Binary-single-star scattering. v. steady state binary distribution in a homogeneous static background of single stars

We compute the rate at which hard (tightly bound) equal-mass binaries form in a homogeneous stellar background, as the solution of an integral equation describing the combined effects of creation, destruction, hardening, and softening of binaries. Most hard binaries are born very soft. The rate of energy production by hard binaries can be (and has already been) directly used in Fokker-Planck models for the evolution of globular clusters past core collapse. We also calculate the survival probability for a binary as a function of its binding energy, and the steady state distribution of binding energies.