The Primordial Excitation and Clearing of the Asteroid Belt

Abstract

In this paper, we use N-body integrations to study the effect that planetary embryos spread between ∼0.5 and 4 AU would have on primordial asteroids. The most promising model for the formation of the terrestrial planets assumes the presence of such embryos at the time of formation of Jupiter. At the end of their runaway growth phase, the embryos are on quasi-circular orbits, with masses comparable to that of the Moon or Mars. Due to gravitational interactions among them, and with the growing Jupiter, their orbits begin to cross each other, and they collide, forming bigger bodies. A general outcome of this model is that a few planets form in a stable configuration in the terrestrial planet region, while the asteroid belt is cleared of embryos. Due to combined gravitational perturbations from Jupiter and the embryos, the primordial asteroids are dynamically excited. Most of the asteroids are ejected from the system in a very short time, the dynamical lifetime being on the order of 1 My. A few asteroids (less than 1%) survive, mostly in the region 2.8–3.3 AU, and their eccentricity and inclination distribution qualitatively resembles the observed one. The surviving asteroids have undergone changes in semimajor axis of several tenths of an AU, which could explain the observed radial mixing of asteroid taxonomic types. When the distribution of massive embryos is truncated at 3 AU, we obtain too many asteroids in the outer part of the belt, especially too many Hildas. This suggests that the formation of Jupiter did not prohibit the formation of large embryos in the outer belt and Jupiter did not accrete them while it was still growing.