Binary stars as dynamical tracers in globular clusters. I. First observations of bimodal spatial distributions

We present the first homogeneous study of the radial distribution of the binary fraction across the full extent of six Galactic globular clusters (GCs) spanning a wide range of dynamical ages, from dynamically young systems to core-collapsed clusters. We measured the radial variation of the binary fraction using a combination of deep optical HST observations and wide-field ground-based data. For the first time, we provide evidence that the binary fraction in GCs does not decrease monotonically with radius, as commonly assumed, but instead exhibits a bimodal distribution characterized by an excess in the outer regions. Specifically, the binary fraction displays a central peak, followed by a minimum at intermediate radii and a rising branch beyond approximately 1–2 half-light radii. The position of this minimum correlates with the cluster relaxation timescale, indicating that it is shaped by long-term dynamical effects of two-body relaxation driving binary evolution, segregation, and disruption. The minimum radius also correlates with the A^+_rh parameter derived from the radial distribution of blue straggler stars, an empirical indicator of a cluster's dynamical age, further supporting the interpretation that this feature is due to internal dynamical processes. Numerical simulations presented in a companion paper show that such bimodal distributions naturally arise from the combined effects of binary disruption and mass segregation of the surviving binaries in clusters.