How do galaxies populate Dark Matter halos?

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 108M⊙ < M∗ < 10 12M⊙. Within the concordance ΛCDM cosmology, the Millennium simulations give precise halo abundances as a function of mass and redshift for all halos 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 is in quite good agreement with gravitational lensing analysis of mean halo mass as a function of stellar mass from SDSS data, but for large stellar masses it is substantially and significantly larger than similar mean halo mass estimates from a stacking analysis of SDSS satellite dynamics. For M∗ = 6 × 10 10M⊙, the stellar mass usually assumed for the Milky Way, the implied halo mass is 2.6×1012M⊙, larger than most (but not all) recent direct estimates, but consistent with 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% at masses somewhat below that of the Milky Way, and falls rapidly at both higher and lower masses. These conversion efficiencies are lower than in most 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 is also consistent with observation, indicating that galaxy luminosity functions and Tully-Fisher relations can be reproduced simultaneously in a ΛCDM cosmology.