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The dynamical structure of the SolarSystem
Wilhelm KleyInstitut fur Astronomie & Astrophysik
& Kepler Center for Astro and Particle Physics Tubingen
March 2015
8. Solar System: Organisation
Lecture overview:8.1 Introduction8.2 Nice model8.3 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 3
8.1 Introduction: Dynamical structure of Kuiper belt
a Classical KBO(Cubewanos)42-47 AUcold: i and e small
b scattered KBO(Scattered Disk)large e, perihel ≈ 35 AUshort-period comets
c PlutinosIn 3:2 Resonance withNeptune(a = 39.4AU), as Pluto⇒ Name
35% of TNOs arePlutinos
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 4
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 5
8.1 Introduction: Migration by scatteringExample: Neptune and the outer planetesimal disk (Gomes, 2003)
Planetesimals are scattered by Neptune into the inner Solar System (loseangular 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 Introduction8.2 Nice model8.3 Grand Tack
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 7
8.2 Nice model: Initial conditions
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 (verticaldashed line)⇒ increase e⇒ chaotic scatterings with N and U⇒ N and Uexchange 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 9
8.2 Nice model: Late Heavy Bombardment - timingLHB after 700 mio. yearsSample calculations:4 Planets on circular orbit:aJ = 5.45AU,aS = 8.18,aN = 11.5,aU = 14.2massless test particles (e = i = 0)a) Dynamical life timeTime until particle is inside ofHill-Radius of a planet⇒ planetesimal diskbegins 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
4 Planets:aJ = 5.45AU,aS = 8.18,aN = 11.5,aU = 14.2Planetesimal diskainn = 15.5 AU,m = 35mEarth
Animation:Initially circular orbitslater elliptic
Jupiter & Saturn cross 2:1 resonanceafter about 880 Mio. years:⇒ Neptun and Uranus swap orbits⇒ intense planetesimal scattering (LHB)
xy -animation (A. Morbidelli)
ae-animation (A. Morbidelli)
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 11
8.2 Nice model: Late Heavy Bombardment II
4 PlanetsaJ = 5.45,aS = 8.18,aN = 11.5,aU = 14.2Planetesimal diskainn = 15.5 AU,m = 35mEarth
Snapshots:a) 100 Myrb) 879 Myrdirectly before LHBc) 882 Myrjust after LHBd) 1082 Myr200 Myr after LHBca. 3% ofPlanetesimals left(Gomes et al., 2005)
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 12
8.2 Nice model: Late Heavy Bombardment III
a)Planet-Migration
Jupiter & Saturn cross2:1 Resonanceafter about 880 Mio. yrsNeptune and Uranusswap 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 ofsimulation basedon Nice model.Right: observeddistributionvertical lines:resonances withNeptunedotted: perihelion= 30AUabove dashedline: only high i orresonant bodiescan be stable overa 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 theSolar Systems
Important for Nice model:Jupiter Trojans
About 4000 in L4 (greeks)and 2050 in L5 (trojans).
Observations:large inclinations andlibration 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 cap-ture during Jupiters forma-tion (damping of e, i bygas friction & collisions)Observations:too large inclinations andlibration in length
Here:Planetesimals are capturedat Lagrange points L4/L5 byJupiter in chaotic evolutiondirectly after 2:1 MMR pas-sage⇒ agreement withobs. orbital parameter(Morbidelli et al., 2005)
• Simulation · Observation
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 Introduction8.2 Nice model8.3 Grand Tack
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 18
8.3 Grand Tack: Resonant migration
A mumericalsimulation:Two Planetsin uniform diskM1 = 1MJup,M2 = .3MJupa1 = 1aJup,a2 = 2aJupMdisk = 2MJupinside aJup
(Masset & Snell-grove 2001)
Jupiter & Saturn: Outer planet less massive than inner oneFast inward migration (type III) of outer planet: crosses 2:1 resonance(upper dashed line). Captured in 3:2 resonance, and subsequent outwardmigrationW. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 19
8.3 Grand Tack: Resonant migration
(F. Masset)
Principle ofOutward MigrationM1 = 1.0MJup,M2 = 0.3MJup
Planets are in joint gap:Inner (Jup): positive torqueOuter (Sat): negative torq.MJup > MSat→ Net torque > 0• Matter funneled fromoutside to inside• replenishes inner disk• Sustained outward migra-tion possible(Masset&Snellgrove, 2001)
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 out-ward migration ofJupiter and Saturn isa robust mechanismfor locally isothermaldisks
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 21
8.3 Grand Tack: Planet migration in Solar SystemJupiter 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 SystemMigration of Jup. & Sat. (red: S-Type) Zoom Out (in blue: C-Type Material)
global evolution Final state
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 23
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 nu-merical simulations.Solid: Inner Solar SystemHorizontal lines: Eccentric ex-cursions
(Walsh ea., Nature 2011)
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 25
8.3 Grand Tack: Summary
W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures, 2015 26
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