On the Constancy of Binary Star Fractions in Local Star Clusters

We investigate the unresolved binary-star fraction in a complete sample of 376 open clusters located within 1 kpc of the Sun using Gaia DR3 and ASteCA based synthetic colour magnitude diagram modelling. The binary fraction is a global photometric quantity, sensitive primarily to unresolved binaries that produce measurable broadening above the single-star main sequence. We find that the median binary fraction of the sample is nearly constant, 0.29 plus or minus 0.03, with no clear dependence on cluster age, core radius, limiting radius or median mass. This apparent constancy suggests that the global binary content of nearby open clusters is regulated by competing dynamical processes, including disruption of soft binaries, survival and hardening of close binaries, mass segregation, evaporation of single stars, and long-term cluster dissolution. The result is consistent with theoretical expectations and previous observational studies indicating that cluster binary populations can evolve internally while maintaining a relatively stable global binary fraction. Our findings provide an observational constraint for models of open-cluster formation and dynamical evolution and highlight the need for future work combining photometric, astrometric, spectroscopic, and N-body approaches to distinguish between primordial and dynamically formed binary populations.