Planetesimal and Gas Dynamics in Binaries

Observations of extrasolar planets reveal that planets can be found in close binary systems, where the semi-major axis of the binary orbit is less than 20 AU. The existence of these planets challenges planet formation theory because the strong gravitational perturbations due to the companion increase encounter velocities between planetesimals and make it difficult for them to grow through accreting collisions. We study planetesimal encounter velocities in binary systems, where the planetesimals are embedded in a circumprimary gas disc that is allowed to evolve under influence of the gravitational perturbations of the companion star. We use the RODEO method to evolve the vertically integrated Navier-Stokes equations for the gas disc. Embedded within this disc is a population of planetesimals of various sizes, that evolve under influence of the gravitational forces of both stars and friction with the gas. The equations of motion for the planetesimals are integrated using a 4 order symplectic algorithm. We find that the encounter velocities between planetesimals of different size strongly depend on the gas disc eccentricity. Depending on the amount of wave damping, we find two possible states of the gas disc: a quiet state, where the disc eccentricity reaches a steady state that is determined by the forcing of the binary, for which the encounter velocities do not differ more than a factor of 2 from the case of a circular gas disc, and an excited state, for which the gas disc obtains a large free eccentricity, which drives up the encounter velocities more substantially. In both cases, inclusion of the full gas dynamics increases the encounter velocity compared to the case of a static, circular gas disc. Full numerical parameter exploration is still impossible, but we derive analytical formulae to estimate encounter velocities between bodies of different sizes given the gas disc eccentricity. The gas dynamical evolution of a protoplanetary disc in a binary system tends to make planetesimal accretion even more difficult than in a static, axisymmetric gas disc.