NEW CONSTRAINTS ON THE EVOLUTION OF THE STELLAR-TO-DARK MATTER CONNECTION: A COMBINED ANALYSIS OF GALAXY-GALAXY LENSING, CLUSTERING, AND STELLAR MASS FUNCTIONS FROM<i>z</i>= 0.2 to<i>z</i>= 1

Using data from the COSMOS survey, we perform the first joint analysis of galaxy-galaxy weak lensing, galaxy spatial clustering, and galaxy number densities. Carefully accounting for sample variance and for scatter between stellar and halo mass, we model all three observables simultaneously using a novel and self-consistent theoretical framework. Our results provide strong constraints on the shape and redshift evolution of the stellar-to-halo mass relation (SHMR) from z = 0.2 to z = 1. At low stellar mass, we find that halo mass scales as Mh vpropM 0.46 * and that this scaling does not evolve significantly with redshift from z = 0.2 to z = 1. The slope of the SHMR rises sharply at M * &gt; 5 × 1010 M ☉ and as a consequence, the stellar mass of a central galaxy becomes a poor tracer of its parent halo mass. We show that the dark-to-stellar ratio, Mh /M *, varies from low to high masses, reaching a minimum of Mh /M * ~ 27 at M * = 4.5 × 1010 M ☉ and Mh = 1.2 × 1012 M ☉. This minimum is important for models of galaxy formation because it marks the mass at which the accumulated stellar growth of the central galaxy has been the most efficient. We describe the SHMR at this minimum in terms of the "pivot stellar mass," M piv *, the "pivot halo mass," M piv h , and the "pivot ratio," (Mh /M *)piv. Thanks to a homogeneous analysis of a single data set spanning a large redshift range, we report the first detection of mass downsizing trends for both M piv h and M piv *. The pivot stellar mass decreases from M piv * = 5.75 ± 0.13 × 1010 M ☉ at z = 0.88 to M piv * = 3.55 ± 0.17 × 1010 M ☉ at z = 0.37. Intriguingly, however, the corresponding evolution of M piv h leaves the pivot ratio constant with redshift at (Mh /M *)piv ~ 27. We use simple arguments to show how this result raises the possibility that star formation quenching may ultimately depend on Mh /M * and not simply on Mh , as is commonly assumed. We show that simple models with such a dependence naturally lead to downsizing in the sites of star formation. Finally, we discuss the implications of our results in the context of popular quenching models, including disk instabilities and active galactic nucleus feedback.