the formation of the solar system re’em sari (caltech) yoram lithwick (ucb) peter goldreich...
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The Formation of The Solar System
Re’em Sari (Caltech)
Yoram Lithwick (UCB)
Peter Goldreich (Caltech & IAS)
Ben Collins (Caltech)
• When did oligarchy end?• What set the number of solar system planets?• How long did it take them to form?• Why are their orbits circular and coplanar?
• Why exoplanets occupy eccentric orbits?• Why Jupiter does not!?
• What happened after planet formation?• When and how did the Oort cloud form?• How long do debris disks live?
Questions
Physical Processes: velocities
• Setup: many small bodies, few big bodies
, u , v
viscous stirring
dynamical friction
accretion
viscous stirring
collisions =
~
= solve for v
Physical Processes: accretion
• Setup: many small bodies, few big bodies
, u , v
viscous stirring
accretion
collisions =
~
Very small bodies (s«R) very fast accretion rate
~
Gravitational Instability of Particle Disk
• From Q~1:
• Required size for setup of such velocities:
€
ustab ≈πGσ
Ω≈
10 cm/s
200 cm/s
⎧ ⎨ ⎩
a ~ 1AU
a ~ 30AU
€
sstab ≈x
a
σ
ρ≈
0.2 cm
0.5 cm
⎧ ⎨ ⎩
a ~ 1AU
a ~ 30AU
Gravitational Disk Instabilities
• In very cold disk:Largest unstable wavelength
Quick collapse
No angular momentum lost
Energy dissipates by collisions€
Rmax ~ α −2 σ
ρ≈
2km
100km
a ~ 1au
a ~ 30au
⎧ ⎨ ⎩
€
S* ~ α −3 / 2 σ
ρ≈
0.05 km
2 km
a ~ 1au
a ~ 30au
⎧ ⎨ ⎩
Early Times: Runaway Accretion• Without gravitational focusing
– Bodies tend to become of equal size
• With focusing
– Few large bodies become larger than their peers.
€
1
R
dR
dt∝
1
R
€
1
R
dR
dt∝
1
R
vesc
v
⎛
⎝ ⎜
⎞
⎠ ⎟2
∝ R+1
Most of the Bodies & mass
Exponentialcutoff
Runawaytail
m
m N(m)
Late Times: Oligarchic Growth
• Big bodies heat their own food larger u around bigger bodies bigger bodies grow more slowly
big bodies are: equal mass, uniformly spaced• Number of big bodies decreases as they grow
• Super Hill - win by competition• Sub Hill - large-large accretion• Thin disk - No sustained Oligarchy
( Kokubo
and Ida
1998)
“Classical” oligarchy:
More refined oligarchy - battles:
• Formation time of Uranus & Neptune fast enough (10 Myr) if small bodies are very small (< 1 m) and very cold (e<0.05)
• In cold (sub Hill) accretion, might expect:
• Observe:
Uranus & Neptune = End of Oligarchy?
30, 000 km
20 AU 30 AUfew Hill radii
20 AU 30 AU
50, 000 km
15 Hill radii
• Formation time of earth isfast (100 Myr) even with no focusing.
• In cold accretion, might expect:
• Observed:
Earth = End of Oligarchy?
4, 000 km
0.72 AU 1 AU~3 Hill radii=0.01AU
0.72 AU 1 AU
13, 000 km
~40 Hill radii
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~30 sub-marsobjects
• Isolation when ~ • we assume u~vH
Uranus & Neptune: Beyond Isolation
50, 000 km
20 AU 30 AUfew Hill radii
• After 10 million years, • Heating > Cooling runaway heating• Planets are ejected in time
Uranus & Neptune: Ejection
50, 000 km
20 AU 30 AUfew Hill radii
• Complete N-body simulations– e.g. Kokubo & Ida (1998)
– Can not realistically treat enough small bodies.
• Statistical treatments– Interactions between mass bins
• Hybrid Codes– e.g. Kenyon
– Still difficult to have very small bodies
– Gravitational instability
• N-body + simple accretion and dynamical friction– Preliminary simulations (Collins and Sari)
Numerical Approaches
• New n-body code• Accretion• Dynamical friction
Numerical n-body Simulation
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– Contrary to current statistical models
• Extended tail up to VH
• Most of energy around VH
• Most bodies at v<<VH
Velocity Distribution
€
∂f
∂t+
r ∇v a f( ) =
∂f
∂t col
€
2 f
τ+
v
τ
∂f
∂v= − p(
r w ) f (
r v −
r w ) − f (
r v )[ ]d2w∫
Encounters within RH
Beginning of Oligarchy
• Radius of circle = Hill sphere ~ 3000R
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• Radius of circle = Hill sphere ~ 3000R
Oligarchic Growth
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End of Oligarchy
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• Radius of circle = Hill sphere ~ 3000R
• At end of oligarchy ~ , v~VH
• Only a few remaining bodies (Uranus & Neptune)• No Chaos = no heating• Cooled by remaining small bodies (explains small
eccentricity)
Uranus & Neptune: regularization
50, 000 km
20 AU 30 AU
• Vesc<Vorbit ejection unlikely
• Collisions • Formation on Geometric timescale (100 Myr)• Giant impacts!
Venus & Earth: Beyond isolation
0.72 AU 1 AU
13, 000 km
~40 Hill radii
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• When did oligarchy end?– When !! GENERAL RESULT
• What set the number of solar system planets?– Stability: No wide range chaos.
• How long did it take them to form?– About 100 Myr at a~1AU.– Faster at a~30AU !– More time until ejection at a~30AU .
• Why are their orbits circular and coplanar?– Velocity damping by small bodies.
Answers
€
=
• Small bodies:
– Inner planetary region:
• Most will be accreted.
• MMSN is sufficient!
– Outer solar system: ~5 MMSN to form Neptune.
• Large ejected bodies:
– ~3 bodies >Mearth could be in Oort cloud.
– Origin in outer planetary system.
– Survival depends on their long term stability and solar environment.
• Giant impacts:
– Expected internal to 3AU.
– Our moon
More Implications
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