Validating Open Cluster Candidates with Photometric Bayesian Evidence

TL;DR

This paper addresses the challenge of validating Gaia-era open-cluster candidates plagued by field-star contamination. It introduces MiMO, a CMD-based Bayesian framework that compares a single stellar population plus field contamination against a pure field model, quantified by the Bayes factor BF. A conservative threshold of $\log_{10}\mathrm{BF} > 2$ robustly separates genuine clusters from random field overdensities, and the method remains effective under substantial field contamination while allowing extension to kinematic and multi-dimensional validation. The framework and its publicly available code enable principled catalog refinement and are broadly applicable to other resolved stellar systems such as moving groups, streams, and dwarf satellites.

Abstract

The thousands of open cluster (OC) candidates identified by the Gaia mission are significantly contaminated by false positives from field star fluctuations, posing a major validation challenge. Based on the Mixture Model for OCs (MiMO), we present a Bayesian framework for validating OC candidates in the color--magnitude diagram. The method compares the Bayesian evidence of two competing models: a single stellar population with field contamination versus a pure field population. Their ratio, the Bayes factor (BF), quantifies the statistical support for cluster existence. Tests on confirmed clusters and random fields show that a threshold of BF > 100 effectively distinguishes genuine clusters from chance field overdensities. This approach provides a robust, quantitative tool for OC validation and catalog refinement. The framework is extendable to multi-dimensional validation incorporating kinematics and is broadly applicable to other resolved stellar systems, including candidate moving groups, stellar streams, and dwarf satellites.

Figures (4)

• Figure 1: Example CMDs for different types of targets. Left: Random field regions ($\log_{10}\mathrm{BF} < 0$). Middle: Ambiguous candidates ($\log_{10}\mathrm{BF} \sim 1$). Right: Confirmed OCs with strong evidence ($\log_{10}\mathrm{BF} > 3$). BF denotes the Bayes factor comparing a mixture model of SSP+field to a pure field-star model.
• Figure 2: Distributions of Bayes factor (BF) for random field samples (orange) and confirmed OCs (blue). To accommodate the wide dynamical range of $\log_{10}\mathrm{BF}$, the $x$-axis adopts an arcsinh scale, which is linear near zero and logarithmic at large values. The probability density on the $y$-axis is computed for $\mathrm{arcsinh}(\log_{10}\mathrm{BF})$ accordingly. A threshold of $\log_{10}\mathrm{BF} \simeq 2$ effectively separates real clusters from field samples.
• Figure 3: CMD examples illustrating the impact of field-star model mismatch. In both panels, black points represent 200 field stars within 100 pc. Left: using a representative field model built from stars in the same distance range (gray points). Right: using a mismatched field model built from a broader distance range ($d < 2$ kpc).
• Figure 4: Relation between the Bayes factor (BF) and the field star fraction ($f_\mathrm{fs}$) for the 1232 confirmed OCs from the MiMO catalog. Points are color-coded by the number of inferred member stars ($N_\mathrm{memb}$).