  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.

Astrophysics of Galaxies