A Kinematic Study of the Old Open Cluster M67

We present a kinematic study of the old open cluster, M67, using recent Gaia data. The photometric and astrometric data of the 934 members were obtained from the member list of our previous study. The structure of M67 was investigated using a surface density map and a radial surface density profile. The apparent and half-number radius of this cluster were determined as approximately 30' (7.6 pc) and 12.'4 (3.1 pc), respectively. The core radius was determined to be approximately 4.'0 (1.0 pc) from the King's empirical density profile fitting. The cluster age was estimated to be approximately 4 Gyr by fitting the theoretical isochrones to its color-magnitude diagram, which is in good agreement with those obtained in previous studies. We investigated the proper motion of individual members relative to the systemic motion of M67. Consequently, the members within the half-number radius appeared to have nearly isotropic motion, whereas the other stars sinked into the cluster center. This indicates that the outskirt of this cluster is contracting. In addition, the signature of cluster rotation was detected from radial velocities of stars within rc, with the rotational axis lying in an east-west direction (position angle 100 degrees-280 degrees) on the sky plane. This implies that the rotation of the cluster can continue for a long time even after its formation. Assuming virial equilibrium, the virial mass of M67 was approximately 1600 M-circle dot. The dynamic relaxation time of M67 was estimated to be approximately 190 Myr, indicating that the cluster had already been relaxed. Indeed, this cluster shows mass segregation in the radial mass distribution of the stars.