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Dissipationless Merging and the Assembly of Central Galaxies

We reanalyze the galaxy-mass correlation function measured by the Sloan Digital Sky Survey to obtain host dark matter halo masses at galaxy and galaxy group scales. We extend the data to galaxy clusters in the 2MASS catalog and study the relation between central galaxy luminosity and halo mass. While the central galaxy luminosity scales as ~M^{0.7-0.8} at low masses, the relation flattens to ~M^{<0.3} above ~4x10^{13} M_sun. The total luminosity of galaxies in the halo, however, continues to grow as a power-law ~M^{0.8-0.9}. Starting from the hypothesis that the central galaxies grow by merging ("galactic cannibalism"), we develop a simple model for the evolution of their luminosities as a consequence of the accretion of satellite galaxies. The luminosity-mass relation flattens when the time scale on which dynamical friction induces orbital decay in the satellite galaxies exceeds the age of the dark matter halo. Then, the growth of the central galaxy is suppressed as it can cannibalize only the rare, massive satellite galaxies. The model takes the dependence of the total luminosity of galaxies in a halo on its mass and the global galaxy luminosity function as input, and reproduces the observed central galaxy luminosity-mass relation over three decades in halo mass, (10^{12}-10^{15}) M_sun. The success of the model suggests that gas cooling and subsequent star formation did not play an important role in the final assembly of central galaxies from sub-L_star precursors.