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 ÿ1 < 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 5% on scales 0:05 < k h Mpc ÿ1 < 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 Mpc ÿ1 , and only show amplification on smaller scales, whereas low mass haloes show strong, 5%-10%, suppression over the range 0:05 < k h Mpc ÿ1 < 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 shotnoise correction is nontrivial, evidence for this in the simulations is marginal.

Combining perturbation theories with halo models

“…In practice, one often replaces the 2-halo term by the linear two-point correlation, or power spectrum, to reproduce linear theory on large scales. Previous works (Cooray & Sheth 2002;Smith et al 2003Smith et al , 2007Giocoli et al 2010) have shown that halo models provide a good match to numerical simulations, especially at high k, whereas Lagrangian mappings based on the stable clustering ansatz (Peebles 1980) do not fare as well.…”

“…It is also possible to combine perturbation theory and nonlinear halo bias to make the expression above consistent with standard perturbation theory while building a model for the halo power spectrum itself, see Smith et al (2007). Of course, in order to describe the weakly nonlinear regime one can as well replace P L (k) by P pert (k) in Eq.…”

What can the spatial distribution of galaxy clusters tell about their scaling relations?

“…Even though it is beyond the scope of this paper to discuss the impact of the systematic effects present on the modeling of the quantities mentioned above, we recognize their relevance in extracting accurate information regarding the parameters describing the observed clustering pattern of galaxy clusters (especially using the luminosity power spectrum) from forthcoming galaxy and galaxy cluster surveys such as eROSITA, DES (The Dark Energy Survey Collaboration 2005), or Euclid (Laureijs et al 2011). We notice that the only model that we have explicitly implemented in our analysis makes the assumption that the halo distribution behaves like a Poisson point process, which is a debatable hypothesis (see, e.g., Casas-Miranda et al 2002;Smith et al 2007). With this assumption, the shot-noise correction of the halo power spectrum is represented by subtracting a white noise from the raw power spectrum.…”

“…We assume that the halo distribution n(r; L) is the result of an inhomogeneous Poisson point process. Strictly speaking, a Poisson model cannot properly describe the distribution of galaxy clusters since these objects are subject to the so-called halo exclusion effects (e.g., Porciani & Giavalisco 2002;Tinker et al 2005;Smith et al 2007). This effect arises because halos are treated as disjointed entities that are not allowed to overlap, leading to a correlation function ξ(r) → −1 on scales below the minimum scale probed by the halo catalog (for an ideal sample of spherical halos, this scale equals twice the radius of the smaller halo, e.g., Peebles 1980).…”

Creating synthetic universes in a computer

“…Following proof-of-concept work (e.g. Blake & Glazebrook 2003;Seo & Eisenstein 2003), it is now apparent that the BAOs are not quite a standard ruler and, furthermore, they can be altered by a range of effects (Seo & Eisenstein 2005Smith et al 2007Smith et al , 2008Angulo et al 2008;Crocce & Scoccimarro 2008;Sánchez et al in press;Seo et al in press). Careful modelling is required to produce accurate predictions for the form of the BAOs and to help devise estimators to exploit these features in order to extract unbiased constraints on the dark energy.…”