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Planetesimal Evolution in Circumbinary Gaseous Disks: A Hybrid Model

We study the dynamics of planetesimals embedded in a circumbinary protoplanetary disk. A hybrid numerical approach is developed where the evolution of the gaseous component of the disk is computed with the hydrodynamical code FARGO while the planetesimal trajectories are computed with an N-body code. The local gas density and velocity derived from the hydrodynamical portion are used to calculate the drag force and the gravitational attraction of the disk on the planetesimals. We explore the effects of spiral density wave patterns and of the disk eccentricity, both excited by the binary tidal perturbations, on the dynamical evolution of planetesimal orbits. A new definition of osculating orbital elements is given to properly account for the gravitational attraction of the disk. The outcomes of the numerical simulations show that the pericenter alignment of the planetesimal orbits is a robust result. It occurs for different values of the binary eccentricity and surface density profiles of the disk. However, the pericenters are less collimated compared to early predictions based on codes adopting a stationary and axisymmetric approximation for the disk. In addition, the eccentricity values are higher and depend on the semimajor axis of the bodies. Both these effects favor higher relative velocities between colliding planetesimals, making accretion less likely than previously thought. Small 100 m size bodies (planetesimal precursors) have a very high inward drift rate that might lead to a high-density belt in the proximity of the inner border of the disk. Fast accretion into larger bodies might occur in this region.