Acceleration of planetary migration: Resonance crossing and planetesimal ring

Planetary migration is a crucial stage in the early solar system, explaining many observational phenomena and providing constraints on details related to the solar system's origins. This paper aims to investigate the acceleration during planetary migration in detail using numerical simulations, delving deeper into the early solar system's preserved information. We confirm that planetary migration is a positive feedback process: the faster the migration, the more efficient the consumption of planetesimals; once the migration slows down, Neptune clears the surrounding space, making further migration more difficult to sustain. Quantitatively, a tenfold increase in migration rate corresponds to an approximately 30% reduction in the mass of planetesimals consumed to increase per unit angular momentum of Neptune. We also find that Neptune's final position is correlated with the initial surface density of planetesimals at that location, suggesting that the disk density at 30au was approximately 0.009$M_{\oplus}/au^2$ in the early solar system. Two mechanisms that can accelerate planetary migration are identified: the first is MMR between Uranus and Neptune. Migration acceleration will be triggered whenever these two giant planets cross their major MMR. The second mechanism is the ring structure within the planetesimal disk, as the higher planetesimal density in this region can provide the material support necessary for migration acceleration. Our research indicates that Neptune in the current solar system occupies a relatively delicate position. In case Neptune crossed the 1:2 MMR with Uranus, it could have migrated to a much more distant location. Therefore, under the influence of the positive feedback mechanism, the evolution of the solar system to its current configuration might be a stochastic outcome rather than an inevitable consequence.