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Global magnetohydrodynamical models of turbulence in protoplanetary disks: I. A cylindrical potential on a Cartesian grid and transport of solids
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Astrophysics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Astrophysics.
2008 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 479, 883-901 p.Article in journal (Refereed) Published
Abstract [en]

Aims.We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to demonstrate that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations while offering advantages, such as the absence of a grid singularity, for certain applications, e.g., circumbinary disks and disk-jet simulations. Methods: We employ the Pencil Code, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation of state. Planets and stars are treated as particles evolved with an N-body scheme. Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle. Results: We find that Cartesian grids are well-suited for accretion disk problems. The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence, in good agreement with published results achieved with cylindrical codes. Models without an inner boundary do not show the spurious build-up of magnetic pressure and Reynolds stress seen in the models with boundaries, but the global stresses and alpha viscosities are similar in the two cases. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 ± 0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of Maxwell to Reynolds stresses decreases with increasing temperature, dropping from 5 to 1 when the sound speed was raised by a factor 4, maintaing the same field strength. We also study the dynamics of solid boulders in the hydromagnetic turbulence, by making use of 106 Lagrangian particles embedded in the Eulerian grid. The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer, forming instead a layer of solids of finite vertical thickness. The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0 ± 0.2 for a model with α≈10-3 and 0.78 ± 0.06 for a model with α≈10-1. That is, the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase. The average bulk density of solids in the turbulent flow is quite low (ρp = 6.0×10-11 kg m-3), but in the high pressure regions, significant overdensities are observed, where the solid-to-gas ratio reached values as great as 85, corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01

Place, publisher, year, edition, pages
2008. Vol. 479, 883-901 p.
Keyword [en]
magnetohydrodynamics (MHD), accretion, accretion disks, instabilities, turbulence, solar system: formation, diffusion
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
URN: urn:nbn:se:uu:diva-97999DOI: 10.1051/0004-6361:20077948ISI: 000253454600026OAI: oai:DiVA.org:uu-97999DiVA: diva2:173150
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Turbulence-Assisted Planetary Growth: Hydrodynamical Simulations of Accretion Disks and Planet Formation
Open this publication in new window or tab >>Turbulence-Assisted Planetary Growth: Hydrodynamical Simulations of Accretion Disks and Planet Formation
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The current paradigm in planet formation theory is developed around a hierarquical growth of solid bodies, from interstellar dust grains to rocky planetary cores. A particularly difficult phase in the process is the growth from meter-size boulders to planetary embryos of the size of our Moon or Mars. Objects of this size are expected to drift extremely rapid in a protoplanetary disk, so that they would generally fall into the central star well before larger bodies can form.

In this thesis, we used numerical simulations to find a physical mechanism that may retain solids in some parts of protoplanetary disks long enough to allow for the formation of planetary embryos. We found that such accumulation can happen at the borders of so-called dead zones. These dead zones would be regions where the coupling to the ambient magnetic field is weaker and the turbulence is less strong, or maybe even absent in some cases. We show by hydrodynamical simulations that material accumulating between the turbulent active and dead regions would be trapped into vortices to effectively form planetary embryos of Moon to Mars mass.

We also show that in disks that already formed a giant planet, solid matter accumulates on the edges of the gap the planet carves, as well as at the stable Lagrangian points. The concentration is strong enough for the solids to clump together and form smaller, rocky planets like Earth. Outside our solar system, some gas giant planets have been detected in the habitable zone of their stars. Their wakes may harbour rocky, Earth-size worlds.

Place, publisher, year, edition, pages
Uppsala: Universitetsbiblioteket, 2009. viii, 102 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 593
Keyword
accretion, accretion disks, hydrodynamics, instabilities, methods: numerical, solar system: formation, planets and satellites: formation, magnetohydrodynamics (MHD), turbulence, diffusion, stars: planetary systems: formation
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-9537 (URN)978-91-554-7395-2 (ISBN)
Public defence
2009-02-26, Polhemsalem, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 14:00
Opponent
Supervisors
Available from: 2009-02-05 Created: 2009-02-05Bibliographically approved

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