Switching integrators reversibly in the astrophysical $N$-body problem

Abstract

We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader. Upgrading an ordinary non-reversible switching integrator to a reversible one is straightforward and introduces no appreciable computational burden in our tests. Our method checks if the integrator during the time step violates a time-symmetric selection condition and redoes the step if necessary. In our experiments a few percent of steps would have violated the condition without our corrections. By eliminating them the algorithm avoids long-term error accumulation, of several orders magnitude in some cases.

arXiv comment10 pages, 8 figures. Matches accepted MNRAS version

References in corpus (32)

• The cosmological simulation code GADGET-2
• IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
• A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems
• PeTar: a high-performance N-body code for modeling massive collisional stellar systems
• Hybrid Symplectic Integrators for Planetary Dynamics
• N-body simulations of gravitational dynamics
• Long-term planetary integration with individual time steps
• New families of symplectic splitting methods for numerical integration in dynamical astronomy
• Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions
• N-body Integrators with Individual Time Steps from Hierarchical Splitting
• High precision Symplectic Integrators for the Solar System
• The fate of planetesimal discs in young open clusters: implications for 1I/'Oumuamua, the Kuiper belt, the Oort cloud and more
• On the minimal accuracy required for simulating self-gravitating systems by means of direct N-body methods
• Time-Symmetrized Kustaanheimo-Stiefel Regularization
• A Time-Symmetric Block Time-Step Algorithm for N-Body Simulations
• Symplectic integrators in the shearing sheet
• A Fast and Accurate Universal Kepler Solver without Stumpff Series
• Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations
• A study of symplectic integrators for planetary system problems: error analysis and comparisons
• Symplectic fourth-order maps for the collisional N-body problem
• Variational Integrators for the Gravitational N-Body Problem
• Symplectic integration for the collisional gravitational $N$-body problem
• Highly stable evolution of Earth's future orbit despite chaotic behavior of the Solar System
• Time-symmetric integration in astrophysics
• Towards time symmetric N-body integration
• Are long-term $N$-body simulations reliable?
• A differentiable N-body code for transit timing and dynamical modeling. I. Algorithm and derivatives
• Stepsize errors in the $N$-body problem: discerning Mercury's true possible long-term orbits
• Should $N$-body integrators be symplectic everywhere in phase space?
• High order regularised symplectic integrator for collisional planetary systems
• EnckeHH: an integrator for gravitational dynamics with a dominant mass that achieves optimal error behaviour
• Improving the accuracy of simulated chaotic $N$-body orbits using smoothness

Cited by in corpus (2)

• TRACE: a code for Time-Reversible Astrophysical Close Encounters
• Close-in compact super-Earth systems emerging from resonant chains: slow destabilization by unseen remnants of formation