The galactic orbital decay and capture process is reevaluated to see whether a very massive galaxy would be expected to form in a relaxed cluster that did not contain one originally, and to derive the dependence of the capture rate on overall cluster properties. A largely analytic description of cluster evolution is first given based on the assumption that relatively little orbital evolution occurs in a Hubble time. The resulting expression for the rate of accumulation of galaxies at low orbital energies is compared with expressions derived earlier by other authors, some of which are shown greatly to overestimate the number of accumulated galaxies, even after a fixed number of decay times. These results are then extended to clusters in which galaxy masses are appreciable. It is concluded from the results that orbital evolution in a rich, relaxed cluster is unlikely to result in the growth of a very massive central galaxy.
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David Merritt (1985) studied this question.