MiMO: Mixture Model for Open Clusters in Color-Magnitude Diagrams
  We propose a mixture model of open clusters (OCs) in the 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, MF 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% to 50%. The photometric and astrometric distances agree well.
