Binding Energy and the Fundamental Plane of Globular Clusters

Abstract

A physical description of the fundamental plane of Galactic globular clusters is developed which explains all empirical trends and correlations in a large number of cluster observables and provides a small but complete set of truly independent constraints on theories of cluster formation and evolution in the Milky Way. Within the theoretical framework of single-mass, isotropic King models, it is shown that (1) 39 regular (non--core-collapsed) globulars with measured core velocity dispersions share a common V-band mass-to-light ratio of 1.45 +/- 0.10, and (2) a complete sample of 109 regular globulars reveals a very strong correlation between cluster binding energy and total luminosity, regulated by Galactocentric position: E_b \propto (L^{2.05} r_{\rm gc}^{-0.4}). The observational scatter about either of these two constraints can be attributed fully to random measurement errors, making them the defining equations of a fundamental plane for globular clusters. A third, weaker correlation, between total luminosity and the King-model concentration parameter, c, is then related to the (non-random) distribution of globulars on the plane. The equations of the FP are used to derive expressions for any cluster observable in terms of only L, r_{\rm gc}, and c. Results are obtained for generic King models and applied specifically to the globular cluster system of the Milky Way.