The Galaxy--Halo Connection in High-Redshift Universe: Details and Evolution of Stellar-to-Halo Mass Ratios of Lyman Break Galaxies on CFHTLS Deep Fields

We present the results of clustering analyses of Lyman break galaxies (LBGs) at $z\sim3$, $4$, and $5$ using the final data release of the Canada--France--Hawaii Telescope Legacy Survey (CFHTLS). Deep- and wide-field images of the CFHTLS Deep Survey enable us to obtain sufficiently accurate two-point angular correlation functions to apply a halo occupation distribution analysis. Mean halo masses, calculated as $\langle M_{h} \rangle=10^{11.7}-10^{12.8}h^{-1}M_{\odot}$, increase with stellar-mass limit of LBGs. The threshold halo mass to have a central galaxy follows the same increasing trend with the low-$z$ results, whereas the threshold halo mass to have a satellite galaxy shows higher values at $z=3-5$ than $z=0.5-1.5$ over the entire stellar mass range. Satellite fractions of dropout galaxies, even at less massive haloes, are found to drop sharply from $z=2$ down to less than $0.04$ at $z=3-5$. These results suggest that satellite galaxies form inefficiently within dark haloes at $z=3-5$ even for less massive satellites with $M_{\star}<10^{10}M_{\odot}$. We compute stellar-to-halo mass ratios (SHMRs) assuming a main sequence of galaxies, which is found to provide consistent SHMRs with those derived from a spectral energy distribution fitting method. The observed SHMRs are in good agreement with the model predictions based on the abundance-matching method within $1\sigma$ confidence intervals. We derive observationally, for the first time, $M_{{\rm h}}^{{\rm pivot}}$, which is the halo mass at a peak in the star-formation efficiency, at $3<z<5$, and it shows a little increasing trend with cosmic time at $z>3$. In addition, $M_{{\rm h}}^{{\rm pivot}}$ and its normalization are found to be almost unchanged during $0<z<5$. Our study shows an observational evidence that galaxy formation is ubiquitously most efficient near a halo mass of $M_{{\rm h}}\sim10^{12}M_{\odot}$ over cosmic time.