2017ApJ...844...64A

The recent detection of two faint and extended star clusters in the central regions of two Local Group dwarf galaxies, Eridanus II and Andromeda XXV, raises the question of whether clusters with such low densities can survive the tidal field of cold dark matter halos with central density cusps. Using both analytic arguments and a suite of collisionless N-body simulations, I show that these clusters are extremely fragile and quickly disrupted in the presence of central cusps ρ∼r^-α^ with α0.2. Furthermore, the scenario in which the clusters were originally more massive and sank to the center of the halo requires extreme fine tuning and does not naturally reproduce the observed systems. In turn, these clusters are long lived in cored halos, whose central regions are safe shelters for α0.2. The only viable scenario for hosts that have preserved their primordial cusp to the present time is that the clusters formed at rest at the bottom of the potential, which is easily tested by measurement of the clusters proper velocity within the host. This offers means to readily probe the central density profile of two dwarf galaxies as faint as L_V∼5×10⁵ L_☉ and L_V∼6×10⁴ L_☉, in which stellar feedback is unlikely to be effective.