The dynamical structure of the Solar
System
Wilhelm Kley
Institut fur
¨ Astronomie & Astrophysik
& Kepler Center for Astro and Particle Physics Tubingen
¨
March 2015
8. Solar System:
Organisation
Lecture overview:
8.1 Introduction
8.2 Nice model
8.3 Grand Tack
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
2
8.1 Introduction:
The Late Heavy Bombardment
From cratering history and Apollo lunar rocks age measurements:
Period of rapid infall of material on the moon about 3.9 bil. yrs ago.
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
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8.1 Introduction:
Dynamical structure of Kuiper belt
a Classical KBO
(Cubewanos)
42-47 AU
cold: i and e small
b scattered KBO
(Scattered Disk)
large e, perihel ≈ 35 AU
short-period comets
c Plutinos
In 3:2 Resonance with
Neptune
(a = 39.4AU), as Pluto
⇒ Name
35% of TNOs are
Plutinos
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
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8.1 Introduction:
Some dynamical contraints
orbital elements of large planets in the Solar System:
- eccentricities of Jupiter, Saturn & Uranus reach 0.06, 0.09 and 0.08
- the inclinations are about 2◦
planet formation scenarios (core accretion model) predicts
- circular orbits and low inclination
- partially caused by dynamical friction with the planetesimals
Late Heavy Bombardment
- maximum of meteorite/asteroid impact on the moon
Dynamical structure in Kuiper-belt
- Resonances and high eccentricities
A solution of the problems is given by the Nice-model:
(Gomez, Levinson, Morbidelli & Tsiganis; Nature 2005a,b,c)
• Idea: Begin with compact configuration then evolve in time
- Jupiter to Uranus very close together (compact system)
- Migration due to interaction with the remaining planetesimals
- Dynamical interaction between planets
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
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8.1 Introduction:
Migration by scattering
Example: Neptune and the outer planetesimal disk (Gomes, 2003)
Planetesimals are scattered by Neptune into the inner Solar System (lose
angular momentum). Neptune gains ang.mom. (orbit expansion)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
6
8. Solar System:
Organisation
Lecture overview:
8.1 Introduction
8.2 Nice model
8.3 Grand Tack
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
7
Initial conditions
8.2 Nice model:
Start with compact system:
- large planets within: 5-17 AU
- on circular orbits
- S within 2:1 resonance with J
Outer planetesimal disk
- total mass 30-50MEarth
- (1000-5000 particles)
- from ca. 18 up to 30-35 AU
Integrate planet orbits
- mutual forces
- influence of planetesimals
- vary simulation parameter
(Tsiganis et al., 2005)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
8
8.2 Nice model:
Evolution of the large planets
(Tsiganis et al., 2005)
Saturn (S) migrates outward, J and S reach 2:1 Resonance (vertical
dashed line) ⇒ increase e ⇒ chaotic scatterings with N and U ⇒ N and U
exchange orbits. Displayed is a, q, Q (semi-major axis, periastron,
apoastron). Final configuration comparable to todays Solar System !
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
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Late Heavy Bombardment - timing
8.2 Nice model:
LHB after 700 mio. years
Sample calculations:
4 Planets on circular orbit:
aJ = 5.45AU, aS = 8.18,
aN = 11.5, aU = 14.2
massless test particles (e = i = 0)
a) Dynamical life time
Time until particle is inside of
Hill-Radius of a planet
⇒ planetesimal disk
begins 1-1.5AU outside of aU
b) Time to cross 2:1 resonance of J-S
⇒ Planetesimal disk density
≈ 1.9MEarth /(1AU ring) (e = 0, i < 0.5o )
Variation of inner boundary
⇒ at ainn ≈ 15 AU
(Gomes et al., 2005)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
10
8.2 Nice model:
Late Heavy Bombardment I
xy -animation (A. Morbidelli)
4 Planets:
aJ = 5.45AU, aS = 8.18,
aN = 11.5, aU = 14.2
Planetesimal disk
ainn = 15.5 AU,
m = 35mEarth
Animation:
Initially circular orbits
later elliptic
ae-animation (A. Morbidelli)
Jupiter & Saturn cross 2:1 resonance
after about 880 Mio. years:
⇒ Neptun and Uranus swap orbits
⇒ intense planetesimal scattering (LHB)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
11
Late Heavy Bombardment II
8.2 Nice model:
4 Planets
aJ = 5.45, aS = 8.18,
aN = 11.5, aU = 14.2
Planetesimal disk
ainn = 15.5 AU,
m = 35mEarth
Snapshots:
a) 100 Myr
b) 879 Myr
directly before LHB
c) 882 Myr
just after LHB
d) 1082 Myr
200 Myr after LHB
ca. 3% of
Planetesimals left
(Gomes et al., 2005)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
12
Late Heavy Bombardment III
8.2 Nice model:
a)
Planet-Migration
Jupiter & Saturn cross
2:1 Resonance
after about 880 Mio. yrs
Neptune and Uranus
swap distances
b)
Mass accretion by the moon
(LHB)
from comets and asteroids
(Gomes et al., 2005)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
13
8.2 Nice model:
Kuiper Belt structure
Left:
Result of
simulation based
on Nice model.
