Planet formation in binary star systems is a complex issue due to the gravitational perturbations of the companion star. One of the crucial steps of the core-accretion model is planetesimal accretion into large protoplanets which finally coalesce into planets. In a planetesimal swarm surrounding the primary star, the average mutual impact velocity determines if larger bodies form or if the population is grinded down to dust, halting the planet formation process. This velocity is strongly influenced by the companion gravitational pull and by gas drag. The combined effect of these two forces may act in favour of or against planet formation, setting a lower or equal probability of the existence of extrasolar planets around single or binary stars.
Planetesimal accretion in binaries has been studied so far with two different approaches. N-body codes based on the assumption that the disk is axisymmetric are very cost-effective since they allow the study of the mutual relative velocity with limited CPU usage. A large amount of planetesimal trajectories can be computed making it possible to outline the regions around the star where planet formation is possible. The main limitation of the N-body codes is the axisymmetric assumption. The companion perturbations affect not only the planetesimal orbits, but also the gaseous disk, by forcing spiral density waves. In addition, the overall shape of the disk changes from circular to elliptic.
Hybrid codes have been recently developed which solve the equations for the disk with a hydrodynamical grid code and use the computed gas density and velocity vector to calculate an accurate value of the gas drag force on the planetesimals. These codes are more complex and may compute the trajectories of only a limited number of planetesimals.