The globular cluster systems of 54 Coma ultra-diffuse galaxies: statistical constraints from HST data.

We use data from the HST Coma Cluster Treasury program to assess the richness of the Globular Cluster Systems (GCSs) of 54 Coma ultra-diffuse galaxies (UDGs), 18 of which have a half-light radius exceeding 1.5 kpc. We use a hierarchical Bayesian method tested on a large number of mock datasets to account consistently for the high and spatially varying background counts in Coma. These include both background galaxies and intra-cluster GCs (ICGCs), which are disentangled from the population of member GCs in a probabilistic fashion. We find no candidate for a GCS as rich as that of the Milky Way, our sample has GCSs typical of dwarf galaxies. For the standard relation between GCS richness and halo mass, 33 galaxies have a virial mass $M_{vir}\leq10^{11}M_\odot$ at 90% probability. Only three have $M_{vir}>10^{11}M_\odot$ with the same confidence. The mean colour and spread in colour of the UDG GCs are indistinguishable from those of the abundant population of ICGCs. The majority of galaxies in our sample are consistent with the relation between stellar mass and GC richness of 'normal' dwarf galaxies. Nine systems, however, display GCSs that are richer by a factor of 3 or more (at 90% probability). Six of these have sizes $\lesssim1.4$ kpc. Our results imply that the physical mechanisms responsible for the extended size of the UDGs and for the enhanced GC richness of some cluster dwarfs are at most weakly correlated.