Excitation and Depletion of the Asteroid Belt in the Early Instability Scenario

Abstract

Containing only a few percentages of the mass of the moon, the current asteroid belt is around three to four orders of magnitude smaller than its primordial mass inferred from disk models. Yet dynamical studies have shown that the asteroid belt could not have been depleted by more than about an order of magnitude over the past ∼4 Gyr. The remainder of the mass loss must have taken place during an earlier phase of the solar system’s evolution. An orbital instability in the outer solar system occurring during the process of terrestrial planet formation can reproduce the broad characteristics of the inner solar system. Here, we test the viability of this model within the constraints of the main belt’s low present-day mass and orbital structure. Although previous studies modeled asteroids as massless test particles because of limited computing power, our work uses graphics processing unit acceleration to model a fully self-gravitating asteroid belt. We find that depletion in the main belt is related to the giant planets’ exact evolution within the orbital instability. Simulations that produce the closest matches to the giant planets’ current orbits deplete the main belt by two to three orders of magnitude. These simulated asteroid belts are also good matches to the actual asteroid belt in terms of their radial mixing and broad orbital structure.