Statistics of Dark Matter Halos in the Excursion Set Peak Framework

TL;DR

This paper develops highly accurate analytical formulas for the abundance and clustering of dark matter halos using an enhanced excursion set peak framework that incorporates realistic filtering, mass-dependent thresholds, and peak theory.

Contribution

It introduces new analytical expressions that improve the modeling of dark matter halo statistics by including realistic physical effects and matches simulation results well.

Findings

Analytical formulas match N-body simulations for various power spectra.

Approximations work well across different filtering methods and thresholds.

Enhanced framework accurately predicts halo bias and mass function.

Abstract

We derive approximated, yet very accurate analytical expressions for the abundance and clustering properties of dark matter halos in the excursion set peak framework; the latter relies on the standard excursion set approach, but also includes the effects of a realistic filtering of the density field, a mass-dependent threshold for collapse, and the prescription from peak theory that halos tend to form around density maxima. We find that our approximations work excellently for diverse power spectra, collapse thresholds and density filters. Moreover, when adopting a cold dark matter power spectra, a tophat filtering and a mass-dependent collapse threshold (supplemented with conceivable scatter), our approximated halo mass function and halo bias represent very well the outcomes of cosmological $N-$body simulations.