Implications for Galaxy Formation Models from Observations of Globular Clusters around Ultra-Diffuse Galaxies

We present an analysis of Hubble Space Telescope observations of globular clusters (GCs) in six ultra-diffuse galaxies (UDGs) in the Coma cluster, a sample that represents UDGs with large effective radii ($R_{\rm e}$), and use the results to evaluate competing formation models. We eliminate two significant sources of systematic uncertainty in the determination of the number of GCs, $N_{\rm GC}$ by using sufficiently deep observations that (i) reach the turnover of the GC luminosity function and (ii) provide a sufficient number of GCs with which to measure the GC number radial distribution. We find that $N_{\rm GC}$ for these galaxies is on average $\sim$20, which implies an average total mass, $M_{\rm total}$, $\sim$ $10^{11}$ $M_{\odot}$ when applying the relation between $N_{\rm GC}$ and $M_{\rm total}$. This value of $N_{\rm GC}$ lies at the upper end of the range observed for dwarf galaxies of the same stellar mass and is roughly a factor of two larger than the mean. The GC luminosity function, radial profile and average colour are more consistent with those observed for dwarf galaxies than with those observed for the more massive ($L^*$) galaxies, while both the radial and azimuthal GC distributions closely follow those of the stars in the host galaxy. Finally, we discuss why our observations, specifically the GC number and GC distribution around these six UDGs, pose challenges for several of the currently favoured UDG formation models.