pdf 3.6 MB

The Role of 

Turbulence in 

Planetesimal 

Formation 

Hubert Klahr, 

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t=36.1 

München, Sep. 5 th, 2012 

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Max-Planck-Institut für Astronomie, 0 100 200Heidelberg 300 400 500 

t=36.3 

t=36.5 

Natalie Raettig, Helen Morrison, Karsten Dittrich, Mario Flock, Natalia Dzyurkevich, Karsten 

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500 

Dittrich, Ana Uribe(MPIA), Rainer Spurzem (NAOC/ARI), Mario Trieloff (HD), Til Birnstiel, Barbara 

Ercolano (USM), Kees Dullemond (ITA), Chris Ormel (Berkley), Neal Turner (JPL), Wlad Lyra 

(AMNH), 12/13/2009 400 

Peter Bodenheimer (UCSC), Hubert Doug Klahr Lin - Planet (KIAA, Formation UCSC) - MPIA 400 

Anders Johansen (Lund), 1 Andrew 

Heidelberg 

Youdin (CfA), Jeffrey S. Oishi (Berkley), Mordecai-Mark Mac Low (AMNH) 

Wednesday, September 5, 12 

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t=36.2 

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Outline: 

• Capturing Dust in Pressure maxima e.g. 

Zonal flows and vortices 

• MHD turbulence and Gravoturbulent 

Planetesimal formation -> Karsten Dittrich 

• Turbulence and vortices in Baroclinic 

disks: Disk Weather 

• Modified Symmetric Instability 

• Dust capturing in 3D vortices 

• Summary, Conclusions 

12/13/2009 Hubert Klahr - Planet Formation - MPIA 

Heidelberg 


The role of 

Turbulence in 

Planet Formation

Turbulence in a non rotating frame: 

Cuzzi et al. 


Heidelberg 


L 

H 

Laboratory Conditions 

Dust collects between 

vortices (high pressure)

Particle response in rotating (DISK) frame: 

Geostophic flow: balance of pressure and Coriolis forces 

VORTICES: 

Barge & Sommeria 1995 ZONAL FLOWS: 


Heidelberg 


H 

L 

H 

Radial Pressure maxima 

Klahr & Lin 2000

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e 

r 

t 

i 

c 

a 

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From dust/gas eq. 1 => Streaming Instability - 

> dust densities larger than local Roche 

density, e.g. Planetesimals can form. 

h o r i z o n t a l 


Heidelberg 


Johansen, Henning & Klahr 2006

V 

e 

r 

t 

i 

c 

a 

l 

From dust/gas eq. 1 => Streaming Instability - 

> dust densities larger than local Roche 

density, e.g. Planetesimals can form. 

h o r i z o n t a l 


Heidelberg 


Johansen, Henning & Klahr 2006

Disk: 


Heidelberg 


…because it is a reliable source for turbulence. 

Box: 

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MHD plus self-gravity for the dust, including particle feed back 

on the gas: 

gas 

dust 

Poisson equation solved via FFT in parallel mode: up to 256 3 cells 


Heidelberg 

Wednesday, September 5, 12

Formation Of 

Planetesimals 

From pressure 

trapped / 

gravitational 

Bound heaps of 

gravel - here 

magnetic 

turbulence: 

Johansen, Klahr & 

Henning 2011. 

Next: Raettig & 

Lyra 

512 ^2 simulation 

64 Mio particles 

Entire project 

used 15 Mio. CPU 

hours. 


Heidelberg 


Concentration in Zonal Flows: 

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At 5123 100 and the usual set 100 up: As before mass of 

planetesimals 0 depends on 0 the available mass. 

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t=36.1 

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t=36.3 

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t=36.2 

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new: Intermediate Formation of Binaries; 

Johansen, Klahr & Henning (2011) 

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t=36.5 

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Fig. 6. The particle column density as a function of time after self-gravity is turned on after t = 35.0Torb. Theinsertshowsanenlargementofthe 

region around the point of highest column density.

Not the process but numerical resolution limit the smallest 

possible planetesimals. Johansen, Klahr & Henning 2011 

To predict an initial mass distribution of 

Planetesimals one needs A: the proper size 

distribution of precursors and B: the likely hood 

12/13/2009 for concentrations Hubert as Klahr a - Planet function Formation - MPIA of particle size. 10 

Heidelberg 



Larger Boxes = better concentration 

Dittrich, Klahr & Johansen submitted 

See Talk by Karsten Dittrich

Natalia Dziurkevich (in prep.) see her POSTER! 

