Reversible time-step adaptation for the integration of few-body systems
arXiv:2212.09745 · doi:10.1093/mnras/stac3777
Abstract
The time step criterion plays a crucial role in direct N-body codes. If not chosen carefully, it will cause a secular drift in the energy error. Shared, adaptive time step criteria commonly adopt the minimum pairwise time step, which suffers from discontinuities in the time evolution of the time step. This has a large impact on the functioning of time step symmetrisation algorithms. We provide new demonstrations of previous findings that a smooth and weighted average over all pairwise time steps in the N-body system, improves the level of energy conservation. Furthermore, we compare the performance of 27 different time step criteria, by considering 3 methods for weighting time steps and 9 symmetrisation methods. We present performance tests for strongly chaotic few-body systems, including unstable triples, giant planets in a resonant chain, and the current Solar System. We find that the harmonic symmetrisation methods (methods A3 and B3 in our notation) are the most robust, in the sense that the symmetrised time step remains close to the time step function. Furthermore, based on our Solar System experiment, we find that our new weighting method based on direct pairwise averaging (method W2 in our notation), is slightly preferred over the other methods.
arXiv commentAccepted by MNRAS. 13 pages, 6 figures
References in corpus (17)
- PeTar: a high-performance N-body code for modeling massive collisional stellar systems
- Hybrid Symplectic Integrators for Planetary Dynamics
- Mercury-T: A new code to study tidally evolving multi-planet systems. Applications to Kepler-62
- N-body Integrators with Individual Time Steps from Hierarchical Splitting
- Stellar triples on the edge; Comprehensive overview of the evolution of destabilised triples leading to stellar and binary exotica
- On the minimal accuracy required for simulating self-gravitating systems by means of direct N-body methods
- The fate of planetesimal discs in young open clusters: implications for 1I/'Oumuamua, the Kuiper belt, the Oort cloud and more
- A Time-Symmetric Block Time-Step Algorithm for N-Body Simulations
- Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
- Return of the TEDI: revisiting the Triple Evolution Dynamical Instability channel in triple stars
- Chaos in self-gravitating many-body systems: Lyapunov time dependence of and the influence of general relativity
- Symplectic fourth-order maps for the collisional N-body problem
- Towards time symmetric N-body integration
- The relativistic Pythagorean three-body problem
- Orbital Divergence and Relaxation in the Gravitational N-Body Problem
- High order regularised symplectic integrator for collisional planetary systems
- Modeling Dense Stellar Systems