A Machine-learning-based Investigation of the Open Cluster M67

In this paper, we use a machine-learning method, random forest (RF), to identify reliable members of the old (4 Gyr) open cluster M67 based on the high-precision astrometry and photometry taken from the second Gaia data release (Gaia-DR2). The RF method is used to calculate membership probabilities of 71,117 stars within 2 degrees.5 of the cluster center in an 11-dimensional parameter space, the photometric data are also taken into account. Based on the RF membership probabilities, we obtain 1502 likely cluster members (>= 0.6), 1361 of which are high-probability cluster members (>= 0.8). Based on high-probability memberships with high-precision astrometric data, the mean parallax (distance) and proper- motion of the cluster are determined to be 1.1327 +/- 0.0018 mas (883 +/- 1 pc) and (<mu(alpha) cos delta >, <mu(delta)>) = (-10.9378 +/- 0.0078, -2.9465 +/- 0.0074) mas yr(-1), respectively. We find the cluster to have a mean radial velocity of +34.06 +/- 0.09 km s(-1), using 74 high-probability cluster members with precise radial-velocity measures. We investigate the spatial structure of the cluster, the core and limiting radius are determined to be 4'.80 +/- 0'.11 (similar to 1.23 +/- 0.03 pc) and 61'.98 +/- 1'.50 (similar to 15.92 +/- 0.39 pc), respectively. Our results reveal that an escaped member with high membership probability (similar to 0.91) is located at a distance of 77' (similar to 20 pc) from the cluster center. Furthermore, our results reveal that at least 26.4% of the main-sequence stars in M67 are binary stars. We confirm that significant mass segregation has taken place within M67.