Dynamical Shake‐up of Planetary Systems. I. Embryo Trapping and Induced Collisions by the Sweeping Secular Resonance and Embryo‐Disk Tidal Interaction

Abstract

We analyze the orbital evolution of terrestrial planetary embryos after oligarchic growth, including the effect of the sweeping Jupiter secular resonance combined with tidal drag during the depletion of the protoplanetary gas disk. Previous studies show that the orbits of isolated embryos become unstable through long-term gravitational interaction. However, the planetary systems formed as a result of giant impacts are generally very eccentric, unlike our solar system. Although mechanisms that damp the eccentricity have been proposed, such mechanisms not only damp the eccentricity of embryos strongly but also prevent their orbital crossing and planetary growth. This dilemma can be solved if the protoplanetary collisions occur in an environment where the damping is still working. We consider the stage of gas depletion after the formation of a Jupiter-like planet in the disk. The gas depletion changes the gravitational potential and causes the sweeping of a secular resonance. We find that the secular resonance passes through the terrestrial region from outside to inside, that the resonance excites the eccentricities of isolated embryos, and that it leads to orbit crossing. Because the remnant disk is still present in this stage, the gas drag due to tidal interaction is still effective. The tidal drag effectively damps the eccentricities of the fully grown embryos. This process allows the system to form circular orbits analogous to our solar system. We also find that the tidal drag induces the decay of the semimajor axes of the embryos. As a result of balance between damping and excitation of eccentricity, the embryos migrate along with the secular resonance. This "secular resonance trapping" can lead to rapid collisions and mergers among the embryos as they migrate from the outer to the inner region, concurrent with the disk depletion. Since the induced migration is strongest near the Jovian orbit, the final terrestrial planets tend to be concentrated in a relatively small region (<2 AU). We suggest that this mechanism may be the origin of the severe present-day mass depletion of the asteroid belt.