Cosmic web anisotropy is the primary indicator of halo assembly bias

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 $α$ 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 $α$, and the other between $α$ 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 $β$) and angular momentum (dimensionless spin $λ$) 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 $α$, $b_1$ and any of the internal properties $c\in\{β,c_v/a_v,c/a,c_{\rm vir},λ\}$ is consistent with $p(α,b_1,c)\simeq p(α)p(b_1|α)p(c|α)$, at all but the largest masses. $\textit{Thus, the assembly bias trends $c-b_1$ reflect the two fundamental correlations $c-α$ and $b_1-α$.}$ 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 $α$ does not explain their assembly bias trends. The overarching importance of $α$ 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.