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We present the results of an halo occupation distribution (HOD) analysis ofstar-forming galaxies at $z \sim 2$. We obtained high-quality angularcorrelation functions based on a large sgzK sample, which enabled us to carryout the HOD analysis. The mean halo mass and the HOD mass parameters are foundto increase monotonically with increasing $K$-band magnitude, suggesting thatmore luminous galaxies reside in more massive dark haloes. The luminositydependence of the HOD mass parameters was found to be the same as in the localUniverse; however, the masses were larger than in the local Universe over allranges of magnitude. This implies that galaxies at $z \sim 2$ tend to form inmore massive dark haloes than in the local Universe, a process known asdownsizing. By analysing the dark halo mass evolution using the extendedPress--Schechter formalism and the number evolution of satellite galaxies in adark halo, we find that faint Lyman break galaxies at $z \sim 4$ could evolveinto the faintest sgzKs $(22.0 < K \leq 23.0)$ at $z \sim 2$ and into theMilky-Way-like galaxies or elliptical galaxies in the local Universe, whereasthe most luminous sgzKs $(18.0 \leq K \leq 21.0)$ could evolve into the mostmassive systems in the local Universe. The stellar-to-halo mass ratio (SHMR) ofthe sgzKs was found to be consistent with the prediction of the model, exceptthat the SHMR of the faintest sgzKs was smaller than the prediction at $z \sim2$. This discrepancy may be attributed that our samples are confined tostar-forming galaxies.

monthly notices of the royal astronomical society

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