the dynamical structure of the solar system · mass structure of inner terrestrial planets (mars...

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.


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


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


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)


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)


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 !


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)


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)


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)


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)


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)


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


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


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


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)


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


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)


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


8.3 Grand Tack: Formation: Earth like planets

(red: planetesimals, green embryos)with outer material (in blue)


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)


8.3 Grand Tack: Summary


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 ?


the dynamical structure of the solar system · mass structure of inner terrestrial planets (mars...

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