Effects of Binaries on Open Cluster Age Determination in Bayesian Inference

We investigate the effects of binaries on the cluster age determination for 561 open clusters in the Galactic disk via the Bayesian statistical framework. Stellar properties of these star clusters, including age, metallicity, distance modulus, color excess, binary fraction, and rotating star fraction, are derived from color-magnitude-diagrams (CMDs) via isochrone fitting to high-precision Gaia EDR3 data. Across the simple stellar population of binary and single-star, age differences can be found with the same star cluster. A Bayesian applied regression modeling software, Stan, is employed to explore how much binaries affect the age determination of open clusters. Our results present less statistically significant difference between the binary-star simple populations (bsSSPs) and the single-star simple populations (ssSSPs) for cluster age determination. For all clusters in our sample, the ages estimated using the bsSSPs models are younger than those estimated using the ssSSPs, with a mean value of similar to 70 Myr. However, it is found that for 52.5% clusters in our sample, ages are relatively sensitive to the presence of binaries, at least similar to 25% younger. This suggests that in studies of open cluster age determinations, the effects of binary interactions on the whole sample are not prominent, but its effects on some clusters should still be included as an essential ingredient.