Formation of Protoplanets from Massive Planetesimals in Binary Systems

More than half of all stars reside in binary or multiple star systems, and many planets have been found in binary systems. From a theoretical point of view, however, whether or not the planetary formation proceeds in a binary system is a very complex problem, because secular perturbation from the companion star can easily stir up the eccentricity of the planetesimals and cause high-velocity, destructive collisions between planetesimals. Early stages of the planetary formation process in binary systems have been studied by a restricted three-body approach with gas drag, and it is commonly accepted that accretion of planetesimals can proceed due to orbital phasing by gas drag. However, the gas drag becomes less effective as the planetesimals become more massive. Therefore, it is uncertain whether the collision velocity remains small and planetary accretion can proceed once the planetesimals become massive. We performed N -body simulations of planetary formation in binary systems, starting from massive planetesimals of size ~100-500 km. We found that the eccentricity vectors of planetesimals quickly converge to the forced eccentricity due to the coupling of the perturbation of the companion and the mutual interaction of planetesimals, if the initial disk model is sufficiently wide in radial distribution. This convergence decreases the collision velocity, and as a result accretion can proceed much in the same way as in isolated systems. The basic processes of the planetary formation, such as runaway and oligarchic growth and final configuration of the protoplanets, are essentially the same in binary systems and single star systems, at least in the late stage, where the effect of gas drag is small.