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The mass and radius evolution of globular clusters in tidal fields

We present a simple theory for the evolution of initially compact clusters in a tidal field. The fundamental ingredient of the model is that a cluster conducts a constant fraction of its own energy through the half-mass radius by two-body interactions every half-mass relaxation time. This energy is produced in a self-regulative way in the core by an (unspecified) energy source. We find that the half-mass radius increases during the first part (roughly half) of the evolution and decreases in the second half, while the escape rate is constant and set by the tidal field. We present evolutionary tracks and isochrones for clusters in terms of cluster half-mass density, cluster mass and galacto-centric radius. We find substantial agreement between model isochrones and Milky Way globular cluster parameters, which suggests that there is a balance between the flow of energy and the central energy production for almost all globular clusters. We also find that the majority of the globular clusters are still expanding towards their tidal radius. Finally, a fast code for cluster evolution is presented.