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In the last decade, several ultra faint objects (UFOs, $M_V\gtrsim-3.5$) havebeen discovered in the outer halo of the Milky Way. For some of these objectsit 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 ofUFOs. We extrapolated the mass and Galactocentric radius distribution of theglobular clusters using a population model, finding that the Milky Way containsabout $3.3^{+7.3}_{-1.6}$ star clusters with $M_V\gtrsim-3.5$ andGalactocentric radius $\geq20\,$kpc. To understand whether dissolving clusterscan appear as UFOs, we run a suite of direct $N$-body models, varying theorbit, the Galactic potential, the binary fraction and the black hole (BH)natal kick velocities. In the analyses, we consider observational biases suchas: luminosity limit, field stars, and line-of-sight projection. We find thatstar clusters contribute to both the compact and the extended population ofUFOs: clusters without BHs appear compact with radii $\sim5\,$pc, whileclusters that retain their BHs after formation have radii $\gtrsim20\,$pc. Theproperties of the extended clusters are remarkably similar to those of dwarfgalaxies: high inferred mass-to-light ratios due to binaries; binary propertiesmildly affected by dynamical evolution; no observable mass segregation; andflattened stellar mass function. We conclude that the slope of the stellar massfunction as a function of Galactocentric radius and the presence/absence ofcold streams can discriminate between DM free and DM dominated UFOs.

The contribution of dissolving star clusters to the population of ultra-faint objects in the outer halo of the Milky Way