Title: Halo assembly bias and the tidal anisotropy of the local halo environment,
Abstract: We study the role of the local tidal environment in determining the assembly
bias of dark matter haloes. Previous results suggest that the anisotropy of a
halo's environment (i.e, whether it lies in a filament or in a more isotropic
region) can play a significant role in determining the eventual mass and age of
the halo. We statistically isolate this effect using correlations between the
large-scale and small-scale environments of simulated haloes at $z=0$ with
masses between $10^{11.6}\lesssim (m/h^{-1}M_{\odot})\lesssim10^{14.9}$. We
probe the large-scale environment using a novel halo-by-halo estimator of
linear bias. For the small-scale environment, we identify a variable $\alpha_R$
that captures the $\textit{tidal anisotropy}$ in a region of radius
$R=4R_{\textrm{200b}}$ around the halo and correlates strongly with halo bias
at fixed mass. Segregating haloes by $\alpha_R$ reveals two distinct
populations. Haloes in highly isotropic local environments
($\alpha_R\lesssim0.2$) behave as expected from the simplest, spherically
averaged analytical models of structure formation, showing a
$\textit{negative}$ correlation between their concentration and large-scale
bias at $\textit{all}$ masses. In contrast, haloes in anisotropic,
filament-like environments ($\alpha_R\gtrsim0.5$) tend to show a
$\textit{positive}$ correlation between bias and concentration at any mass. Our
multi-scale analysis cleanly demonstrates how the overall assembly bias trend
across halo mass emerges as an average over these different halo populations,
and provides valuable insights towards building analytical models that
correctly incorporate assembly bias. We also discuss potential implications for
the nature and detectability of galaxy assembly bias.