quantum pressure on characteristic $\sim$kpc de Broglie scales. In the Galaxy,
this halo region can be probed by means of S-stars orbiting the supermassive
black hole Sagittarius A* to unveil the presence of such a solitonic core and,
ultimately, to bound the boson mass $m_\psi$. Employing a Monte Carlo Markov
Chain algorithm, we compare the predicted orbital motion of S2 with publicly
available data and set an upper bound $m_\psi \lesssim 3.2\times 10^{-19}$ eV
on the boson mass, at 95 \% confidence level. When combined with other galactic
and cosmological probes, our constraints help to reduce the allowed range of
the bosonic mass to $(2.0 \lesssim m_\psi \lesssim 32.2)\times 10^{-20}$ eV, at
the 95 \% confidence level, which opens the way to precision measurements of
the mass of the ultralight bosonic dark matter.
