Globular Cluster Scale Sizes in Giant Galaxies: The Case of M87 and the Role of Orbital Anisotropy and Tidal Filling

We present new Hubble Space Telescope imaging of the outer regions of M87 in order to study its globular cluster (GC) population out to large galactocentric distances. We discuss particularly the relationship between GC effective radii $r_h$ and projected galactocentric distance $R_{gc}$. The observations suggest a shallow trend $r_h \propto R_{gc}^{0.14}$ out to $R_{gc} \sim 100$ kpc, in agreement with studies of other giant elliptical galaxies. To theoretically reproduce this relationship we simulate GC populations with various distributions of orbits. For an isotropic distribution of cluster orbits we find a steeper trend of $r_h \propto R_{gc}^{0.4}$. Instead we suggest that (a) if the cluster system has an orbital anisotropy profile, where orbits become preferentially radial with increasing galactocentric distance, AND (b) if clusters become more tidally under-filling with galactocentric distance, the observed relationship can be recovered. We also apply this approach to the red and blue GC populations separately and predict that red clusters are preferentially under-filling at large $R_{gc}$ and have a more isotropic distribution of orbits than blue clusters.