Halo Mass-observable Proxy Scaling Relations and Their Dependencies on Galaxy and Group Properties

Based on the DECaLS shear catalog, we study the scaling relations between halo mass (M h) and various proxies for Sloan Digital Sky Survey central galaxies, including stellar mass (M *), stellar velocity dispersion (sigma *), abundance-matching halo mass (M AM), and satellite velocity dispersion (sigma s), and their dependencies on galaxy and group properties. In general, these proxies all have strong positive correlations with M h, consistent with previous studies. We find that the M h-M * and M h-sigma * relations depend strongly on group richness (N sat), while the M h-M AM and M h-sigma s relations are independent of it. Moreover, the dependence on the star formation rate (SFR) is rather weak in the M h-sigma * and M h-sigma s relations, but very prominent in the other two. sigma s is thus the best proxy among them, and its scaling relation is in good agreement with hydrodynamical simulations. However, estimating sigma s accurately for individual groups/clusters is challenging because of interlopers and the requirement for sufficient satellites. We construct new proxies by combining M *, sigma *, and M AM, and find that the proxy with 30% contribution from M AM and 70% from sigma * can minimize the dependence on N sat and the SFR. We obtain the M h-supermassive black hole (SMBH) mass relation via the SMBH scaling relation and find indications for rapid and linear growth phases for the SMBH. We also find that correlations among M h, M *, and sigma * change with M *, indicating that different processes drive the growth of galaxies and SMBHs at different stages.