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, Omega(Mecl,rh)(dyn)(t), exists, which uniquely transforms an initial (t = 0) orbital-parameter distribution function for binaries, D-in, into a new distribution, D-Mecl,D-rh(t), depending on the initial cluster mass, M-ecl, and half-mass radius, r(h), after some time t of dynamical evolution. For D-in 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 Omega 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 Omega(Mecl,rh)(dyn)(t) can be well parametrized as a function of the cluster density, rho(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, rho(ecl), which are found to be in the range of 10(2) less than or similar to rho(ecl)(<= r(h))/M-circle dot pc (3) less than or similar to 2 x 10(5) for open clusters and a few x 10(3) less than or similar to r(ecl)(<= r(h))/M-circle dot pc (3) less than or similar to 10(8) for globular clusters.