1:1 orbital resonance of circumbinary planets

The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of these systems we have performed two-dimensional hydrodynamic simulations of the circumbinary disc with two embedded planets for several Kepler systems. In two cases, Kepler-47 and -413, the planets are captured in a 1:1 mean-motion resonance at the planet "parking position" near the inner edge of the disc. The orbits are fully aligned and have mean eccentricities of about 0.25 to 0.30; the planets are entangled in a horseshoe-type motion. Subsequent n-body simulations without the disc show that the configurations are stable. Our results point to the existence of a new class of stable resonant orbits around binary stars. It remains to be seen if such orbits exist in reality.