Two-point Correlation Function of Member Stars in the Open Star Cluster M67

In this paper, we study the two-point correlation function of the old open cluster M67. We discuss the spatial distribution and mass segregation of M67 member stars. The result suggests that spatial distribution of all member stars can be well described by power law. This implies that M67 is characterized by significant spatial clustering and self-similarity. The result of two-point self-correlation function analysis shows that brighter member stars tend to have greater correlation strength and larger correlation index. This indicates that the spatial mass segregation in M67 exists and brighter stars have larger spatial concentration. Further cross-correlation analysis reveals that there is no absolute mass segregation for M67 member stars and all of stars mingle with each other in spatial distribution.