2009MNRAS.392..341C

We have previously reported a measure which both quantifies and distinguishes between a (relatively smooth) large-scale radial density gradient and multiscale (fractal) subclustering. Here, we extend the applicability of to clusters which deviate significantly from an overall circular shape.

varies systematically as clusters assume a more elongated shape, and it is therefore possible to correct for the effect, if the elongation of the cluster is also quantified. therefore remains a useful and robust analytical technique for classifying and quantifying the internal structure of star clusters, even when their overall shape is far from circular.

The corrections required are small for individual clusters which are not extremely elongated (not more than three times longer than they are wide) of the same order as the uncertainty in the value of for a particular cluster type. We therefore recommend that no correction be applied to the calculation of for individual clusters, unless they are more than three times longer than their width, but that correction for elongation be applied when is used for statistical analyses of large numbers of observed or simulated clusters.