Mass functions from the excursion set model

TL;DR

This paper develops an improved stochastic model for the evolution of density fluctuations to better match dark matter halo mass functions observed in N-body simulations, using a novel kernel and a lower collapse threshold.

Contribution

It introduces a new kernel-based stochastic evolution model for density fluctuations that aligns more closely with simulation results, especially for lower mass halos.

Findings

Enhanced agreement with N-body simulations for mass functions

Accurate modeling for halos with   1

Lower collapse threshold improves fit across redshifts

Abstract

Aims. We aim to study the stochastic evolution of the smoothed overdensity $\delta$ at scale $S$ of the form $\delta(S) = \int_{0}^S K(S,u)\mathrm{d}W(u)$, where $K$ is a kernel and $\mathrm{d}W$ is the usual Wiener process. Methods. For a Gaussian density field, smoothed by the top-hat filter, in real space, we used a simple kernel that gives the correct correlation between scales. A Monte Carlo procedure was used to construct random walks and to calculate first crossing distributions and consequently mass functions for a constant barrier. Results. We show that the evolution considered here improves the agreement with the results of N-body simulations relative to analytical approximations which have been proposed from the same problem by other authors. In fact, we show that an evolution which is fully consistent with the ideas of the excursion set model, describes accurately the mass function of dark matter haloes for values of $\nu \leq 1$ and underestimates the number of larger haloes. Finally, we show that a constant threshold of collapse, lower than it is usually used, it is able to produce a mass function which approximates the results of N-body simulations for a variety of redshifts and for a wide range of masses. Conclusions. A mass function in good agreement with N-body simulations can be obtained analytically using a lower than usual constant collapse threshold.