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 the migration rate corresponds to a reduction of approximately 30% in the mass of planetesimals consumed to increase per unit of 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 30,au was approximately 0.009,M_⊕/au^2 in the early Solar System. Furthermore, we identify two mechanisms that can accelerate planetary migration. The first is mean motion resonance between Uranus and Neptune: migration acceleration will be triggered whenever these two giant planets cross their major mean motion resonance. 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 resonance with Uranus, it could have migrated to a much more distant location. Our results demonstrate that giant planet instability is fundamentally required; otherwise, reconstructing the migration histories of Uranus and Neptune would yield physically implausible orbital configurations. Furthermore, even without introducing the giant planet instability, under the influence of the positive feedback mechanism, the evolution of the Solar System to its current configuration might still be a stochastic outcome rather than an inevitable consequence.