Effects of Tidal Shocks on the Evolution of Globular Clusters

We present new Fokker-Planck models of the evolution of globular clusters, including gravitational tidal shocks. We extend our calculations beyond the core collapse by adopting three-body binary heating. Effects of the shocks are included by adding the tidal shock terms to the ordinary Fokker-Planck equation: the first order heating term, , and the second order energy dispersion term, . As an example, we investigate the evolution of models for the globular cluster NGC 6254. Using the Hipparcos proper motions, we are now able to construct the orbits of this cluster in the Galaxy. Tidal shocks significantly accelerate both core collapse and the evaporation of the cluster. We examine various types of adiabatic corrections and find that they are critical for accurate calculation of the evolution. Without adiabatic corrections, the destruction time of the cluster is twice as short. We examine cluster evolution for a wide range of concentration and tidal shock parameters, and determine the region of the parameter space where tidal shocks dominate the evolution. We present fitting formulae for the core collapse time and the destruction time, covering all reasonable initial conditions. The effects of tidal shocks are rapidly self-limiting: as clusters lose mass and become more compact, the importance of the shocks diminishes. This implies that tidal shocks were more important in the past.