Astrometric and Photometric Investigation of Three Old Age Open Clusters in the Gaia Era: Berkeley 32, Berkeley 98, and King 23

Using the photometric and kinematical data from Gaia Data Release 2, three old open clusters namely Berkeley 32 (Be 32), Berkeley 98 (Be 98), and King 23 are investigated. The latter two of these clusters are poorly studied in the literature. The numbers of the most probable cluster members are 563, 260, and 114 for Be 32, Be 98, and King 23, respectively, with membership probabilities higher than 80% and lying within the clusters' limiting radii. Mean proper motions (PMs; mu(alpha) cos delta and mu(delta)) of the clusters are determined as (-0.34 +/- 0.008, -1.60 +/- 0.006), (-1.34 +/- 0.007, -3.22 +/- 0.008), and (-0.46 +/- 0.009, -0.87 +/- 0.012) mas yr(-1). The errors mentioned in the PMs are the Gaussian fitting errors. The blue straggler stars (BSS) in all three old clusters were found to exhibit centralized radial distribution. The clusters' radii are determined as 9'.4, 12'.95, and 66 for Be 32, Be 98, and King 23 using radial density profiles. Ages of the clusters determined by isochrone fitting are 4.90 +/- 0.22, 3.23 +/- 0.15, and 1.95 +/- 0.22 Gyr. The errors given in the clusters' ages are the internal errors. The mass function slopes are found to be flatter than Salpeter's value for all three clusters. All three clusters are found to be dynamically relaxed. Galactic orbits are derived for these clusters, which demonstrate that the studied clusters follow a circular path around the Galactic center.