[Paper Review] Rapid formation of Gas Giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores

Hiroshi Kobayashi, Hidekazu Tanaka|arXiv (Cornell University)|Oct 3, 2021

Astrophysics and Star Formation StudiesPhysics and Astronomy70 references39 citations

TL;DR

This paper proposes a unified collisional coagulation model from dust grains to planetary cores in protoplanetary disks, showing that drifting pebbles in the outer disk grow into planetesimals that suppress radial drift and enable rapid core formation via planetesimal accretion. The model achieves massive core growth (10 M⊕) in 0.2–0.4 million years—before Type I migration destroys cores—explaining gas giant formation at 2–7 au in typical disks.

ABSTRACT

Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust to planets are still uncertain. Here we report the result of full simulations for collisional evolution from dust to planets in a whole disk. Dust growth with realistic porosity allows the formation of icy planetesimals in the inner disk (> 10 au), while pebbles formed in the outer disk drift to the inner disk and there grow to planetesimals. The growth of those pebbles to planetesimals suppresses their radial drift and supplies small planetesimals sustainably in the vicinity of cores. This enables rapid formation of sufficiently massive planetary cores within 0.2-0.4 million years, prior to the planetary migration. Our models shows first gas giants form at 2-7 au in rather common protoplanetary disks, in agreement with the exoplanet and solar systems.

Motivation & Objective

• To resolve the core formation timescale problem in protoplanetary disks, where standard planetesimal accretion is too slow and pebble accretion requires rare massive disks.
• To investigate whether collisional growth of pebbles into planetesimals in the outer disk can enable sustained, rapid core growth via planetesimal accretion in the inner disk.
• To determine if this mechanism can form massive planetary cores (10 M⊕) within the disk lifetime and before Type I migration destroys them.
• To explain the observed orbital locations of gas giants in the Solar System and exoplanet systems (2–7 au) via a physically consistent, full-disk simulation from dust to planets.
• To quantify the minimum disk mass required for successful gas giant core formation via pebble accretion, addressing the issue of disk rarity in current models.

Proposed method

• Developed a full-disk, multi-scale simulation (Dust-to-Planet Simulation, DTPS) tracking collisional evolution from dust grains to planetesimals and planetary cores.
• Incorporated realistic dust aggregate porosity and bulk density evolution, allowing pebbles to grow into icy, porous planetesimals in the inner disk (≤10 au).
• Modeled radial drift of pebbles from the outer disk (where they form) to the inner disk, where they grow into planetesimals, reducing their drift speed and enabling sustained supply to cores.
• Used a hybrid accretion model combining planetesimal accretion (for 1–10 km bodies) and pebble accretion (for sub-km bodies), with gravitational focusing and atmospheric drag effects.
• Applied detailed collisional probability models (Inaba et al. 2001; Ormel & Kobayashi 2012) that account for relative velocities, Stokes numbers, and gas drag, including collisional damping and stirring.
• Simulated orbital evolution with Type I migration, using a disk model with surface densities Σg ∝ r⁻¹, Σs ∝ r⁻¹, and temperature T ∝ r⁻¹/², consistent with observed disks and the MMSN beyond the snow line.

Experimental results

Research questions

• RQ1 Can pebble drift and collisional growth in the outer disk lead to sustained planetesimal delivery to forming cores in the inner disk?
• RQ2 What is the maximum core growth timescale achievable via planetesimal accretion when planetesimals are supplied by drifting pebbles?
• RQ3 Can this mechanism form massive cores (10 M⊕) before Type I migration destroys them, given typical disk lifetimes (~1 Myr)?
• RQ4 What is the minimum disk mass required for successful gas giant core formation via pebble accretion, and is this feasible in common protoplanetary disks?
• RQ5 Why do gas giants form at 2–7 au in both the Solar System and exoplanet systems, and can this be explained by the proposed mechanism?

Key findings

• Pebbles formed in the outer disk (beyond ~10 au) drift inward and grow into planetesimals via collisional coagulation, suppressing their radial drift and enabling sustained delivery to cores.
• The growth of pebbles into planetesimals in the inner disk (≤10 au) provides a continuous supply of 1–10 km bodies, enabling rapid core growth via planetesimal accretion.
• Massive planetary cores (10 M⊕) form in 0.2–0.4 million years—well within the disk lifetime and before Type I migration destroys them—enabling gas accretion.
• The model successfully reproduces the observed formation locations of gas giants at 2–7 au in both the Solar System and exoplanet systems.
• The required disk mass for core formation via pebble accretion is feasible in common protoplanetary disks (≈220 M⊕ in solids), resolving the issue of rare massive disks in prior models.
• The mechanism is robust: even with low pebble accretion efficiency (ε ≈ 0.1), the sustained supply of planetesimals from drifting pebbles enables core growth on timescales comparable to migration.