Testing Galaxy Formation Models with the Stellar Mass-Halo Mass Relations for Star-forming and Quiescent Galaxies

The tight relationship between the stellar mass and halo mass of galaxies is one of the most fundamental scaling relations in galaxy formation and evolution. It has become a critical constraint for galaxy formation models. Over the past decade, growing evidence has convincingly shown that the stellar mass-halo mass relations (SHMRs) for star-forming and quiescent central galaxies differ significantly: at a given stellar mass, the average host halo mass of quiescent centrals is more massive than that of star-forming centrals. Despite the importance of this feature, its scientific implications have not yet been fully recognized or thoroughly explored in the field. In this work, we demonstrate that the semi-analytical model L-GALAXIES successfully reproduces these observational results, whereas three state-of-the-art hydrodynamic galaxy formation simulations (TNG, Illustris, and EAGLE) do not. Consequently, in L-GALAXIES, star-forming central galaxies are more efficient at converting baryons into stars than quiescent central galaxies at a given halo mass, while the other models predict similar efficiencies for both populations. Further analysis reveals that these fundamental discrepancies stem from distinct evolutionary paths on the stellar mass-halo mass plane. We show that the observed SHMRs for star-forming and quiescent galaxies support galaxy formation models in which quenching only weakly correlates with halo assembly histories and the stellar mass of star-forming galaxies can increase significantly after cosmic noon. In contrast, models in which quenching strongly preferentially happens in early-formed halos are not very favored. Additionally, we find that galaxy downsizing is present in L-GALAXIES and TNG but absent in Illustris and EAGLE.