Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

TL;DR

This paper develops a perturbative phase space distribution function approach to model redshift space distortions in dark matter, systematically including higher order effects and small scale velocity dispersions, with comparisons to simulations.

Contribution

It introduces a systematic perturbation theory framework for RSD that incorporates all relevant terms at a given order and models small scale velocity dispersions using the halo model.

Findings

Standard PT models many terms well, others require higher order corrections.

Small scale velocity dispersions significantly affect RSD, modeled via halo model.

The approach successfully models several key RSD features, but not all.

Abstract

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of \mu, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of \mu and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion.