Oligarchic Growth of Protoplanets

We investigate the growth and the orbital evolution of protoplanets embedded in a swarm of planetesimals using three-dimensionalN-body simulations. We find that among protoplanets, larger ones grow more slowly than smaller ones, while the growth of protoplanets is still faster than that of planetesimals. As a result, in the stage after rapid runaway growth, protoplanets with the same order mass grow oligarchically, while most planetesimals remain small. While the protoplanets grow, orbital repulsion keeps their orbital separations wider than about 5 Hill radius of the protoplanets. The typical orbital separation is about 10 Hill radius, which only weakly depends on the mass and the semimajor axis of protoplanets. We explain how this self-organized protoplanet-planetesimal system forms.