Space Velocities of Globular Clusters. III. Cluster Orbits and Halo Substructure

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Abstract
We have compiled a catalog of absolute proper motions of globular clusters from various sources. The sample consists of 38 clusters, from which most of the southern ones (15 clusters) were measured in our previous papers in this series. We have integrated orbits assuming two different Galactic potential models adopted from the literature and have calculated orbital parameters. The uncertainties associated with the orbital parameters were derived in a Monte Carlo approach, and we conclude that, overall, at the present level of measurement errors, orbital differences due to Galactic potential models are not significant. Three metal-poor clusters are found to have orbits similar to prototypical metal-rich disk clusters. These clusters are NGC 6254 (M10), NGC 6626 (M28), and NGC 6752. We interpret this as a potentially significant constraint on the formation of the disk. It is thus possible that part of the inner metal-poor halo is the low-metallicity tail of the thick disk. In this case, the ages of these clusters indicate that the formation of the disk partially overlapped with that of the halo. The clusters classified as "young halo" or "red horizontal-branch" by Zinn show a radially anisotropic velocity distribution, their orbits are of high total energy, with apocentric radii larger than 10 kpc and highly eccentric. In this sense they may represent an accreted component of our Galaxy. We also discuss ω Cen's orbit characteristics in the view of an accreted origin. We investigate the effect of the orbital motion on the internal dynamics of clusters. Adopting the formalism from Gnedin & Ostriker and their destruction rates due to two-body relaxation, we find that, in most cases, this internal process is more important than the destruction processes due to disk and bulge shocking. Hubble Space Telescope (HST) observations argue that NGC 6397's luminosity function is depleted at the faint end, and this is blamed on its high total destruction rate. We propose a list of clusters with similar destruction rates that may also have depleted luminosity functions. We also note the bias toward deriving higher destruction rates in studies that statistically assign tangential velocities based on a kinematic model of the globular cluster system, in contrast to the rates derived from the measured tangential velocities. Clusters prone to such biases are those that have circular orbits (kinematically thick-disk clusters) and some of those with orbits of high total energy.

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