Origin and full characterization of the secondary (assembly) halo bias

Abstract

The clustering of dark matter halos depends not only on their mass, the so-called primary bias, but also on theirinternal properties, the so-called secondary bias. While the former effect is well understood within the Press–Schechter and excursion set models of structure formation, the latter is not. In those models, protohalos are fullycharacterized by their height and scale, which determine the halo mass and collapse time, so there is no room forany other halo property. This is why the secondary bias was believed not to be innate but due to the distinct mergerrate of halos lying in different backgrounds, and dubbed assembly bias. However, it has now been determined thatmergers leave no imprint in the inner halo properties. In fact, the innate origin of the secondary bias cannot bediscarded because, in the more realistic peak model of structure formation, halo seeds are characterized by oneadditional property: the peak curvature. Here, we use the confluent system of peak trajectory formalism to showthat peaks lying in different backgrounds have different mean curvatures, which in turn cause them to evolve intohalos with different typical inner properties. The dependence we find of the properties on halo background (or haloclustering) reproduces the results of simulations.