Binary Aggregations in Hierarchical Galaxy Formation: The Evolution of the Galaxy Luminosity Function

We develop a semi-analytic model of hierarchical galaxy formation with an improved treatment of the evolution of galaxies inside dark matter haloes. 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 described using the kinetic Smoluchowski equation. The description of gas cooling, star formation and evolution, and Supernova feedback follows the standard prescriptions widely used in semi-analytic modelling. 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~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 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 semi-analytic models with the observations is considerably reduced at z>1 and even more at z ~ 3 by the effect of binary aggregations. The predictions from our dynamical model are discussed and compared with the effects of complementary processes which may conspire in affecting the shape of the luminosity function.