planetesimal formation in turbulent protoplanetary discsiccg/pub/associated/fy2009/...planetesimal...

Planetesimalformation in

turbulentprotoplanetary

discs

AndersJohansen

Planetformation

Dust in MHDturbulence

Planetesimalformation

Zonal flows

Analyticalmodel

Global models

Streaming andself-gravity

Dead zones

Conclusions

Planetesimal formation inturbulent protoplanetary discs

Anders JohansenLeiden Observatory, Leiden University

“Workshop on the Magnetorotational Instability in Protoplanetary Disks” (Kobe University, June 2009)

Collaborators: Andrew Youdin, Hubert Klahr, Wladimir Lyra, Mordecai-Mark Mac Low, Thomas Henning



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Planet formation

Planets form in protoplanetary discs from dust grains that collide andstick together (planetesimal hypothesis of Safronov, 1969).

From dust to planetesimalsµm → m: Contact forces in collisions cause stickingm → km: ???From planetesimals to protoplanetskm → 1,000 km: GravityFrom protoplanets to planetsTerrestrial planets: Protoplanets collideGas planets: Solid core attracts gaseous envelope

→ → → →



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Planetesimals

Kilometer-sized objects massive enoughto attract each other by gravity(two-body encounters)

Building blocks of planets

Formation:

µm → cm: Dust grains collide andstick(Blum & Wurm 2000)

cm → km: Sticking or gravitationalinstability(Safronov 1969, Goldreich & Ward 1973, Weidenschilling &

Cuzzi 1993)

Dynamics of turbulent gas importantfor modelling dust grains and boulders

William K. Hartmann



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Overview of planets

Protoplanetary discs

Dust grains

Pebbles

Gas giants andice giants

Terrestrial planets

Dwarf planets+ Countless asteroids and Kuiper belt objects+ Moons of giant planets+ More than 300 exoplanets



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Particle dynamics

Gas accelerates solid particles through drag force:

∂w∂t = . . .− 1

τf(w − u)

@@

@I

Particle velocity @@I

Gas velocity

In the Epstein drag force regime, when the particle is muchsmaller than the mean free path of the gas molecules, thefriction time is (Weidenschilling 1977)

τf =a•ρ•csρg

a•: Particle radius

ρ•: Material density

cs: Sound speed

ρg : Gas density

Important nondimensional parameter in protoplanetary discs:

ΩKτf (Stokes number)

At r = 5 AU we can approximately write a•/m ∼ 0.3ΩKτf .



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Diffusion-sedimentation equilibrium

Diffusion-sedimentationequilibrium:

Hdust

Hgas=

√δt

ΩKτf

Hdust = scale height of dust-to-gasratio

Hgas = scale height of gas

δt = turbulent diffusion coefficient,like α-value

ΩKτf = Stokes number, proportional

to radius of solid particles(Johansen & Klahr 2005)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Diffusion coefficient

Definition of Schmidtnumber:Sc = νt/Dt = αt/δt

From thescale-height of thedust one cancalculate thediffusion coefficient:δt = δt(Hdust)

0.001 0.010 0.100 1.000α

1

10

Sc

Scx

Scz

Scx (Ly=4)Scz (Ly=4)

Johansen & Klahr (2005): Scz ' 1.5, Scx ' 1(Turner et al. 2006: Scz ' 1; Fromang & Papaloizou 2006: Scz ' 3)

Carballido, Stone, & Pringle (2005): Scx ' 10

Johansen, Klahr, & Mee (2006):The ratio between diffusion and viscosity depends on thestrength of an imposed magnetic field



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

The role of the Schmidt number

Safronov (1969):

Dust grains coagulate and gradually decouple from the gas

Sediment to form a thin mid-plane layer in the disc

Planetesimals form by continued coagulation orself-gravity (or combination) in dense mid-plane layer

HOWEVER:MRI-driven turbulence very efficient at diffusing dust

Need to look at how larger particles react to turbulence



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Dust nomenclature

My suggestion for naming solid particles (not official):

Diameter Name

<1 mm Dust

1 mm Sand

1 cm Pebble, gravel

10 cm Cobble, rock

> 1 m Boulder



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Radial drift

Balance between drag force and head wind gives radial driftspeed (Weidenschilling 1977)

vdrift = − 2

ΩKτf + (ΩKτf)−1ηvK

for Epstein drag law (solids smaller than gas mean free path).

