The Laplace resonance in the Kepler-60 planetary system

We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We 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 similar to 4 M-circle plus and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace mean-motion resonance (MMR) exhibits the critical angle librating around similar or equal to 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 similar to 30 degrees and apsidal lines in planet's pairs are antialigned. The system is simultaneously locked in a three-body MMR with librations amplitude similar or equal to 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.