[Paper Review] Planet formation inside proto-giants: First 3D simulations

Sergei Nayakshin|arXiv (Cornell University)|Aug 15, 2018

Astrophysics and Star Formation Studies1 references3 citations

TL;DR

This study presents the first 3D simulations of pebble dynamics inside gravitationally unstable gas clumps in protoplanetary discs, demonstrating that dust-mediated Rayleigh-Taylor instabilities rapidly transport pebbles inward, accelerating sedimentation by up to two orders of magnitude. The simulations show that even mm-sized pebbles can form solid planetary cores within hundreds of years, depending on clump temperature and composition, supporting gravitational instability as a viable pathway for forming cores from sub-Earth to Neptune masses and gas giants with solid or fuzzy cores.

ABSTRACT

Numerical simulations of pebble dynamics inside gas clumps formed by gravitational instability of protoplanetary discs are presented. We find that dust-mediated Rayleigh-Taylor instabilities transport pebbles inward rapidly via dense metal-rich "fingers". This speeds up sedimentation of small pebbles by up to two orders of magnitude and yet does not impede grain growth because grains of all sizes sediment at the same collective speed as long as Stokes number is less than unity. In simulations with a fixed pebble size, solid planetary cores form if pebble size exceeds a few cm. Pebble growth leads to core formation in some hundreds of years even when pebbles injected into clumps are of mm or smaller sizes. Properties of the gas clump dictate what kind of cores can be made. Low central temperature clumps allow formation of solid cores out of refractory materials, whereas in the highest temperature clumps pebbles of any composition are vaporised and make fuzzy cores only. These results confirm that gravitational instability of protoplanetary discs is a robust mechanism of hatching cores from sub-Earth to Neptune mass, as well as gas giants with massive cores, solid or fuzzy. This mode of planet formation is especially promising for environs too young and distant (such as the ALMA-observed HL Tau disc) or too violent (such as circum-binary planets) to form via the Core Accretion scenarios.

Motivation & Objective

• To investigate how pebbles accreted from the protoplanetary disc sediment and grow inside self-gravitating gas clumps formed by disc fragmentation.
• To determine whether gravitational instability can efficiently form planetary cores under realistic conditions, especially where core accretion fails.
• To assess the role of dust-mediated Rayleigh-Taylor instabilities in enhancing core formation timescales compared to 1D models.
• To evaluate how clump temperature, pebble size, and composition influence core formation outcomes, including solid vs. fuzzy cores.

Proposed method

• 3D hydrodynamical simulations of gas and dust coupling in isolated, polytropic gas clumps with initial masses of 3 M_J and central temperatures of 300 K.
• Use of the Epstein drag law to model aerodynamic friction between gas and pebble particles, with Stokes number < 1 for all grains.
• Incorporation of dust Rayleigh-Taylor instability via numerical modeling of metal-rich, dense fingers that transport pebbles inward rapidly.
• Simulation of grain growth and fragmentation in high-metallicity central regions, assuming collisional equilibrium.
• Fixed pebble size simulations to isolate sedimentation dynamics, followed by variable pebble size and non-spherical initial conditions.
• Comparison of results with 1D models and observational constraints, including ALMA observations of HL Tau and Juno data on Jupiter’s core.

Experimental results

Research questions

• RQ1 Can dust-mediated Rayleigh-Taylor instabilities significantly accelerate pebble sedimentation in proto-giant clumps compared to standard 1D models?
• RQ2 What is the minimum pebble size required for efficient core formation in clumps with varying central temperatures?
• RQ3 How quickly can solid planetary cores form from mm-sized pebbles in a 3D environment with turbulent mixing and instability?
• RQ4 To what extent does clump metallicity and temperature determine whether a solid or fuzzy core forms?
• RQ5 Can gravitational instability of protoplanetary discs produce cores rapidly enough to explain young, distant, or circum-binary planets?

Key findings

• Dust-mediated Rayleigh-Taylor instabilities transport pebbles inward up to two orders of magnitude faster than in 1D models, enabling rapid core formation.
• Pebble sedimentation speed is independent of grain size as long as Stokes number remains below unity, allowing collective inward motion of mixed-size grains.
• Solid planetary cores form within a few hundred years if pebble size exceeds a few centimeters, even in low-metallicity clumps.
• Even mm-sized pebbles can form cores in a few hundred years due to efficient inward transport via instabilities, not just size-dependent settling.
• In clumps with central temperatures above ~1500 K, pebbles are vaporized, leading to the formation of fuzzy cores instead of solid ones.
• The simulations suggest that gravitational instability can produce cores in environments too distant, young, or violent for core accretion, such as the HL Tau disc or circum-binary systems.