Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. IV. High Precision Constraints on the Evolution of Stellar-Halo Mass Relation at Redshift $z<0.7$

Abstract: Taking advantage of the Photometric objects Around Cosmic webs (PAC) method developed in Paper I, we measure the excess surface density $\bar{n}2w{{\rm{p}}}$ of photometric objects around spectroscopic objects down to stellar mass $10^{8.0}M_{\odot}$, $10^{9.2}M_{\odot}$ and $10^{9.8}M_{\odot}$ in the redshift ranges of $z_s<0.2$, $0.2<z_s<0.4$ and $0.5<z_s<0.7$ respectively, using the data from the DESI Legacy Imaging Surveys and the spectroscopic samples of Slogan Digital Sky Survey (i.e. Main, LOWZ and CMASS samples). We model the measured $\bar{n}2w{{\rm{p}}}$ in N-body simulation using abundance matching method and constrain the stellar-halo mass relations (SHMR) in the three redshift ranges to percent level. With the accurate modeling, we demonstrate that the stellar mass scatter for given halo mass is nearly a constant, and that the empirical form of Behroozi et al describes the SHMR better than the double power law form at low mass. Our SHMR accurately captures the downsizing of massive galaxies since $z_s=0.7$, while it also indicates that small galaxies are still growing faster than their host halos. The galaxy stellar mass functions (GSMF) from our modeling are in perfect agreement with the {\it model-independent} measurements in Paper III, though the current work extends the GSMF to a much smaller stellar mass. Based on the GSMF and SHMR, we derive the stellar mass completeness and halo occupation distributions for the LOWZ and CMASS samples, which are useful for correctly interpreting their cosmological measurements such as galaxy-galaxy lensing and redshift space distortion.