Dynamical Evolution of Clusters of Galaxies, I

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Abstract
Numerical integrations of the classical N -body problem have been carried out on a fast computer for a variety of clusters in the range N = 25 to N = 100. Newtonian forces are slightly modified to give convergence for collisions. The solutions are completely general and the results are applied to clusters of galaxies. It is found that the moment of inertia increases considerably even if bodies are not lost by ejection. At the same time there is an increase of mass in the central regions. The derived relaxation times are substantially longer than predicted by the theory of Chandrasekhar, but even so there is a deficiency of escapers for N ≳ 50. Some of the light cluster members are lost when the effect of cosmic expansion is included. The dynamical formation rate of binaries is found to be small but this is compensated by long life-times for heavy doubles. Radially contracting clusters of irregular shapes are studied and a common feature is the formation of a compact sub-system of high stability. Field galaxies moving through a cluster do not affect the bound members significantly, but there is a likelihood of capture. In some cases the integration time corresponds to a physical time ∼ 10 10 yrs for a typical model cluster, but maximum errors in total energy may still be ≲ 0.5 per cent. The estimated computer time depends on the expression N2t where t is the physical integration time.

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