Soliton Random Walk and the Cluster-Stripping Problem in Ultralight Dark
  Matter
  Simulations of ultralight, $\sim 10^{-22}\,\rm eV$, bosonic dark matter
exhibit rich wave-like structure, including a soliton core within a surrounding
halo that continuously self-interferes on the de Broglie scale. We show here
that as an inherent consequence, the soliton undergoes a confined random walk
at the base of the halo potential. This is significant for the fate of the
ancient central star cluster in Eridanus II, as the agitated soliton
gravitationally shakes the star cluster in and out of the soliton on a time
scale of $\sim 100\,\rm Myr$, so complete tidal disruption of the star cluster
can occur within $\sim 1\,\rm Gyr$. This destructive effect can be mitigated by
tidal stripping of the halo of Eridanus II, thereby reducing the agitation,
depending on its orbit around the Milky Way. Our simulations show the Milky Way
tide affects the halo much more than the soliton, so the star cluster in
Eridanus II can survive for over $5\,\rm Gyr$ within the soliton if it formed
after significant halo stripping.
