The stellar-to-halo mass relation over the past 12 Gyr

Aims. Understanding the link between the galaxy properties and the dark matter halos they reside in and their coevolution is a powerful tool for constraining the processes related to galaxy formation. In particular, the stellar-to-halo mass relation (SHMR) and its evolution throughout the history of the Universe provides insights on galaxy formation models and allows us to assign galaxy masses to halos in N-body dark matter simulations. To address these questions, we determine the SHMR throughout the entire cosmic history from z ∼ 4 to the present. Methods. We used a statistical approach to link the observed galaxy stellar mass functions on the COSMOS field to dark matter halo mass functions up to z ∼ 4 from the ΛCDM DUSTGRAIN-pathfinder simulation, which is complete for Mh > 1012.5 M⊙, and extended this to lower masses with a theoretical parameterization. We propose an empirical model to describe the evolution of the SHMR as a function of redshift (either in the presence or absence of a scatter in stellar mass at fixed halo mass), and compare the results with several literature works and semianalytic models of galaxy formation. We also tested the reliability of our results by comparing them to observed galaxy stellar mass functions and to clustering measurements. Results. We derive the SHMR from z = 0 to z = 4, and model its empirical evolution with redshift. We find that M*/Mh is always lower than ∼0.05 and depends both on redshift and halo mass, with a bell shape that peaks at Mh ∼ 1012 M⊙. Assuming a constant cosmic baryon fraction, we calculate the star-formation efficiency of galaxies and find that it is generally low; its peak increases with cosmic time from ∼30% at z ∼ 4 to ∼35% at z ∼ 0. Moreover, the star formation efficiency increases for increasing redshifts at masses higher than the peak of the SHMR, while the trend is reversed for masses lower than the peak. This indicates that massive galaxies (i.e., galaxies hosted at halo masses higher than the SHMR peak) formed with a higher efficiency at higher redshifts (i.e., downsizing effect) and vice versa for low-mass halos. We find a large scatter in results from semianalytic models, with a difference of up to a factor ∼8 compared to our results, and an opposite evolutionary trend at high halo masses. By comparing our results with those in the literature, we find that while at z ∼ 0 all results agree well (within a factor of ∼3), at z > 0 many differences emerge. This suggests that observational and theoretical work still needs to be done. Our results agree well (within ∼10%) with observed stellar mass functions (out to z = 4) and observed clustering of massive galaxies (M* > 1011 M⊙ from z ∼ 0.5 to z ∼ 1.1) in the two-halo regime.