N-body Integrators with Individual Time Steps from Hierarchical Splitting

TL;DR

This paper introduces a new class of N-body integrators that use hierarchical splitting and individual time steps, achieving excellent energy, momentum, and angular momentum conservation without iterative schemes.

Contribution

The paper presents a novel momentum-conserving N-body integrator with individual time steps derived from Hamiltonian splitting, improving energy conservation and computational efficiency.

Findings

Excellent energy conservation with minimal drift

Conservation of momentum and angular momentum to machine precision

Effective for long-term N-body simulations

Abstract

We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping, these integrators are momentum conserving and show excellent energy conservation in conjunction with a symmetrized time step criterion. We use an explicit but approximate formula for the time symmetrization that is compatible with the use of individual time steps. No iterative scheme is necessary. We implement these ideas in the HUAYNO (available online at www.amusecode.org) code and present tests of the integrators and show that the presented integration schemes shows good energy conservation, with little or no systematic drift, while conserving momentum and angular momentum to machine precision for long term integrations.