The Formation of The Solar System Re’em Sari (Caltech) Yoram Lithwick (UCB) Peter Goldreich...

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

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.



















~30 sub-marsobjects

• Isolation when ~ • we assume u~vH

Uranus & Neptune: Beyond Isolation

50, 000 km


• After 10 million years, • Heating > Cooling runaway heating• Planets are ejected in time

Uranus & Neptune: Ejection

50, 000 km


• 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

QuickTime™ and aPhoto - JPEG decompressor


QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.• Non thermal distribution

– 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

Simulation - Oligarchy Begins

Beginning of Oligarchy

• Radius of circle = Hill sphere ~ 3000R




Oligarchic Growth



End of Oligarchy




• At end of oligarchy ~ , v~VH

Simulation - Oligarchy Ends

• 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





• 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





The Formation of The Solar System Re’em Sari (Caltech) Yoram Lithwick (UCB) Peter Goldreich...

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