Formation rates of Dark Matter Haloes

TL;DR

This paper presents a method to estimate the formation rate of dark matter halos across different masses and redshifts, using the excursion set formalism and differentiating between merger types, with results aligning well with N-Body simulations.

Contribution

It introduces a novel approach to compute positive dark matter halo formation rates, distinguishing major and minor mergers, and compares these estimates with simulation data.

Findings

Formation rates are positive at all scales.

Good agreement with N-Body simulation results.

Provides insights into halo survival and formation redshift distributions.

Abstract

We derive an estimate of the rate of formation of dark matter halos per unit volume as a function of the halo mass and redshift of formation. Analytical estimates of the number density of dark matter halos are useful in modeling several cosmological phenomena. We use the excursion set formalism for computing the formation rate of dark matter halos. We use an approach that allows us to differentiate between major and minor mergers, as this is a pertinent issue for semi-analytic models of galaxy formation. We compute the formation rate for the Press-Schechter and the Sheth-Tormen mass function. We show that the formation rate computed in this manner is positive at all scales. We comment on the Sasaki formalism where negative halo formation rates are obtained. Our estimates compare very well with N-Body simulations for a variety of models. We also discuss the halo survival probability and the formation redshift distributions using our method.