Redshift-Space Distortions, Pairwise Velocities and Nonlinearities

Details Redshift-Space Distortions, Pairwise Velocities and Nonlinearities Redshift-Space Distortions, Pairwise Velocities and Nonlinearities

2004-07-12

arxiv.org/abs/astro-ph/0407214v2

Phys.Rev. D70 (2004) 083007

Astronomy and Astrophysics

Astrophysics

30 pages, 7 figures

Scientific paper

10.1103/PhysRevD.70.083007

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.

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