How large are the globular cluster systems of early-type galaxies and do they scale with galaxy halo properties?

The globular cluster (GC) systems of galaxies are well known to extend to large galactocentric radii. Here, we quantify the size of GC systems using the half number radius of 22 GC systems around early-type galaxies (ETGs) from the literature. We compare GC system sizes to the sizes and masses of their host galaxies. We find that GC systems typically extend to 4 times that of the host galaxy size; however, this factor varies with galaxy stellar mass from about 3 times for M* galaxies to 5 times for the most massive galaxies in the universe. The size of a GC system scales approximately linearly with the virial radius (R-200) and with the halo mass (M-200) to the 1/3 power. The GC system of the Milky Way follows the same relations as for ETGs. For ultra diffuse galaxies (UDGs), their GC system size scales with halo mass and virial radius as for more massive, larger galaxies. UDGs indicate that the linear scaling of GC system size with stellar mass for massive galaxies flattens out for low stellar mass galaxies. Our scalings are different to those reported recently by Hudson & Robison.