A Binary-Based Reassessment of the Age and Stellar Properties of NGC 7789 Using Twelve Binary Components

TL;DR

This study applies a binary-based, multi-observable approach to determine a precise age and fundamental properties for the open cluster NGC 7789 by jointly modelling radial velocities, TESS light curves, and broadband spectral-energy distributions for six SB2 binaries (twelve stars), anchored by Gaia DR3 astrometry. The analysis yields a self-consistent solution with an age of $1.26 \pm 0.09$ Gyr, $A_V = 0.90 \pm 0.05$ mag, and a Gaia-based distance of $d \approx 2.08 \pm 0.14$ kpc, with metallicity around ${\rm [Fe/H]} \approx +0.20$. The twelve components probe the MSTO and subgiant regime and show excellent agreement with modern stellar evolution models in multiple parameter planes, demonstrating the method’s precision and robustness. This work positions NGC 7789 as a valuable benchmark for binary-based cluster dating and highlights the consistency between dynamical, photometric, and astrometric constraints in open clusters.

Abstract

We present a binary-based reassessment of the age of the intermediate-age open cluster NGC 7789, together with well-constrained stellar parameters for twelve components in six SB2 systems, including two eclipsing binaries. Our analysis employs a unified modelling framework that combines radial-velocity orbits, TESS light curves, and blue-to-IR spectral energy distributions (SEDs), providing a robust alternative to traditional isochrone-based age determinations. By adopting common cluster-wide parameters (age, distance, and line-of-sight extinction) when solving for the stellar parameters of the binary components, we obtain a coherent set of masses, radii, effective temperatures, and luminosities for all twelve stars. The combined SED, eclipsing-binary, and radial-velocity analysis yields a well-constrained cluster age of $1.26 \pm 0.09$ Gyr and an extinction of $A_V = 0.90 \pm 0.05$ mag, while remaining consistent with the Gaia DR3 distance of $d \simeq 2.06$ kpc used as an external prior. An independent Gaia DR3 astrometric analysis gives a distance of $2082 \pm 142$ pc and confirms the membership of all six systems. The twelve binary components occupy the turnoff and subgiant regions of the cluster, enabling stringent evolutionary tests: in the radius--mass, radius--temperature, and temperature--mass diagrams, they show excellent agreement with modern stellar evolution models for the derived cluster parameters. NGC 7789 thus serves as a valuable benchmark for multi-observable, binary-based age determinations in open cluster studies.

Figures (7)

• Figure 1: Observed (circles) and modelled (lines) radial velocities for the six selected binary systems in NGC 7789. Residuals (O-C) are shown below each panel. Red color denote the primary component, blue for the secondary.
• Figure 2: The observed and the modelled (solid lines) light curves of WOCS 14014 and WOCS 17028; insets provide zoomed views of the primary (Min I) and secondary (Min II) minima to illustrate the goodness of fit.
• Figure 3: We performed a joint SED fit for six binary systems, assuming a common age, distance, and extinction ($A_V$). The models were computed for a metallicity of [Fe/H] = 0.20. Figure \ref{['fig:age_Fe']} illustrates how the derived age depends on metallicity. In the figure, blue and red lines represent the best-fit models for the individual components of each binary, while the black line corresponds to the combined (composite) SED. Observational data are shown as orange circles with associated error bars.
• Figure 4: Age of NGC 7789 vs. the assumed metallicity [Fe/H]. The same type of SED fits used to produce Table \ref{['tab:ngc7789_sedresults']} and Fig. \ref{['fig:seds']} was carried out for additional metallicities. We find a linear relation between the age of NGC 7789 and metallicity given in Sec. \ref{['sec:SEDs']}. The $\chi^2$ value at each metallicity tested is also plotted to provide an idea of which metallicities are acceptable, i.e., for [Fe/H] $\gtrsim 0$.
• Figure 5: Top: Proper–motion density map of the NGC 7789 field based on Gaia DR3 data. The cluster population is clearly identified as the prominent red overdensity centred at $(\mu_{\alpha*},\mu_\delta) \simeq (-0.97,\,-1.89)$ mas yr$^{-1}$, corresponding to the mean cluster motion. Middle: Cumulative distribution of proper–motion displacements $\Delta\mu$ from the cluster centroid. The vertical dashed line at $\Delta\mu = 0.3$ mas yr$^{-1}$ marks the adopted membership boundary separating the dense cluster core from the surrounding field population. Bottom: Mean cumulative density (number of stars per $\Delta\mu^{2}$) as a function of $\Delta\mu$, showing a rapid decline in source density beyond the adopted cutoff and confirming the effectiveness of the membership selection.