# Cosmic web anisotropy is the primary indicator of halo assembly bias

## TL;DR

This paper demonstrates that cosmic web anisotropy is the main factor driving halo assembly bias, revealing that internal halo properties are statistically linked to the local web environment characterized by tidal anisotropy.

## Contribution

It identifies cosmic web anisotropy as the primary indicator of halo assembly bias and clarifies the statistical relationships between internal properties, large-scale bias, and web environment.

## Key findings

- Cosmic web anisotropy strongly correlates with halo assembly bias.
- Internal properties are statistically linked to tidal anisotropy.
- Results are robust against recent mergers and splashback objects.

## Abstract

The internal properties of dark matter haloes correlate with the large-scale halo clustering strength at fixed halo mass $-$ an effect known as assembly bias $-$ and are also strongly affected by the local, non-linear cosmic web. Characterising a halo's local web environment by its tidal anisotropy $\alpha$ at scales $\sim4$ x the halo radius, we demonstrate that these multi-scale correlations represent two distinct statistical links: one between the internal property and $\alpha$, and the other between $\alpha$ and large-scale ( $>30h^{-1}$Mpc) halo bias $b_1$. We focus on scalar internal properties of haloes related to formation time (concentration $c_{\rm vir}$), shape (mass ellipsoid asphericity $c/a$), velocity dispersion structure (velocity ellipsoid asphericity $c_v/a_v$ and velocity anisotropy $\beta$) and angular momentum (dimensionless spin $\lambda$) in the mass range $8\times10^{11}< M_{\rm vir}/(h^{-1}M_\odot)<5\times10^{14}$. Using conditional correlation coefficients and other detailed tests, we show that the joint distribution of $\alpha$, $b_1$ and any of the internal properties $c\in\{\beta,c_v/a_v,c/a,c_{\rm vir},\lambda\}$ is consistent with $p(\alpha,b_1,c)\simeq p(\alpha)p(b_1|\alpha)p(c|\alpha)$, at all but the largest masses. $\textit{Thus, the assembly bias trends $c-b_1$ reflect the two fundamental correlations $c-\alpha$ and $b_1-\alpha$.}$ Our results are unaffected by the exclusion of haloes with recent major merger events or splashback objects, although the latter are distinguished by the fact that $\alpha$ does not explain their assembly bias trends. The overarching importance of $\alpha$ provides a new perspective on the nature of assembly bias of distinct haloes, with potential ramifications for incorporating realistic assembly bias effects into mock catalogs of future large-scale structure surveys and for detecting galaxy assembly bias.