Lu Li

Almost all stars are formed in clusters, and most of them are thought to form in binary or multiple systems. The properties of binaries in clusters provide essential constraints on the star formation scenario. Moreover, binaries are deeply involved in the dynamical evolution of stellar clusters. In the early stage, according to the Heggie-Hill law, close encounters in stellar clusters involving binary systems may disrupt soft (i.e., generally wide) binaries efficiently. Only hard (close) binaries remain. Subsequently, in the central (dense) region of a cluster, with the frequent encounters, hard binaries may get harder due to the kinematic energy exchanges. This process actually provides a gravitational fuel that can delay and eventually stop the gravitational collapse. Thus the binary properties of open clusters place crucial constraints on star formation theory and dynamical evolution. If an open cluster is a city of stars and binary stars are the lovers. What is the fate of these couples?

To answer these questions, we develop a comprehensive approach that models the color-magnitude diagram (CMD) distribution of the members of a cluster as a mixture of single stars and photometric unresolved binaries. This method enables us to infer the binary properties, including the binary fraction f_b and binary mass ratio distribution index γ_q, with high accuracy and precision, which was unfeasible in conventional methods. Since the inference of these binary parameters is sensitive to the exact location and extension of the main sequence, we also employ a robust Gaussian process based on iterative trimming to determine the main sequence ridgeline and its scatter from the observed CMD as model input. We test the validity and accuracy of the method with mock clusters. We apply the method to the open cluster NGC 3532 with the Gaia DR2 photometry. For the main sample of cluster members constrained within a magnitude range corresponding to FGK dwarfs, we obtain f_b = 0.267±0.019 and γ_q = -0.10±0.22 for binaries with mass ratio q > 0.2. The f_b value is consistent with the previous work on this cluster and smaller than the binary fraction of field stars. The close-to-zero γ_q indicates that the mass ratios of binaries follow a nearly uniform distribution. For the first time, we unveil that the stars with smaller mass or in the inner region tend to have lower f_b and a more positive value of γ_q due to the lack of low mass-ratio binaries. The clear dependencies of binary properties on mass and radius are most likely caused by the internal dynamics. In this scheme, binaries with smaller primary mass or lower mass-ratio have smaller binding energy; hence, they are more vulnerable to dynamical disruption, especially in the inner region where stars interact more frequently.

In plain words, many stars (30%) in open clusters are in marriage (binary system). The most stable style of marriage is monogamy, open relations (higher-order systems) would be destroyed by dynamics efficiently. If we compare the stellar mass to a star’s wealth, the marriage is fragile when you are both poor (less massive); you are much poorer than your partner (low q); you live in the downtown (inner region) where there are too many temptations (dynamical encounter)! But there is an exception: the Heggie-Hill law told us, very loved ones (hard binary stars) tend to love each other even more (harden) under the encounters. So, if two stars do not love each other so much, they would better be rich!