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.