MMSN at r=5 AU

10−3 10−2 10−1 100 101

a [m]

10−1

100

101

102

v drif

t [m

/s]

Epstein drag Sto

kes

drag

MMSN η from Cuzzi et al.1993

Maximum drift speed of 50m/s

Drift time-scale of 50-100orbits for solids of 30 cm inradius at 5 AU, but 1 cm at100 AU



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Boulders in turbulence

Johansen, Klahr, & Henning (2006):2,000,000 boulders moving in magnetorotational turbulence



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Gas density bumps

Strong correlation between high gas density and highparticle density (Johansen, Klahr, & Henning 2006)

Solid particles are caught in gas overdensities(Whipple 1972, Klahr & Lin 2001, Haghighipour & Boss 2003)

Gravoturbulent formation of planetesimals



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Pressure gradient trapping

Outer edge:Gas sub-Keplerian. Particles forced by gas drag to moveinwards.

Inner edge:Gas super-Keplerian. Particles forced by gas drag to moveoutwards.



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Global models

Fromang & Nelson (2005):Dust concentrates in long-lived vortex

Dust density (5 cm and 25 cm):

Gas density and vorticity (ωz):



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Increasing box size

Stratified shearing box simulations with increasing box size

−0.5 0.0 0.50.00.0x/H

0

20

40

60

80

100

t/Tor

b−1.0 −0.5 0.0 0.5 1.00.00.0

x/H

0

20

40

60

80

100

t/Tor

b

−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0 2.5x/H

0

20

40

60

80

100

t/Tor

b0.95

1.00

1.05

Σ g/<

Σ g>

Orbital advection algorithm with Pencil Code(Fourier interpolate the Keplerian advection term)

No spurious density depression in box centre(Johnson et al. 2008)

Pressure bumps of few percent amplitude appear andreappear at time-scales of many orbitsPlot by T. Sano



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Zonal flow

1 10kx

−2•10−5

−1•10−5

0

1•10−5

2•10−5

3•10−5d/

dt[k

x ^ u y2 (kx,0

,0)]

AdvCorLor

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

ρ/<ρ> 0.95 1.05

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

uy/cs −0.05 +0.05

Large scale variation in Maxwell stress launches zonal flows

Pressure bumps form as zonal flows are slightlycompressive

Balance between turbulent diffusion and compression gives|ρ| ∝ k−2

x

Johansen, Youdin, & Klahr (2009):Zonal flows in accretion discs



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Examples of zonal flow – planets

Definition of zonal flow:

Axisymmetric large scale variation in rotation velocity

Saturn and Jupiter showsteady zonal flows

Driven by convection(inverse hydrodynamicalcascade)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Examples of zonal flow – the Sun

On top of the Sun’s differentialrotation there is a zonal flow ofamplitude approximately 3 m/s

Discovered in 1980 from veryprecise measurements of thesolar rotation(Howard & Bonte 1980)

Migrates with the solar cycle

Zonal flows (or torsionaloscillations) are launched by themagnetic tension associated withlarge scale magnetic fields(Schußler 1981, Yoshimura 1981)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Stress variation

Resistive 2.56H × 2.56H × 1.28H simulation at256× 256× 128 grid points (ReM = 12500, Pm = 3.75):

BxBy(x,t)/<BxBy(t)>

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

0.7

1.3

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

ρ/<ρ> 0.95 1.05

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

uy/cs −0.05 +0.05

Turbulent viscosity α ≈ 0.005

Stress variation of 10%–20%

Stress correlation time of a few orbits

Density bumps and zonal flows correlated on tens of orbits



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Analytical model

BxBy(x,t)/<BxBy(t)>

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50t/T

orb

0.7

1.3

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

ρ/<ρ> 0.95 1.05

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

uy/cs −0.05 +0.05

Analytical model of zonal flow excitation and saturation

Need to connect a known (measured) stress and stress variationto amplitude of density bumps and zonal flows

