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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
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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.
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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.
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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.
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)]
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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.
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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
Planetesimalformation inturbulent
traffic jams
AndersJohansen
Planetesimalformation
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)
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