Collapse Barriers and Halo Abundance: Testing the Excursion Set Ansatz

TL;DR

This paper tests the excursion set ansatz for predicting dark matter halo abundance using large-scale simulations, revealing inconsistencies and suggesting the need for improved models of halo collapse.

Contribution

It demonstrates that the standard collapse barrier models do not accurately predict halo mass functions, highlighting limitations of the excursion set approach.

Findings

Relation between overdensity and variance aligns with ellipsoidal collapse models.

Excursion set ansatz predicts halo mass functions inconsistent with simulations.

Highlights need for refined collapse models in analytical frameworks.

Abstract

Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier", for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance sigma^2(M). Several such barriers based on the spherical, Zel'dovich, and ellipsoidal collapse models have been extensively discussed. Using large scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.