We developed a rigorous Bayesian frame that treats the open clusters (OC) in CMD as a mixture of members and field stars. The advanced statistics and comprehensive physical models make our method the state of the art of determining the basic properties (Age, Distance, [Fe/H], extinction AV) along with the slope of MF and the binary fraction of OCs in using photometric data of Gaia EDR3. We also accurately determine the binary fraction fb and γq for NGC3532 by using the mixture model method. For the first time, we unveil that the stars with smaller mass or in the inner region tend to have lower fb and a more positive value of γq due to the lack of low mass ratio binaries. It is strong evidence of the internal dynamics in a cluster.

This work is supported by the National Key Basic R&D Program of China 2019YFA0405501, and NSFC, China U2031139.

{"references": ["Li, L., Shao, Z., Li, Z.-Z., et al. 2020, ApJ, 901, 49"]}