The pumping up of orbital inclinations of asteroids caused by sweeping secular resonances associated with depletion of a proto-planetary disk is discussed, focusing on the dependence on the disk inclinations and surface density distribution. The asteroids have large mean inclinations that cannot be explained by present planetary perturbations alone. It has been suggested that the sweeping secular resonances caused by disk depletion are responsible for these high inclinations. Nagasawa et al. (2000, Astron. J. 119, 1480-1497) showed that the inclinations of asteroids are pumped up if the disk is depleted in an inside-out manner on a time scale longer than 3 × 105 years. Their assumed disk midplane is not on the invariant plane. However, it should be affected by the inclination of the disk plane. Here we investigate the dependence on the disk inclinations. We assume a disk depletion model in which the disk inside the jovian orbit has been removed and the residual outer disk is uniformly depleted. We calculate the locations of the secular resonances and the excitation magnitude of the inclinations with analytical methods. We found that the inclinations are pumped up to the observational level for a depletion time scale longer than 106 years in the case of the disk plane that coincides with the invariant plane. The required time scale is longest (3 × 106 years) if the disk plane coincides with the jovian orbital plane. However, it is still within the observationally inferred depletion time scale. We also studied dependence on a disk surface density gradient and found that the results do not change significantly as long as the inner disk depletion is faster than the outer disk one.
ASJC Scopus subject areas