A relationship between X-ray luminosity and cluster velocity dispersion is derived, which improves on the results of Solinger and Tucker (1972) in several important respects, and a simple model for primordial gas accretion by a cluster of galaxies is described. It is argued that the accreted gas may be causally related to the occurrence of a central active radio or giant cD or galaxy in X-ray clusters. Accretion and subsequent dissipation lead to a decrease with time in the amount of hot gas and in the X-ray luminosity as well as to an increase in mass of the dominant central galaxy.
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Joseph Silk (1976) studied this question.