Globular Cluster Scale Sizes in Giant Galaxies: Orbital Anisotropy and Tidally Under-filling 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 under-filling 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 under-filling. 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 fitted 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.