ZOMG-I. How the cosmic web inhibits halo growth and generates assembly bias

The clustering of dark matter haloes with fixed mass depends on their formation history, an effect known as assembly bias. We use zoom N -body simulations to investigate the origin of this phenomenon. For each halo at redshift z=0, we determine the time in which the physical volume containing its final mass becomes stable. We consider five examples for which this happens at z~1.5 and two that do not stabilize by z=0. The zoom simulations show that early-collapsing haloes do not grow in mass at z=0 while late-forming ones show a net inflow. The reason is that 'accreting' haloes are located at the nodes of a network of thin filaments feeding them. Conversely, each 'stalled' halo lies within a prominent filament that is thicker than the halo size. Infalling material from the surroundings becomes part of the filament while matter within it recedes from the halo. We conclude that assembly bias originates from quenching halo growth due to tidal forces following the formation of non-linear structures in the cosmic web, as previously conjectured in the literature. Also the internal dynamics of the haloes change: the velocity anisotropy profile is biased towards radial (tangential) orbits in accreting (stalled) haloes. Our findings reveal the cause of the yet unexplained dependence of halo clustering on the anisotropy. Finally, we extend the excursion-set theory to account for these effects. A simple criterion based on the ellipticity of the linear tidal field combined with the spherical collapse model provides excellent predictions for both classes of haloes.