The statistical properties of LCDM halo formation

TL;DR

This paper compares the statistical properties of dark matter halo merger trees from the Millennium Simulation with EPS formalism and Monte-Carlo methods, highlighting their strengths and limitations in modeling hierarchical structure growth.

Contribution

It provides a detailed comparison of merger tree statistics from simulations and analytical models, and introduces a fitting function to improve progenitor mass predictions.

Findings

EPS and Monte-Carlo methods qualitatively match simulation trends

Both methods underestimate the masses of the most massive progenitors at high redshift

A new fitting function improves the accuracy of progenitor mass distribution predictions

Abstract

We present a comparison of the statistical properties of dark matter halo merger trees extracted from the Millennium Simulation with Extended Press-Schechter (EPS) formalism and the related GALFORM Monte-Carlo method for generating ensembles of merger trees. The volume, mass resolution and output frequency make the Millennium Simulation a unique resource for the study of the hierarchical growth of structure. We construct the merger trees of present day friends-of-friends groups and calculate a variety of statistics that quantify the masses of their progenitors as a function of redshift; accretion rates; and the redshift distribution of their most recent major merger. We also look in the forward direction and quantify the present day mass distribution of halos into which high redshift progenitors of a specific mass become incorporated. We find that EPS formalism and its Monte-Carlo extension capture the qualitative behaviour of all these statistics but, as redshift increases they systematically underestimate the masses of the most massive progenitors. This shortcoming is worst for the Monte-Carlo algorithm. We present a fitting function to a scaled version of the progenitor mass distribution and show how it can be used to make more accurate predictions of both progenitor and final halo mass distributions.