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

Abstract

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.°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 (< {μ }_α \cos δ > , < {μ }_δ > ) = (-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 (∼1.23 ± 0.03 pc) and 61.‧98 ± 1.‧50 (∼15.92 ± 0.39 pc), respectively. Our results reveal that an escaped member with high membership probability (∼0.91) is located at a distance of 77‧ (∼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.