Halo assembly bias in the quasi-linear regime

We address the question of whether or not assembly bias arises in the absence of highly non-linear effects such as tidal stripping of haloes near larger mass concentrations. Therefore, we use a simplified dynamical scheme where these effects are not modelled. We choose the punctuated Zel'dovich (PZ) approximation, which prevents orbit mixing by coalescing particles coming within a critical distance of each other. A numerical implementation of this approximation is fast, allowing us to run a large number of simulations to study assembly bias. We measure an assembly bias from 60 PZ simulations, each with 512(3) cold particles in a 128 h(-1) Mpc cubic box. The assembly bias estimated from the correlation functions at separations of less than or similar to 5 h(-1) Mpc for objects (haloes) at z = 0 is comparable to that obtained in full N-body simulations. For masses 4 x 10(11) h(-1) M-circle dot, the 'oldest' 10 per cent haloes are three to five times more correlated than the 'youngest' 10 per cent. The bias weakens with increasing mass, also in agreement with full N-body simulations. We find that halo ages are correlated with the dimensionality of the surrounding linear structures as measured by the parameter (lambda(1) + lambda(2) + lambda(3))/(lambda 0(1)(2) + lambda(2)(2) + lambda(2)(3))(1/2) where lambda(i) is proportional to the eigenvalues of the velocity deformation tensor. Our results suggest that assembly bias may already be encoded in the early stages of the evolution.