The Criterion for Chaos in Three-Planet Systems
arXiv:2110.02956 · doi:10.3847/1538-4357/ac5f57
Abstract
We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances MMR's), only agrees with numerical simulations at a very crude level. (ii) Much greater accuracy is attained by considering neighboring MMR's that do not overlap. We work out the width of the chaotic zones around each of the neighbors, and also provide simple approximate expressions for the widths. (iii) Even greater accuracy is provided by the overlap of three-body resonances (3BR's), which accounts for fine-grained structure seen in maps from N-body simulations, and also predicts the Lyapunov times. Previous studies conflict on whether overlap of MMR's or of 3BR's drive interplanetary chaos. We show that both do, and in fact they are merely different ways of looking at the same effect. (iv) We compare both criteria with high-resolution maps of chaos from N-body simulations, and show that they agree at a high level of detail.
References in corpus (22)
- REBOUND: An open-source multi-purpose N-body code for collisional dynamics
- A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11
- WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
- First order resonance overlap and the stability of close two planet systems
- All Six Planets Known to Orbit Kepler-11 Have Low Densities
- The Origin of Chaos in the Outer Solar System
- Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
- Predicting the long-term stability of compact multiplanet systems
- Theory of Secular Chaos and Mercury's Orbit
- A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets
- Chaotic Disintegration of the Inner Solar System
- Rapid dynamical chaos in an exoplanetary system
- The path to instability in compact multi-planetary systems
- Dynamical Evolution of Multi-Resonant Systems: the Case of GJ876
- Stability of the Kepler-11 System and its Origin
- Is the outer Solar System chaotic?
- An Integrable Model for the Dynamics of Planetary Mean Motion Resonances
- Dynamical instabilities in systems of multiple short-period planets are likely driven by secular chaos: a case study of Kepler-102
- Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System
- The width of a chaotic layer
- How Close are Compact Multi-Planet Systems to the Stability Limit?
- A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems
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- A Criterion for the Stability of Planets in Chains of Resonances
- celmech: A Python package for celestial mechanics
- The instability mechanism of compact multiplanet systems
- High-resolution resonant portraits of a single-planet white dwarf system
- Resonant chains in triple-planetary systems
- Higher-Order Mean-Motion Resonances Can Form in Type-I Disk Migration
- Secular Dynamics of Compact Three-Planet Systems
- An Adolescent and Near-Resonant Planetary System Near the End of Photoevaporation
- Dynamical Evolution of Planetary Systems