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 similar to M-0.7 to M-0.8 at low masses, the relation flattens to shallower than similar to M-0.3 above similar to 4 x 10(13) M-circle dot. The total luminosity of galaxies in the halo, however, continues to grow as a power law similar to M-0.8-M-0.9. Starting from the hypothesis that the central galaxies grow by hierarchical merging ("galactic cannibalism"), we develop a simple model for the evolution of their luminosities as a consequence of the accretion of satellite galaxies, tracking the merging of dark matter halos. The luminosity-mass relation flattens when the timescale 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 3 decades in halo mass, 10(12)-10(15) M,. 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-* precursors.