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

TL;DR

This paper introduces a new method using a stellar-dynamical operator derived from N-body models to predict how binary star orbital parameters evolve in star clusters based on initial conditions, enabling efficient analysis without additional simulations.

Contribution

It presents a novel analytical approach to describe binary orbital-parameter evolution in star clusters using a stellar-dynamical operator based on extensive N-body simulations.

Findings

Binary populations evolve on a crossing time-scale.

The operator depends on initial cluster density.

Observed binary populations constrain initial stellar densities.

Abstract

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 exists, which uniquely transforms an initial orbital parameter distribution function for binaries into a new distribution depending on the initial cluster mass and half-mass radius, after some time of dynamical evolution. For the initial distribution the distribution functions derived by Kroupa (1995a,b) 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 stellar-dynamical 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 the stellar dynamical operator can be well parametrized as a function of the initial cluster density. 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 which are found to be in the range 10^2 - 2x10^5 M_sun pc^-3 for open clusters and a few x 10^3 - 10^8 M_sun pc^-3 for globular clusters, respectively.