Not so fuzzy: excluding FDM with sizes and stellar kinematics of
  ultra-faint dwarf galaxies
  We use observations of ultra-faint dwarf (UFD) galaxies to constrain the
particle mass of ultra-light dark matter. Potential fluctuations created by
wave interference in virialized "fuzzy" dark matter (FDM) halos dynamically
heat stellar orbits in UFDs, some of which exhibit velocity dispersions of
$\lesssim$ 3 km/s and sizes $\lesssim$ 40 pc. Using simulations of FDM halos,
and existing measurements of sizes and stellar radial velocities in Segue 1 and
Segue 2 UFDs, we derive a lower limit on the dark matter particle mass of
$m_{fdm} > 3\times 10^{-19}$ eV at 99% confidence, marginalized over host halo
circular velocity. This constraint is conservative as it is derived under the
assumption that soliton heating is negligible, and that no other sources of
non-FDM dynamical heating of stars operate to increase velocity dispersion. It
can potentially be strengthened by future spectroscopic observations of
additional stars in ultra-faint galaxies and by tightening theoretical
constraints on the soliton size-halo mass relation. However, even the current
conservative lower limit on the FDM mass makes this model indistinguishable
from Cold Dark Matter at the scales probed by existing astronomical
observations.
