Modelling Circumbinary Planets: The case of Kepler-38

Received; accepted Context. Recently, a number of planets orbiting binary stars have been discovered by the Kepler space telescope. In a few systems the planets reside close to the dynamical stability limit. Due to the difficulty of forming planets in such close orbits, it is believed that they have formed further out in the disk and migrated to their present locations. Aims. Our goal is to construct more realistic models of planet migration in circumbinary disks, and to determine the final position of these planets more accurately. In our work, we focus on the system Kepler-38 where the planet is close to the stability limit. Methods. The evolution of the circumbinary disk is studied using two-dimensional hydrodynamical simulations. We study locally isothermal disks as well as more realistic models that include full viscous heating, radiative cooling from the disk surfaces, and radiative diffusion in the disk midplane. After the disk has been brought into a quasi-equilibrium state, a 115 Earth-mass planet is embedded and its evolution is followed. Results. In all cases the planets stop inward migration near the inner edge of the disk. In isothermal disks with a typical disk scale height of H/r = 0.05, the final outcome agrees very well with the observed location of planet Kepler-38b. For the radiative models, the disk thickness and location of the inner edge is determined by the mass in the system. For surface densities in the order of 3000 g/cm2 at 1 AU, the inner gap lies close to the binary and planets stop in the region between the 5:1 and 4:1 mean-motion resonance