Tidal interactions in star cluster simulations

Abstract

We describe the implementation of tidal circularization of binaries in an N-body code for star cluster simulations. The first part contains the theoretical framework for normal and chaotic tidal interactions, including capture from hyperbolic orbits. This formulation yields convenient expressions which are used to modify the binary elements. Stars are represented as polytropes, with a time-dependent effective polytropic index calculated for evolving stars. Stellar evolution is treated using a fast look-up table for stellar masses and radii. This gives a consistent astrophysical description of open clusters containing a significant proportion of primordial binaries with 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 chaotic motion for perturbed binaries which are studied by the classical Kustaanheimo—Stiefel two-body regularization method and also outline a similar treatment for multiple regularization of temporary subsystems involving 3–6 members. Strong interactions in the latter lead to the formation of chaotic binaries and stable hierarchical systems in which the eccentricity of the inner binary may be subject to systematic changes on relatively short time-scales. Finally, we illustrate the effect of tidal circularization by presenting some results of a realistic cluster simulation involving 104 single stars and 500 primordial binaries.