Modelling unresolved binaries of open clusters in color-magnitude diagram. I. method and application of NGC3532

TL;DR

This paper introduces a new method to model unresolved binaries in open clusters using color-magnitude diagrams, allowing precise inference of binary properties like fraction and mass-ratio distribution, demonstrated on NGC3532.

Contribution

The paper presents a novel approach combining Gaussian processes and CMD modeling to accurately determine binary fractions and mass-ratio distributions in open clusters.

Findings

Binary fraction in NGC3532 is approximately 0.267.

Mass-ratio distribution is nearly uniform with a slope near zero.

Binary properties vary with stellar mass and cluster radius.

Abstract

The binary properties of open clusters place crucial constraints on star formation theory and clusters' dynamical evolution. We develop a comprehensive approach that models the color-magnitude diagram (CMD) of the cluster members as the mixture of single stars and photometric unresolved binaries. This method enables us to infer the binary properties, including the binary fraction $f_\mathrm{b}$ and binary mass-ratio distribution index $\gamma_q$ when a power-law is assumed, with high accuracy and precision, which were unfeasible in conventional methods. We employ a modified Gaussian process to determine the main sequence ridge line and its scatter from the observed CMD as model input. As a first example, we apply the method to the open cluster NGC3532 with the Gaia DR2 photometry. For the cluster members within a magnitude range corresponding to FGK dwarfs, we obtain $f_\mathrm{b} = 0.267\pm0.019$ and $\gamma_q = - 0.10\pm0.22$ for binaries with mass ratio $q > 0.2$. The $f_\mathrm{b}$ value is consistent with the previous work on NGC3532 and smaller than that of field stars. The close to zero $\gamma_q$ 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 $f_\mathrm{b}$ and more positive value of $\gamma_q$ due to the lack of low mass-ratio binaries. The clear dependences of binary properties on mass and radius are most likely caused by the internal dynamics.