Hierarchical models of structure formation predict that dark matter halo assembly histories are characterised by episodic mergers and interactions with other haloes. An accurate description of this process will provide insights into the dynamical evolution of haloes and the galaxies that reside in them. Using large cosmological N-body simulations, we characterise halo orbits to study the interactions between substructure haloes and their hosts, and how different evolutionary histories map to different classes of orbits. We use two new software tools - WhereWolf, which uses halo group catalogues and merger trees to ensure that haloes are tracked accurately in dense environments, and OrbWeaver, which quantifies each halos orbital parameters. We demonstrate how WhereWolf improves the accuracy of halo merger trees, and we use OrbWeaver to quantify orbits of haloes. We assess how well analytical prescriptions for the merger timescale from the literature compare to measured merger timescales from our simulations and find that existing prescriptions perform well, provided the ratio of substructure-to-host mass is not too small. In the limit of small substructure-to-host mass ratio, we find that the prescriptions can overestimate the merger timescales substantially, such that haloes are predicted to survive well beyond the end of the simulation. This work highlights the need for a revised analytical prescription for the merger timescale that more accurately accounts for processes such as catastrophic tidal disruption.
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