Binary aggregations in hierarchical galaxy formation: The evolution of the galaxy luminosity function

We develop a semianalytic model of hierarchical galaxy formation with an improved treatment of the evolution of galaxies inside dark matter halos. We take into account not only dynamical friction processes building up the central dominant galaxy but also binary aggregations of satellite galaxies inside a common halo. These deplete small to intermediate mass objects, affecting the slope of the luminosity function at its faint end, with significant observable consequences. We model the effect of two-body aggregations using the kinetic Smoluchowski equation. This flattens the mass function by an amount that depends on the histories of the host halos as they grow by hierarchical clustering. The description of gas cooling, star formation and evolution, and supernova feedback follows the standard prescriptions widely used in semianalytic modeling. We find that binary aggregations are effective in depleting the number of small/intermediate mass galaxies over the redshift range 1 < z < 3, thus flattening the slope of the luminosity function at the faint end. At z approximate to 0 the flattening occurs for -20 < M-B < 18, but an upturn is obtained at the very faint end for M-B > 16. We compare our predicted luminosity functions with those obtained from deep multicolor surveys in the Hubble Deep Field North, Hubble Deep Field South, and New Technology Telescope Deep Field in the rest-frame B and UV bands for the redshift ranges 0 < z < 1 and 2.5 < z < 3.5, respectively. The comparison shows that the discrepancy of the predictions of other semianalytic models with the observations is considerably reduced at z > 1 and even more at z approximate to 3 by the effect of the binary aggregations. The predictions from our dynamical model are discussed and compared with the effects of complementary processes ( additional starburst recipes, alternative sources of feedback, different mass distribution of the dark matter halos) that may conspire in affecting the shape of the luminosity function.