  Observational surveys have found that the dynamical masses of ultra-diffuse
galaxies (UDGs) correlate with the richness of their globular cluster (GC)
system. This could be explained if GC-rich galaxies formed in more massive dark
matter haloes. We use simulations of galaxies and their GC systems from the
E-MOSAICS project to test whether the simulations reproduce such a trend. We
find that GC-rich simulated galaxies in galaxy groups have enclosed masses that
are consistent with the dynamical masses of observed GC-rich UDGs. However,
simulated GC-poor galaxies in galaxy groups have higher enclosed masses than
those observed. We argue that GC-poor UDGs with low stellar velocity
dispersions are discs observed nearly face on, such that their true mass is
underestimated by observations. Using the simulations, we show that galactic
star-formation conditions resulting in dispersion-supported stellar systems
also leads to efficient GC formation. Conversely, conditions leading to
rotationally-supported discs leads to inefficient GC formation. This result may
explain why early-type galaxies typically have richer GC systems than late-type
galaxies. This is also supported by comparisons of stellar axis ratios and GC
specific frequencies in observed dwarf galaxy samples, which show GC-rich
systems are consistent with being spheroidal, while GC-poor systems are
consistent with being discs. Therefore, particularly for GC-poor galaxies,
rotation should be included in dynamical mass measurements from stellar
dynamics.
