Dynamical and Photometric Analysis of NGC 146 and King 14: Evidence for a Co-Moving, Unbound Cluster Pair

Abstract

To understand the nature of the NGC 146-King 14 cluster pair, we conducted a detailed photometric, astrometric, and dynamical study using multiwavelength data from Gaia DR3, Pan-STARRS1, WISE, and TESS. Using a probabilistic approach, we identified 770 and 690 high-probability members of NGC 146 and King 14, respectively. Both clusters exhibit well-defined radial density profiles consistent with King models. We estimate the cluster ages as 20 $\pm$ 5 Myr and 50 $\pm$ 10 Myr from isochrone fitting, and distances of 2.98 $\pm$ 0.33 kpc and 2.51 $\pm$ 0.23 kpc from parallaxes after applying the Bailer-Jones criteria. The clusters show consistent mean proper motions. The mass function slopes (1.51 $\pm$ 0.18 and 1.50 $\pm$ 0.15) are close to the Salpeter value, and the extinction follows a normal Galactic reddening law (RV ~ 3.1). Three-dimensional mapping gives a projected separation of ~ 9 pc. Orbit integration using the galpy MWPotential2014 model shows that NGC 146 and King 14 move in nearly circular, disk-like orbits with similar mean orbital radii (Rm ~ 9 kpc) and orbital periods of roughly 255 Myr. A dynamical separation of ~ 32 pc indicates that both clusters share a common spatial and kinematic association, consistent with a co-moving pair. However, their relative velocity exceeds the escape velocity set by their combined mass, indicating they are not gravitationally bound. TESS light curves reveal seven variable stars, including $\gamma$ Doradus, SPB stars, and eclipsing binaries, though only one is a likely member. Overall, the clusters likely formed within the same giant molecular cloud and now exist as an unbound co-moving pair.