  We use the Milky Way's nuclear star cluster (NSC) to test the existence of a
dark matter 'soliton core', as predicted in ultra-light dark matter (ULDM)
models. Since the soliton core size is proportional to mDM^{-1}, while the core
density grows as mDM^{2}, the NSC (dominant stellar component within about 3
pc) is sensitive to a specific window in the dark matter particle mass, mDM. We
apply a spherical isotropic Jeans model to fit the NSC line-of-sight velocity
dispersion data, assuming priors on the precisely measured Milky Way's
supermassive black hole (SMBH) mass and the well-measured NSC density profile.
We find that the current observational data reject the existence of a soliton
core for a single ULDM particle with mass in the range 10^{-20.4} < mDM <
10^{-18.5} eV, assuming that the soliton core structure is not affected by the
Milky Way's SMBH. We test our methodology on mock data, confirming that we are
sensitive to the same range in ULDM mass as for the real data. Dynamical
modelling of a larger region of the Galactic centre, including the nuclear
stellar disc, promises tighter constraints over a broader range of mDM. We will
consider this in future work.
