How do galaxies populate dark matter haloes?

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<inf>⊙</inf> < <it>M</it><inf>*</inf> < 1012 M<inf>⊙</inf>. 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…