## 1. IntroductionTheoretical models for the evolution of star clusters are generally
too idealized for comparison with observations. However, detailed
model calculations with direct If we could scale the results of The inclusion of realistic effects such as mass loss due to stellar evolution and the effect of galactic tidal fields (with the galaxy approximated as a point mass, but also with the inclusion of disc shocking) further complicate the scaling problem (see, e.g., Heggie 1996). A proper treatment of stellar evolution is particularly problematic, since its characteristic timescale changes as stars evolve. Chernoff & Weinberg (1990, CW90) performed an extensive study of the survival of star clusters using Fokker-Planck calculations which included 2-body relaxation and some rudimentary form of mass loss from the evolving stellar population. In their simulations the number of particles is not specified. Their models are defined by the initial half-mass relaxation time and by the initial mass function of the cluster. Since their models do not specify the number of stars per cluster, each of their model calculations corresponds to a one-dimensional series of models, when plotted in a plane of observational values, such as total mass versus distance to the galactic center (Fig. 1). All points of the solid line in that figure correspond to a single calculations by CW90, since they have an identical relaxation time. As we will see later, it is useful to consider other series of models, for which the crossing time is held constant while varying the mass. An example of such a series is indicated by the dashed line in Fig. 1. The shapes of these lines are derived under the assumption of a flat rotation curve for the parent galaxy.
The main conclusion of CW90 was that the majority of the simulated
star clusters dissolve in the tidal field of the galaxy within a few
hundred million years. Fukushige & Heggie (1995, FH95) studied the
evolution of globular clusters using direct FH95 found lifetimes much longer than those in CW90's Fokker-Planck calculations, for the majority of the models used in CW90. However, the reason for the discrepancy is rather unclear, because the calculations of FH95 and those of CW90 differ in several important respects. The relaxation times differ because FH95 held the cluster crossing time fixed in scaling from the model to the real system. However, the crossing times themselves are also different, since the crossing time is by definition zero in a Fokker-Planck calculation. Finally, the implementation of the galactic tidal field is also quite different. CW90 used a simple boundary condition in energy space (spherically symmetric in physical space), in which stars were removed once they acquired positive energy, but the underlying equations of motion included no tidal term. FH95 adopted a much more physically correct treatment, including tidal acceleration terms in the stellar equations of motion and a proper treatment of centrifugal and coriolis forces in the cluster's rotating frame of reference (see FH95). In order to study the behavior of star clusters with limited numbers of stars, and to compare with the results of the Fokker-Planck simulations of CW90, we selected one of their models and perform a series of collisional N-body simulations in which the evolution of the individual stars is taken into account. According to CW90 the results should not depend on the number of stars in the simulation as long as the relaxation time is taken to be the same for all models. It is, among others, this statement which we intend to study. We find that for this set of initial conditions Fokker-Planck models do not provide a qualitatively correct picture of the evolution of star clusters. The effects of the finite dynamical time scale are large, even for models whose lifetime is several hundred times longer than the dynamical time. The main purpose of this paper is to study the survival
probabilities of star clusters containing up to a few tens of
thousands of single stars, in order to gain a deeper understanding of
the influence of the galactic tidal field and the fundamental scaling
of small The dynamical model, stellar evolution, initial conditions and scaling are discussed in Sect. 2. Sect. 3 reviews the software environment and the GRAPE-4 hardware, and discusses the numerical methods used. The results are presented in Sect. 4 and discussed in Sect. 5; Sect. 6 sums up. © European Southern Observatory (ESO) 1998 Online publication: August 17, 1998 |