How to Grow a Healthy Merger Tree

TL;DR

This paper evaluates seven Monte Carlo algorithms for constructing dark matter halo merger trees, comparing their accuracy against the extended Press-Schechter formalism, and introduces three new algorithms that accurately reproduce the progenitor mass function across redshifts.

Contribution

The paper introduces three new Monte Carlo algorithms that accurately generate progenitor mass functions consistent with EPS at all redshifts, improving upon previous methods.

Findings

KW93 algorithm matches EPS progenitor mass function across redshifts

Three new algorithms reliably reproduce the progenitor mass function at each timestep

Differences among algorithms are demonstrated through additional statistical tests

Abstract

We investigate seven Monte Carlo algorithms -- four old and three new -- for constructing merger histories of dark matter halos using the extended Press-Schechter (EPS) formalism based on both the spherical and ellipsoidal collapse models. We compare, side-by-side, the algorithms' abilities at reproducing the analytic EPS conditional (or progenitor) mass function over a broad range of mass and redshift (z=0 to 15). Among the four old algorithms (Lacey & Cole 1993, Kauffmann & White 1993, Somerville & Kolatt 1999, Cole et al 2000), we find that only KW93 produces a progenitor mass function that is consistent with the EPS prediction for all look-back redshifts. The origins of the discrepancies in the other three algorithms are discussed. Our three new algorithms are designed to generate the correct progenitor mass function at each timestep. We show that this is a necessary and sufficient condition for consistency with EPS at any look-back time. We illustrate the differences among the three new algorithms and KW93 by investigating two other conditional statistics: the mass function of the i_{th} most massive progenitors and the mass function for descendants with N_p progenitors.