Simulations of Fractal Star Cluster Formation: I. New Insights for Measuring Mass Segregation of Star Clusters with SubStructure

We compare the existent methods including the minimum spanning tree based method and the local stellar density based method, in measuring mass segregation of star clusters. We find that the minimum spanning tree method reflects more the compactness, which represents the global spatial distribution of massive stars, while the local stellar density method reflects more the crowdedness, which provides the local gravitational potential information. It is suggested to measure the local and the global mass segregation simultaneously. We also develop a hybrid method that takes both aspects into account. This hybrid method balances the local and the global mass segregation in the sense that the predominant one is either caused either by dynamical evolution or purely accidental, especially when such information is unknown a priori. In addition, we test our prescriptions with numerical models and show the impact of binaries in estimating the mass segregation value. As an application, we use these methods on the Orion Nebula Cluster (ONC) observations and the Taurus cluster. We find that the ONC is significantly mass segregated down to the 20th most massive stars. In contrast, the massive stars of the Taurus cluster are sparsely distributed in many different subclusters, showing a low degree of compactness. The massive stars of Taurus are also found to be distributed in the high-density region of the subclusters, showing significant mass segregation at subcluster scales. Meanwhile, we also apply these methods to discuss the possible mechanisms of the dynamical evolution of the simulated substructured star clusters.