Investigating 16 Open Clusters in the Kepler/K2-Gaia DR3 Field. I. Membership, Binary Systems, and Rotation

Using data from Gaia Data Release 3 and Kepler/K2, we present a catalog of 16 open clusters with ages ranging from 4-4000 Myr that provides detailed information on membership, binary systems, and rotation. We assess the memberships in 5D phase space, and estimate the basic parameters of each cluster. Among the 20,160 members, there are 4381 stars identified as binary candidates and 49 stars identified as blue straggler stars. The fraction of binaries varies in each cluster, and the range is between 9% and 44%. We obtain the rotation periods of 5467 members, of which 4304 are determined in this work. To establish a benchmark for the rotation-age-color relation, we construct color-period diagrams. We find that the rotational features of binaries are similar to that of single stars, while the features for binaries are more scattered in the rotation period. Moreover, the morphology of the color-period relationship is already established for Upper Scorpius at the age of 19 Myr, and some stars of varying spectral types ( i.e., FG, K, and M type) show different spin-down rates after the age of similar to 110 Myr. By incorporating the effects of stalled spin-down into our analysis, we develop an empirical rotation-age-color relation, which is valid with ages between 700-4000 Myr and colors corresponding to a range of 0.5 < (G(BP) - G(RP))(0) < 2.5 mag.