Journal Article

On the dynamics of planetesimals embedded in turbulent protoplanetary discs

Richard P. Nelson and Oliver Gressel

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 409, issue 2, pages 639-661
Published in print December 2010 | ISSN: 0035-8711
Published online November 2010 | e-ISSN: 1365-2966 | DOI:
On the dynamics of planetesimals embedded in turbulent protoplanetary discs

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Angular momentum transport and accretion in protoplanetary discs are generally believed to be driven by magnetohydrodynamics (MHD) turbulence via the magnetorotational instability (MRI). The dynamics of solid bodies embedded in such discs (dust grains, boulders, planetesimals and planets) may be strongly affected by the turbulence, such that the formation pathways for planetary systems are determined in part by the strength and spatial distribution of the turbulent flow.

We examine the dynamics of planetesimals, with radii between 1 m and 10 km, embedded in turbulent protoplanetary discs, using 3D MHD simulations. The planetesimals experience gas drag and stochastic gravitational forces due to the turbulent disc. We use, and compare the results from, local shearing box simulations and global models in this study.

The main aims of this work are to examine: the growth, and possible saturation, of the velocity dispersion of embedded planetesimals as a function of their size and disc parameters; the rate of radial migration and diffusion of planetesimals; the conditions under which the results from shearing box and global simulations agree.

We find good agreement between local and global simulations when shearing boxes of dimension 4H× 16H× 2H are used (H being the local scaleheight). The magnitude of the density fluctuations obtained is sensitive to the box size, due to the excitation and propagation of spiral density waves. This affects the stochastic forcing experienced by planetesimals. The correlation time associated with the stochastic forcing is also found to be a function of the box size and aspect ratio.

The equilibrium radial velocity dispersion, σ(vr), obtained depends on the radii, Rp, of the planetesimals. Bodies with Rp= 50 m achieve the smallest value with σ(vr) ≃ 20 m s−1. Smaller bodies are tightly coupled to the gas, and boulders with Rp= 1 m attain a value of σ(vr) similar to the turbulent velocity of the gas (∼100 m s−1). Equilibrium values of σ(vr) for bodies larger than 100 m are not achieved in our simulations, but in all models we find rapid growth of the velocity dispersion for planetesimals of size 1 and 10 km, such that σ(vr) ≥ 160 m s−1 after a run time of 1200 orbits at a distance of 5 au from the central star. These values are too large to allow for the runaway growth of planetesimals, and mutual collisions would lead to catastrophic disruption. Radial migration due to gas drag is observed for bodies with Rp≃ 1 m, and is only modestly affected by the turbulence. Larger bodies undergo a random walk in their semimajor axes, leading to radial diffusion through the disc. For our fiducial disc model, we estimate that radial diffusion across a distance of ≃2.5 au would occur for typical planetesimals in a swarm located at 5 au over a disc lifetime of 5 Myr. Radial diffusion of this magnitude appears to be inconsistent with Solar system constraints.

Our models show that fully developed magnetohydrodynamics (MHD) turbulence in protoplanetary discs would have a destructive effect on embedded planetesimals. Relatively low levels of turbulence are required for traditional models of planetesimal accretion to operate, this being consistent with the existence of a dead zone in protoplanetary discs.

Keywords: accretion, accretion discs; MHD; methods: numerical; planets and satellites: formation; protoplanetary discs

Journal Article.  19280 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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