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

TL;DR

This study combines Gaia DR3 astrometry, multiwavelength photometry, and TESS time-series data to characterize the young open clusters NGC 146 and King 14. Through probabilistic membership, King-profile structural fits, isochrone-based parameter estimation, and galpy orbit integrations in MWPotential2014, the authors show that the clusters share a common origin and kinematic coherence but are not gravitationally bound, forming an unbound co-moving pair with S0 ≈ 32 pc and similar orbital properties. The clusters display near-Salpeter mass-function slopes, ages of 20 ± 5 Myr and 50 ± 10 Myr, and disk-like orbits with small Zmax, consistent with formation in the Perseus arm, while TESS uncoveries of a SPB member and several field variables add time-domain context. Collectively, the results illuminate the transition from bound binaries to unbound co-moving pairs in the Galactic disk and provide a benchmark for primordial cluster pairing and disruption processes.

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 $γ$ 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.

Figures (12)

• Figure 1: Top: Identification charts of the clusters NGC 146 (blue circle) and King 14 (red circle), based on Digitized Sky Survey (DSS) images. The circles indicate the approximate angular extent of each cluster, and the denser central regions correspond to their probable cores. The identified variable stars towards the cluster regions are marked as triangles. Bottom: Stellar surface density maps of the cluster pair, where the color scale represents the stellar density in stars per arcmin$^{2}$.
• Figure 2: Top: Vector point diagrams (VPDs) for NGC 146 (left group) and King 14 (right group), showing the distribution of proper motions in right ascension ($\mu_{\alpha}\cos\delta$) and declination ($\mu_{\delta}$). For each cluster, the three panels correspond to all stars (left), stars lying on the cluster sequence (middle), and field stars (right). The red circles with radii of 0.5 and 0.6 mas yr$^{-1}$ for NGC 146 and King 14, respectively, indicate the proper-motion selection used to define probable cluster members. Bottom: Corresponding Gaia DR3 colour--magnitude diagrams, $G$ versus $(G_{\rm BP}-G_{\rm RP})$, for the same samples (all stars, probable members, and field stars) in the direction of NGC 146 (left) and King 14 (right).
• Figure 3: Membership probability as a function of $Gaia$$G$-band magnitude for stars in the regions of NGC 146 (left) and King 14 (right), derived using the method of balaguer1998determination. Red circles indicate stars with membership probability greater than 80$\%$, considered as probable cluster members.
• Figure 4: RDPs of NGC 146 (left) and King 14 (right), constructed using the surface stellar density in concentric annuli centered on each cluster. The observed data points (black dots) represent the stellar density, with vertical error bars indicating Poisson uncertainties. The solid red curves show the best-fit king1962structure model profiles. The horizontal dashed lines represent the estimated background field star density, while the arrows mark the adopted cluster radii ($r_{\mathrm{cluster}}$) of 7.0 arcmin for NGC 146 and 10.5 arcmin for King 14. These fits enable the determination of structural parameters such as core radius, background density, and limiting radius.
• Figure 5: Two-color diagrams (TCDs) for the clusters NGC 146 (left panels) and King 14 (right panels), constructed using combinations of optical to near-infrared photometric bands (e.g., $B$, $V$, $g$, $r$, $i$, $z$, $y$, $J$, $H$, $K$, $W1$, $W2$, $G$) against $Gaia$$G_{\rm RP}$ magnitudes. The diagrams illustrate the photometric transformations and inter-band correlations, with linear fits overplotted in each panel. These TCDs are employed to probe the interstellar extinction law across different wavelengths and help in constraining the total-to-selective extinction ratio ($R_{\rm V}$), offering insights into the dust properties along the line of sight toward the clusters.