Toward a Universal Formulation of the Halo Mass Function

TL;DR

This paper develops a refined theoretical model for the dark matter halo mass function using the excursion set formalism, achieving high accuracy in agreement with N-body simulations across a wide mass range.

Contribution

It introduces a diffusive barrier with a linearly drifting average in the excursion set formalism, incorporating non-Markovian corrections for improved modeling of halo formation.

Findings

Achieves ~5% agreement with N-body data

Validates the excursion set approach with realistic collapse thresholds

Provides a robust theoretical framework for halo mass function estimation

Abstract

We compute the dark matter halo mass function using the excursion set formalism for a diffusive barrier with linearly drifting average which captures the main features of the ellipsoidal collapse model. We evaluate the non-Markovian corrections due to the sharp filtering of the linear density field in real space with a path-integral method. We find an unprecedented agreement with N-body simulation data with deviations within ~5% level over the range of masses probed by the simulations. This indicates that the Excursion Set in combination with a realistic modelling of the collapse threshold can provide a robust estimation of the halo mass function.