Redshift-Space Distortions, Pairwise Velocities and Nonlinearities

TL;DR

The paper addresses how peculiar velocities distort observed galaxy clustering in redshift space by deriving an exact relation between real-space and redshift-space two-point statistics through the line-of-sight pairwise velocity distribution. It demonstrates that the pairwise velocity distribution is strongly non-Gaussian at all scales and that the dispersion model yields an unphysical velocity PDF, making it inappropriate to infer the true PDF from redshift-space clustering. The authors show that deviations from the Kaiser limit at large scales arise from both Gaussian and non-Gaussian contributions to large-scale velocity dispersion and that linear theory fails to fully capture velocity evolution. They discuss implications for recovering the real-space power spectrum from redshift-space measurements, noting biases in monopole-based inferences but a simple reconstruction can recover large-scale real-space power; they also outline a framework for modeling redshift distortions via the velocity-difference PDF with further Work on non-Gaussian terms in a companion paper.

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.