Halo assembly bias in hierarchical structure formation

We investigate the origin of halo assembly bias, the dependence of halo clustering on assembly history. We relate halo assembly to peak properties measured in the Lagrangian space of the initial linear Gaussian random density field and show how these same Lagrangian properties determine large-scale bias. We focus on the two regimes where assembly bias has been observed to be significant: at masses very large and very small compared to the nonlinear mass scale. At high masses, we show that assembly bias is expected from the statistics of the peaks of Gaussian random fluctuations, and we show that the extent of assembly bias found in N-body simulations of rare halos is in excellent agreement with our theoretical prediction. At low masses, we argue that assembly bias largely arises from a subpopulation of low-mass halos whose mass accretion has ceased. Due to their arrested development, these halos naturally become unbiased, in contrast to their antibiased peers. We show that a simple toy model incorporating these effects can roughly reproduce the bias trends found in N-body simulations.