Sweeping Secular Resonances in the Kuiper Belt Caused by Depletion of the Solar Nebula

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Abstract
We have investigated excitations of orbital eccentricities and inclinations of Kuiper belt objects (KBOs) caused by the sweeping secular resonances during the primitive solar nebula depletion. Since nebula gravitational potential rotates the longitudes of perihelia and ascending nodes, the nebula depletion leads to migration of secular resonances. In the outer (classical) Kuiper belt (the region beyond 42 AU), inclinations and eccentricities are respectively distributed up to 0.6 (radian) and 0.2, and their root mean squares are about 0.2 (radian) and 0.1. These large values are not explained by present planetary perturbations alone. We have investigated the sweeping secular resonances in the Kuiper belt with both direct orbital integration and the analytical method and have found that the sweeping secular resonances can account for the eccentricity and inclination in the outer belt. Inclinations of objects in the outer belt are excited to the observational level if the residual nebula with about 0.1% of the density in the minimum mass nebula model is depleted in a timescale of 107–108 yr. For inclination excitation, Jovian perturbations and nebula potential are the most important, and Neptunian perturbations do not play an important role during the residual nebula depletion, although Neptune with more than one-fifth of its present mass is needed for enough eccentricity excitation. If further observation of the KBOs at semimajor axis 50 AU confirms our model, it would give important clues about Neptune's formation and the depletion of the solar nebula.