Dynamical behaviour of multiplanet systems close to their stability limit

TL;DR

This study investigates the dynamical stability of two- and three-planet systems near their stability limits, revealing that traditional criteria may underestimate their stability regions and that complex behaviors like stable chaos are common.

Contribution

It provides new insights into the stability boundaries of multiplanet systems, highlighting the limitations of Hill radius-based criteria and emphasizing the need for a multidimensional stability analysis.

Findings

Two-planet systems exhibit stable chaos near the Hill limit.

Three-planet systems can be stable within regions previously considered unstable.

Traditional Hill radius criteria may underestimate the stability of packed planetary systems.

Abstract

The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of systems is numerically computed and their dynamical behaviour is investigated with the frequency map analysis as chaos indicator. Following the guidance of this analysis, it is found that for two-planet systems the dependence of the Hill limit on the planet mass, usually made explicit through the Hill's radius parametrization, does not appear to be fully adequate. In addition, frequent cases of stable chaos are found in the proximity of the Hill limit. For three-planet systems, the usual approach adopted in numerical explorations of their stability, where the planets are initially separated by multiples of the mutual Hill radius, appears too reducing. A detailed sampling of the parameter space reveals that systems with more packed inner planets are stable well within previous estimates of the stability limit. This suggests that a two-dimensional approach is needed to outline when three-planet systems are dynamically stable.