Dust settling in local simulations of turbulent protoplanetary disks
Astronomy Unit, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK e-mail: S.Fromang@damtp.cam.ac.uk
Accepted: 25 February 2006
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.
Key words: accretion, accretion disks / magnetohydrodynamics (MHD) / methods: numerical / planets and satellites: formation
© ESO, 2006