The influence of galaxy mergers on the mass dispersion of brightest
  cluster galaxies
  The absolute magnitude of the brightest galaxy of clusters varies remarkably
little and is nearly independent of all other physical properties of the
cluster as, e.g., its spatial extension or its richness. The question arises
whether the observed small scatter is compatible with the assumption of
dynamical evolution of the cluster. This is investigated with the help of
statistical analysis of the results of cluster simulation. The underlying
interaction process is merging (and also destruction) of smaller galaxies
forming the giant galaxy. The cluster itself is supposed to be in virial
equilibrium.
  We find that the evolutionary importance of merger processes grows with
decreasing scale. Rich clusters as well as their brightest members evolve
merely slowly whereas compact groups as well as their brightest members evolve
more rapidly and more violently. We also find that the number of merger
processes leading to the growth of the brightest cluster galaxy (BCG) is small
enough to keep the BCG mass dispersion below the measured value. Our
simulations substantiate that just the combination of the initial distribution
function and the following merging to form the BCG can explain the remarkably
small variance of mean BCG masses between clusters of different size and
different number of galaxies.
