MiMO: Mixture Model for Open Clusters in Color-Magnitude Diagrams

We propose a mixture model of open clusters (OCs) in color-magnitude diagrams (CMDs) to measure the OC properties, including isochrone parameters (age, distance, metallicity, and dust extinction), stellar mass function (MF), and binary parameters (binary fraction and mass-ratio distribution), with high precision and reliability. The model treats an OC in the CMD as a mixture of single and binary member stars and field stars in the same region. The cluster members are modeled using a theoretical stellar model, mass function, and binary properties. The field component is modeled nonparametrically using a separate field-star sample in the vicinity of the cluster. Unlike conventional methods that rely on stringent member selection, ours allows us to use a sample of more complete cluster members and attendant field stars. The larger star sample reduces the statistical error and diminishes the potential bias by retaining more stars that are crucial for age estimation and MF measurement. After validating the method with 1000 mock clusters, we measured the parameters of 10 real OCs using Gaia EDR3 data. The best-fit isochrones are consistent with previous measurements in general but with more precise age estimates for several OCs. The inferred MF slope is -2.7 to -1.6 for clusters younger than 2 Gyr, while older clusters appear to have significantly flatter MFs. The binary fraction is 30%-50%. The photometric and astrometric distances agree well.