Luminosity segregation from merging in clusters of galaxies

We compute the evolution of the space-dependent mass distribution of galaxies in clusters that arise from binary aggregations by solving a space-dependent Smoluchowski equation. From the solutions, we derive the distribution of intergalactic distances for different ranges of mass (and corresponding magnitudes). We compare the results with the observed distributions and find that the different degrees of luminosity segregation observed in clusters are well accounted for by our merging model. In addition, the presence of luminosity segregation is related to dynamical effects that also show up in different but connected observables, such as galaxy velocity profiles that decrease toward the center and X-ray-measured beta-parameters smaller than 1. We predict that both luminosity segregation and the observables above (being a product of binary aggregations) are inversely correlated with the core radius and with the galaxy velocity dispersion; we also discuss how the whole set of predictions compares with up-to-date observations.