Dependence of Halo Bias and Kinematics on Assembly Variables

TL;DR

This study investigates how halo bias and kinematics depend on various assembly variables using large N-body simulations, revealing complex joint dependencies and the influence of assembly history on halo velocities.

Contribution

It presents a detailed analysis of the joint dependence of halo bias on multiple assembly variables and explores how assembly history affects halo kinematics, highlighting the complexity of these relationships.

Findings

Halo bias increases outward from a global minimum in the mass-assembly variable plane.

No single assembly variable can fully account for all assembly bias effects.

Halo assembly influences pairwise velocity dispersion, with earlier-formed low-mass haloes showing higher velocities.

Abstract

Using dark matter haloes identified in a large $N$-body simulation, we study halo assembly bias, with halo formation time, peak maximum circular velocity, concentration, and spin as the assembly variables. Instead of grouping haloes at fixed mass into different percentiles of each assembly variable, we present the joint dependence of halo bias on the {\it values} of halo mass and each assembly variable. In the plane of halo mass and one assembly variable, the joint dependence can be largely described as halo bias increasing outward from a global minimum. We find it unlikely to have a combination of halo variables to absorb all assembly bias effects. We then present the joint dependence of halo bias on two assembly variables at fixed halo mass. The gradient of halo bias does not necessarily follow the correlation direction of the two assembly variables and it varies with halo mass. Therefore in general for two correlated assembly variables one cannot be used as a proxy for the other in predicting halo assembly bias trend. Finally, halo assembly is found to affect the kinematics of haloes. Low-mass haloes formed earlier can have much higher pairwise velocity dispersion than those of massive haloes. In general, halo assembly leads to a correlation between halo bias and halo pairwise velocity distribution, with more strongly clustered haloes having higher pairwise velocity and velocity dispersion. However, the correlation is not tight, and the kinematics of haloes at fixed halo bias still depends on halo mass and assembly variables.