Conditional Mass Functions and Merger Rates of Dark Matter Halos in the Ellipsoidal Collapse Model

TL;DR

This paper derives accurate analytic formulas for the conditional mass function and merger rates of dark matter halos within the ellipsoidal collapse model, improving agreement with simulations for small time steps.

Contribution

It provides the first simple, accurate analytic expressions for the conditional mass function and merger rates in the ellipsoidal collapse model for small look-back times.

Findings

Better match to Millennium simulation results than previous models.

Analytic formulas applicable for small time steps in halo merger trees.

Improved understanding of halo formation and merger processes.

Abstract

Analytic models based on spherical and ellipsoidal gravitational collapse have been used to derive the mass functions of dark matter halos and their progenitors (the conditional mass function). The ellipsoidal model generally provides a better match to simulation results, but there has been no simple analytic expression in this model for the conditional mass function that is accurate for small time steps, a limit that is important for generating halo merger trees and computing halo merger rates. We remedy the situation by deriving accurate analytic formulae for the first-crossing distribution, the conditional mass function, and the halo merger rate in the ellipsoidal collapse model in the limit of small look-back times. We show that our formulae provide a closer match to the Millennium simulation results than those in the spherical collapse model and the ellipsoidal model of Sheth & Tormen (2002).