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 ($0.01<k[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]<0.15$), due to nonlinear effects from dynamics and halo bias. We pursue a two line offensive: high-resolution numerical simulations are used to establish some old and some 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 $\ensuremath{\sim}5%$ on scales $0.05<k[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]<0.075$; (ii) that, indeed, halo bias is nonlinear 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 $k<0.07[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]$, and only show amplification on smaller scales, whereas low mass haloes show strong, $\ensuremath{\sim}5%--10%$, suppression over the range $0.05<k[h\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}]<0.15$. These results were primarily established through the use of the cross-power spectrum of dark matter and haloes, which circumvents the thorny issue of shot-noise correction. The halo-halo power spectrum, however, is highly sensitive to the shot-noise correction; we show that halo exclusion effects make this sub-Poissonian and a new correction is presented. Our results have special relevance for studies of the baryon acoustic oscillation features in the halo power spectra. Nonlinear 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. We show that these effects on halo clustering are important over the redshift range relevant to such studies $(0<z<2)$, and so will need to be accounted for when extracting information from precision measurements of galaxy clustering. Our analytic model is described in the language of the ``halo model.'' The halo-halo clustering term is propagated into the nonlinear regime using ``1-loop'' perturbation theory and a nonlinear halo bias model. Galaxies are then inserted into haloes through the halo occupation distribution. We show that, with nonlinear bias parameters derived from simulations, this model produces predictions that are qualitatively in agreement with our numerical results. We then use it to show that the power spectra of red and blue galaxies depend differently on scale, thus underscoring the fact that proper modeling of nonlinear bias parameters will be crucial to derive reliable cosmological constraints. In addition to showing that the bias on very large scales is not simply linear, the model also shows that the halo-halo and halo-dark matter spectra do not measure precisely the same thing. This complicates interpretation of clustering in terms of the stochasticity of bias. However, because the shot-noise correction is nontrivial, evidence for this in the simulations is marginal.