Abstract
The evolution of globular clusters due to 2-body relaxation results in an outward flow of energy and at some stage all clusters need a central energy source to sustain their evolution. Henon provided the insight that we do not need to know the details of the energy production in order to understand the relaxation-driven evolution of the cluster, at least outside the core. He provided two self-similar solutions for the evolution of clusters based on the view that the cluster as a whole determines the amount of energy that is produced in the core: steady expansion for isolated clusters, and homologous contraction for clusters evaporating in a tidal field. We combine these models: the half-mass radius increases during the first half of the evolution, and decreases in the second half; while the escape rate approaches a constant value set by the tidal field. We refer to these phases as `expansion dominated' and `evaporation dominated'. These simple analytical solutions immediately allow us to construct evolutionary tracks and isochrones in terms of cluster half-mass density, cluster mass and galacto-centric radius. From a comparison to the Milky Way globular clusters we find that roughly 1/3 of them are in the second, evaporation-dominated phase and for these clusters the density inside the half-mass radius varies with the galactocentric distance R as rho_h ~ 1/R^2. The remaining 2/3 are still in the first, expansion-dominated phase and their isochrones follow the environment-independent scaling rho_h ~ M^2; that is, a constant relaxation time-scale. We find substantial agreement between Milky Way globular cluster parameters and the isochrones, which suggests that there is, as Henon suggested, a balance between the flow of energy and the central energy production for almost all globular clusters.