Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

Abstract

Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are non-perturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k 2 R 2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. We adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k 2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the "CMASS" sample of the BOSS survey, we find that our predictions for the redshift-space power spectra are accurate up to k ≃ 0.4 h Mpc −1 within 1% if the halo power spectrum is measured using N -body simulations and within 3% if it is modeled using perturbation theory.

Constraining the relative velocity effect using the Baryon Oscillation Spectroscopic Survey

“…30 and (5) introducing the leading scale dependent bias term 2b1R 2 k 2 P lin (k) to eq. 16 (Okumura et al 2015). None of these changes to the model was able to explain the biases we measure.…”

The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions atz∼ 1.4

“…There are numerous models for nonlinear RSD of biased objects based on a halo model, perturbation theory and N -body simulations (e.g., Seljak 2001;White 2001;Tinker 2007;Matsubara 2008;Taruya et al 2010;Reid & White 2011;Nishimichi & Taruya 2011;Okumura et al 2012a;Vlah et al 2013;Song et al 2014;Kitaura et al 2014;Uhlemann et al 2015;Okumura et al 2015). However, our galaxy sample lies at a relatively high redshift z ∼ 1.3 where density perturbations have not grown as much as today, we will use only the clustering information on large scales, so the nonlinear effect is weaker.…”

“…They smear the anisotropies in the correlation function. Without any assumption, the measured correlation function can be decomposed into three terms: the auto correlation of real galaxies, that of the auto correlation of fake galaxies (the blunders), and their cross correlation (see e.g., Okumura et al 2015 for a decomposition scheme of a measured redshift-space power spectrum). The simplest approximation is that the fake signals are assumed to be distributed randomly so that the latter two terms are equal to zero, and the true clustering amplitude is obtained by the simple scaling of Blake et al 2010).…”

Interloper bias in future large-scale structure surveys

“…Interloper bias-to-noise ratio (BNR) for P(k). Nishizawa et al 2013;Saito et al 2014;Vlah et al 2015) and nonlinear RSD (Scoccimarro 2004;Matsubara 2008;Taruya et al 2010;Reid & White 2011;Okumura et al 2012aOkumura et al , 2012bOkumura et al , 2015White 2014), yet here we will only consider a basic nonlinear clustering model. Specifically, as an example we consider the nonlinear power spectrum using the HALOFIT prescription computed from CAMB (Lewis et al 2000) along with a FoG damping term given in equation (10) of Blake et al (2011) with σ v = 2 Mpc h −1 .…”