Implementing Few-Body Algorithmic Regularization with Post-Newtonian Terms

We discuss the implementation of a new regular algorithm for simulation of the gravitational few-body problem. The algorithm uses components from earlier methods, including the chain structure, the logarithmic Hamiltonian, and the time-transformed leapfrog. This algorithmic regularization code, AR-CHAIN, can be used for the normal N-body problem, as well as for problems with softened potentials and/or with velocity-dependent external perturbations, including post-Newtonian terms, which we include up to order PN2.5. Arbitrarily extreme mass ratios are allowed. Only linear coordinate transformations are used and thus the algorithm is somewhat simpler than many earlier regularized schemes. We present the results of performance tests which suggest that the new code is either comparable in performance or superior to the existing regularization schemes based on the Kustaanheimo-Stiefel (KS) transformation. This is true even for the two-body problem, independent of eccentricity. An important advantage of the new method is that, contrary to the older KS-CHAIN code, zero masses are allowed. We use our algorithm to integrate the orbits of the S stars around the Milky Way supermassive black hole for one million years, including PN2.5 terms and an intermediate-mass black hole. The three S stars with shortest periods are observed to escape from the system after a few hundred thousand years.