Modelling and interpreting the dependence of clustering on the spectral energy distributions of galaxies

We extend our previous physically-based halo occupation distribution models to include the dependence of clustering on the spectral energy distributions of galaxies. The high resolution Millennium Simulation is used to specify the positions and the velocities of the model galaxies. The stellar mass of a galaxy is assumed to depend only on M_{infall}, the halo mass when the galaxy was last the central dominant object of its halo. Star formation histories are parametrized using two additional quantities that are measured from the simulation for each galaxy: its formation time (t_{form}), and the time when it first becomes a satellite (t_{infall}). Central galaxies begin forming stars at time t_{form} with an exponential time scale tau_c. If the galaxy becomes a satellite, its star formation declines thereafter with a new time scale tau_s. We compute 4000 \AA break strengths for our model galaxies using stellar population synthesis models. By fitting these models to the observed abundances and projected correlations of galaxies as a function of break strength in the Sloan Digital Sky Survey, we constrain tau_c and tau_s as functions of galaxy stellar mass. We find that central galaxies with large stellar masses have ceased forming stars. At low stellar masses, central galaxies display a wide range of different star formation histories, with a significant fraction experiencing recent starbursts. Satellite galaxies of all masses have declining star formation rates, with similar e-folding times, tau_s ~ 2.5Gyr. One consequence of this long e-folding time is that the colour-density relation is predicted to flatten at redshifts > 1.5, because star formation in the majority of satellites has not yet declined by a significant factor. This is consistent with recent observational results from the DEEP and VVDS surveys