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. EUects of the shocks are included by adding the tidal shock diUusion coefficients to the ordinary Fokker-Planck equation: the —rst-order heating term, S*ET, and the second-order energy dispersion term, S*E2T. 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 orbits of this cluster in the Galaxy. Tidal shocks accelerate signi—cantly both core collapse and the evaporation of the cluster and shorten the destruction time from 24 to 18 Gyr. We examine various types of adiabatic corrections and —nd 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 the concentration and tidal shock parameters and determine the region of the parameter space where tidal shocks domi- nate the evolution. We present —tting formulae for the core collapse time and the destruction time, covering all reasonable initial conditions. In the limit of strong shocks, the typical value of the core collapse time decreases from to or less, while the destruction time is just twice that number. 10t rh 3t rh The eUects 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. Subject headings: celestial mechanics, stellar dynamicsglobular clusters: general ¨ globular clusters: individual (NGC 6254)