The statistical Analysis of Star Clusters

Abstract

We review a range of stastistical methods for analyzing the structures of star clusters, and derive a new measure $\mathcal{Q}$ which both quantifies, and distinguishes between, a (relatively smooth) large-scale radial density gradient and multi-scale (fractal) sub-clustering. Q is derived from the normalised correlation length and the normalised edge length of the minimal spanning tree for each cluster.