Dust settling in local simulations of turbulent protoplanetary disks

By Sébastien Fromang, J. Papaloizou. 2006

159 citations recorded by the source corpus.

Aims. In this paper, we study the effect of MHD turbulence on the dynamics of dust particles in protoplanetary disks. We vary the size of the particles and relate the dust evolution to the turbulent velocity fluctuations. Methods. We performed numerical simulations using two Eulerian MHD codes, both based on finite difference techniques: ZEUS-3D and NIRVANA. These were local shearing box simulations incorporating vertical stratification. Both ideal and non ideal MHD simulations with midplane dead zones were carried out. The codes were extended to incorporate different models for the dust as an additional fluid component. Good agreement between results obtained using the different approaches was obtained. Results. The simulations show that a thin layer of very small dust particles is diffusively spread over the full vertical extent of the disk. We show that a simple description obtained using the diffusion equation with a diffusion coefficient simply expressed in terms of the velocity correlations accurately matches the results. Dust settling starts to become apparent for particle sizes of the order of 1 to 10 centimeters for which the gas begins to decouple in a standard solar nebula model at 5.2 AU. However, for particles which are 10 centimeters in size, complete settling toward a very thin midplane layer is prevented by turbulent motions within the disk, even in the presence of a midplane dead zone of significant size. Conclusions. These results indicate that, when present, MHD turbulence affects dust dynamics in protoplanetary disks. We find that the evolution and settling of the dust can be accurately modelled using an advection diffusion equation that incorporates vertical settling. The value of the diffusion coefficient can be calculated from the turbulent velocity field when that is known for a time of several local orbits.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/c304cafecc68619ddd93f582e6d1492954caa809

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Citations in the corpus

The subcritical baroclinic instability in local accretion disc models (2009, methodology): “NIRVANA has been used frequently in the past to study Page 2 of 12 various problems involving MHD turbulence in the shearing box (Fromang & Papaloizou 2006; Papaloizou et al. 2004).”
Standing on the shoulders of giants : Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids (2008, background): “Johansen & Klahr (2005), Fromang & Papaloizou (2006) and Lyra et al. (2008a) show that the particles are stirred up by the hydromagnetic turbulence to form a layer of finite vertical thickness, maintained by turbulent diffusion.”
Dust Evolution and the Formation of Planetesimals (2016, background): “…is commonly called the Schmidt number2 Sc which was shown to be (Youdin & Lithwick 2007) Sc = Dg Dd ' 1 + St2, (13) and it is commonly assumed that the gas diffusivity Dg equals the gas viscosity ν (but see Johansen & Klahr 2005; Fromang & Papaloizou 2006; Pavlyuchenkov & Dullemond 2007).”
DUST AND GAS IN THE DISK OF HL TAURI: SURFACE DENSITY, DUST SETTLING, AND DUST-TO-GAS RATIO (2015, methodology): “Larger values than our assumed SC = 1.5 have been reported from numerical simulations e.g. 2.8 in Fromang & Papaloizou (2006) and 11 in Carballido et al. (2005).”
A Three-dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk Using DCO+ (2017, background): “This lifting can occur even for modest levels of turbulence, vturb ∼ 0.1cs (Fromang & Papaloizou 2006), and is especially prominent for the smallest grains (Fromang & Nelson 2009).”
Probing dust grain evolution in IM Lupi's circumstellar disc. Multi-wavelength observations and mo (2008, background): “In parallel to grain growth, dust grains are expected to settle towards the disc midplane and then to migrate inward as a result of the conjugate actions of the stellar gravity and gas drag (e.g. Barrière-Fouchet et al. 2005; Fromang & Papaloizou 2006).”
Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations (2007, background): “If eddies are destroyed in a shear time, then τe ∼ 1, and some local MRI simulations support this choice (Fromang and Papaloizou, 2006).”
MHD simulations of the magnetorotational instability in a shearing box with zero net flux II. The effect of transport coefficients (2007, methodology): “It has been used frequently in the past to study various problems involving MHD turbulence in the shearing box (Papaloizou et al. 2004; Fromang & Papaloizou 2006).”
Dynamics of Protoplanetary Disks (2010, methodology): “Settling can also be rapid, but will be inhibited for small particles if there is any significant level of turbulence within the gas (Dubrulle, Morfill & Sterzik 1995; Fromang & Papaloizou 2006).”
On the Migration of Protogiant Solid Cores (2006, background): “…that the total torque, in a turbulent disk, can be considered as the sum of the fluctuations arising from turbulence and of the laminar torque, which remains to date an open question. than that of the active layers (Fleming & Stone 2003; Reyes-Ruiz et al. 2003; Fromang & Papaloizou 2006).”
Dust dynamics during protoplanetary disc clearing (2007, background): “(18) The relationship between the dust diffusion coefficient D and the gas diffusion coefficient (viscosity) ν is not fully understood, with hydrodynamics models suggesting ratios of ν/D that range from ≃ 0.5–10 (Carballido, Stone & Pringle 2005; Johansen & Klahr 2005; Turner et al. 2006; Fromang & ”