We present a new technique to probe the central dark matter (DM) density profile of galaxies that harnesses both the survival and observed properties of star clusters. As a first application, we apply our method to the `ultra-faint dwarf Eridanus II (Eri II) that has a lone star cluster ~45 pc from its centre. Using a grid of collisional $N$-body simulations, incorporating the effects of stellar evolution, external tides and dynamical friction, we show that a DM core for Eri II naturally reproduces the size and the projected position of its star cluster. By contrast, a dense cusped galaxy requires the cluster to lie implausibly far from the centre of Eri II (>1 kpc), with a high inclination orbit that must be observed at a particular orbital phase. Our results, therefore, favour a dark matter core. This implies that either a cold DM cusp was `heated up at the centre of Eri II by bursty star formation, or we are seeing an evidence for physics beyond cold DM.
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