Large-scale halo velocity correlations and the impact of finite simulation volumes

TL;DR

This paper examines how finite simulation volumes suppress large-scale halo velocity correlations, demonstrating the importance of accounting for missing long-wavelength modes to accurately model velocity statistics.

Contribution

It quantifies the impact of finite box sizes on velocity correlations and introduces a method to correct biases in growth rate measurements.

Findings

Larger simulation boxes reduce suppression of velocity correlations.

Marginalizing over the minimum wavenumber corrects growth rate biases.

Suppression of velocity correlations depends on halo mass.

Abstract

The velocity correlation functions directly measured from the peculiar velocity field of dark matter in numerical simulations are known to have an amplitude lower than that predicted by theoretical models at large scales. The trend persists for dark-matter halos or galaxies that are more closely related to the observables. We investigate the impact of the finite simulation box sizes on the measured velocity correlation functions of halos, utilizing N-body simulations with different box sizes. We measure the halo velocity correlations from N-body simulations with side lengths of $1{\rm Gpc}/h$ and $2{\rm Gpc}/h$, confirming the former is more suppressed compared to the linear theory prediction on large scales due to the lack of large-scale modes beyond the box size. In contrast, even though we subdivide the larger-box simulations into those with side lengths of $1{\rm Gpc}/h$, the amount of the suppression is the same as that from the original boxes, as the large-scale modes are already imprinted. Introducing the lower limit of the integral in the Hankel transform, $k_{\rm min}$, as a free parameter and marginalizing it over, we find that the constrained growth rate parameter, $f(z)\sigma_8(z)$, returns the correct value assumed in the simulations. However, when we ignore the effect and set $k_{\rm min}=0$, the constraint on $f\sigma_8$ is significantly biased if the correlation between different separation bins is also ignored. Furthermore, we find that the suppression of the velocity correlation amplitude on large scales depends on halo mass, with more massive halos exhibiting a systematically stronger suppression. These results highlight the importance of accounting for missing long-wavelength modes when developing simulation-based modeling of velocity statistics, such as emulators.