Tidal interactions in star cluster simulations

We describe the implementation of tidal circularization of binaries in an N -body code for star cluster simulations. The first part contains the theore tical framework for normal and chaotic tidal interactions, including captur e from hyperbolic orbits. This formulation yields convenient expressions wh ich are used to modify the binary elements. Stars are represented as polytr opes, with a time-dependent effective polytropic index calculated for evolv ing stars. Stellar evolution is treated using a fast look-up table for stel lar masses and radii. This gives a consistent astrophysical description of open clusters containing a significant proportion of primordial binaries wi th a wide range of masses and periods. An analytic expression for the chaos boundary for arbitrary mass ratio and polytropic indices is presented. We provide detailed correction procedures for tidal circularization and chaoti c motion for perturbed binaries which are studied by the classical Kustaanh eimo-Stiefel two-body regularization method and also outline a similar trea tment for multiple regularization of temporary subsystems involving 3-6 mem bers. Strong interactions in the latter lead to the formation of chaotic bi naries and stable hierarchical systems in which the eccentricity of the inn er binary may be subject to systematic changes on relatively short time-sca les. Finally, we illustrate the effect of tidal circularization by presenti ng some results of a realistic cluster simulation involving 10(4) single st ars and 500 primordial binaries.