The fundamental properties of clusters of galaxies

The combination of optical and X-ray data provides a key to the fundamental properties of clusters of galaxies. For our analysis, we choose a complete sample of nearby clusters in the redshift range from 0.02 to 0.05. Using the COSMOS-and ROSAT-data we derive robust optical and X-ray parameters from surface brightness profiles. In particular, we use the optical and Xray luminosity and the half-light radii in both energy bands for the analysis. We derive several monovariant relations for different morphological classes of galaxy clusters. Under the assumption that the cluster is virialized and in hydrostatic equilibrium we estimate the mass to light ratio and the dark matter fraction. The remarkably low scatter in this relation reveals the existence of a fundamental plane of clusters of galaxies in the optical and X-ray parameter space. In addition, the comparison with structures on smaller scales supports the hierarchical clustering scenario.