The contribution of dissolving star clusters to the population of
  ultra-faint objects in the outer halo of the Milky Way
  In the last decade, several ultra faint objects (UFOs, $M_V\gtrsim-3.5$) have
been discovered in the outer halo of the Milky Way. For some of these objects
it is not clear whether they are star clusters or (ultra-faint) dwarf galaxies.
In this work we quantify the contribution of star clusters to the population of
UFOs. We extrapolated the mass and Galactocentric radius distribution of the
globular clusters using a population model, finding that the Milky Way contains
about $3.3^{+7.3}_{-1.6}$ star clusters with $M_V\gtrsim-3.5$ and
Galactocentric radius $\geq20\,$kpc. To understand whether dissolving clusters
can appear as UFOs, we run a suite of direct $N$-body models, varying the
orbit, the Galactic potential, the binary fraction and the black hole (BH)
natal kick velocities. In the analyses, we consider observational biases such
as: luminosity limit, field stars, and line-of-sight projection. We find that
star clusters contribute to both the compact and the extended population of
UFOs: clusters without BHs appear compact with radii $\sim5\,$pc, while
clusters that retain their BHs after formation have radii $\gtrsim20\,$pc. The
properties of the extended clusters are remarkably similar to those of dwarf
galaxies: high inferred mass-to-light ratios due to binaries; binary properties
mildly affected by dynamical evolution; no observable mass segregation; and
flattened stellar mass function. We conclude that the slope of the stellar mass
function as a function of Galactocentric radius and the presence/absence of
cold streams can discriminate between DM free and DM dominated UFOs.
