Lund Observatory

department of Astronomy and Theoretical Physics

Turbulence in protoplanetary disks

Planets form in protoplanetary discs around young stars as dust grains collide and stick together to form larger and larger bodies. Protoplanetary discs are observed around most young stars. They play two important roles: they are birth sites of planets and they feed gas to the star via accretion.

The stresses associated with turbulent gas motion can transport angular momentum outwards and mass inwards. Our best candidate for driving turbulence in protoplanetary discs is the magnetorotational instability. Keplerian gas flow is in itself stable and will not transition to turbulence, despite of the free energy in the shear. The presence of a weak magnetic field changes the situation entirely and constitutes a robust path to turbulence in the regions where the disc is sufficiently ionised.

At Lund Observatory we study the details of protoplanetary disc turbulence caused by the magnetorotational instability. We use the Pencil Code to simulate the magnetohydrodynamics of gas in protoplanetary discs.

The figure shows the turbulent gas velocity (the azimuthal velocity component)
in a local box simulation of magnetorotational turbulence.

Our research is particularly focused on the effect of gas turbulence on the embedded dust particles. Small particles (dust grains) are strongly coupled to the gas and experience turbulent diffusion. This prevents sedimentation to the mid-plane. Small particles are also transported radially outwards by the turbulence, and this may explain why crystalline silicate dust grains, believed to form in the inner regions of the solar nebula close to the sun, are found in comets.

The figure shows the density of micrometer-sized dust grains. An equilibrium has been achieved between sedimentation to the mid-plane and turbulent diffusion.

Larger dust particles - pebbles, rocks, and boulders - partially decouple from the gas drag. This gives them freedom to move more independently of the gas. We have studied the dynamics of such large particles in protoplanetary discs turbulence and found that the particles concentrate strongly in large-scale pressure bumps that form spontaneously in the turbulent flow. The pressure bumps are supported by axisymmetric zonal flows similar to the banded wind structure of Jupiter and Saturn.

The figure shows the gas density at the sides of the simulation box (left) and the directional column density of gas normalised by the mean column density. The vertically extended and axisymmetric pressure bump is clearly visible in the column density.

Pressure bumps may concentrate particles enough that the particle component contracts gravitationally to form planetesimals. In regions where the ionisation fraction is too low to support magnetic turbulence, the streaming instability constitutes another possible path to planetesimals.

For more information and references see Anders Johansen's web page.
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