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The very wide-field $gzK$ galaxy survey -- II. The relationship between star-forming galaxies at $z \sim 2$ and their host haloes based upon HOD modelling

We present the results of an halo occupation distribution (HOD) analysis of star-forming galaxies at $z \sim 2$. We obtained high-quality angular correlation functions based on a large sgzK sample, which enabled us to carry out the HOD analysis. The mean halo mass and the HOD mass parameters are found to increase monotonically with increasing $K$-band magnitude, suggesting that more luminous galaxies reside in more massive dark haloes. The luminosity dependence of the HOD mass parameters was found to be the same as in the local Universe; however, the masses were larger than in the local Universe over all ranges of magnitude. This implies that galaxies at $z \sim 2$ tend to form in more massive dark haloes than in the local Universe, a process known as downsizing. By analysing the dark halo mass evolution using the extended Press--Schechter formalism and the number evolution of satellite galaxies in a dark halo, we find that faint Lyman break galaxies at $z \sim 4$ could evolve into the faintest sgzKs $(22.0 < K \leq 23.0)$ at $z \sim 2$ and into the Milky-Way-like galaxies or elliptical galaxies in the local Universe, whereas the most luminous sgzKs $(18.0 \leq K \leq 21.0)$ could evolve into the most massive systems in the local Universe. The stellar-to-halo mass ratio (SHMR) of the sgzKs was found to be consistent with the prediction of the model, except that the SHMR of the faintest sgzKs was smaller than the prediction at $z \sim 2$. This discrepancy may be attributed that our samples are confined to star-forming galaxies.