# Intrinsic alignment statistics of density and velocity fields at large scales: Formulation, modeling, and baryon acoustic oscillation features

## TL;DR

This paper develops theoretical models and measures intrinsic alignment statistics of density and velocity fields at large cosmic scales, revealing their potential to enhance cosmological insights, especially through baryon acoustic oscillation features.

## Contribution

It introduces new velocity alignment statistics, derives their theoretical expressions assuming Gaussian density fluctuations, and demonstrates their consistency with simulations and potential for cosmological studies.

## Key findings

- Velocity intrinsic alignments extend beyond density alignments.
- Linear alignment model accurately predicts velocity IAs.
- Baryon acoustic oscillations are detectable in velocity statistics.

## Abstract

The kinematic Sunyaev-Zel'dovich effect enables us to directly probe the density-weighted velocity field up to very large cosmic scales. We investigate the effects of intrinsic alignments (IAs) of dark-matter halo shapes on cosmic density and velocity fields on such large scales. In the literature IAs have been detected up to $\sim 100~h^{-1}{\rm Mpc}$ using the gravitational shear-intrinsic ellipticity correlation and the alignment correlation function. In this paper we introduce the corresponding various velocity statistics: the (density-weighted) velocity-intrinsic ellipticity correlation as well as the alignment pairwise infall momentum, momentum correlation function, and density-weighted pairwise velocity dispersion. We derive theoretical expressions for these velocity alignment statistics for the first time based on the assumption that the density fluctuation is a Gaussian random field. Using large-volume, high-resolution $N$-body simulations, we measure the alignment statistics of density and velocity fields. The behaviors of IAs in the velocity statistics are similar to those in the density statistics, except that the halo orientations are aligned with the velocity field up to scales larger than those with the density field, $r\gg 100~h^{-1}{\rm Mpc}$, because of a factor of the wave number in the linear relation between the density and velocity fields in Fourier space, $v\propto \delta/k$. We show that the detected IAs of the velocity field can be well predicted by the linear alignment model. We also demonstrate that the baryon acoustic oscillation features can be detected in both the conventional and alignment velocity statistics. Our results indicate that observations of IAs with the velocity field on large scales can provide additional information on cosmological models, complementary to those with the density field.