Self-consistent $N$-body simulation of Planetesimal-Driven Migration. II. The effect of PDM on planet formation from a planetesimal disk

TL;DR

This work demonstrates that planetesimal-driven migration (PDM) can dynamically redistribute planetary embryos even during runaway growth, challenging the classic in-situ formation paradigm. By performing high-resolution, self-consistent N-body simulations from a large-scale, MMSN-like disk with gas drag and Type-I torques, the authors show protoplanets undergo substantial inward and outward migration, with mutual orbital repulsion organizing embryos into dense migrating groups. The results indicate that a standard MMSN can support the migration-driven assembly of Earth-like cores and ice-giant cores, and that extending the disk or modulating drag enhances outward transport to large radii. These findings provide a coherent pathway to explain diverse exoplanet architectures and imply that disk outer edges and ring-like substructures may play a pivotal role in planet formation via PDM.

Abstract

According to the canonical planet formation theory, planets form "in-situ" within a planetesimal disk via runaway and oligarchic growth. This theory, however, cannot naturally account for the formation timescale of ice giants or the existence of diverse exoplanetary systems. Planetary migration is a key to resolving these problems. One well-known mechanism of planetary migration is planetesimal-driven migration (PDM), which can let planets undergo significant migration through gravitational scattering of planetesimals. In our previous paper (Jinno et al. 2024, PASJ, 76, 1309), we investigated the migration of a single planet through PDM, addressing previously unexplored aspects of both the gravitational interactions among planetesimals and the interactions with disk gas. Here we perform the first high-resolution simulations of planet formation from a large-scale planetesimal disk, incorporating planet-gas disk interactions, planet-planetesimal interactions, gravitational interactions among all planetesimals, and physical collisions between planetesimals to investigate the role of PDM in the planet formation process. Our results show that protoplanets undergo dynamic inward/outward migrations during the runaway growth stage via PDM. Moreover, orbital repulsion combined with PDM tends to make two groups of protoplanets, outer ones going outward and inner ones going inward. Such dynamic migration significantly influences the early stages of planetary formation. These findings provide a viable pathway for the formation of Earth-like planets and ice giants' cores. Furthermore, they suggest that a standard protoplanetary disk model can account for the planetary migration necessary to explain diverse exoplanetary systems without the need for additional hypotheses.

Figures (13)

• Figure 1: Two different planet formation scenarios starting from the same smoothed protoplanetary disk model. [a] The classic scenario illustrating the formation of the solar system 1972epcf.book.....S1981PThPS..70...35H1985prpl.conf.1100H: Runaway growth of planetesimals form protoplanets and the orbital repulsion between them results in their in-situ oligarchic growth in the disk (a--1). Subsequently, as the disk gas dissipates, orbital crossings, giant impacts, and gas accretion take place, eventually forming the solar system (a-2 & a-3). [b] The dynamic planet formation scenario realizing the formation of diverse planetary systems (this study): Planetary embryos formed through runaway growth migrate within the disk via outward/inward PDM and Type-I migration (b-1). Eventually, diverse planetary systems will be formed through planetary migration (b-2). Alt text: Two schematic panels comparing two different planet formation scenarios. Panel a shows the classical view of static planet formation through in-situ runaway and oligarchic growth. Panel b shows dynamic planet formation from this study, where migrating embryos form diverse planetary systems.
• Figure 2: The time evolution of the semi-major axes for the heaviest 30 bodies at 2.5 Myr (including a body that collided with another body at approximately 1.87 Myr, indicated by a dotted curve). The color of each curve represents each mass. The black hatched regions on the left show the initial planetesimal disk size. Alt text: The line graph showing the time evolution of semi-major axes and masses of planetary embryos formed in model 1-5. The horizontal axis represents time, and the vertical axis displays the semi-major axis in au.
• Figure 3: The time evolution of the semi-major axis and mass for the top 15 heaviest bodies at 2.5 Myr (including protoplanet I (thin yellow curve), II (green curve), and III (blue curve), which collided with another body at approximately 1.87 Myr). (a) The width of each curve represents the orbital repulsion for each body, calculated as $a \pm 5r_{\mathrm{Hill}}$, where $a$ and $r_{\mathrm{Hill}}$ are the semi-major axis and the Hill radius. The black-hatched regions indicate the initial planetesimal disk size. The numbers on the right indicate the ranks based on the masses of the planetary embryos. (b) The color of each curve corresponds to the rank shown in (a). Alt text: Two line graphs showing the orbital and mass evolution of the 15 heaviest protoplanets formed in model 1-5. Panel (a) shows the semi-major axis and orbital repulsion of planetary embryos, and panel (b) shows the color-coded mass ranking of the 15 heaviest protoplanets.
• Figure 4: The time evolution of the system during planet formation within the initially smoothed planetesimal disk. Bodies with $0.1M_{\oplus}\leq M\leq M_{\oplus}$ and $M_{\oplus}\leq M$ are represented by black and green stars, respectively, scaled by $M^{1/3}$, where $M$ is the mass. The dots, colored red, blue, green, yellow, and purple, represent planetesimals. Each color indicates their initial semi-major axes: red for 2-4 au, blue for 4-6 au, green for 6-8 au, yellow for 8-10 au, and purple for 10-12 au. (a) Initial planetesimal disk with a surface density distribution of 4$\times$MMSN. (b) By 0.5 Myr, a single planetary embryo migrates outward to approximately 7 au. (c) By 0.75 Myr, two planetary embryos reach the outer edge of the disk ($\sim12$ au). (d) By 1 Myr, one of the two planetary embryos that reached the disk's outer edge changes its migration direction inward and reaches near 10 au, while a new embryo from the inner disk begins migrating outward. (e) By 1.25 Myr, the inward migrating planetary embryo encounters the outward migrating one, causing both to migrate outward. (f) By 1.5 Myrs, all planetary embryos that migrated outward begin migrating inward. (g) By 2 Myr, they encounter a group of outward migrating planetary embryos, (h) prompting them to begin migrating outwards again by 2.5 Myr. Alt text: Snapshots of model 1-5, arranged chronologically from panel (a) to panel (h). The horizontal axis represents semi-major axis in au, and the vertical axis displays eccentricity.
• Figure 5: The time evolution of the semi-major axes for the heaviest 30 bodies at 4 Myr. From left to right, the panels represent models 1-1 (left), 1-2 (middle), and 1-3 (right). The black hatched regions show the initial planetesimal disk size. Alt text: The line graphs showing the time evolution of semi-major axes and masses of protoplanets formed in model 1-1, 1-2 and 1-3. The horizontal axis represents time, and the vertical axis displays the semi-major axis in au.