The galactic globular cluster system

We explore correlations between various properties of Galactic globular clusters, using a database on 143 objects. Our goal is identify correlations and trends which can be used to test and constrain theoretical models of cluster formation and evolution. We use a set of 13 cluster parameters, 9 of which are independently measured. Several arguments suggest that the number of clusters still missing in the obscured regions of the Galaxy is of the order of 10, and thus the selection effects are probably not severe for our sample. Known clusters follow a power-law density distribution with a slope approximately -3.5 to -4, and an apparent core with a core radius approximately 1 kpc. Clusters show a large dynamical range in many of their properties, more so for the core parameters (which are presumably more affected by dynamical evolution) than for the half-light parameters. There are no good correlations with luminosity, although more luminous clusters tend to be more concentrated. When data are binned in luminosity, several trends emerge: more luminous clusters tend to have smaller and denser cores. We interpret this as a differential survival effect, with more massive clusters surviving longer and reaching more evolved dynamical states. Cluster core parameters and concentrations also correlate with the position in the Galaxy, with clusters closer to the Galactic center or plane being more concentrated and having smaller and denser cores. These trends are more pronounced for the fainter (less massive) clusters. This is in agreement with a picture where tidal shocks form disk or bulge passages accelerate dynamical evolution of clusters. Cluster metallicities do not correlate with any other parameter, including luminosity and velocity dispersion; the only detectable trend is with the position in the Galaxy, probably reflecting Zinn's disk-halo dichotomy. This suggests that globular clusters were not self-enriched systems. Velocity dispersions show excellent correlations with luminosity and surface brightness. Their origin is not well understood, but they may well reflect initial conditions of cluster formation, and perhaps even be used to probe the initial density perturbation spectrum on a approximately 106 solar mass scale. Core radii and concentrations play a role of a 'second parameter' in these correlations. While a global manifold of cluster properties has a high statistical dimensionality (D greater than 4), a subset of structural, photometric, and dynamical parameters forms a statistically three-dimensional family, as expected from objects following King models; we propose to call this set of quantities the King Manifold. <Some of the observed correlations may be usable as distance indicator relations for globular clusters.