The Scale Dependence of Halo and Galaxy Bias: Effects in Real Space

Abstract

We examine the scale dependence of dark matter, halo and galaxy clustering on very large scales (0.01<k[h/Mpc]<0.15), due to non-linear effects from dynamics and halo bias. We pursue a two line offensive: high resolution numerical simulations are used to establish several new results, and an analytic model is developed to understand their origins. Our simulations show: (i) that the z=0 dark matter power spectrum is suppressed relative to linear theory by ~5% on scales (0.05<k[h/Mpc]<0.075); (ii) that, indeed, halo bias is non-linear over the scales we probe and that the scale dependence is a strong function of halo mass. High mass haloes show no suppression of power on scales (k<0.07[h/Mpc]), and only show amplification on smaller scales, whereas low mass haloes show strong, ~5-10%, suppression over the range (0.05 <k[h/Mpc] <0.15). Our results have relevance for studies of the baryon acoustic oscillation features. Non-linear mode-mode coupling: (i) damps these features on progressively larger scales as halo mass increases; (ii) produces small shifts in the positions of the peaks and troughs which depend on halo mass. Our analytic model is described in the language of the `halo-model'. However, for the first time the halo-halo clustering term is propagated into the non-linear regime using `1-loop' perturbation theory and a non-linear halo bias model. We show that, with bias parameters derived from simulations, the model predictions are in agreement with the numerical results. We then use the model to explore the scale dependence of galaxies of different colour and find significant differences between the power spectra of the two populations. Thus understanding the scale dependent bias for a given galaxy sample will be crucial for deriving accurate cosmological constraints. (Abridged)