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
astrophysically large de Broglie wavelength. A striking feature of this model
is $\mathcal{O}(1)$ 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 $m_a\gtrsim
0.6\rightarrow 1\times 10^{-19}\text{ eV}$ within modelling 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 $m_a\gtrsim
0.8\times 10^{-21}\text{ eV}$ to successfully form Eridanus II. The window
between $10^{-21}\text{ eV}\lesssim m_a\lesssim 10^{-20}\text{ eV}$ is affected
by narrow band resonances, and the limited applicability of the diffusion
approximation. Some of this window may be consistent with observations of
Eridanus II and more detailed investigations are required.
