Most clusters have a giant elliptical or cD galaxy near their spatial and kinematic center. (They are generically known as brightest cluster galaxies or BCGs). There have been various theories put forward for the origin of these galaxy giants including star formation in X-ray cooling flows (Fabian 1994), galactic cannibalism and tidal destruction of small galaxies (Richstone 1976; Ostriker & Tremaine 1975), and early galaxy merging during the collapse of cluster core in hierarchical structure formation (Merritt 1985). There is little evidence of young stars in BCG's which refutes the cooling flow idea and galactic cannibalism can only account for a small fraction of the luminosity of a BCG since merging is inefficient in virialized clusters - galaxies are moving fast and tidally truncated so dynamical friction timescales are too long to allow much merging.
The idea that seems to work the best is rapid galaxy merging in a cosmological
hierarchy and has recently been illustrated by Dubinski (1998) in a
simulation of a poor cluster.
The 7 most massive galaxies in the collapsing cluster merge rapidly
forming a BCG by 
building up the bulk of its luminosity.
The BCG accretes a further 6 ``dwarf'' galaxies (
km/s) but they do not add much extra mass. The structure and
kinematics of the resulting simulated BCG agree quantitatively with real
ones (cf. Fisher et al. 1995)
with de Vaucouleurs light profiles (
kpc) and central velocity dispersions in the right range
km/s). Furthermore, the BCG displays the alignment effect: its
long axis is closely aligned with the long axis of the galaxy distribution
(Sastry 1968; Carter & Metcalfe 1980). This can be traced back to the
collapse of the cluster along the filament present in the cosmological
initial conditions supporting conjectures that BCG's show alignment
correlations with large-scale structure (Binggeli 1982).
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