Star cluster simulations: The state of the art

This paper concentrates on four key tools for performing star cluster simul ations developed during the last decade which are sufficient to handle all the relevant dynamical aspects. First we discuss briefly the Hermite integr ation scheme which is simple to use and highly efficient for advancing the single particles. The main numerical challenge is in dealing with weakly an d strongly perturbed hard binaries. A new treatment of the classical Kustaa nheimo-Stiefel two-body regularization has proved to be more accurate for s tudying binaries than previous algorithms based on divided differences or H ermite integration. This formulation employs a Taylor series expansion comb ined with the Stumpff functions, still with one force evaluation per step, which gives exact solutions for unperturbed motion and is at least comparab le to the polynomial methods for large perturbations. Strong interactions b etween hard binaries and single stars or other binaries are studied by chai n regularization which ensures a non-biased outcome for chaotic motions. A new semi-analytical stability criterion for hierarchical systems has been a dopted and the long-term effects on the inner binary are now treated by ave raging techniques for cases of interest. These modifications describe consi stent changes of the orbital variables due to large Kozai cycles and tidal dissipation. The range of astrophysical processes which can now be consider ed by N-body simulations include tidal capture, circularization, mass trans fer by Roche-lobe overflow as well as physical collisions, where the masses and radii of individual stars are modelled by synthetic stellar evolution.