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

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