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.

We show that dissipationless LCDM simulations predict that the majority of the most massive subhaloes of the Milky Way are too dense to host any of its bright satellites (L_V > 10^5 L_sun). These dark subhaloes have circular velocities at infall of 30-70 km/s and infall masses of [0.2-4] x 10^10 M_sun. Unless the Milky Way is a statistical anomaly, this implies that galaxy formation becomes effectively stochastic at these masses. This is in marked contrast to the well-established monotonic relation between galaxy luminosity and halo circular velocity (or halo mass) for more massive haloes. We show that at least two (and typically four) of these massive dark subhaloes are expected to produce a larger dark matter annihilation flux than Draco. It may be possible to circumvent these conclusions if baryonic feedback in dwarf satellites or different dark matter physics can reduce the central densities of massive subhaloes by order unity on a scale of 0.3 - 1 kpc.Comment: 6 pages, 5 figures; matches version accepted by MNRAS Letter

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.

The Feedback In Realistic Environments (FIRE) project explores feedback in cosmological galaxy formation simulations. Previous FIRE simulations used an identical source code ("FIRE-1") for consistency. Motivated by the development of more accurate numerics -including hydrodynamic solvers, gravitational softening, and supernova coupling algorithms -and exploration of new physics (e.g. magnetic fields), we introduce "FIRE-2", an updated numerical implementation of FIRE physics for the GIZMO code. We run a suite of simulations and compare against FIRE-1: overall, FIRE-2 improvements do not qualitatively change galaxy-scale properties. We pursue an extensive study of numerics versus physics. Details of the star-formation algorithm, cooling physics, and chemistry have weak effects, provided that we include metal-line cooling and star formation occurs at higher-than-mean densities. We present new resolution criteria for high-resolution galaxy simulations. Most galaxy-scale properties are robust to numerics we test, provided: (1) Toomre masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved. Stellar masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followed by properties of winds and circum-galactic media (CGM). Central (∼kpc) mass concentrations in massive (> L * ) galaxies are sensitive to numerics (via trapping/recycling of winds in hot halos). Multiple feedback mechanisms play key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels late star formation; radiative feedback suppresses accretion onto dwarfs and instantaneous star formation in disks. We provide all initial conditions and numerical algorithms used.