Planetesimal Formation in Zonal Flows

Karsten Dittrich (PhD student, MPIA Heidelberg)

Hubert Klahr (Supervisor, MPIA Heidelberg)

Anders Johansen (Lund Observatory)

Dittrich, Klahr, & Johansen 2013, ApJ, 763, 117

Scales of Planet Formation

Credit: Cornelis Dullemond

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Zonal flows and axisymmetric pressure bumps - Theory

Magnetic pressure

Azimuthal gas velocity

Gas pressure (gas density)

• Magnetic pressure forms large-scale structures

• Orbital shear converts magnetic to kinetic energy

– Zonal flows!

• Geostrophic balance excites axisymmetric pressure bumps

Magnetic pressure

Azimuthal gas velocity

Gas pressure

www.spitzer.caltech.edu, Johansen & Klahr 2005

Zonal flows in numerical simulations

• View from the top of the disk; integrated over vertical direction

• Snapshot of the gas surface density shows many short-lived high frequency oscillations

Zonal flows in numerical simulations

• Time-average over 5 orbits reveals radial structure

– Sinusodial radial structure

– About 5 scale heights H

5H 1.25AU (at 5AU)

Zonal flows in numerical simulations

• Sinusoidal structure has constant width

• Stable for several tens of local orbits

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Zonal flows in numerical simulations

• Life time up to 50 local orbits

• Radial scale of 5-7 pressure scale heights

Planetesimal formation in zonal flows

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• Radial drift is slowed down by pressure bumps

• Leads to high dust densities

• All simulations start with a dust-to-gas ratio of 10-2

• Maximal concentrations reached during simulation: – 104 for meter-

sized particles

– Some 100 for decimeter-sized particles

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Particle Size [cm]

Planetesimal formation in zonal flows

Summary • Zonal flows and the resulting pressure

bumps are a physical feature of magneto-rotationally-unstable protoplanetary disks – Life-time of several tens of local orbits

– Radial size of 5-7 scale heights (1.5AU at a 5AU orbit); in agreement with global simulations (e.g., Uribe et al. 2011)

• Dust gets trapped at pressure bumps and forms over-densities – Decimeter-sized pebbles can trigger

streaming instability

– Meter-sized boulders can undergo gravitational collapse to form planetesimals

Tim

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Particle Size [cm]

zonal flow simulation +back-reaction - no self-gravity + initial dust-to-gas ratio: 0.001 + particle size: St=0.1 Physical size: 5.28 x 5.28 x 2.64 H³ Resolution: 512 x 512 x 256 using 4096 CPUs on Juqueen

More recently…

zonal flow simulation +back-reaction + no self-gravity + initial dust-to-gas ratio: 0.01 + particle size: St=0.1 Physical size: 5.28 x 5.28 x 5.28 H³ Resolution: 512 x 512 x 512 using 8192 CPUs on Juqueen

More recently…