planetesimal formation in turbulent traffic jams formation in turbulent traﬃc jams anders johansen...

Planetesimalformation inturbulent

traffic jams

AndersJohansen

Planetesimalformation

Densityenhancements

Self-gravity

Conclusions

Planetesimal formation in turbulent traffic jams

Anders Johansen (Max-Planck-Institut fur Astronomie)

“From Stars to Planets”Gainesville, April 2007

Collaborators: Hubert Klahr, Thomas Henning, Andrew Youdin, Jeff

Oishi, Mordecai-Mark Mac Low


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Planetesimal formation

1. Problems with forming planetesimals through collisions:

Macroscopic bodies do not stick(Chokshi, Tielens, & Hollenbach 1993; Benz 2000)

Radial drift of rocks and boulders in a few 10 rotation periodsimposes severe time-scale constraint(Weidenschilling 1977)

2. Problems with forming planetesimals by gravitational instability:

Need to increase solids-to-gas ratio by about factor 104

Turbulence prevents sedimentation of solids(Goldreich & Ward 1973, Weidenschilling 1980, Weidenschilling & Cuzzi 1993)

Planetesimal formation is a major unsolved problem of modernastrophysics.We propose that planetesimals form as regions of transientoverdensity of solids collapse under their own gravity.


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions








Planetesimal formation is a major unsolved problem of modernastrophysics.

We propose that planetesimals form as regions of transientoverdensity of solids collapse under their own gravity.


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions








Planetesimal formation is a major unsolved problem of modernastrophysics.We propose that planetesimals form as regions of transientoverdensity of solids collapse under their own gravity.


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Magnetorotational turbulence

Robust and reliable source of turbulence in protoplanetary discswith a sufficient degree of ionization.

Disc

Simulation box

Shearing box, no vertical gravity on the gas.

Code: The Pencil Code [MHD code, finite differences, 6thorder in space, 3rd order in time, Brandenburg (2003)]


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Concentration in transient gas high pressures

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/(csΩ0

−1)

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

y/(c

sΩ0−1

)

0.97 1.03Σ/Σ0

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/(csΩ0

−1)

−0.6

−0.4

−0.2

0.0

0.2

0.4

0.6

y/(c

sΩ0−1

)

0.0 5.0Σd/(ε0Σ0)

Strong correlation between high gas density and highparticle densitySolid particles are caught in transient gas high pressures ofmagnetorotational turbulenceGravoturbulent formation of planetesimals(Johansen, Klahr, & Henning 2006)


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Concentration in transient gas high pressures

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/(csΩ0

−1)

20

40

60

80

100

t/(2

πΩ 0−

1 )

0.98 1.02<Σ>y/Σ0

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6x/(csΩ0

−1)

20

40

60

80

100

t/(2

πΩ 0−

1 )

0.0 3.0<Σd>y/(ε0Σ0)

Strong correlation between high gas density and highparticle densitySolid particles are caught in transient gas high pressures ofmagnetorotational turbulenceGravoturbulent formation of planetesimals(Johansen, Klahr, & Henning 2006)


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

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.

(Klahr & Lin 2001, Haghighipour & Boss 2003; see also poster by Nader Haghighipour and talk by Ken Rice)


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Streaming instability (Youdin & Goodman 2005)

Bulk density of cm-sized pebbles in mid-plane of non-magneticdisc (Johansen, Henning, & Klahr 2006):

The “traffic jam” view of the streaming instability:

Regions with slightly more solids have less radial drift

Lower density material piles up from upstream, increasing thelocal solids-to-gas ratio

(see also Youdin & Johansen 2007, Johansen & Youdin 2007)


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

High pressure trapping vs. streaming

x

y

z

0 20 40 60 80 100t/Torb

100

101

102

103

max

(ρp/

ρ gas)

Withoutback−reaction

0 20 40 60 80 100t/Torb

100

101

102

103

max

(ρp/

ρ gas)

Withback−reaction

Σp(x,t)/Σg

−0.6 −0.2 0.2 0.6x/H

0

20

40

60

80

100

t/Tor

b

Σp(x,t)/Σg

−0.6 −0.2 0.2 0.6x/H

0

20

40

60

80

100

t/Tor

b

0.0 0.1

−0.6 −0.2 0.2 0.6z/H

10−3

10−2

10−1

100

ρ p(z

)/ρ g

as

−0.6 −0.2 0.2 0.6z/H

10−3

10−2

10−1

100

ρ p(z

)/ρ g

as

ΩKτf=0.2ΩKτf=0.5ΩKτf=1.0

a)

b)

c)

d)


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Self-gravity

New term in equation of motion of the particles:

dvi

dt= . . .−∇Φself

The gravitational potential of the particles Φself is found by solving thePoisson equation

∇2Φself = 4πGρpar

We have developed a fully parallel shearing sheet Poisson equationsolver. Technical details:

Solids are treated as particlesGravity potential is solved on the mesh using FFT methodTriangular Shaped Cloud assignment/interpolation scheme(Hockney & Eastwood 1981)Much faster than direct summation, but resolution limited bymesh

Collaboration with Jeff Oishi and Mordecai Mac Low at the American

Museum of Natural History in New York.


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

The kitchen sink simulation

Combine known effects (but never before studied together):

Magnetorotational turbulence (2563 grid points)

Sedimentation of boulders (8,000,000 superparticles)

Concentrations in transient gas high pressures

Streaming instability (traffic jams)

with some new physics:

Self-gravity of boulders

Several particle sizesRadii from 15 cm to 60 cm

Differential radial drift of different particle sizes potentially

disrupts gravitational collapse (Weidenschilling 1995)

Collisional coolingCollisions between boulders dynamically important forsolids-to-gas ratio & 10 . . . 100.

Collisions are highly inelastic ⇒ local rms speed of particles

damped on collisional time-scale


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Clump condensation

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>)

2 × MMSN

Mclump ∼ MCeres


traffic jams

AndersJohansen


Densityenhancements

Self-gravity

Conclusions

Conclusions

Turbulent concentrationsand streaming instabilityinteract constructively andproduce overdensities ofseveral 100 in the mid-planelayerGravitationally boundclumps condense out even indiscs comparable tominimum mass solar nebula.Differential radial drift ofdifferent particle sizes doesnot disrupt the collapse(Weidenschilling 1995).Clumps have masses similarto dwarf planets andcontinue to accrete.

−10.0 −5.0 0.0 5.0t/Torb

100

101

102

103

104

max

(ρp/

ρ g)

Self−gravitySedimentation

MHill /MCeres −−−> t

ΩKτf = 0.250.500.751.00

0.8

0.4

0.8

1.2

2.0

2.3

3.2

Growth from boulders toplanetesimals does not relyon sticking efficiency.Collapse happens muchfaster than the radial drifttime-scale.

Johansen, Oishi, Mac Low, Klahr, Henning, & Youdin (submitted)

Image:

NA

SA,ESA,J.

Par

ker

(SRI)

planetesimal formation in turbulent traffic jams formation in turbulent traﬃc jams anders johansen...

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