Decoupling of a giant planet from its disk in an inclined binary system

We explore the dynamical evolution of a planet embedded in a disk surrounding a star part of a binary system where the orbital plane of the binary is significantly tilted respect to the initial disk plane. Our aim is to test whether the planet remains within the disk and continues to migrate towards the star in a Type I/II mode in spite of the secular perturbations of the companion star. This would explain observed exoplanets with significant inclination respect to the equatorial plane of their host star. We have used two different SPH codes, vine and phantom, to model the evolution of a system star+disk+planet and companion star with time. After an initial coupled evolution, the inclination of the disk and that of the planet begin to differ significantly. The period of oscillation of the disk inclination, respect to the initial plane, is shorter than that of the planet which evolves independently after about 10^4 yr following a perturbed N-body behavior. However, the planet keeps migrating towards the star because during its orbital motion it crosses the disk plane and the friction with the gas causes angular momentum loss. Disk and planet in a significantly inclined binary system are not dynamically coupled for small binary separations but evolve almost independently. The planet abandons the disk and, due to the onset of a significant mutual inclination, it interacts with the gas only when its orbit intersects the disk plane. The drift of the planet towards the star is not due to type I/II with the planet embedded in the disk but to the friction with the gas during the disk crossing.