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: Eb propto (L 2.05 rrm 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, rrm gc, and c. Results are obtained for generic King models and applied specifically to the globular cluster system of the Milky Way.