Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected. We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)' Lambda(MSR) = 8.0 +/- 3.5 (where Lambda(MSR) = 1 is no mass segregation) down to 16M(circle dot), and also that the ONC is mass segregated at a lower level (similar to 2.0 +/- 0.5) down to 5M(circle dot). Below 5M(circle dot) we find no evidence for any further mass segregation in the ONC.