The Fundamental Plane of Galaxy Clusters

Abstract

Velocity dispersion $σ$, radius $R$ and luminosity $L$ of elliptical galaxies are known to be related, leaving only two degrees of freedom and defining the so-called ``fundamental plane". In this {\em Letter} we present observational evidence that rich galaxy clusters exhibit a similar behaviour. Assuming a relation $L \propto R^ασ^{2 β}$, the best-fit values of $α$ and $β$ 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 $L-σ$ 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.