A Common Origin for Binary Fractions in the Field and in Dense Clusters

Abstract Globular clusters (GCs) display much lower binary fractions than found among main-sequence (MS) stars in the solar neighborhood. The physical cause of this difference is debatable: does it reflect different star formation outcomes at low metallicity and/or high density, the dynamical processing of primordial binaries over cluster lifetimes, or a combination of the two? Starting from the assumption that the initial binary distribution in GCs is the same as the binary distribution observed in the solar neighborhood, we show with a straightforward analytical calculation that the dynamical dissolution of “soft” primordial binaries can largely explain the MS binary fractions in present-day GCs. We validate our estimates against a set of detailed N -body simulations with the Cluster Monte Carlo code. We find broad agreement between the binary populations and dynamical characteristics of the theoretical models and a sample of well-studied GCs in the Milky Way. The process of “black hole burning” provides a major energy source for soft binary dissolution on gigayear timescales; in the densest clusters (initial virial radii ≲ 0.5 pc), direct collisions between stars rapidly reduce the binary fraction at early times. Our results reinforce the need to include realistic initial conditions in the numerical modeling of GCs.