The Likelihood of Undiscovered Globular Clusters in the Outskirts of the
  Milky Way
  The currently known Galactic globular cluster population extends out to a
maximum galactocentric distance of $\sim$ 145 kpc, with the peculiarity that
the outermost clusters predominantly have an inward velocity. Orbit averaging
finds that this configuration occurs by chance about $6\%$ of the time,
suggesting that several globular clusters with positive radial velocities
remain undiscovered. We evaluate the expected number of undiscovered clusters
at large distances under the assumption that the cluster population has a
smooth radial distribution and is in equilibrium within the Milky Way's virial
radius. By comparing the present day kinematic properties of outer clusters to
random orbital configurations of the Galactic globular cluster system through
orbit averaging, we estimate a likelihood of $73\%$ of there being at least one
undiscovered globular cluster within the Milky Way. This estimate assumes the
current population is complete out to 50 kpc, and increases to $91\%$ if the
population is complete out to 150 kpc. The likelihood of there being two
undiscovered clusters is between $60\%$ and $70\%$, with the likelihood of
there being three undiscovered clusters being on the order of $50\%$. The most
likely scenario is that the undiscovered clusters are moving outwards, which
results in the outer cluster population being consistent with an equilibrium
state. Searches for distant and possibly quite low concentration and very low
metallicity globular clusters will be enabled with upcoming deep imaging
surveys.