Forcing of the zonal flow by stress variation

Geostrophic balance between pressure bump and zonalflow envelope

Damped random walk model



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Variation in stress

Linearised, axisymmetric evolution equation for uy :

∂u′y∂t

= −1

2Ωu′x + T ′

The tension term T ′ describes momentum transport byMaxwell stress:

T ′ =1

ρ0

1

µ0

∂〈BxBy 〉∂x

M = −µ−10 〈BxBy 〉

In shearing sheet the tension is simply the derivative of theMaxwell stress variation:

T ′ = − 1

ρ0

∂M ′

∂x



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Zonal flow dynamical equations

Linearised equation system for zonal flow excitation(hats denote wave amplitudes):

0 = 2Ωuy −c2s

ρ0ik0ρ

duy

dt= −1

2Ωux + T

dρdt

= −ρ0ik0ux −1

τmixρ

Assumed geostrophic balance between zonal flow andpressure bump

Density evolution includes turbulent diffusion term actingon time-scale τmix



discs

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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Solutions

Combine the three equations to get

Master equation

dρdt

=1

1 + k20 H2

(F − ρ(t)

τmix

)

F = −2ik0ρ0Ω−1T

Straight forward solution:

ρeq = τmixF

Only valid if correlation time of stress variation larger thanmixing time-scale. Need to model as damped random walk.Exciting at time-scale τfor and damping on time-scale τmix.



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Damped random walk

Re( )ρ

ρIm( )

Turbulent

diffusion

Stress

Correlation time equal to turbulent diffusion time-scale

What is the ampitude?



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Random walk solution

Solution involves product of forcing and mixing time-scales:

Random walk solution

ρeq

ρ0= 2√

ckτforτmixHk0T

cs

ck =1

1 + k20 H2

ρeq ∝ k−10 for k0H 1

ρeq ∝ const for k0H 1

How to find amplitude of zonal flow:

Take ρ0, H, Ω from disc modelRead off T , τmix and τfor from simulationSolution gives ρeq at a given scale k0

Geostrophic balance gives uy from ρeq



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Comparison to simulation

BxBy(x,t)/<BxBy(t)>

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50t/T

orb

0.7

1.3

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

ρ/<ρ> 0.95 1.05

−1.0 −0.5 0.0 0.5 1.0x/H

0

10

20

30

40

50

t/Tor

b

uy/cs −0.05 +0.05

Turbulent mixing time-scale τmix ≈ 1/(k20 D) ≈ 6 Torb

Stress variation of BxBy ∼ 10−3

Stress correlation time of a few orbits

Formula predicts pressure bump amplitude of ρeq ≈ 0.08

In fairly good agreement with the measured ρeq ≈ 0.05



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Global models

Lyra, Johansen, Klahr, & Piskunov (2008):

Global disc with boulders on Cartesian grid (disk-in-a-box)

Gas density (320× 320× 32) Particle density (106 particles)



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AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Space-time plots

Gas density structure from Lyra et al. (2008):

Gas Density

0

20

40

60

80100

Model A

0.5 1.0 1.5 2.0s

020

40

60

80100

Model C

t/(

2πΩ 0-1

)

0.5

1.0

1.5

Gas Densities - Comparison

0.5 1.0 1.5 2.0 2.5s

0.40.6

0.8

1.0

1.2

1.4

1.6ρ

Model A (cs0=0.05)Model C (cs0=0.20)



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AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Stress variation

At any given time there are approximately 10% variationsin the α-value

This is enough to launch zonal flows

Similar variations reported in Fromang & Nelson (2006)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Inverse cascade

Plots show power contribution ofdifferent terms in the inductionequation:

