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 their internal 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 fully characterized by their height and scale, which determine the halo mass and collapse time, so there is no room for any other halo property. This is why the secondary bias was believed not to be innate but due to the distinct merger rate of halos lying in different backgrounds, and dubbed assembly bias. However, it has now been determined that mergers leave no imprint in the inner halo properties. In fact, the innate origin of the secondary bias cannot be discarded because, in the more realistic peak model of structure formation, halo seeds are characterized by one additional property: the peak curvature. Here, we use the confluent system of peak trajectory formalism to show that peaks lying in different backgrounds have different mean curvatures, which in turn cause them to evolve into halos with different typical inner properties. The dependence we find of the properties on halo background (or halo clustering) reproduces the results of simulations.