Title: Probing dark matter with star clusters: a dark matter core in the ultra-faint dwarf Eridanus II,
Abstract: 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.