Understanding redshift space distortions in density-weighted peculiar velocity

TL;DR

This paper develops an analytical model to predict the redshift space power spectrum and correlation function of density-weighted velocities, aiding the interpretation of kinetic Sunyaev-Zel'dovich (kSZ) observations for cosmology.

Contribution

It introduces a simple relation linking density and velocity power spectra and extends perturbation techniques to model non-linear redshift space distortions in kSZ data.

Findings

Accurately predicts non-linear velocity statistics up to ~30 h^{-1} Mpc.

Explains sign change in density-velocity cross-correlation due to redshift distortions.

Model matches simulations at multiple redshifts without free parameters.

Abstract

Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to $\sim30\ h^{-1} {\rm Mpc}$ for dark matter particles at the redshifts of $z=0.0$, $0.5$, and $1.0$.