Accurate determination of halo velocity bias in simulations and its cosmological implications

TL;DR

This paper presents a high-precision method to measure halo velocity bias in cosmological simulations, revealing deviations from unity at small scales and their dependence on mass and redshift, with significant implications for cosmological measurements.

Contribution

The authors develop a novel hybrid approach that eliminates sampling artifacts and cosmic variance, enabling the first 0.1-1% accurate determination of halo velocity bias in large simulations.

Findings

Halo velocity bias deviates from unity at small scales, increasing with wavenumber.

The deviation depends on halo mass and redshift, sometimes exceeding 0.05.

Results challenge existing peak model predictions, showing weaker deviation and redshift dependence.

Abstract

A long-standing issue in peculiar velocity cosmology is whether the halo/galaxy velocity bias $b_v=1$ at large scale. The resolution of this important issue must resort to high precision cosmological simulations. However, this is hampered by another long-standing `sampling artifact' problem in volume weighted velocity measurement. We circumvent this problem with a hybrid approach. We first measure statistics free of sampling artifact, then link them to volume weighted statistics in theory, finally solve for the velocity bias. $b_v$ determined by our method is not only free of sampling artifact, but also free of cosmic variance. We apply this method to a $\Lambda$CDM N-body simulation of $3072^3$ particles and $1200 Mpc/{\rm h}$ box size. For the first time, we determine the halo velocity bias to $0.1\%$-$1\%$ accuracy. Our major findings are as follows: (1) $b_v\neq 1$ at $k>0.1 h/{\rm Mpc}$. The deviation from unity ($|b_v-1|$) increases with $k$. Depending on halo mass and redshift, it may reach $\mathcal{O}(0.01)$ at $k=0.2 h/{\rm Mpc}$ and $\mathcal{O}(0.05)$ at $k\sim 0.3 h/{\rm Mpc}$. The discovered $b_v\neq 1$ has statistically significant impact on structure growth rate measurement by spectroscopic redshift surveys, including DESI, Euclid and SKA. (2) Both the sign and the amplitude of $b_v-1$ depend on mass and redshift. These results disagree with the peak model prediction in that $b_v$ has much weaker deviation from unity, varies with redshift, and can be bigger than unity. (3) Most of the mass and redshift dependences can be compressed into a single dependence on the halo density bias. Based on this finding, we provide an approximate two-parameter fitting formula.