Correlation of macroscopic instability and Lyapunov times in the general three-body problem

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small bodies in the Solar System. Numerical integrations of several sets of differently randomised initial conditions produced the same relationship of the instability time and Lyapunov time. Marginal probability densities of the various times in the three-body experiments are also discussed. Our high accuracy numerical method for three-body orbit computations and Lyapunov time determinations is concisely described.Comment: 4 pages, 7 figures. accepted for publication in MNRA

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. The code 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. Arbitarily extreme mass ratios are allowed. Coordinate transformations are not used and thus the algorithm is somewhat simpler than many earlier regularized schemes. We present the results of performance tests, then 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

Evolution of Binary Supermassive Black Holes via Chain Regularization

A chain regularization method is combined with special purpose computer hardware to study the evolution of massive black hole binaries at the centers of galaxies. Preliminary results with up to N=260,000 particles are presented. The decay rate of the binary is shown to decrease with increasing N, as expected on the basis of theoretical arguments. The eccentricity of the binary remains small.Comment: 8 pages. To appear in "Nonlinear Dynamics in Astronomy and Physics, A Workshop Dedicated to the Memory of Professor Henry E. Kandrup", ed. J. R. Buchler, S. T. Gottesman and M. E. Maho