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($M_{\rm h}$) and various proxies for SDSS central galaxies, including stellar mass($M_*$), stellar velocity dispersion($\sigma_*$), abundance matching halo mass($M_{\rm AM}$) and satellite velocity dispersion($\sigma_{\rm s}$), and their dependencies on galaxy and group properties. In general, these proxies all have strong positive correlations with $M_{\rm h}$, consistent with previous studies. We find that the $M_{\rm h}$-$M_*$ and $M_{\rm h}$-$\sigma_*$ relations depend strongly on group richness($N_{\rm sat}$), while the $M_{\rm h}$-$M_{\rm AM}$ and $M_{\rm h}$-$\sigma_{\rm s}$ relations are independent of it. Moreover, the dependence on star formation rate(SFR) is rather weak in the $M_{\rm h}$-$\sigma_*$ and $M_{\rm h}$-$\sigma_{\rm s}$ relations, but very prominent in the other two. $\sigma_{\rm s}$ is thus the best proxy among them, and its scaling relation is in good agreement with hydro-dynamical simulations. However, estimating $\sigma_{\rm s}$ 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 $M_{\rm AM}$, and find the proxy with 30\% contribution from $M_{\rm AM}$ and 70\% from $\sigma_*$ can minimize the dependence on $N_{\rm sat}$ and SFR. We obtain the $M_{\rm h}$-supermassive black hole(SMBH) mass relation via the SMBH scaling relation and find indications for rapid and linear growth phases for SMBH. We also find that correlations among $M_{\rm h}$, $M_*$ and $\sigma_*$ change with $M_*$, indicating that different processes drive the growth of galaxies and SMBH at different stages.