LAUSR

The star formation and quenching of central galaxies are regulated by the assembly histories of their host halos. In this work, we use the central stellar mass to halo mass ratio as a proxy of halo formation time, and we devise three different models, from the physical hydrodynamical simulation to the empirical statistical model, to demonstrate its robustness. With this proxy, we inferred the dependence of the central galaxy properties on the formation time of their host halos using the SDSS main galaxy sample, where central galaxies are identified with the halo-based group finder. We found that central galaxies living in late-formed halos have higher quiescent fractions and lower spiral fractions than their early-formed counterparts by $\lesssim 8\%$. Finally, we demonstrate that the group finding algorithm has a negligible impact on our results.