The Laplace resonance in the Kepler-60 system

TL;DR

This paper analyzes the dynamical stability of the Kepler-60 system, revealing two possible resonant configurations involving three planets, with implications for planetary formation theories.

Contribution

It identifies and characterizes the Laplace resonance in Kepler-60, demonstrating its potential formation pathways and stability through TTV data analysis.

Findings

The system is stable with planets around 4 Earth masses.

Two resonant configurations are possible: true three-body MMR and chain of two-body MMRs.

The true three-body MMR remains a plausible, yet puzzling, configuration.

Abstract

We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We first determine their orbital elements and masses by Transit Timing Variation (TTV) data spanning quarters Q1-Q16 of the KEPLER mission. The system is dynamically active but the TTV data constrain masses to ~4 Earth masses and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace MMR exhibits the critical angle librating around 45 degrees and aligned apsides of the inner and outer pair of planets. In the Laplace MMR formed through a chain of two-planet 5:4 and 4:3 MMRs, all critical angles librate with small amplitudes of ~30 degrees and apsidal lines in planet's pairs are anti-aligned. The system is simultaneously locked in a three-body MMR with librations amplitude of ~10 degrees. The true Laplace MMR can evolve towards a chain of two-body MMRs in the presence of planetary migration. Therefore the three-body MMR formed in this way seems to be more likely state of the system. However, the true three-body MMR cannot be disregarded a priori and it remains a puzzling configuration that may challenge the planet formation theory.