We have updated and extended our semi-analytic galaxy formation modelling capabilities and applied them simultaneously to the stored halo/subhalo merger trees of the Millennium and Millennium-II Simulations (MS and MS-II, respectively). These differ by a factor of 125 in mass resolution, allowing explicit testing of resolution effects on predicted galaxy properties. We have revised the treatment of the transition between the rapid infall and cooling flow regimes of gas accretion, of the sizes of bulges, and of gaseous and stellar discs, of supernova feedback, of the transition between central and satellite status as galaxies fall into larger systems, and of gas and star stripping, once they become satellites. Plausible values of efficiency and scaling parameters yield an excellent fit not only to the observed abundance of low-redshift galaxies over five orders of magnitude in stellar mass and 9 mag in luminosity, but also to the observed abundance of Milky Way satellites. This suggests that reionization effects may not be needed to solve the 'missing-satellite' problem, except, perhaps, for the faintest objects. The same model matches the observed large-scale clustering of galaxies as a function of stellar mass and colour. The fit remains excellent down to ∼30 kpc for massive galaxies. For M * < 6 × 10 10 M , however, the model overpredicts clustering at scales below ∼1 Mpc, suggesting that the assumed fluctuation amplitude, σ 8 = 0.9, is too high. The observed difference in clustering between active and passive galaxies is matched quite well for all masses. Galaxy distributions within rich clusters agree between the simulations and match those observed, but only if galaxies without dark matter subhaloes (so-called orphans) are included. Even at MS-II resolution, schemes which assign galaxies only to resolved dark matter subhaloes cannot match observed clusters. Our model predicts a larger passive fraction among low-mass galaxies than is observed, as well as an overabundance of ∼10 10 M galaxies beyond z ∼ 0.6. (The abundance of ∼10 11 M galaxies is matched out to z ∼ 3.) These discrepancies appear to reflect deficiencies in the way star formation rates are modelled.

For any assumed standard stellar initial mass function, the Sloan Digital Sky Survey (SDSS) gives a precise determination of the abundance of galaxies as a function of their stellar mass over the full stellar mass range 108 M⊙ < M* < 1012 M⊙. Within the concordance Λ cold dark matter (ΛCDM) cosmology, the Millennium Simulations give precise halo abundances as a function of mass and redshift for all haloes within which galaxies can form. Under the plausible hypothesis that the stellar mass of a galaxy is an increasing function of the maximum mass ever attained by its halo, these results combine to give halo mass as a function of stellar mass. The result agrees quite well with observational estimates of mean halo mass as a function of stellar mass from stacking analyses of the gravitational lensing signal and the satellite dynamics of SDSS galaxies. For M*∼ 5.5 × 1010 M⊙, the stellar mass usually assumed for the Milky Way (MW), the implied halo mass is ∼2 × 1012 M⊙, consistent with most recent direct estimates and inferences from the MW/M31 timing argument. The fraction of the baryons associated with each halo which are present as stars in its central galaxy reaches a maximum of 20 per cent at masses somewhat below that of the MW and falls rapidly at both higher and lower masses. These conversion efficiencies are lower than in almost all recent high‐resolution simulations of galaxy formation, showing that these are not yet viable models for the formation of typical members of the galaxy population. When inserted in the Millennium‐II Simulation, our derived relation between stellar mass and halo mass predicts a stellar mass autocorrelation function in excellent agreement with that measured directly in the SDSS. The implied Tully–Fisher relation also appears consistent with observation, suggesting that galaxy luminosity functions and Tully–Fisher relations can be reproduced simultaneously in a ΛCDM cosmology.

We estimate the galaxy stellar mass function and stellar mass density for star-forming and quiescent galaxies with 0.2 < z < 4. We construct a large, deep (K s < 24) sample of 220 000 galaxies selected using the new UltraVISTA DR1 data release. Our analysis is based on precise 30-band photometric redshifts. By comparing these photometric redshifts with 10,800 spectroscopic redshifts from the zCOSMOS bright and faint surveys, we find a precision of σ Δz/(1+z) = 0.008 at i + < 22.5 and σ Δz/(1+z) = 0.03 at 1.5 < z < 4. We derive the stellar mass function and correct for the Eddington bias. We find a mass-dependent evolution of the global and starforming populations, with the low-mass end of the mass functions evolving more rapidly than the high-mass end. This mass-dependent evolution is a direct consequence of the star formation being "quenched" in galaxies more massive than M 10 10.7−10.9 M . For the mass function of the quiescent galaxies, we do not find any significant evolution of the high-mass end at z < 1; however we observe a clear flattening of the faint-end slope. From z ∼ 3 to z ∼ 1, the density of quiescent galaxies increases over the entire mass range. Their comoving stellar mass density increases by 1.6 dex between z ∼ 3 and z ∼ 1 and by less than 0.2 dex at z < 1. We infer the star formation history from the mass density evolution. This inferred star formation history is in excellent agreement with instantaneous star formation rate measurements at z < 1.5, while we find differences of 0.2 dex at z > 1.5 consistent with the expected uncertainties. We also develop a new method to infer the specific star formation rate from the mass function of star-forming galaxies. We find that the specific star formation rate of 10 10−10.5 M galaxies increases continuously in the redshift range 1 < z < 4. Finally, we compare our results with a semi-analytical model and find that these models overestimate the density of low mass quiescent galaxies by an order of magnitude, while the density of low-mass star-forming galaxies is successfully reproduced.Key words. galaxies: distances and redshifts -galaxies: evolution -galaxies: formation -galaxies: star formationgalaxies: stellar content Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID 179.A-2005 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium.Catalogues are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via