In a previous paper, we presented an approach (based on the perturbative solution of a Boltzmann-Liouville equation) aimed at deriving the velocity distribution for aggregating galaxies in the potential well of galaxy clusters, averaged over the cluster volume. This approach succeeded in explaining both the value β < 1 of the ratio of galaxy to gas energy density measured in several clusters and the velocity bias found in several N-body simulations. Further evidence for galaxy aggregations in the cluster cores may be constituted by the rising velocity dispersion profiles found recently in the central regions of many clusters. In this paper, we develop our previous approach to derive the velocity distribution as a function of the distance r from the cluster center, and hence we compute the galaxy velocity dispersion as a function of r (velocity dispersion profiles [VDPs]). The results depend upon the depth of the cluster potential wells, which can be measured by the X-ray temperature T. We find that, in clusters with T < 6.5 keV, the efficiency of galaxy merging in the central, denser regions causes the dissipation of galaxy orbital energy. The decrease of this effect with the distance from the cluster center (due to the decrease of galaxy density) gives rise to rising VDPs, associated with a galaxy average velocity dispersion smaller than that, of the dark matter. Thus, in such clusters, increasing VDPs are expected to be correlated with a β parameter (measured from combined optical and X-ray observations) smaller than 1. In clusters with T > 8 keV, merging is not efficient and the galaxy velocity dispersion follows the radial decrease of the dark matter velocity dispersion, characterizing most models of cluster dark matter distribution. In clusters with X-ray temperature in the range 6.5 keV approx < T approx < 8 keV, the VDPs depend critically on the shape of the gravitational potential. We discuss the dependence of such effects upon the parameters defining the cluster potential wells in the usual King models. Finally, we compare our results with recent data, finding quantitative agreement with the predictions of our model.
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