Monte Carlo Models of Star Clusters
The dynamical evolution of spherical star clusters under the effect of internal encounters is followed numerically using a Monte Carlo procedure. Successive states of the system are computed, separated by a time step which is a fraction of the relaxation time. In any given state, each star is characterized by its total energy and its angular momentum with respect to the centre. Changes in these two quantities from one state to the next are computed by randomly selecting the position of the star on its orbit, randomly choosing a field star, letting the two stars interact, and multiplying the effect by an appropriate factor. This procedure can be shown to reproduce correctly the behaviour of the system as given by the Fokker-Planck equation. The computation is much faster than the exact N-body integration. Multiple-encounter effects are neglected, but this is probably not of serious consequence when N is large.
Some provisional results are presented. Once more it is found that N-body systems develop a very high central density peak. The velocity distribution becomes isotropic in the central parts, radially elongated in the halo. Models started with widely different initial conditions tend to become similar after a few relaxation times. The presence of a tidal field, or a distribution of masses, accelerate the evolution of the system.
A companion paper gives a detailed technical description of the method.
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