We explore the origin of a population of stars recently detected in the inner parsec of the Milky Way Nuclear Cluster (NC), which exhibit sub-solar metallicity and a higher rotation compared to the dominant population. Using state-of-the-art $N$-body simulations, we model the infall of a massive stellar system into the Galactic center, both of Galactic and extra-galactic origin. We show that the newly discovered population can either be the remnant of a massive star cluster formed a few kpc away from the Galactic center (Galactic scenario) or be accreted from a dwarf galaxy originally located at 10-100 kpc (extragalactic scenario) and that reached the Galactic center 3-5 Gyr ago. A comparison between our models and characteristic Galactocentric distance and metallicity distributions of Milky Way satellites and globular clusters favours the Galactic scenario. A comparison with clusters associated with the Enceladus-Sausage, Sequoia, Sagittarius and Canis Major structures suggests that the progenitor of the observed metal-poor substructure formed in-situ rather than being accreted.
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