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.
