Positions of the secular resonances in the primordial Kuiper Belt disk
Résumé
In current dynamical evolution models aiming at reproducing the orbital structure of the Kuiper Belt, the giant planets start from a compact multiresonant orbital configuration and migrate to their current positions by interacting with a planetesimal disk extending beyond the orbit of Neptune. In order to stop the migration of Neptune at 30 AU and to reproduce the distinction between the dynamically cold and hot populations, it is often assumed that the primordial planetesimal disk was divided into two parts: a massive disk extending from Neptune to 30 AU and a low mass extension of the disk extending beyond 30 AU, the outer limit of which is quite uncertain. Before the dynamical instability between the giant planets, which strongly depletes the mass of the planetesimal disk, the massive part of the disk can have a significant influence on the apsidal and nodal precessions of the giant planets and of the planetesimals, leading to the shift of the positions of the secular resonances. In particular, the presence of the massive disk removes the degenaracy of the f5 nodal frequency and allows for a new secular resonance. We investigate these effects in the linear secular theory of Lagrange-Laplace and find the locations of the secular resonances for different orbital configurations. We show that during the pre-instability period, for some orbital configurations the f5 nodal secular resonance is located in the region where the primordial cold classical Kuiper belt formed. If the inclination between the plane orthogonal to the total angular momentum of the giant planets and the mean plane of the massive disk is high enough, this nodal secular resonance is efficient at rising the inclinations of objects located in it. Thus, this could be a potential solution for the problem of the low density of the cold objects in the region near 45-47 AU.