The dynamical structure of the Solar System
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1 The dynamical structure of the Solar System Wilhelm Kley Institut für Astronomie & Astrophysik & Kepler Center for Astro and Particle Physics Tübingen March 2015
2 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,
3 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,
4 8.1 Introduction: Dynamical structure of Kuiper belt a Classical KBO (Cubewanos) 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,
5 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 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,
6 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,
7 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,
8 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 30-50M Earth - ( particles) - from ca. 18 up to 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,
9 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,
10 8.2 Nice model: Late Heavy Bombardment - timing LHB after 700 mio. years Sample calculations: 4 Planets on circular orbit: a J = 5.45AU, a S = 8.18, a N = 11.5, a U = 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 a U b) Time to cross 2:1 resonance of J-S Planetesimal disk density 1.9M Earth /(1AU ring) (e = 0, i < 0.5 o ) Variation of inner boundary at a inn 15 AU (Gomes et al., 2005) W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures,
11 8.2 Nice model: Late Heavy Bombardment I xy-animation (A. Morbidelli) 4 Planets: a J = 5.45AU, a S = 8.18, a N = 11.5, a U = 14.2 Planetesimal disk a inn = 15.5 AU, m = 35m Earth 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,
12 8.2 Nice model: Late Heavy Bombardment II 4 Planets a J = 5.45, a S = 8.18, a N = 11.5, a U = 14.2 Planetesimal disk a inn = 15.5 AU, m = 35m Earth 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,
13 8.2 Nice model: Late Heavy Bombardment III 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,
14 8.2 Nice model: Kuiper Belt structure Left: Result of simulation based on Nice model. Right: observed distribution vertical resonances Neptune dotted: = 30AU lines: with perihelion 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,
15 8.2 Nice model: Trojans - todays positions Some minor bodies in the Solar Systems Important for Nice model: Jupiter Trojans About 4000 in L 4 (greeks) and 2050 in L 5 (trojans). Observations: large inclinations and libration in length W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures,
16 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 Here: Planetesimals are captured at Lagrange points L 4 /L 5 by Jupiter in chaotic evolution directly after 2:1 MMR passage agreement with obs. orbital parameter (Morbidelli et al., 2005) Simulation Observation W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures,
17 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,
18 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,
19 8.3 Grand Tack: Resonant migration A mumerical simulation: Two Planets in uniform disk M 1 = 1M Jup, M 2 =.3M Jup a 1 = 1a Jup, a 2 = 2a Jup M disk = 2M Jup inside a Jup (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 migration Planet Formation, The Solar System, 45th Saas-Fee Lectures,
20 8.3 Grand Tack: Resonant migration Principle of Outward Migration M 1 = 1.0M Jup, M 2 = 0.3M Jup Planets are in joint gap: Inner (Jup): positive torque Outer (Sat): negative torq. M Jup > M Sat 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,
21 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,
22 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 M out /M in 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,
23 8.3 Grand Tack: The inner Solar System Migration 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,
24 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,
25 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,
26 8.3 Grand Tack: Summary W. Kley Planet Formation, The Solar System, 45th Saas-Fee Lectures,
27 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,
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