Binary fractions and mass ratio distribution indices of 61 open clusters

Open clusters (OCs) are crucial for studying stellar formation and evolution, while understanding binary stellar formation and star cluster dynamics is key to advancing the field of stellar astrophysics. The binary fraction (f_ b) and mass ratio distribution index (γ_ q) provide key insights into stellar formation and evolution mechanisms. When conventional methods are applied to datasets characterized by small sample sizes and optical binary contamination, the resulting uncertainties often preclude definitive interpretations. Using data from the LI team’s Star Cluster (LISC) I b) and (γ_ q) for 61 OCs. We used the advanced stellar population synthesis model and the Powerful CMD code to perform isochrone fitting and constructed a mixture model of single and binary stars. To correct observational errors, we applied convolution and normalization techniques. A Bayesian framework combined with the Markov chain Monte Carlo method was used to jointly estimate (b) and (γ_ q) from observational data. For the 61 OCs in the LISC catalog, the initial f_ I b mainly ranges from 0. 333 to 0. 611, and it decreases with time. The values of γ_ q are mostly uniform, ranging between -0. 131 and 0. 113, and only a few clusters fall outside the 2σ range. We find that there is a significant positive correlation between the f_ b values and the LISC catalog, with a linear regression analysis yielding an R² of 0. 83, demonstrating the reliability of Powerful CMD code of this work. I