Publication : t93/067

Abstract:
Velocity dispersion $ \sigma , $ radius $ R $ and luminosity $ L $ of elliptical galaxies are known to be related, leaving only two degrees of freedom and defining the so-called \lq\lq fundamental plane\rq\rq . In this {\sl Letter\/} we present observational evidence that rich galaxy clusters exhibit a similar behaviour. Assuming a relation $ L\propto R^\alpha \sigma^{ 2\beta} , $ the best-fit values of $ \alpha $ and $ \beta $ are very close to those defined by galaxies. The dispersion of this relation is lower than 10 percent, i.e. significantly smaller than the dispersion observed in the $ L-\sigma $ and $ L-R $ relations. We briefly suggest some possible implications on the spread of formation times of objects and on peculiar velocities of galaxy clusters.