Modelling galaxy clustering in a high-resolution simulation of structure formation

We use the Millennium Simulation, a 10 billion particle simulation of the growth of cosmic structure, to construct a new model of galaxy clustering. We adopt a methodology that falls midway between the traditional semi-analytic approach and the halo occupation distribution (HOD) approach. In our model, we adopt the positions and velocities of the galaxies that are predicted by following the orbits and merging histories of the substructures in the simulation. Rather than using star formation and feedback `recipes' to specify the physical properties of the galaxies, we adopt parametrized functions to relate these properties to the quantity M₈₍₅₀₋₋, defined as the mass of the halo at the epoch when the galaxy was last the central dominant object in its own halo. We test whether these parametrized relations allow us to recover the basic statistical properties of galaxies in the semi-analytic catalogues, including the luminosity function, the stellar mass function and the shape and amplitude of the two-point correlation function evaluated in different stellar mass and luminosity ranges. We then use our model to interpret recent measurements of these quantities from Sloan Digital Sky Survey data. We derive relations between the luminosities and the stellar masses of galaxies in the local Universe and their host halo masses. Our results are in excellent agreement with recent determinations of these relations by Mandelbaum et al using galaxy-galaxy weak lensing measurements from the SDSS.