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M. Nagasawa, H. Tanaka, S. Ida (T.I.Tech.)
The pumping-up of inclinations and eccentricities due to sweeping secular resonances in the asteroid belt is studied. Present observations show the asteroids have large mean eccentricities and inclinations that cannot be explained by planetary perturbations only. Sweeping of secular resonances associated with the depletion of the primitive solar nebula had been proposed for the origin of asteroids' orbits (e.g., Ward et al. 1976, Icarus, 28, 441). According to this idea, several studies had been done. Lecar & Franklin (1997, Icarus, 129, 134) found that most of asteroids spiral into the Sun by gas drag if depletion time scale is longer than 105 years. However, this time scale is too short compared with the time inferred from observed T-Tauri stars (106-107 years). Moreover, they only studied the two-dimensional nebula model and assumed that the nebula depleted uniformly.
We performed three-dimensional orbital integration of asteroids with a three-dimensional nebula disk. We consider three types of nebula depletion models: (1) uniform depletion model, (2) inside-out depletion model, (3) gap-opening model. In the first model, inclinations of asteroids are not pumped up enough to account for the observed magnitude in our simulation. On the other hand, in the second and third models, inclinations are pumped up, too. Our linear analysis shows that non-uniform depletion of the nebula is essential for pumping up of inclinations in the asteroid belt. Furthermore, in non-uniform depletion models, secular resonances pass the asteroid belt after nebula gas has already been depleted, which prevents migration of asteroids due to gas drag. In the case of inside-out depletion model, we can take a long nebula depletion time scale as inferred from observed T-Tauri stars.