2011A&A...528A..86L

We explore the orbital evolution of the four Jovian planets embedded in a self-gravitating planetesimal disk, along with the simultaneous accretion of small bodies by proto-Uranus and proto-Neptune. We adopt the code NBODY4 running on the GRAPE-type special-purpose computer for numerically simulating the primordial evolution of the outer Solar System, where the total gravitational forces due to the Sun, the four Jovian planets, and the massive planetesimals are all taken into account. There is no significant accretion of proto-Uranus and proto-Neptune during their migration stage, only on the order of 0.1 Earth mass. The self-gravitating disk can provide a new replenishment of planetesimals outside a few AU beyond Neptune into the scattering zone, resulting in larger radial displacement of Neptune than in the non-self-gravitating disk. The present location of Neptune requires an original planetesimal disk outer edge at ∼35AU. The distribution of the surviving planetesimals is very similar to the observed Kuiper belt.