From Stability to Instability: Characterizing the Eccentricities of Multi-planet Systems in the California Kepler Survey as a Means of Studying Stability

TL;DR

This study uses machine learning and N-body simulations to analyze the stability and eccentricities of multi-planet systems from the California Kepler Survey, revealing key correlations and insights into their dynamical history.

Contribution

It introduces the use of SPOCK for stability characterization and identifies the relationship between period ratios and eccentricities in multi-planet systems.

Findings

Characteristic eccentricities are about 20% of the resonance overlap threshold.

Minimum period ratio strongly correlates with characteristic eccentricity.

Systems with high eccentricities (>0.15) are likely remnants of past giant impacts.

Abstract

Understanding the stability of exoplanet systems is crucial for constraining planetary formation and evolution theories. We use the machine-learning stability indicator, SPOCK, to characterize the stability of 126 high-multiplicity systems from the California Kepler Survey (CKS). We constrain the range of stable eccentricities for each system, adopting the value associated with a 50% chance of stability as the characteristic eccentricity. We confirm characteristic eccentricities via a small suite of N-body integrations. In studying correlations between characteristic eccentricity and various planet-pair and system-level metrics we find that minimum period ratio correlates most strongly with characteristic eccentricity. These characteristic eccentricities are approximately 20% of the eccentricities necessary for two-body mean-motion resonance overlap, suggesting three-body dynamics are needed to drive future instabilities. Systems in which the eccentricities would need to be high (> 0.15) to drive instability are likely dynamically relaxed and might be the fossils of a previous epoch of giant impacts that increased the typical planet-planet spacing.