Globular cluster scale sizes in giant galaxies: orbital anisotropy and tidally underfilling clusters in M87, NGC 1399 and NGC 5128

We investigate the shallow increase in globular cluster half-light radii with projected galactocentric distance Rgc observed in the giant galaxies M87, NGC 1399, and NGC 5128. To model the trend in each galaxy, we explore the effects of orbital anisotropy and tidally underfilling clusters. While a strong degeneracy exists between the two parameters, we use kinematic studies to help constrain the distance Rβ beyond which cluster orbits become anisotropic, as well as the distance Rfα beyond which clusters are tidally underfilling. For M87 we find Rβ > 27 kpc and 20 < Rfα < 40 kpc and for NGC 1399 Rβ > 13 kpc and 10 < Rfα < 30 kpc. The connection of Rfα with each galaxy's mass profile indicates the relationship between size and Rgc may be imposed at formation, with only inner clusters being tidally affected. The best-fitting models suggest the dynamical histories of brightest cluster galaxies yield similar present-day distributions of cluster properties. For NGC 5128, the central giant in a small galaxy group, we find Rβ > 5 kpc and Rfα > 30 kpc. While we cannot rule out a dependence on Rgc, NGC 5128 is well fitted by a tidally filling cluster population with an isotropic distribution of orbits, suggesting it may have formed via an initial fast accretion phase. Perturbations from the surrounding environment may also affect a galaxy's orbital anisotropy profile, as outer clusters in M87 and NGC 1399 have primarily radial orbits while outer NGC 5128 clusters remain isotropic.