Formation of Protoplanets from Planetesimals in the Solar Nebula

Abstract

Planetary accretion from planetesimals to protoplanets is investigated using three-dimensional N-body simulations. The effect of gas drag due to solar nebula is included and realistic-sized planetesimals with a standard material density are used, with which the growth time scale of planetesimals is realistic. In agreement with the earlier works (E. Kokubo and S. Ida 1996, Icarus 123, 180–191; 1998, Icarus 131, 171–178) that investigated gas-free accretion of planetesimals with enlarged sizes, it is found that a bimodal protoplanet–planetesimal system is formed through runaway and oligarchic growth. In the intermediate accretion stage, the growth mode of planetesimals is runaway growth where the mass distribution relaxes into isolated runaway bodies and the continuous power-law mass distribution with dn c/ dm∝ m α, where n c is the cumulative number of bodies and α≃−2.5. While thinning out some runaway bodies, the growth mode shifts to oligarchic growth where larger protoplanets tend to grow more slowly than smaller ones. The orbital separations of the protoplanets are kept wider than about 5 Hill radii of the protoplanets through orbital repulsion. In the late accretion stage, similar-sized protoplanets grow, while most planetesimals remain small. Protoplanets with mass 10 26 g are formed at 1 AU in 500,000 years.