Stability of the Kepler-11 System and its Origin

TL;DR

This study analyzes the long-term stability of the Kepler-11 six-planet system using frequency maps, revealing it is stable but near resonances, and discusses implications for its formation history involving in-situ assembly or migration.

Contribution

The paper introduces the use of frequency maps as a fast stability indicator for Kepler-11 and explores how its stability constrains its formation scenarios.

Findings

Kepler-11 is stable but close to mean-motion resonances.

Planet eccentricities must be below ~0.04 for stability.

Masses could be more than twice the reported values.

Abstract

A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called `frequency maps' as fast indicators for long-term stability, we explore the stability of Kepler-11 system by analyzing the neighbourhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few percent of several dynamically dangerous 2-body mean-motion resonances. Planet eccentricities are restricted below a small value, $\sim 0.04$, for long-term stability, but planet masses can be more than twice their reported values (thus, allowing for the possibility of mass-loss by past photoevaporation). Based on our frequency maps, we speculate on the origin for instability in closely-packed systems. We then proceed to investigate how the system can have been assembled. The stability constraints on Kepler-11 (mainly, eccentricity constraints) suggest that if the system were assembled in-situ, a dissipation mechanism must have been at work to neutralize eccentricity excitation. On the other hand, if migration was responsible for assembling the planets, there has to be little differential migration among the planets, to avoid them either getting trapped into mean motion resonances, or crashing into each other.