Dynamical Evolution of Clusters of Galaxies--III

Previous numerical studies of simulated galaxy clusters are extended to include rotation. The initial velocity distribution contains 26 retrograde and 74 direct orbits. The inclusion of rotation shortens the mean relaxation time and gives rise to a significant flattening. A large proportion of positive angular momentum is transferred to the halo but the flattening remains frozen in. There is preferential escape of direct orbits but two out of 20 escapers are retrograde. The direct escapers do not carry away any excess angular momentum per unit mass but the loss of rotational energy is increased considerably by the removal of 61 distant halo orbits. After a total integration time of 139 initial crossing times the cluster contains 19 bodies representing 37.5 per cent of the total mass and only 13 per cent of the angular momentum. An upper limit of 370 initial crossing times is estimated for the time to lose all non-nuclear members inside $$r \simeq 10$$ by replacing the compact nucleus with one central body. Six further cases with different types of rotation have also been studied in order to explore the initial condition dependence. There is significant correlation between total angular momentum and flattening but fluctuations can mask the rotation effect when the rotational energy is small.