Stellar mass segregation as separating classifier between globular clusters and ultra-faint dwarf galaxies

We have determined the amount of stellar mass segregation in over 50 globular clusters and ultra-faint dwarf galaxy candidates based on deep HST and ground-based photometry. We find that the amount of mass segregation in globular clusters is strongly correlated with their relaxation time and that all clusters with relaxation times of the order of their ages or longer have little to no mass segregation. For each cluster, the amount of mass segregation seen is fully compatible with the amount expected by dynamical evolution from initially unsegregated clusters, showing that globular clusters formed without primordial mass segregation among their low-mass stars. Ultra-faint dwarf galaxy candidates split into two groups, star clusters which follow the same trend between relaxation time and amount of mass segregation as globular clusters and dark-matter dominated dwarf galaxies that are unsegregated despite having relaxation times smaller than a Hubble time. Stellar abundance and velocity dispersion data, where available, confirm our classification. After classification of the ultra-faint dwarf galaxy candidates, we find that outer halo star clusters have average densities inside their half-light radii of 0.03 M$_\odot$/pc$^3 \lesssim \rho_h \lesssim$ 1 M$_\odot$/pc$^3$, while dwarf galaxies have stellar densities of 0.001 M$_\odot$/pc$^3 \lesssim \rho_h \lesssim $ 0.03 M$_\odot$/pc$^3$. The reason for this separation in density is most likely a combination of the initial conditions by which the systems formed and the requirement to withstand external tidal forces.