Nuclear star clusters as probes of dark matter halos: the case of the Sagittarius Dwarf Spheroidal Galaxy

The Sagittarius dwarf spheroidal (Sgr dSph) galaxy is currently being accreted and disrupted by the tidal field of the Milky Way. Recent observations have shown that the central region of the dwarf hosts at least three different stellar populations, ranging from old and metal-poor over intermediate metal-rich to young metal-rich. While the intermediate-age metal-rich population has been identified as part of the galaxy, the oldest and youngest populations belong to M54, the nuclear star cluster (NSC) of the Sgr dSph galaxy. The old metal-poor component of M54 has been interpreted as at least one decayed GC which was initially orbiting its host galaxy. The youngest population formed in situ from gas accreted into M54 after its arrival at the centre of the host. In this work, we use the observed properties of M54 to explore the shape of the inner density profile of the Sgr dSph galaxy. To do so, we simulate the decay of M54 towards the centre of the dark matter (DM) halo of its host. We model the DM density profile using different central slopes, and we compare the results of the simulations to the most recent observations of the structural properties of M54. From this comparison, we conclude that a GC that decays in a DM halo with a density profile \(\propto r^{-\gamma}\) and \(\gamma \leq 1\) shows a rotational signal and flattening comparable to those observed for M54. Steeper profiles produce, instead, highly rotating and more flattened NSCs which do not match the properties of M54.