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 R-gc 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 R-beta beyond which cluster orbits become anisotropic, as well as the distance R-f alpha beyond which clusters are tidally underfilling. For M87 we find R-beta > 27 kpc and 20 < R-f alpha < 40 kpc and for NGC 1399 R-beta > 13 kpc and 10 < R-f alpha < 30 kpc. The connection of R-f alpha with each galaxy's mass profile indicates the relationship between size and R-gc 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 R-beta > 5 kpc and R-f alpha > 30 kpc. While we cannot rule out a dependence on R-gc, 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.