Halo Assembly Bias in Hierarchical Structure Formation

TL;DR

This paper explores the origins of halo assembly bias in hierarchical structure formation, linking it to initial conditions and demonstrating agreement with simulations for both high and low mass regimes.

Contribution

It provides a theoretical framework connecting halo assembly bias to initial peak properties and explains observed bias trends with a simple toy model.

Findings

Assembly bias at high masses aligns with peak statistics in Gaussian fluctuations.

Low mass halos with halted growth tend to be unbiased, explaining low-mass bias trends.

A toy model can roughly reproduce the bias behaviors observed in simulations.

Abstract

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 sub-population of low mass halos whose mass accretion has ceased. Due to their arrested development, these halos naturally become unbiased, in contrast to their anti-biased peers. We show that a simple toy model incorporating these effects can roughly reproduce the bias trends found in N-body simulations.