Spatial network characterizations of centrally-concentrated artificial star clusters

Abstract

We explore both two- and three-dimensional spatial network characterization of a centrally-concentrated artificial star cluster (ASC) model with respect to its central concentration parameter α. Using the minimum spanning tree (MST) and Delaunay triangulation network (DT network) construction we show that we can determine not only the core and coronal regions of star clusters, but also the member stars of these regions of interest. The influence of α on a set of convex hull-based star cluster spatial distribution parameters and the network properties are investigated. For α ∈ [0, 2.9], the well-established 𝒬-parameter indicates that 𝒬 ≥ 0.8 indicates a two-dimensional cluster with smooth large-scale radial density gradient. We were able to confirm this result, however we find that this does not extend to three-dimensions; we obtain 𝒬 ≥ 0.6 instead. Most significantly, we find that using the mean of the closeness centrality, as cutoff threshold on the DT networks can clearly define the core and coronal region of each star cluster, with the core regions having considerable spatial overdensities compared to the cluster proper. By determining the roundness and sphericity of the identified two- and three-dimensional core regions respectively, we find that the identified core region has a near-perfect circular or spherical border defined by convex hull between the coronal regions. We propose a modified Q-parameter Q_DT based on the DT network for a faster computation since compared to Q, which takes O(n² log n), Q_DT takes only O(n log n) to compute.