Self-consistency of the Excursion Set Approach

TL;DR

This paper examines the self-consistency of the excursion set approach in predicting dark matter halo abundance, comparing theoretical predictions with numerical simulations to validate assumptions, especially for low mass halos.

Contribution

The paper analyzes the assumptions of the excursion set approach and demonstrates its self-consistency for low mass halos through comparison with numerical simulations.

Findings

Excursion set predictions align with simulations for low mass halos.

The approach's assumptions are valid for certain mass ranges.

Comparison supports the theoretical framework's applicability.

Abstract

The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism comes from the physics of halo formation: the specification of a critical overdensity threshold (barrier) which protohalos must exceed if they are to form bound virialized halos at a later time. Another ingredient is statistical, as it requires the specification of the appropriate statistical ensemble over which to average when making predictions. The excursion set approach explicitly averages over all initial positions, thus implicitly assuming that the appropriate ensemble is that associated with randomly chosen positions in space, rather than special positions such as peaks of the initial density field. Since halos are known to collapse around special positions, it is not clear that the physical and statistical assumptions which underlie the excursion set approach are self-consistent. We argue that they are at least for low mass halos, and illustrate by comparing our excursion set predictions with numerical data from the DEUS simulations.