Stellar masses and mass ratios for Gaia open cluster members

Context: Unresolved binaries in star clusters can bias stellar and cluster mass estimates, making their proper treatment essential for studying cluster dynamics and evolution. Aims: We aim to develop a fast and robust framework for jointly deriving stellar masses and multiplicity statistics of member stars, together with optimal cluster parameters. Methods: We use Gaia DR3 parallaxes together with multi-band photometry of open cluster (OC) members to infer stellar masses and binary mass-ratios through simulation-based inference (SBI), while iteratively fitting the cluster parameters. The validation of our SBI framework on simulated clusters demonstrates that the inclusion of infrared photometry significantly improves the detection of low mass-ratio binaries. The minimum mass-ratio threshold for reliably identifying unresolved binaries depends on cluster properties and the available photometry, but typically lies below $q=0.5$. Results: Applying our method to 42 well-populated OCs, we derive a catalogue of stellar masses and mass-ratios for 27201 stars, achieving typical uncertainties of 0.08 in $q$ and $0.01,\mathrm{M}\odot$ in the primary stellar mass. We analyse the archetype OCs M67 and NGC 2360 in detail, including mass segregation and mass-ratio distribution among other characteristics, while deriving multiplicity fractions for the rest of the sample. We find evidence that the high mass-ratio ($q\geq 0.6$) binary fraction shows a strong correlation with the age and a weak anti-correlation with the cluster metallicity. Furthermore, the variation of the binary fraction with stellar mass in OCs shows strong accordance with the observed dependence for field stars heavier than $\gtrsim0.6,\mathrm{M}\odot$. Conclusions: Our work paves a path for future population-level investigations of multiplicity statistics and precision stellar masses in extended samples of OCs.

💡 Research Summary

This paper presents a novel, fast, and robust framework for simultaneously deriving individual stellar masses and binary mass‑ratios (q) for members of open clusters (OCs) by exploiting Gaia DR3 parallaxes together with multi‑band photometry from Gaia, 2MASS, and WISE. The authors adopt a simulation‑based inference (SBI) approach, specifically Neural Posterior Estimation (NPE), to bypass explicit likelihood calculations. They generate a training set of roughly two million synthetic stars using the PARSEC isochrone library, sampling broad priors for primary mass (0.1–9 M⊙), mass‑ratio (0–1), metallicity (‑2.0 to +0.45 dex), log(age) (6.5–10.0), distance modulus (0–13.5 mag), and extinction (0–4 mag). Observational uncertainties are injected directly into the simulated magnitudes and parallaxes, ensuring that the neural network learns to handle realistic noise.

For each real cluster member, the trained network returns 20 000 posterior samples of the six astrophysical parameters. To enforce cluster coherence, the authors assign Gaussian weights to each sample based on provisional cluster parameters (age, distance, metallicity, extinction) and compute weighted averages. These weighted estimates are fed back into the next iteration, updating the cluster priors until convergence. This iterative weighting scheme replaces computationally expensive Markov Chain Monte Carlo sampling while still achieving self‑consistent estimates of both stellar and cluster properties.

A key methodological insight is the inclusion of infrared photometry (J, H, K_s, W1) alongside Gaia’s optical bands. Tests on simulated clusters demonstrate that infrared data dramatically improve the detection of low‑mass‑ratio binaries, lowering the reliable q‑threshold to ≈0.5 for typical Gaia‑depth clusters. The minimum detectable q depends on cluster distance, age, and extinction, but generally remains below 0.5 for well‑populated, nearby OCs.

The authors apply the pipeline to 42 “Very Good” OCs selected from an initial pool of 144 candidates (itself drawn from 7167 HR24‑identified clusters within 2 kpc). The final catalogue contains 27 201 stars with typical uncertainties of 0.01 M⊙ in primary mass and 0.08 in q. Detailed case studies of M 67 and NGC 2360 illustrate the method’s ability to recover mass segregation signatures and to map the q‑distribution across the main sequence. Across the full sample, they find that the high‑q (q ≥ 0.6) binary fraction correlates strongly with cluster age (older clusters host a larger fraction of high‑q binaries) and shows a weak anti‑correlation with metallicity. Moreover, the binary fraction’s dependence on stellar mass mirrors that observed in the field for stars above ≈0.6 M⊙, suggesting that dynamical processing within OCs preserves the mass‑dependent binary statistics seen in the Galactic disk.

The paper discusses several limitations. The reliance on a single set of stellar models (PARSEC) introduces systematic uncertainties, especially in the low‑mass regime where model‑data colour discrepancies are known. The treatment of systems with companion masses below 0.1 M⊙ as single stars creates an artificial excess of q = 0 in the training set. Additionally, clusters lacking full infrared coverage will have higher q detection limits, and very metal‑poor or highly extincted clusters may suffer from biased priors.

In conclusion, the presented SBI framework offers a scalable solution for deriving precise stellar masses and binary mass‑ratios across large OC samples, paving the way for population‑level studies of multiplicity evolution, cluster dynamics, and Galactic stellar demographics. Future extensions could incorporate spectroscopic radial velocities, Gaia astrometric binaries, and hierarchical triple modeling to further refine the multiplicity census.