Stellar Cores Live Long and Prosper in Cuspy Dark Matter Halos

Abstract The existence of cuspy or cored centers of dark matter halos is a crucial discriminant between different dark matter models. It has recently been claimed based on dynamical arguments that perfectly cored stellar systems cannot survive inside cuspy dark matter halos, which would make the observation of stellar cores in ultrafaint dwarf galaxies, where dark matter cores cannot form through baryonic processes, a direct falsification of the cold dark matter paradigm. Here, we use idealized simulations to show explicitly that cored stellar systems like those observed in dwarf galaxies can be stable within cuspy dark matter halos over at least several Hubble times. We also demonstrate that observations of ultrafaint dwarf galaxies cannot distinguish mildly positive, flat, or negative inner density slopes, further precluding the dynamical inference of the gravitational potential from the stellar configuration.