Measuring clustering in 2dv space

The statistical descriptor is a robust and useful tool for distinguishing and quantifying the degree of radial or multiscale clustering in objects such as open clusters. is calculated as m/s, where is the mean edge length of the minimum spanning tree and is the mean distance between cluster members, or correlation length. is obtained using only two-dimensional position data. Here, we investigate the performance of in three dimensions, both when true three-dimensional data are available and when the radial velocity of cluster components is used as a proxy for position: this is known as 2dv space. True three-dimensional data offer an improvement in the resolution of and as diagnostic indicators of clustering, a scatter plot of versus proving to be a particularly clear method of interpreting the information. Results are not satisfactory when 2dv information is used, as the data from cluster types which are clearly distinguishable using 2d information alone become overlapping and confused when 2dv information is used. We therefore recommend that the 2d method is used, unless true 3d positions of cluster members are available. The use of the versus plot is particularly recommended, as adding extra discrimination between cluster types, compared with that achieved using alone.