Origin of the correlation between stellar kinematics and globular cluster system richness in ultradiffuse galaxies

Observational surveys have found that the dynamical masses of ultradiffuse 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 lead 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.