We use the Milky Ways 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 Milky Ways supermassive black hole (SMBH) mass taken from the Gravity Collaboration et al. (2020) and stellar density profile taken from Gallego-Cano et al. (2018). 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^{-20.0} < mDM < 10^{-18.5} eV, assuming that the soliton core structure is not affected by the Milky Ways 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.
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