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.
