Oligarchic Growth of Protoplanets

and N-body calculations (e.g., Ida 1990, Ida and Makino 1992b). It is shown that dynamical friction is effective in We investigate the growth and the orbital evolution of proa Keplerian potential as well as in a free space. Kokubo toplanets embedded in a swarm of planetesimals using threedimensional N-body simulations. We find that among protoplaand Ida (1996), hereafter referred to as Paper I, performed nets, larger ones grow more slowly than smaller ones, while 3-D N-body simulation of planetary accretion, including the growth of protoplanets is still faster than that of planetesiboth gravitational interaction and accretion between planmals. As a result, in the stage after rapid runaway growth, etesimals. They directly showed that runaway growth is an protoplanets with the same order mass grow oligarchically, inevitable outcome of a 3-D planetesimal system where while most planetesimals remain small. While the protoplanets gravitational focusing and dynamical friction are effective. grow, orbital repulsion keeps their orbital separations wider Runaway growth is a kind of instability phenomenon. than about 5 Hill radius of the protoplanets. The typical orbital It is not likely that runaway growth continues till the end separation is about 10 Hill radius, which only weakly depends of planetary accretion, since runaway growth itself breaks on the mass and the semimajor axis of protoplanets. We explain the uniformity of the velocity and the spatial distributions how this self-organized protoplanet–planetesimal system of planetesimals on which runaway growth is based. It is forms.  1998 Academic Press necessary to consider the back reaction of a planetesimal