The statistical Analysis of Star Clusters.pdfVIP

A Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 February 2008 (MN L T X style file v1.4) E The Statistical Analysis of Star Clusters Annabel Cartwright, Anthony P. Whitworth Department of Physics and Astronomy, Cardiff University 4 0 ABSTRACT 0 2 We review a range of stastistical methods for analyzing the structures of star r clusters, and derive a new measure Q which both quantifies, and distinguishes between, a a (relatively smooth) large-scale radial density gradient and multi-scale (fractal) sub- M clustering. The distribution of separations p (s) is considered, and the Normalised Correlation 9 Length s¯ (i.e. the mean separation between stars, divided by the overall radius of the 1 cluster), is shown to be a robust indicator of the extent to which a smooth cluster is 1 centrally concentrated. For spherical clusters having volume-density n ∝ r−α (with v α between 0 and 2) s¯ decreases monotonically with α, from ∼ 0.8 to ∼ 0.6. Since s¯ 4 reflects all star positions, it implicitly incorporates edge effects. However, for fractal 7 star clusters (with fractal dimension D between 1.5 and 3) s¯ decreases monotonically 4 with D (from ∼ 0.8 to ∼ 0.6). Hence s¯, o