A new smooth-$k$ space filter approach to calculate halo abundances

TL;DR

This paper introduces a smooth-$k$ space filter for the Press-Schechter model, improving the accuracy of halo mass function predictions across various power spectra compared to traditional filters.

Contribution

A novel smooth-$k$ space filter is proposed, addressing limitations of existing filters in modeling the halo mass function within the Press-Schechter framework.

Findings

The smooth-$k$ filter better matches simulation data across a wider mass range.

It outperforms sharp-$k$ and real-space top-hat filters in accuracy.

The approach works for both damped and undamped power spectra.

Abstract

We propose a new filter, a smooth-$k$ space filter, to use in the Press-Schechter approach to model the dark matter halo mass function which overcomes shortcomings of other filters. We test this against the mass function measured in N-body simulations. We find that the commonly used sharp-$k$ filter fails to reproduce the behaviour of the halo mass function at low masses measured from simulations of models with a sharp truncation in the linear power spectrum. We show that the predictions with our new filter agree with the simulation results over a wider range of halo masses for both damped and undamped power spectra than is the case with the sharp-$k$ and real-space top-hat filters.