Strong Constraints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II

The fuzzy dark matter (FDM) model treats DM as a bosonic field with an astrophysically large de Broglie wavelength. A striking feature of this model is O(1) fluctuations in the dark matter density on time scales which are shorter than the gravitational timescale. Including, for the first time, the effect of core oscillations, we demonstrate how such fluctuations lead to heating of star clusters and, thus, an increase in their size over time. From the survival of the old star cluster in Eridanus II, we infer m(a) greater than or similar to 0.6 -> 1 x 10(-19) eV within modeling uncertainty if FDM is to compose all of the DM and derive constraints on the FDM fraction at lower masses. The subhalo mass function in the Milky Way implies m(a) less than or similar to 0.8 x 10(-21) eV to successfully form Eridanus II. The region between 10(-21) and 10(-20) eV is affected by narrow band resonances. However, the limited applicability of the diffusion approximation means that some of this region may still be consistent with observations of Eridanus II.