Nonlinear stochastic biasing of halos: Analysis of cosmological N-body simulations and perturbation theories

It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological $N$-body simulations for a standard $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range $0\ensuremath{\le}z\ensuremath{\le}3$. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with $N$-body simulation results down to $r\ensuremath{\sim}15(10){h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.