The effect of a cusped matter distribution on the formation of brightest   cluster members
  We present N-body simulations of galaxy groups embedded in a common halo of matter. We study the influence of the different initial conditions upon the evolution of the group and show that denser configurations evolve faster, as expected. We then concentrate on the influence of the initial radial density profile of the common halo and of the galaxy distribution. We select two kinds of density distributions, a singular profile (modeled by a Hernquist distribution) and a profile with a flat core (modeled by a Plummer sphere). In all cases we witness the formation of a central massive object due to mergings of individual galaxies and to accretion of stripped material, but both its formation history and its properties depend heavily on the initial distribution. In Hernquist models the formation is due to a ``burst'' of mergings in the inner parts, due to the large initial concentration of galaxies in the center. The merging rate is much slower in the initial phases of the evolution of a Plummer distribution, where the contribution of accretion to the formation of the central object is much more important. The central objects formed within Plummer distributions have projected density profiles which are not in agreement with the radial profiles of observed brightest cluster members, unless the percentage of mass in the common halo is small. On the contrary the central object formed in initially cusped models has projected radial profiles in very good agreement with those of brightest cluster members, sometimes also showing luminosity excess over the $r^{1/4}$ law in the outer parts, as is observed in cD galaxies. 
E. Athanassoula, A. Garijo and C. Garcia