Active (Blue) and Dead (Yellow/Orange) Zones 

12/13/2009 => Planetesimals Hubert are Klahr - needed Planet Formation in - MPIA the Dead Zone. 12 

Heidelberg 



Heidelberg 


Baroclinic Effects on Earth: 

Formation of Hurricanes 

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Heidelberg 


Geophysical Baroclinic Instability 

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�[g/cm 2 ] 

Klahr & Raettig in prep. 

Using data from Sean Andrews 

alpha = 0.001; Mdot = 1E-7 Msol/yr; 

Plus irradiation: Tstar = 4300; Rstar = 2 Rsol 

10 5 

10 4 

10 3 

10 2 

0.1 1.0 10.0 100.0 

r[AU] 


Heidelberg 


T[K] 

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10 

0.1 1.0 10.0 100.0 

r[AU] 

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Ri 

0.001 

0.000 

�0.001 

�0.002 

�0.003 

Richardson number & 

Thermal diffusion time 

�0.004 

0.1 1.0 10.0 100.0 

r[AU] 

� therm 


Heidelberg 

N 2 = 1 

100.0 

10.0 

1.0 

⇤ 

Ri 2 = 

H 

R ⇥s⇥p 

N 2 

3 

2 

⇥ 2 

⇧therm = H 2 / D 

The saturated state presents a turbulent flow dominated b 

(Mamatsashvili & Chagelishvili 2007 ;Heinemann & Papaloizo 

fluctuation of 10% of the speed of sound and producing -valu 

10 3. Vortices are forming spontaneously out of the creation o 

⌅cv 

0.1 

0.1 1.0 10.0 100.0 

r[AU] 

vortices show no sign of decay, yet draw the energy out of the g 

providing entropy flux downward the gradient, like in standard 


MRI BI 

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2


Heidelberg 


Strength of alpha? 

Raettig, Klahr and Lyra, submitted 

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Heidelberg 


Pluto Code: 1024^2; WENO3-RK3; HLLE; FARGO 

vortices migrate inward, but are recreated by 

waves from other vortices. 

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Pluto Code: 1024^2; WENO3-RK3; 

HLLE; FARGO 

Spirals spawn new vortices further 

out, many cycles of vortices! 


Heidelberg 


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2D axissymetric Pluto Simulation: Temperature 

due to irradiation from star and thermal 

relaxation tau = 0.1 (also works for flux limited 

diffusion in irradiated disks) 


Heidelberg 


Star-> 

Thermal wind: 

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2D axissymetric Pluto Simulation: 

Overstability due to thermal wind leads to 

convection like motion: Symmetric Instability 


Heidelberg 


Modification of Solberg-Hoiland Criterion, including thermal relaxation: 

In collaboration with Alexander Hubbard 

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2D axissymetric Pluto Simulation: Resulting 

vorticity perturbations 


Heidelberg 


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Full 3D Pluto Simulation: Spontanous Formation 

of Vortices from tiny perturabtions 


Heidelberg 


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Interface 

MRI - Dead Zone 

linear 

axisymmetric 

Instability: 

Solberg-Hoiland 

Disk Weather 

Papaloizou-Pringle 

Rossby Wave Inst. 

classic 

baroclinic 

instability 

Radial Buoyancy : dS/dr < 0 & dP/dr thermal wind dVphi/dz < 0 plus: thermal relaxation 

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Interface 

MRI - Dead Zone 

linear 

axisymmetric 

Instability: 

Solberg-Hoiland 

Disk Weather 

Papaloizou-Pringle 

Rossby Wave Inst. 

classic 

baroclinic 

instability 

Radial Buoyancy : dS/dr < 0 & dP/dr thermal wind dVphi/dz < 0 plus: thermal relaxation 

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Small particles in pressure maxima e.g. a vortex 

e.g. Vortex is in balance between Coriolis forces and 

pressure = same for Zonal flow. 

H 


Heidelberg 


L

St = 0.05 particles (few millimeter) 

(white = x 1000) Natalie Raettig 


Heidelberg 


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St = 0.05 particles (few millimeter) 

(white = x 1000) Natalie Raettig 


Heidelberg 


NEXT STEP: 

SELF GRAVITY 

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Dust Concentration in 3D Vortices: 

Raettig and Klahr, in prep 


Heidelberg 


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Conclusions: 

Johansen and Klahr: High resolution simulations of planetesimal formation 7 

t=35.0 

500 

400 

t=35.7 

• Disk turbulence can be magnetic in nature, but in 

resistive regions the entropy structure of the disk 

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creates a thermal wind and eventually vortices. 

• Any turbulence with 200 gravity can form rapidly 

planetesimals over a broad range of sizes 

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• Vortices can concentrate St = 0.05 dust at initial 

abundance of eps = 1E-4 to the streaming 

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200instability 300 400and 500 planetesimal 0 100 formation. 

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t=36.1 t=36.2 


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Heidelberg 


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