The statistical analysis of star clusters
By A. Cartwright, A. Whitworth. 2004
240 citations recorded by the source corpus.
We review a range of statistical methods for analysing the structures of star clusters, and derive a new measure , which both quantifies and distinguishes between a (relatively smooth) large-scale radial density gradient and multiscale (fractal) subclustering. The distribution of separations p(s) is considered, and the normalized correlation length (i.e. the mean separation between stars, divided by the overall radius of the cluster) is shown to be a robust indicator of the extent to which a smooth cluster is centrally concentrated. For spherical clusters having volume-density n?r? (with between 0 and 2) decreases monotonically with , from ?0.8 to ?0.6. Since reflects all star positions, it implicitly incorporates edge effects. However, for fractal star clusters (with fractal dimension D between 1.5 and 3) decreases monotonically with D (from ?0.8 to ?0.6). Hence , on its own, can quantify, but cannot distinguish between, a smooth large-scale radial density gradient and multiscale (fractal) subclustering. The minimal spanning tree (MST) is then considered, and it is shown that the normalized mean edge length [i.e. the mean length of the branches of the tree, divided by , where A is the area of the cluster and is the number of stars] can also quantify, but again cannot on its own distinguish between, a smooth large-scale radial density gradient and multiscale (fractal) subclustering. However, the combination does both quantify and distinguish between a smooth large-scale radial density gradient and multiscale (fractal) subclustering. IC348 has and ? Ophiuchus has , implying that both are centrally concentrated clusters with, respectively, ? 2.2
Subfields: Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/2386eb428baf5cffafcc939e97ac547ca7d98937
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In Astronomy and Astrophysics
Citations in the corpus
- BANYAN. XI. The BANYAN Σ Multivariate Bayesian Algorithm to Identify Members of Young Associations with 150 pc (2018, methodology): “For each association containing a total of Nk members, the algorithm of Cartwright & Whitworth (2004) was used to build Nk+1 MSTs, in both XY Z and UVW spaces separately.”
- DYNAMICAL MASS SEGREGATION ON A VERY SHORT TIMESCALE (2009, background): “Detailed statistical studies also show the presence of substructure in young clusters, and that substructure is rapidly erased (Cartwright & Whitworth 2004; Schmeja et al. 2008).”
- Clustered and Triggered Star Formation in W5: Observations with Spitzer (2008, methodology): “In this paper we use the so-called ‘minimal spanning tree’ (MST) method to identify and characterize clustering in W5 (see recent work by Cartwright & Whitworth 2004; Bastian et al. 2007).”
- The big problems in star formation: The star formation rate, stellar clustering, and the initial mass function (2014, methodology): “Other quantitative techniques include fractal dimensions (which are closely related to twopoint correlation functions) (Larson 1995), parameters extracted from minimum spanning trees (Cartwright & Whitworth 2004), and dendrograms (Rosolowsky et al. 2008b; Gouliermis et al. 2010), to name only a few.”
- Merging black holes in young star clusters (2019, background): “Furthermore, observations suggest that young embedded SCs are characterised by clumpiness (e.g. Cartwright & Whitworth 2004; Gutermuth et al. 2005) and high fractions of binaries (e.g. Sana et al. 2012), whereas most simulations of young SCs adopt idealized initial conditions, consisting of…”
- A SPITZER SURVEY OF YOUNG STELLAR CLUSTERS WITHIN ONE KILOPARSEC OF THE SUN: CLUSTER CORE EXTRACTION AND BASIC STRUCTURAL ANALYSIS (2009, methodology): “The MST is more convenient than the NN2 links because it allows immediate partitioning of substructured distributions (e.g., Cartwright & Whitworth 2004; Schmeja & Klessen 2006; Bastian et al. 2007, 2009) upon adoption of a surface density threshold as expressed by a critical branch length.”
- Using the minimum spanning tree to trace mass segregation (2009, methodology): “We have used the algorithm of Prim (1957) (see also Cartwright & Whitworth (2004)) to construct our MSTs.”
- The dynamical state of stellar structure in star‐forming regions (2011, methodology): “…the advantageous property of not imposing any geometrical symmetry on the data set, has also been used to quantify the amount of substructure (e.g. Cartwright & Whitworth 2004; Schmejat l. 2008; Maschberger et al. 2010) and mass segregation (e.g. Allison et al. 2009a,b; Maschberger et al. 2010;…”