A connected component-based method for efficiently integrating multiscale $N$-body systems

We present a novel method for efficient direct integration of gravitational N-body systems with a large variation in characteristic time scales. The method is based on a recursive and adaptive partitioning of the system based on the connected components of the graph generated by the particle distribution combined with an interaction-specific time step criterion. It uses an explicit and approximately time-symmetric time step criterion, and conserves linear and angular momentum to machine precision. In numerical tests on astrophysically relevant setups, the method compares favourably to both alternative Hamiltonian-splitting integrators as well as recently developed block time step-based GPU-accelerated Hermite codes. Our reference implementation is incorporated in the HUAYNO code, which is freely available as a part of the AMUSE framework.