Right:
observed
distribution
vertical
lines:
resonances with
Neptune
dotted: perihelion
= 30AU
above
dashed
line: only high i or
resonant
bodies
can be stable over
a few Gyrs.
(Morbidelli ea. 2007)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
14
8.2 Nice model:
Trojans - todays positions
Some minor bodies in the
Solar Systems
Important for Nice model:
Jupiter Trojans
About 4000 in L4 (greeks)
and 2050 in L5 (trojans).
Observations:
large inclinations and
libration in length
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
15
8.2 Nice model:
Trojans
Properties of Trojans:
difficult to explain by capture during Jupiters formation (damping of e, i by
gas friction & collisions)
Observations:
too large inclinations and
libration in length
• Simulation
· Observation
Here:
Planetesimals are captured
at Lagrange points L4 /L5 by
Jupiter in chaotic evolution
directly after 2:1 MMR passage
⇒ agreement with
obs. orbital parameter
(Morbidelli et al., 2005)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
16
8.2 Nice model:
Success and extensions
The Nice-model provides explanations for:
• orbital elements of large planets in todays Solar System
• the LHB on the moon
• the dynamics of the trojans of Jupiter
But still further problems:
• initial compact configuration of large planets
• mass structure of inner terrestrial planets (Mars too big)
A possible solution is provided by the:
Grand-Tack-Modell (Walsh, Morbidelli, Raymond, O’Brian, Mandell; Nature 2011)
• Idea: Early migration of Jupiter and Saturn
- first inward, then outward
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
17
8. Solar System:
Organisation
Lecture overview:
8.1 Introduction
8.2 Nice model
8.3 Grand Tack
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
18
8.3 Grand Tack:
Resonant migration
A mumerical
simulation:
Two Planets
in uniform disk
M1 = 1MJup ,
M2 = .3MJup
a1 = 1aJup ,
a2 = 2aJup
Mdisk = 2MJup
inside aJup
(Masset & Snellgrove 2001)
Jupiter & Saturn: Outer planet less massive than inner one
Fast inward migration (type III) of outer planet: crosses 2:1 resonance
(upper dashed line). Captured in 3:2 resonance, and subsequent outward
W. Kley
Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015
migration
19
8.3 Grand Tack:
Resonant migration
Principle of
Outward Migration
M1 = 1.0MJup ,
M2 = 0.3MJup
Planets are in joint gap:
Inner (Jup): positive torque
Outer (Sat): negative torq.
MJup > MSat
→ Net torque > 0
• Matter funneled from
outside to inside
• replenishes inner disk
• Sustained outward migration possible
(Masset&Snellgrove, 2001)
(F. Masset)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
20
8.3 Grand Tack:
Planet migration in Solar System
Jupiter & Saturn in gas disk (Pierens & Raymond, 2011)
Inward and then outward migration of
Jupiter and Saturn is
a robust mechanism
for locally isothermal
disks
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
21
8.3 Grand Tack:
Planet migration in Solar System
Jupiter in Type-II migration (slow), Saturn in Type-I (faster), either path A or B
capture in 3:2 resonance (typical, if Mout /Min ≈ 1/3), then outward migration
(Masset & Snellgrove, 2001; Pierens & Nelson, 2008; Pierens & Raymond, 2011)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
22
8.3 Grand Tack:
The inner Solar System
Migration of Jup. & Sat. (red: S-Type) Zoom Out (in blue: C-Type Material)
global evolution
W. Kley
Planet Formation,
Final state
The Solar System, 45th Saas-Fee Lectures, 2015
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8.3 Grand Tack:
Formation: Earth like planets
(red: planetesimals, green embryos)
with outer material (in blue)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
24
8.3 Grand Tack:
Formation: Terrestrial planets
Mass distribution: Earth type planets
Open symbols: Results of numerical simulations.
Solid: Inner Solar System
Horizontal lines: Eccentric excursions
(Walsh ea., Nature 2011)
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
25
8.3 Grand Tack:
W. Kley
Planet Formation,
Summary
The Solar System, 45th Saas-Fee Lectures, 2015
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8.3 Grand Tack:
Grand-Tack: Successes
Quote from Walsh ea. (2011)
The Grand-Tack model provides explanations for:
• mass distribution of terrestrial planets
• spatial distribution of S-type and C-type asteroids
• compact configuration of the planets (start for Nice-model)
Criticism:
• How robust is outward migration for J-S in real disks ?
• very special choice of initial parameter ?
W. Kley
Planet Formation,
The Solar System, 45th Saas-Fee Lectures, 2015
27