Peculiar velocity decomposition, redshift space distortion, and velocity reconstruction in redshift surveys. II. Dark matter velocity statistics

Abstract

Massive spectroscopic redshift surveys open a promising window to accurately measure peculiar velocity at cosmological distances through redshift space distortion (RSD). In Paper I Zhang et al. [Phys. Rev. D 87, 063526 (2013)] of this series of work, we proposed decomposing peculiar velocity into three eigenmodes (v , v S , and v B ) in order to facilitate the RSD modeling and peculiar velocity reconstruction. In the current paper we measure the dark matter RSD-related statistics of the velocity eigenmodes through a set of N-body simulations. These statistics include the velocity power spectra, correlation functions, onepoint probability distribution functions, cumulants, and the damping functions describing the Finger of God effect. We have carried out a number of tests to quantify possible numerical artifacts in these measurements and have confirmed that these numerical artifacts are under control. Our major findings are as follows: (1) The power spectrum measurement shows that these velocity components have distinctly different spatial distribution and redshift evolution, consistent with predictions in Paper I. In particular, we measure the window functionWðk; zÞ.W describes the impact of nonlinear evolution on the v -density relation. We confirm that the approximationW ¼ 1 can induce a significant systematic error of Oð10%Þ in RSD cosmology. We demonstrate thatW can be accurately described by a simple fitting formula with one or two free parameters. (2) The correlation function measurement shows that the correlation length is Oð100Þ, Oð10Þ, and Oð1Þ Mpc for v , v S , and v B , respectively. These correlation lengths determine where we can treat the velocity fields as spatially uncorrelated. Hence, they are important properties in RSD modeling.(3) The velocity probability distribution functions and cumulants quantify non-Gaussianities of the velocity fields. We confirm speculation in Paper I that v is largely Gaussian, but with non-negligible non-Gaussianity. We confirm that v B is significantly non-Gaussian. We also measure the damping functions. Despite the observed non-Gaussianities, the damping functions and hence the Finger of God effect are all well approximated as Gaussian ones at scales of interest.

Determination of the large scale volume weighted halo velocity bias in simulations

“…It has been robustly detected for the case of DM simulation particles [19,21]. Therefore it must also exist for DM halos [20].…”

Sampling artifact in volume weighted velocity measurement. II. Detection in simulations and comparison with theoretical modeling

“…The measurement can be done using one's favorite velocity assignment method, such as the ones based on the Voronoi and Delaunay tessellations [1]. Throughout this paper, we restrict to the NP (nearest particle) method [12]. As discussed in paper I, sampling artifacts in other velocity assignment methods are similar, so results on the sampling artifact in the NP method also provide a useful reference for that in other methods.…”

“…These works found that its impact increases with decreasing number density. This behavior can be used to diagnose the sampling artifact [12,13]. For example, by comparing the velocity power spectrum P v of two halo populations at equal volume density, the difference in P v is significantly suppressed [13], manifesting the existence of a sampling artifact.…”

Tests of redshift-space distortions models in configuration space for the analysis of the BOSS final data release

“…Recent, complementary, tests of models in Fourier space have been presented in Jennings, Baugh & Pascoli (2011); Blake et al (2011); Kwan, Lewis & Linder (2012); Okumura, Seljak & Descjacques (2012); Zheng et al (2013); Okumura et al (2014); Beutler et al (2014) and N-body based models for fitting the data to smaller scales have been presented in Reid et al (2014). The outline of the paper is as follows.…”