Magnetic energy cascades tolargest scales in the box

Happens through theadvection term

Excites large scale variation inMaxwell stress

Very little large scale activityin the vertical fieldcomponent

−4·10−5

−2·10−5

0

2·10−5

4·10−5

dBx2 /d

t^

AdvAdv (K)Com

StrRes

−4·10−4

−2·10−4

0

2·10−4

4·10−4

dBy2 /d

t^

AdvAdv (K)Com

StrStr (K)Res

1 10k

−2·10−5

−1·10−5

0

1·10−5

2·10−5

dBz2 /d

t^

AdvAdv (K)Com

StrRes



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Streaming instability

Gas rotates slightly slower than KeplerianParticles lose angular momentum due to headwindParticle clumps locally reduce headwind and are fed byisolated particles

Fg Fp

v η(1− )Kep

Nakagawa, Sekiya, & Hayashi (1986): Equilibrium flow solutionYoudin & Goodman (2005): “Streaming instability” (also Goodman & Pindor 2000)Johansen, Henning, & Klahr (2006); Youdin & Johansen (2007);Johansen & Youdin (2007); Ishitsu, Inutsuka, & Sekiya (2009)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Streaming instability

Youdin & Goodman (2005) :“Streaming Instabilities in Protoplanetary Disks”

Gas rotates slower than Keplerian because of radialpressure gradientGas and solid components “stream” relative to each otherRadial drift flow of solids is linearly unstableGrowth on dynamical time-scale for marginally coupledsolids (rocks/boulders)

NSH86 equilibrium



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Clumping

Linear and non-linear evolution of radial drift flow ofmeter-sized boulders (ΩKτf = 1):

t=40.0 Ω−1

−20.0 −10.0 +0.0 +10.0 +20.0x/(ηr)

−20.0

−10.0

+0.0

+10.0

+20.0

z/(

ηr)

t=80.0 Ω−1

−20.0 −10.0 +0.0 +10.0 +20.0x/(ηr)

−20.0

−10.0

+0.0

+10.0

+20.0

z/(

ηr)

t=120.0 Ω−1

−20.0 −10.0 +0.0 +10.0 +20.0x/(ηr)

−20.0

−10.0

+0.0

+10.0

+20.0

z/(

ηr)

t=160.0 Ω−1

−20.0 −10.0 +0.0 +10.0 +20.0x/(ηr)

−20.0

−10.0

+0.0

+10.0

+20.0

z/(

ηr)

Strong clumping in non-linear state of the streaming instability(Youdin & Johansen 2007, Johansen & Youdin 2007)



discs

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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Clumping in 3-D

3-D evolution of the streaming instability:

DiscSimulation box

Particle clumps have up to 100 times the gas density

Clumps dense enough to be gravitationally unstable

But still too simplified: no vertical gravity

Particle size:

30 cm @ 5 AU or 1 cm @ 40 AU



discs

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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Pebbles

t = 0.1Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

0.0 2.0

ρp

Pebbles

t = 10.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 20.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 30.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

Some overdense regions occur, but weak, and couplingwith gas too strong for self-gravity to be important



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AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Pebbles

t = 0.1Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

0.0 2.0

ρp

Pebbles

t = 10.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 20.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 30.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

Baroclinic instability of uy (z) shear?(Ishitsu & Sekiya 2002; Ishitsu et al. 2009)



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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Baroclinic instability?

Particles (Ωτf=0.02)

−0.10 −0.05 0.00 0.05 0.10x/H

−0.04

−0.02

0.00

0.02

0.04

z/H

Single fluid (Ωτf=0)

−0.10 −0.05 0.00 0.05 0.10x/H

−0.04

−0.02

0.00

0.02

0.04

z/H

Ishitsu & Sekiya (2002), Ishitsu et al. (2009)



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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Rocks

t = 0.1Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

0.0 2.0

ρp

Rocks

t = 10.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 20.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 30.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

Higher overdensities, due to the streaming instability, butstill with short correlation times



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Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Boulders

t = 0.1Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

0.0 5.0

ρp

Boulders

t = 10.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 40.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

t = 100.0Ω−1

−0.10 −0.05 0.00 0.05 0.10x/H

−0.10

−0.05

0.00

0.05

0.10

z/H

Almost no overdensities. Violent turbulent motion puffsup and dilutes mid-plane layer.



