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We have assembled from the literature a data base on on 394 clusters of galaxies, with up to 16 parameters per cluster. They include optical and x-ray luminosities, x-ray temperatures, galaxy velocity dispersions, central galaxy and particle densities, optical and x-ray core radii and ellipticities, etc. In addition, derived quantities, such as the mass-to-light ratios and x-ray gas masses are included. Doubtful measurements have been identified, and deleted from the data base. Our goal is to explore the correlations between these parameters, and interpret them in the framework of our understanding of evolution of clusters and large-scale structure, such as the Gott-Rees scaling hierarchy. Among the simple, monovariate correlations we found, the most significant include those between the optical and x-ray luminosities, x-ray temperatures, cluster velocity dispersions, and central galaxy densities, in various mutual combinations. While some of these correlations have been discussed previously in the literature, generally smaller samples of objects have been used. We will also present the results of a multivariate statistical analysis of the data, including a principal component analysis (PCA). Such an approach has not been used previously for studies of cluster properties, even though it is much more powerful and complete than the simple monovariate techniques which are commonly employed. The observed correlations may lead to powerful constraints for theoretical models of formation and evolution of galaxy clusters.
P.M.O. was supported by a Caltech graduate fellowship. S.D. acknowledges a partial support from the NASA contract NAS5-31348 and the NSF PYI award AST-9157412.
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