Long-term stability and dynamical spacing of compact planetary systems

TL;DR

This paper reviews how interactions between triplet resonances cause chaos and instability in compact multi-planet systems, explaining their long-term stability limits and the inadequacy of Hill radius as a measure.

Contribution

It presents a detailed model of resonance-driven chaos in compact planetary systems and derives a scaling law for stability based on planet-star mass ratio.

Findings

Resonance interactions lead to chaotic semi-major axis diffusion.

The critical spacing for stability scales with the planet-star mass ratio to the 1/4 power.

The Hill radius is not an appropriate measure of dynamical compactness.

Abstract

Exoplanet detection surveys revealed the existence of numerous multi-planetary systems packed close to their stability limit. In this proceeding, we review the mechanism driving the instability of compact systems, originally published in Petit et al. (2020). Compact systems dynamics are dominated by the interactions between resonances involving triplets of planets. The complex network of three-planet mean motion resonances drives a slow chaotic semi-major axes diffusion, leading to a fast and destructive scattering phase. This model reproduces quantitatively the instability timescale found numerically. We can observe signpost of this process on exoplanet systems architecture. The critical spacing ensuring stability scales as the planet-to star mass ratio to the power 1/4. It explains why the Hill radius is not an adapted measure of dynamical compactness of exoplanet systems, particularly for terrestrial planets. We also provide some insight on the theoretical tools developed in the original work and how they can be of interest in other problems.