Abstract
We perform a statistical analysis of the properties of 170 rich clusters of galaxies. We confirm the existence of correlations between the X-ray luminosity and temperature of the cluster intergalactic medium (IGM) and between the velocity dispersion of the galaxies and the X-ray luminosity of the IGM. In addition, we have found a new anti-correlation between the optical luminosity in Hα and the X-ray luminosity of the cluster IGM: log \( \left( {\frac{{L_{H\alpha } }} {{L_ \odot }}} \right) = a - b\log \left( {\frac{{L_x }} {{L_ \odot }}} \right) \). Clusters form sequences with different values of a but similar values of b.
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