Basic N-body modelling of the evolution of globular clusters - I. Time scaling

We consider the use of N-body simulations for studying the evolution of rich star clusters (i.e. globular clusters).The dynamical processes included in this study are restricted to gravitational (point-mass) interactions, the steady tidal field of a galaxy, and instantaneous mass loss resulting from stellar evolution. With evolution driven by these mechanisms, it is known that clusters fall roughly into two broad classes: those that dissipate promptly in the tidal field, as a result of mass loss; and those that survive long enough for their evolution to become dominated by two-body relaxation. The time-scales of the processes we consider scale in different ways with the number of stars in the simulation, and the main aim of the paper is to suggest how the scaling of a simulation should be done so that the results are representative of the evolution of a 'real' cluster. We investigate three different ways of scaling time. One of these is appropriate to the first type of cluster, i.e. those that dissipate rapidly; similarly, a second scaling is appropriate only to the second (relaxation-dominated) type. We also develop a hybrid scaling, which is a satisfactory compromise for both types of cluster. Finally we present evidence that the widely used Fokker-Planck method produces models that are in good agreement with N-body models of those clusters that are relaxation-dominated, at least for N-body models with several thousand particles, but that the Fokker-Planck models evolve too fast for clusters that dissipate promptly.