[论文解读] Formation of planetary systems by pebble accretion and migration: How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode

Michiel Lambrechts, Alessandro Morbidelli+5 more|arXiv (Cornell University)|Feb 22, 2019

Astro and Planetary Science参考文献 137被引用 65

一句话总结

Pebble flux 决定增长模式：低 pebble flux 产生缓慢的类似地球的成长且迁移最小，而大约高出一个因子二的 flux 驱动快速迁移并在内边形成紧密的超地球；消散后的演化随后分化为类地行星或不稳定的超地球系统。

ABSTRACT

Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of two in the pebble mass-flux is enough to change the evolution from the terrestrial to the super-Earth growth mode. If the pebble mass-flux is small, then the initial embryos within the ice line grow slowly and do not migrate substantially, resulting in a widely spaced population of Mars-mass embryos when the gas disc dissipates. Without gas being present, the embryos become unstable and a small number of terrestrial planets are formed by mutual collisions. The final terrestrial planets are at most 5 Earth masses. Instead, if the pebble mass-flux is high, then the initial embryos within the ice line rapidly become sufficiently massive to migrate through the gas disc. Embryos concentrate at the inner edge of the disc and growth accelerates through mutual merging. This leads to the formation of a system of closely spaced super-Earths in the 5 to 20 Earth-mass range, bounded by the pebble isolation mass. Generally, instabilities of these super-Earth systems after the disappearance of the gas disc trigger additional merging events and dislodge the system from resonant chains. The pebble flux - which controls the transition between the two growth modes - may be regulated by the initial reservoir of solids in the disc or the presence of more distant giant planets that can halt the radial flow of pebbles.

研究动机与目标

• Motivate whether terrestrial planets and super-Earths form via distinct pebble-driven pathways.
• Quantify how the integrated pebble flux influences embryo growth, migration, and system architecture.
• Explore post-gas-dispersion evolution and stability of the resulting planetary systems.

提出的方法

• Use a modified N-body code (SyMBA) with prescriptions for a gas disc, Type-I migration, eccentricity/inclination damping, and pebble accretion.
• Model a protoplanetary disc with H/r=0.04, Sigma_g = 610 (r/AU)^-1/2 exp(-t/t_disc) g/cm^2, alpha=1e-4, t_disc=1 Myr, disc phase = 3 Myr.
• Implement pebble flux F_peb(t) = F_peb,0 exp(-t/t_peb) with t_peb = t_disc and F_peb,nom = 120 M_E/Myr.
• Simulate 25 Moon-mass embryos from 0.5–3 AU with initial total mass 0.25 M_E.
• Assume a constant Stokes number tau_f = 3e-3 and allow pebble filtering and isolation mass M_iso ≈ 10 (H/r)^3 M_E.
• Explore four pebble-flux suites (runf1, runf3, runf5, runf9) to cover low-to-high flux regimes.

实验结果

研究问题

• RQ1 Does the integrated inward pebble flux determine whether a system forms Earth-like terrestrial planets or a compact set of super-Earths?
• RQ2 What are the final architectural differences (masses, separations, resonances) between low and high pebble-flux outcomes after disc dissipation?
• RQ3 How do migration and pebble accretion interact during the gas disc phase to shape post-dissipation evolution?
• RQ4 What observational criteria can distinguish Earth-like planets from super-Earths based on formation history, architecture, and atmospheres?

主要发现

• Low pebble flux (< ~110 M_E) yields embryos growing to ~ Mars-mass with little migration, producing widely spaced terrestrial planets after gas dispersal.
• Increasing pebble flux by about a factor of two triggers rapid migration and inward concentration, forming a compact system of 5–20 M_E super-Earths near the inner disc edge (0.1 AU).
• Pebble isolation mass (~10 M_E) halts inner-planet accretion and slows pebble flux to inner embryos, influencing final masses and spacing.
• Post-disc-dissipation evolution is strongly unstable for super-Earth systems with >90% undergoing mergers and non-resonant orbits, while terrestrial systems form Earth- to Mars-sized planets via giant impacts over tens of Myr.
• Terrestrial growth yields planets at wider orbits with small atmospheres, whereas super-Earth growth yields close-in planets likely with primordial H/He envelopes unless lost to irradiation.
• Final architectures show compact configurations during gas disc, with many planet pairs near first-order resonances (e.g., 4:3), but destabilization post-dispersion reduces resonant chains.