We report results of collisional N-body simulations aimed to study the
N-dependance of the dynamical evolution
of star clusters. Our clusters consist of equal-mass stars and are
in virial equilibrium. Clusters moving in external tidal fields and clusters
limited by a cut-off radius are simulated. Our main focus is to study the
dependence of the lifetimes of the clusters on the number of cluster stars and
the chosen escape condition.
We find that star clusters in external tidal fields exhibit a scaling problem
in the sense that their lifetimes do not scale with the relaxation time.
Isolated clusters show a similar problem if stars are removed only after
their distance to the cluster centre exceeds a certain cut-off radius. If
stars are removed immediately after their energy exceeds the energy
necessary for escape, the scaling problem disappears.
We show that some stars which gain the energy necessary for escape are
scattered to lower energies before they can leave the cluster.
Since the efficiency of this process decreases with increasing
particle number, it causes the lifetimes not to scale with the
relaxation time. Analytic formulae are derived for
the scaling of the lifetimes in the different cases.