Study on the mapping of dark matter clustering from real space to redshift space

TL;DR

This paper develops a systematic approach to accurately model the mapping of dark matter clustering from real to redshift space, effectively handling non-linearities and velocity effects to match observed power spectra.

Contribution

It introduces a new perturbative mapping formula that separates and controls systematics, validated with simulations up to small scales.

Findings

Gaussian FoG function with one parameter is effective

Mapping formula accurately reproduces 2D power spectrum up to k~0.2h/Mpc

Systematics are controlled by direct measurement and polynomial expansion

Abstract

The mapping of dark matter clustering from real space to redshift space introduces the anisotropic property to the measured density power spectrum in redshift space, known as the redshift space distortion effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite cross correlations between the density and velocity fields, and the Finger-of-God effect due to the randomness of the peculiar velocity field. Whilst the full higher order polynomials remain unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non-linear density and velocity fields is removed by separately measuring all terms in the expansion directly using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the "one-point" FoG term being independent of the separation vector between two different points, and 2) the "correlated" FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. Using 100 realizations of simulations, we find that the Gaussian FoG function with only one scale-independent free parameter works quite well, and that our new mapping formulation accurately reproduces the observed 2-dimensional density power spectrum in redshift space at the smallest scales by far, up to $k\sim 0.2h$Mpc, considering the resolution of future experiments.