Regularization Tools for Binary Interactions

Abstract

We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies, whereas the latter deals with strong interactions involving binaries. Combined with a powerful stability criterion for hierarchical systems, this versatile treatment provides an efficient way of studying all dynamical processes in globular clusters containing a realistic population of primordial binaries. These algorithms are also ideal for modelling a variety of astrophysical effects, such as averaging over Kozai cycles, tidal circularization, spin-orbit coupling and stellar collisions, where well-defined elements are used to describe near-singular solutions. We also describe a new time-transformed leapfrog scheme which has been developed to deal with black-hole binaries in galactic centres. This formulation is valid for large mass ratios and dominant two-body motions in a compact subsystem can be treated accurately in the post-Newtonian approximation. This method has been combined with the existing regularization algorithms into a new simulation code NBODY7. Some preliminary results of a test problem illustrating possible applications are presented.