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

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 $n_{\mathrm{p}}\gtrsim 75$ across a factor of 512 in mass resolution, but substructure rates converge more slowly with mass resolution, reaching convergence of $\sim 10$% for $n_{\mathrm{p}}\gtrsim 100$ and particle mass $m_{\mathrm{p}}\lesssim 10^9{M}_{\odot }$. 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.

arXiv commentAccepted for publication in MNRAS. 25 pages, 17 figures. Movies available at http://www.astronomy.swin.edu.au/~gpoole/gbpTrees.html . Code available at https://github.com/gbpoole/gbpCode

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