An application of the k-th nearest neighbor method to open cluster membership determination
We introduce a non-parametric method for open cluster membership determination in three-dimensional (3D) velocity space (proper motion and radial velocity). Clean 3D cluster members can be obtained by statistically analyzing the Euclidean distance between each star and its k-th nearest neighbor in 3D velocity space. We use 513 sample stars in the direction of open cluster M67 to construct a 3D velocity space and test our method; 291 3D cluster members are obtained. The color-magnitude diagram, proper motions, radial velocities and spatial distribution of these 3D cluster members demonstrate the effectiveness of our method. From the 291 3D cluster members, the mean radial velocity and absolute proper motion of M67 are Vr = +33.46 ± 0.05 km s−1 and (PMRA, PMDEC) = (−7.64 ± 0.07, −5.98 ± 0.07) mas yr−1, respectively. In addition, we use 640 sample stars with precise proper motions and radial velocities in the direction of open cluster NGC 188 to test our method. The test results also show that our method is effective.
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