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Using membership of 85 open clusters from previous studies (Pang et al.2021a,b, 2022b; Li et al. 2021) based on Gaia DR3 data, we identify binarycandidates in the color-magnitude diagram, for systems with mass ratio q > 0.4.The binary fraction is corrected for incompleteness at different distances dueto the Gaia angular resolution limit. We find a decreasing binary fraction withincreasing cluster age, with substantial scatter. For clusters with a totalmass > 200$M_\odot$, the binary fraction is independent of cluster mass. Thebinary fraction depends strongly on stellar density. Among four types ofcluster environments, the lowest-density filamentary and fractal stellar groupshave the highest mean binary fraction: 23.6% and 23.2%, respectively. The meanbinary fraction in tidal-tail clusters is 20.8%, and is lowest in the densesthalo-type clusters: 14.8%. We find clear evidence of early disruptions ofbinary stars in the cluster sample. The radial binary fraction depends stronglyon the cluster-centric distance across all four types of environments, with thesmallest binary fraction within the half-mass radius $r_h$, and increasingtowards a few $r_h$. Only hints of mass segregation is found in the targetclusters. The observed amount of mass segregation is not significant togenerate a global effect inside the target clusters. We evaluate the bias ofunresolved binary systems (assuming a primary mass of 1$M_\odot$) in 1Dtangential velocity, which is 0.1-1$\,\rm km\,s^{-1}$. Further studies arerequired to characterize the internal star cluster kinematics using Gaia propermotions.

Binary Star Evolution in Different Environments: Filamentary, Fractal, Halo and Tidal-tail Clusters