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

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 $f_{\mathrm{b}}=0.267\pm 0.019$ and ${\gamma }_q=-0.10\pm 0.22$ 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.

18 pages, 10 figures, 4 tables; accepted for publication in ApJ

References in corpus (11)

• The NumPy array: a structure for efficient numerical computation
• A maximum likelihood method for fitting colour-magnitude diagrams
• The primordial binary population II: Recovering the binary population for intermediate mass stars in Sco OB2
• ASteCA - Automated Stellar Cluster Analysis
• Exploring the consequences of pairing algorithms for binary stars
• The exclusion of a significant range of ages in a massive star cluster
• Wide binaries are rare in open clusters
• A new detailed examination of white dwarfs in NGC3532 and NGC2287
• What a Local Sample of Spectroscopic Binaries can tell us about the Field-Binary Population
• Spectroscopic membership for the populous 300 Myr-old open cluster NGC 3532
• Unresolved binaries and Galactic clusters' mass estimates

Cited by in corpus (22)

• The multiplicity fraction in 202 open clusters from Gaia
• Rotation periods for cool stars in the open cluster NGC 3532. The transition from fast to slow rotation
• High Mass-ratio Binary Population in Open Clusters: Segregation of early type binaries and an increasing binary fraction with mass
• MiMO: Mixture Model for Open Clusters in Color-Magnitude Diagrams
• Mass Segregation in the Hyades Cluster
• Kepler meets Gaia DR3: homogeneous extinction-corrected color-magnitude diagram and binary classification
• Unresolved Binaries in the Intermediate Mass Range in the Pleiades Star Cluster
• The Stellar "Snake" I: Whole Structure and Properties
• Photometric Determination of Unresolved Main-sequence Binaries in the Pleiades: Binary Fraction and Mass Ratio Distribution
• An empirical isochrone archive for nearby open clusters
• Unresolved multiple stars and Galactic clusters' mass estimates
• Goodness-of-fit test for isochrone fitting in the Gaia era. Statistical assessment of the error distribution
• Uniform Modelling of the Stellar Density of Thirteen Tidal Streams within the Galactic Halo
• Cluster aggregates surrounding Pismis 5 in the Vela Molecular Ridge
• Multiple stellar populations at less evolved stages-II: no evidence of significant helium spread among NGC 1846 dwarfs
• Tidal Tails of Nearby Open Clusters. II. A Review of Simulated Properties and the Reliability of Observational Catalogues
• Mass-Dependent Radial Distribution of Single and Binary Stars in the Pleiades and their Dynamical Implications
• Half a Million Binary Stars from the low resolution spectra of LAMOST
• Multiple stellar populations at less evolved stages-III: a possible helium spread in NGC 2210
• A Census of Pulsars in Possible Association with Galactic Open Clusters
• Stellar masses and mass ratios for Gaia open cluster members
• Tidal tails in open clusters: Morphology, binary fraction, dynamics, and rotation