Distribution function approach to redshift space distortions. Part II: N-body simulations

TL;DR

This paper uses N-body simulations to analyze the distribution function approach for redshift space distortions, identifying key contributions of velocity moments and their convergence properties, with implications for modeling cosmic growth.

Contribution

It provides a detailed investigation of the distribution function expansion for RSD using simulations, highlighting the convergence limits and resummation techniques for better modeling.

Findings

Higher order terms dominate at small scales (k>0.15h/Mpc).

Expansion achieves percent accuracy for kmu<0.15h/Mpc at 6th order.

FoG kernels are approximately Lorentzian, extending convergence.

Abstract

Measurement of redshift-space distortions (RSD) offers an attractive method to directly probe the cosmic growth history of density perturbations. A distribution function approach where RSD can be written as a sum over density weighted velocity moment correlators has recently been developed. We use Nbody simulations to investigate the individual contributions and convergence of this expansion for dark matter. If the series is expanded as a function of powers of mu, cosine of the angle between the Fourier mode and line of sight, there are a finite number of terms contributing at each order. We present these terms and investigate their contribution to the total as a function of wavevector k. For mu^2 the correlation between density and momentum dominates on large scales. Higher order corrections, which act as a Finger-of-God (FoG) term, contribute 1% at k~0.015h/Mpc, 10% at k~0.05h/Mpc at z=0, while for k>0.15h/Mpc they dominate and make the total negative. These higher order terms are dominated by density-energy density correlations which contribute negatively to the power, while the contribution from vorticity part of momentum density auto-correlation is an order of magnitude lower. For mu^4 term the dominant term on large scales is the scalar part of momentum density auto-correlation, while higher order terms dominate for k>0.15h/Mpc. For mu^6 and mu^8 we find it has very little power for k<0.15h/Mpc. We also compare the expansion to the full 2D P^ss(k,mu) as well as to their multipoles. For these statistics an infinite number of terms contribute and we find that the expansion achieves percent level accuracy for kmu<0.15h/Mpc at 6th order, but breaks down on smaller scales because the series is no longer perturbative. We explore resummation of the terms into FoG kernels, which extend the convergence up to a factor of 2 in scale. We find that the FoG kernels are approximately Lorentzian.