An analytical description of the evolution of binary orbital-parameter distributions in N-body computations of star clusters

A new method is presented to describe the evolution of the orbital-parameter distributions for an initially universal binary population in star clusters by means of the currently largest existing library of N-body models. It is demonstrated that a stellar-dynamical operator, Ω^{Mecl, rh}_dyn(t), exists, which uniquely transforms an initial (t= 0) orbital-parameter distribution function for binaries, ?, into a new distribution, ?, depending on the initial cluster mass, M_ecl, and half-mass radius, r_h, after some time t of dynamical evolution. For ? distribution functions derived are used, which are consistent with constraints for pre-main-sequence and Class I binary populations. Binaries with a lower energy and a higher reduced mass are dissolved preferentially. The Ω operator can be used to efficiently calculate and predict binary properties in clusters and whole galaxies without the need for further N-body computations. For the present set of N-body models, it is found that the binary populations change their properties on a crossing time-scale such that Ω^{Mecl, rh}_dyn(t) can be well parametrized as a function of the cluster density, ρ_ecl. Furthermore, it is shown that the binary fraction in clusters with similar initial velocity dispersions follows the same evolutionary tracks as a function of the passed number of relaxation times. Present-day observed binary populations in star clusters put constraints on their initial stellar densities, ρ_ecl, which are found to be in the range of 10²≲ρ_ecl(≤r_h)/ M_⊙ pc^-3≲ 2 × 10⁵ for open clusters and a few ×10³≲ρ_ecl(≤r_h)/ M_⊙ pc^-3≲ 10⁸ for globular clusters.