We have used the ESO Nearby Abell Cluster Survey (ENACS) in combination with the Cosmos Galaxy Catalogue, to investigate the existence of a Fundamental Plane (FP) for rich clusters of galaxies. The 20 clusters with the most regular projected galaxy distributions appear to define a quite narrow FP, which is similar to the FP found by Schaeffer et al., who used other clusters. Our cluster FP appears to be different from that of ellipticals, as well as from the virial prediction. The latter fact may have several physical explanations, or a combination thereof. If M/L varies with L this will change the FP slope away from the virial slope. Differences in dynamical structure between clusters will also produce deviations from the virial FP. In view of the long virialization time-scales in all but the very central parts of galaxy clusters, the deviation of the cluster FP from the virial expectation may also result from clusters not being totally virialized. The scatter of the observations around the cluster FP is fairly small. An important part of the observed scatter is likely to be intrinsic. If this intrinsic spread were due exclusively to deviations from the Hubble flow it would imply cluster peculiar velocities of at most about 1000 km.s-1.
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