The instability mechanism of compact multiplanet systems

Abstract

To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that account for small sets of resonant interactions between the planets can accurately recover $N$-body instability times. This points toward a simple physical picture in which a handful of three-body resonances, generated by interactions between nearby two-body mean motion resonances, overlap and drive chaotic diffusion, leading to instability. Motivated by this, we show that instability times are well described by a power law relating instability time to planet separations, measured in units of fractional semi-major axis difference divided by the planet-to-star mass ratio to the $1/4$ power, rather than the frequently adopted $1/3$ power implied by measuring separations in units of mutual Hill radii. For idealized systems, the parameters of this power-law relationship depend only on the ratio of the planets' orbital eccentricities to the orbit-crossing value, and we report an empirical fit to enable quick instability time predictions. This relationship predicts that observed systems comprised of three or more sub-Neptune-mass planets must be spaced with period ratios $P\gtrsim 1.35$ and that tightly spaced systems ($P\lesssim 1.5$) must possess very low eccentricities ($e\lesssim 0.05$) to be stable for more than $10^9$ orbits.

20 pages, 13 figures. Accepted for publication in ApJ

References in corpus (32)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The false positive rate of Kepler and the occurrence of planets
• REBOUND: An open-source multi-purpose N-body code for collisional dynamics
• Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data
• Architecture and Dynamics of Kepler's Candidate Multiple Transiting Planet Systems
• Architecture of Kepler's Multi-transiting Systems: II. New investigations with twice as many candidates
• WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
• The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced
• About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of their Intrinsic Architecture
• Kepler Planet Masses and Eccentricities from TTV Analysis
• First order resonance overlap and the stability of close two planet systems
• Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems
• Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
• Are Planetary Systems Filled to Capacity? A Study Based on Kepler Results
• Predicting the long-term stability of compact multiplanet systems
• The stability of tightly-packed, evenly-spaced systems of Earth-mass planets orbiting a Sun-like star
• A Criterion for the Onset of Chaos in Systems of Two Eccentric Planets
• The path to instability in compact multi-planetary systems
• An Integrable Model for the Dynamics of Planetary Mean Motion Resonances
• Orbital Stability of Multi-Planet Systems: Behavior at High Masses
• Formation of compact systems of super-Earths via dynamical instabilities and giant impacts
• Resonant Chains and Three-body Resonances in the Closely-Packed Inner Uranian Satellite System
• Long-term dynamics of the solar system inner planets
• Intra-system uniformity: a natural outcome of dynamical sculpting
• The origin of chaos in the Solar System through computer algebra
• Orbital Architectures of Kepler Multis From Dynamical Instabilities
• The Criterion for Chaos in Three-Planet Systems
• celmech: A Python package for celestial mechanics
• Orbital stability of compact three-planet systems, I: Dependence of system lifetimes on initial orbital separations and longitudes
• Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems
• Long-term instability of the inner Solar System: numerical experiments
• On the Degree of Dynamical Packing in the Kepler Multi-planet Systems

Cited by in corpus (4)

• Dynamical Instability of Multi-planet Systems and Free-floating Planets
• Higher-Order Mean-Motion Resonances Can Form in Type-I Disk Migration
• Orbital stability of compact three-planet systems III. The role of three-body resonances
• Dynamical Evolution of Planetary Systems