Convergence properties of halo merger trees; halo and substructure merger rates across cosmic history

TL;DR

This paper introduces gbpTrees, an algorithm for constructing accurate halo merger trees from cosmological simulations, analyzing convergence properties, and providing analytic fits for merger rates across cosmic history.

Contribution

The paper presents gbpTrees, a novel algorithm that improves halo merger tree accuracy by correcting for pathologies and analyzing convergence across different resolutions and snapshots.

Findings

Merger counts converge within 5% for FoF haloes at specified resolutions.

Substructure merger rates converge within 10% at higher particle counts.

Analytic fits for merger rates match observed galactic history up to redshift 8.5.

Abstract

We introduce gbpTrees: an algorithm for constructing merger trees from cosmological simulations, designed to identify and correct for pathological cases introduced by errors or ambiguities in the halo finding process. gbpTrees is built upon a halo matching method utilising pseudo-radial moments constructed from radially-sorted particle ID lists (no other information is required) and a scheme for classifying merger tree pathologies from networks of matches made to-and-from haloes across snapshots ranging forward-and-backward in time. Focusing on Subfind catalogs for this work, a sweep of parameters influencing our merger tree construction yields the optimal snapshot cadence and scanning range required for converged results. Pathologies proliferate when snapshots are spaced by $\lesssim{0.128}$ dynamical times; conveniently similar to that needed for convergence of semi-analytical modelling, as established by Benson etal Total merger counts are converged at the level of $\sim{5}$% for friends-of-friends (FoF) haloes of size $n_{\rm p}\gtrsim{75}$ across a factor of 512 in mass resolution, but substructure rates converge more slowly with mass resolution, reaching convergence of $\sim{10}$% for $n_{\rm p}\gtrsim{100}$ and particle mass $m_{\rm p}{\lesssim}10^{9}M_\odot$. We present analytic fits to FoF and substructure merger rates across nearly all observed galactic history ($z{\le}8.5$). While we find good agreement with the results presented by Fakhouri etal for FoF haloes, a slightly flatter dependance on merger ratio and increased major merger rates are found, reducing previously reported discrepancies with extended Press-Schechter estimates. When appropriately defined, substructure merger rates show a similar mass ratio dependance as FoF rates, but with stronger mass and redshift dependencies for their normalisation.