Redshift-Space Distortions, Pairwise Velocities and Nonlinearities

Abstract

We derive the exact relationship, including all non-linearities, between real-space and redshift-space two-point statistics through the pairwise velocity distribution function. We show using numerical simulations that the pairwise velocity PDF is strongly non-Gaussian at all scales, and explain why this is so. We caution that a commonly used ansatz to model the redshift-space power spectrum gives rise to an unphysical distribution of pairwise velocities, and show that it is in general impossible to derive the distribution from measurements of redshift-space clustering. Methods that claim to do this obtain instead something else, whose properties we derive. We provide a general derivation of the large-scale limit of the redshift-space power spectrum and show that it differs from the Kaiser formula by terms that depend on Gaussian and non-Gaussian contributions to the velocity dispersion of large-scale flows. We also show that the large-scale evolution of velocity fields is not well described by linear theory and discuss how this impacts the redshift-space power spectrum. Finally, we stress that using the monopole of the redshift-space power as an indicator of the real-space power spectrum shape can lead to systematic effects in the determination of cosmological parameters; nevertheless a simple procedure is able to recover the large-scale real-space power spectrum rather well.

30 pages, 7 figures

References in corpus (1)

• Fingers of God

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• Nonlinear stochastic growth rates and redshift space distortions
• BAO Extractor: bias and redshift space effects
• Power Spectrum Precision for Redshift Space Distortions
• Modeling galaxy clustering on small scales to tighten constraints on dark energy and modified gravity
• Fast Calculation of Nonlinear Redshift-space Galaxy Power Spectrum Including Selection Bias
• Quantification of the multi-streaming effect in Redshift Space Distortion
• Halo Profile Evolution and Velocity Bias
• Type Ia supernovae as speed sensors at intermediate redshifts
• Self-calibrating interloper bias in spectroscopic galaxy clustering surveys
• Constraining Brans-Dicke cosmology with the CSST galaxy clustering spectroscopic survey
• A rising tide: Intrinsic alignments since the turn of the millennium
• The FLAMINGO project: cosmology with the redshift dependence of weak gravitational lensing peaks
• Impact of cosmological signatures in two-point statistics beyond the linear regime
• The galaxy power spectrum on the lightcone: deep, wide-angle redshift surveys and the turnover scale
• Beyond boundaries of redshift surveys: assessing mass fluctuations on "super-survey" scales
• Impact of lensing magnification on the analysis of galaxy clustering in redshift space
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• Dynamics of pairwise motions in the fully non-linear regime in LCDM and Modified Gravity cosmologies
• Brisk estimator for the angular multipoles of the redshift space bispectrum
• Chasing Unbiased Spectra of the Universe
• Galaxy and Mass Assembly (GAMA): Probing galaxy-group correlations in redshift space with the halo streaming model
• Breaking the ${\tau }_{\mathrm{T}}-f$ degeneracy of the kinetic Sunyaev Zel'dovich cosmology in redshift space
• Non-Linearity-Free prediction of the growth-rate $f{\sigma }_8$ using Convolutional Neural Networks
• Nonlinear Redshift-Space Distortions on the Full Sky
• Proca-stinated Cosmology II: Matter, Halo, and Lensing Statistics in the vector Galileon
• Information content in anisotropic cosmological fields: Impact of different multipole expansion scheme for galaxy density and ellipticity correlations
• Modelling the tightest relation between galaxy properties and dark matter halo properties from hydrodynamical simulations of galaxy formation
• Determining accurate measurements of the growth rate from the galaxy correlation function in simulations
• The RSD Sorting Hat: Unmixing Radial Scales in Projection
• Bayesian inference methodology for Primordial Power Spectrum reconstructions from Large Scale Structure
• Mixing Bispectrum Multipoles Under Geometric Distortions
• Experimental evaluation of complete safe coordination of astrobots for Sloan Digital Sky Survey V
• Extending evolution mapping to massive neutrinos with COMET
• Clustering of K-band selected local galaxies
• Phenomenological power spectrum models for H$\alpha$ emission line galaxies from the Nancy Grace Roman Space Telescope
• Neural Network Reconstruction of Non-Gaussian Initial Conditions from Dark Matter Halos
• A model of the anisotropic correlation function xi(rp, pi) in redshift space including redshift errors
• Glass-Like Random Catalogues for Two-Point Estimates on the Light Cone
• Reconstruction of real-space linear matter power spectrum from multipoles of BOSS DR12 results
• The imprints of massive neutrinos on the three-point correlation function of large-scale structures
• Direct Determination of Expansion History Using Redshift Distortions
• Perturbation theory challenge for cosmological parameters estimation II.: Matter power spectrum in redshift space
• Fullshape power spectrum for the Symmetron modified gravity model
• Lagrangian-space Gaussian ansatz for the matter redshift-space power spectrum and correlation function
• Note on Redshift Distortion in Fourier Space
• Transients from Initial Conditions Based on Lagrangian Perturbation Theory in $N$-body Simulations III: The Case of GADGET-2 Code
• The Origin of the Orbital Parameter Distribution of Merging Halos
• Gravitational redshift from large-scale structure: nonlinearities, antisymmetries, and the dipole
• Hybrid $P_{\ell }(k)$: general, unified, non-linear matter power spectrum in redshift space
• Improved Methods for Estimating Peculiar Velocity Correlation Functions Using Volume Weighting
• Skewness as a Probe of Gravity: Real and Redshift Space Counts-In-Cells
• Testing Large-Scale Structure Measurements Against Fisher Matrix Predictions
• Turning dispersion into signal: density-split analyses of pairwise velocities
• Anisotropic Counts-in-Cells in Redshift Space: A New Route to Cosmological Constraints from Galaxy Surveys
• Cosmological implications of the full shape of anisotropic clustering measurements in BOSS and eBOSS
• A redshift distortion free correlation function at third order in the nonlinear regime
• Probing the large-scale structure with 21cm-galaxy cross-bispectrum: Estimates from simulations and forecasts for upcoming cosmological surveys
• Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference
• Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling