Aims. The discovery of planets in close orbits around binary stars raises questions about their formation. It is believed that these planets formed in the outer regions of the disc and then migrated through planet-disc interaction to their current location. Considering five different systems (Kepler-16, -34, -35, -38, and -413) we model planet migration through the disc, with special focus on the final orbital elements of the planets. We investigate how the final orbital parameters are influenced by the disc and planet masses.
Methods. Using two-dimensional, locally isothermal, and viscous hydrodynamical simulations, we first model the disc dynamics for all five systems, followed by a study of the migration properties of embedded planets with different masses. To strengthen our results, we apply two grid-based hydrodynamical codes using different numerics (PLUTO and FARGO3D).
Results. For all systems, we find that the discs become eccentric and precess slowly. We confirm the bifurcation feature in the precession period – gap-size diagram for different binary mass ratios. The Kepler-16, -35, -38, and -413 systems lie on the lower branch and Kepler-34 on the upper one. For systems with small binary eccentricity, we find a new non-monotonic, loop-like feature.
In all systems, the planets migrate to the inner edge of the disc cavity. Depending on the planet-disc mass ratio, we observe one of two different regimes. Massive planets can significantly alter the disc structure by compressing and circularising the inner cavity and they remain on nearly circular orbits. Lower-mass planets are strongly influenced by the disc, their eccentricity is excited to high values, and their orbits are aligned with the inner disc in a state of apsidal corotation.
In our simulations, the final locations of the planets are typically too large with respect to the observations because of the large inner gaps of the discs. The migrating planets in the most eccentric discs (around Kepler-34 and -413) show the largest final eccentricity in agreement with the observations.
Calibrating core overshooting parameters with two-dimensional hydrodynamical simulations
