The non-linear redshift-space power spectrum of galaxies

Heavens, Alan; Matarrese, S.; Verde, Licia

doi:10.1046/j.1365-8711.1998.02052.x

Cited by 117 publications

(196 citation statements)

References 40 publications

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“…(ii) Second, the halo-halo spectrum has a term that corresponds to constant power on very large scales, whereas the cross spectrum does not. Both of these points were independently noted by [73,74], but for the case of nonlinear galaxy biasing (also see [35]). …”

Section: A Halo Center Power Spectramentioning

confidence: 62%

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Scale dependence of halo and galaxy bias: Effects in real space

2007

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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.

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Section: A Halo Center Power Spectramentioning

confidence: 62%

“…This has been explored by [73,74]. Second, consider the case where we integrate over one of the halo masses, say M 2 , weighting by M 2 and its abundance n M 2 .…”

Section: A Halo Center Power Spectramentioning

confidence: 99%

Scale dependence of halo and galaxy bias: Effects in real space

2007

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“…Many more accurate models for connecting the dark matter field to halos in redshift space have been developed and their performance tested against Nbody simulations [26][27][28][29][30][31][32][33][34]. Here we focus on the Gaussian Streaming Model (GSM), [35][36][37], according to which one can approximate the redshift space halo correlation function by a convolution of the real space correlation and an approximately Gaussian velocity distribution whose mean and variance are given by the scale-dependent mean and dispersion of the pairwise velocity.…”

Section: Introductionmentioning

confidence: 99%

Gaussian streaming with the truncated Zel’dovich approximation

2016

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We calculate the dark matter halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale dependent functions entering the streaming model we use local Lagrangian bias together with Convolution Lagrangian perturbation theory (CLPT) which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of proto-halos. Based on this observation we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimised if the coarse graining scale is chosen to be 1 Mpc/h at z = 0, while the pairwise velocity dispersion is optimised if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon Run 2 N-body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM+CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos.

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“…A perturbative analysis using third-order Newtonian perturbation theory is given in Ref. [47], but a detailed investigation of the effect on the small scale 21cm power spectrum is beyond the scope of this paper. Since higher order corrections to ∆ s (χ ′ ) are large on small scales, but the correction to the power spectrum is small due to the large coherence length of the displacement, a perturbative treatment will involve delicate cancellations between different independently large terms.…”

Section: Other Non-linear Effectsmentioning

confidence: 99%

21 cm angular-power spectrum from the dark ages

2007

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At redshifts z 30 neutral hydrogen gas absorbs CMB radiation at the 21cm spin-flip frequency. In principle this is observable and a high-precision probe of cosmology. We calculate the lineartheory angular power spectrum of this signal and cross-correlation between redshifts on scales much larger than the line width. In addition to the well known redshift-distortion and density perturbation sources a full linear analysis gives additional contributions to the power spectrum. On small scales there is a percent-level linear effect due to perturbations in the 21cm optical depth, and perturbed recombination modifies the gas temperature perturbation evolution (and hence spin temperature and 21cm power spectrum). On large scales there are several post-Newtonian and velocity effects; although negligible on small scales, these additional terms can be significant at l 100 and can be non-zero even when there is no background signal. We also discuss the linear effect of reionization re-scattering, which damps the entire spectrum and gives a very small polarization signal on large scales. On small scales we also model the significant non-linear effects of evolution and gravitational lensing. We include full results for numerical calculation and also various approximate analytic results for the power spectrum and evolution of small scale perturbations.

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The non-linear redshift-space power spectrum of galaxies

Abstract: 13.02.13 KB. Accepted version ok to add to Spiral. RAS/Wile

Cited by 117 publications

References 40 publications

Scale dependence of halo and galaxy bias: Effects in real space

Scale dependence of halo and galaxy bias: Effects in real space

Gaussian streaming with the truncated Zel’dovich approximation

21 cm angular-power spectrum from the dark ages

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