Acceleration of planetary migration: Resonance crossing and planetesimal ring

TL;DR

This work investigates acceleration mechanisms in planetary migration driven by planetesimal disks, resonant crossings, and ring structures using GPU-accelerated N-body simulations of a four-giant-planet system with an extended disk. It demonstrates a positive feedback where faster migration consumes more planetesimals, enabling further migration, while slower migration depletes the surrounding region and stalls continuation; resonance crossings, particularly the Uranus–Neptune 1:2 MMR, act as triggers that can substantially extend migration, and dense planetesimal rings can supply material to sustain rapid movement. A key quantitative finding is that the mass of planetesimals consumed per unit angular momentum gained scales roughly as M_loss/DeltaL_N ~ dot a_N^(-0.155), so a tenfold increase in migration rate reduces required planetesimals by about 30% for the same angular momentum change. The results indicate Neptune’s current position sits at a delicate threshold in the early Solar System, where a modest increase in disk mass could have driven a much farther outward migration, underscoring the role of stochastic outcomes and the potential necessity of giant-planet instability to reach the present configuration.

Abstract

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.

Figures (6)

• Figure 1: Evolution of $a_N$ in a plain planetesimal disk. The horizontal and vertical axes represent time and $a_N$, respectively. The four subplots correspond to different $M_{disk}$, with five different-colored lines representing various $\alpha$.
• Figure 2: Acceleration of migration at crossing MMRs. The upper panel shows the evolution of $a_U$, while the lower panel displays the period ratio between Neptune and Uranus. Different $\alpha$ are represented by different colors. The $M_{disk}$ are not explicitly distinguished, but their relative positions are fixed, with four lines of the same color representing $M_{disk}$ of 30 $M_{\oplus}$, 40 $M_{\oplus}$, 50 $M_{\oplus}$, and 60 $M_{\oplus}$ from bottom to top. In the lower panel, two dashed black lines indicate positions where the period ratio between Neptune and Uranus is 2 and 1.5.
• Figure 3: Neptune's migration versus the mass loss of the planetesimal disk. The upper panel illustrates the connection between the total mass loss of the planetesimal disk (horizontal axis) and the total migration distance of Neptune (vertical axis). Different colors represent different $\alpha$, while different line styles indicate different $M_{disk}$. In the lower panel, we calculated the time interval takes for Neptune to migrate per 1 au (from 18 au). The horizontal axis displays the average migration rate during each interval (logarithmic scale), and the vertical axis represents the ratio of consumed planetesimal mass to the angular momentum gained by Neptune within this interval.
• Figure 4: Evolution of the positions of Uranus and Neptune. The horizontal and vertical axes represent the $a_N$ and $a_U$, respectively. The color of the points indicates the migration rate of Uranus at each position. The orange dots denote the initial $a_N$ and $a_U$ in each set of simulations. The points with black borders represent hypothetical extensions of the real Solar System's migration, while the dotted black line shows the linear fit of these points with black borders. The hollow circles mark the positions where $a_U$ reaches its minimum value, and the solid black line represents the linear fit of all black circles. The dashed black line indicates the location corresponding to the $R_{2N:1U}$.
• Figure 5: Evolution of Neptune with the presence of a planetesimal ring. The horizontal and vertical axes represent time and $a_N$, respectively. Lines of different colors correspond to different planetesimal ring masses. The horizontal gray line represents the initial center of the planetesimal ring (34.5 au). The hollow triangles, circles, and squares mark the positions where Neptune crosses $R_{3N:2U}$, $R_{2N:1U}$, and $R_{5N:2U}$, respectively.