2006MNRAS.369.1411C

We have previously reported a dimensionless measure,, which can both quantify, and distinguish between, the extent to which a star cluster is centrally concentrated, and the extent to which it contains small-scale subclusters. is the ratio of the normalized correlation length,, (i.e. the mean projected separation between stars, divided by the overall radius of the cluster), to the mean length,, of the segments of a minimal spanning tree (MST) joining all star positions:.

In this paper, we attempt to adapt the correlation-length method to the characterization of gas clouds, with a view to comparing directly the structures of gas clouds and star clusters. We also compare the results of the correlation-length method with fractal dimensions estimated using the more familiar perimeter-area method whereby the lengths of closed contours are plotted against the areas they enclose, on a log-log plot.

We find that the normalized correlation length, when modified to deal with pixellated grey-scale data, is a robust indicator of either central concentration or fractal subclustering of gas clouds, but cannot distinguish between the two types of structure. It is, however, extremely reliable, easy to implement and works accurately at all scales and over all dynamic ranges, even with poorly sampled data. It implicitly incorporates edge effects, so all the data in the complete cloud are used, and it therefore provides a useful method for comparing the structures of molecular clouds and star clusters.

The normalized correlation length produces comparable results to the perimeter-area method when used on molecular cloud data. However, the perimeter-area method is unable to distinguish the degree of clustering in three-dimensional objects with fractal dimensions greater than 2.0. It also suffers from measurement noise and lack of objectivity, particularly if only a few contours are selected for analysis. It cannot be used to compare clouds with star clusters.

It is not found possible to construct an MST algorithm which works reliably for grey-scale data and is immune to scaling problems. The previously reported parameter is therefore not useful when considering gas clouds.