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 ( σ _* ), abundance-matching halo mass ( M _AM ), and satellite velocity dispersion ( σ _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 – σ _* relations depend strongly on group richness ( N _sat ), while the M _h – M _AM and M _h – σ _s relations are independent of it. Moreover, the dependence on the star formation rate (SFR) is rather weak in the M _h – σ _* and M _h – σ _s relations, but very prominent in the other two. σ _s is thus the best proxy among them, and its scaling relation is in good agreement with hydrodynamical simulations. However, estimating σ _s accurately for individual groups/clusters is challenging because of interlopers and the requirement for sufficient satellites. We construct new proxies by combining M _* , σ _* , and M _AM , and find that the proxy with 30% contribution from M _AM and 70% from σ _* 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 σ _* change with M _* , indicating that different processes drive the growth of galaxies and SMBHs at different stages.