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AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Clumping depends strongly on metallicity

Increase Σpar/Σgas from 0.01 to 0.03

All particles between 1.5 and 15 centimetres

ε=0.01

−0.1 0.0 0.1x/H

0

10

20

30

40

50

t/Tor

b

0.0

0.1

Σp(x,t)/Σg

ε=0.02

−0.1 0.0 0.1x/H

ε=0.03

−0.1 0.0 0.1x/H

0

10

20

30

40

50

t/Tor

b

0 10 20 30 40 50t/Torb

100

101

102

103

104

max

(ρp)

0 10 20 30 40 50t/Torb

0 10 20 30 40 50t/Torb

10−3

10−2

10−1

Hp/

Hg

Johansen, Youdin, & Mac Low (in preparation)



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Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

The exoplanet zoo

First planet around solar-type star discovered in 1995(Mayor & Queloz)Since then 340 planets discoveredExoplanet probability rises steeply with heavy elementabundance of host star:

(Santos et al. 2004)



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AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

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Dead zones

Conclusions

Overdense seeds

Dust column density as a function of radial coordinate x andtime t measured in orbits:

No back−reaction

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/H

0

20

40

60

80

100

t/Por

b

With back−reaction

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/H

0

20

40

60

80

100

t/Por

b

Turbulent overdensities combined with streaming instabilitycreate transient, overdense “seeds” where self-gravity isimportant.



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Formation of Ceres-mass object from rocks andboulders

Turbulenceandsedimentationdevelop 20orbits withoutself-gravity

Different-sized particlesconcentrateat the samelocations

t=0.0 Torb t=1.0 Torb t=2.0 Torb t=3.0 Torb

−0.66 0.00 0.66x/H

−0.66

0.00

0.66

y/H

t=4.0 Torb

t=5.0 Torbt=6.0 Torbt=6.5 Torbt=7.0 Torb

ΩKτ f = 0.25 ΩKτ f = 0.50

ΩKτ f = 0.75 ΩKτ f = 1.000.0

20.0

Σ p(i) /<

Σ p(i) >

0.0 20.0Σp/<Σp>

0.0 3.0log10(Σp/<Σp>)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Forming planet embryos

Time is in Keplerian orbits (1 orbit ≈ 10 years)

6

Keplerian flow

?

Keplerian flow

Johansen et al. 2007 (Nature, 448, 1022)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Dead zones

Transition from active accretion to dead zones triggersRossby wave instability in pile up of gas(Varniere & Tagger 2006; Inaba & Barge 2006)Rossby vortices trap particlesFormation of Mars or Earth size planets by self-gravityLyra et al. (2008, 2009)



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Mass spectrum



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Conclusions

MRI can play a crucial role in the formation of planets

Zonal flows are excited by ≈10% radial variation in the Maxwellstress of magnetorotational turbulence

MRI and streaming instability can interact constructively

Convergence zones concentrate solids and allow the formationof 1000 km sized planet embryos by gravity

MRI good for planet formation even in its absence – Rossbyvortices excited at transition from dead to active regions



discs

AndersJohansen

Planetformation



Zonal flows

Analyticalmodel

Global models


Dead zones

Conclusions

Open questions

What sets the scale of zonal flows?

Do collision speeds of MRI turbulence lead to growth or todestruction of dust agglomorates?

Can we even assume MRI to be operative in planetforming regions?

Would turbulent simulations of dead zones lead to Rossbywave instability and vortices?

How do you grow enough pebbles to launch the streaminginstability?

How does coagulation and fragmentation proceed in agravitationally contracting clump?

What is the relative importance of streaming,Kelvin-Helmholtz and baroclinic instabilities in themid-plane layer?

...

planetesimal formation in turbulent protoplanetary discsiccg/pub/associated/fy2009/...planetesimal...

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