The Hierarchical Structure of Galactic Haloes: Differentiating Clusters from Stochastic Clumping with AstroLink

We present AstroLink, an efficient and versatile clustering algorithm designed to hierarchically classify astrophysically-relevant structures from both synthetic and observational data sets. We build upon CluSTAR-ND, a hierarchical galaxy/(sub)halo finder, so that AstroLink now generates a two-dimensional representation of the implicit clustering structure as well as ensuring that clusters are statistically distinct from the noisy density fluctuations implicit within the $n$-dimensional input data. This redesign replaces the three cluster extraction parameters from CluSTAR-ND with a single parameter, $S$ -- the lower statistical significance threshold of clusters, which can be automatically and reliably estimated via a dynamical model-fitting process. We demonstrate the robustness of this approach compared to AstroLink's predecessors by applying each algorithm to a suite of simulated galaxies defined over various feature spaces. We find that AstroLink delivers a more powerful clustering performance while being $\sim27\%$ faster and using less memory than CluSTAR-ND. With these improvements, AstroLink is ideally suited to extracting a meaningful set of hierarchical and arbitrarily-shaped astrophysical clusters from both synthetic and observational data sets -- lending itself as a great tool for morphological decomposition within the context of hierarchical structure formation.