Dynamics of the young Solar system Kleomenis Tsiganis Dept. of Physics - A.U.Th. Collaborators: Alessandro Morbidelli (OCA) Hal Levison (SwRI) Rodney Gomes (ON-Brasil) Tsiganis et al. (2005), Nature 435, p. 459 Morbidelli et al. (2005), Nature 435, p. 462 Gomes et al. (2005), Nature 435, p. 466 Institut fur Astronomie - Universitats Wien, Vienna 27/4/2006

Overview Solar system architecture Planet migration Two unsolved problems: - orbits of the giant planets - Late Heavy Bombardment (LHB) A new migration model ResultsConclusions

Inner (terrestrial) planets: Mercury – Venus – Earth - Mars (1.5 AU) Main Asteroid Belt (2 – 4 AU) Gas giants: Jupiter (5 AU), Saturn (9.5 AU) Ice giants: Uranus (19 AU), Neptune (30 AU) Kuiper Belt (36 – 50 AU) + Pluto +... Solar system architecture

The Kuiper Belt - 3 Populations Classical (stable) Belt Resonant Objects, 3/4, 2/3, 1/2 with Neptune Scattered Disk Objects Orbital distribution cannot be explained by present planetary perturbations  planetary migration

Planet migration (late stages) Gravitational interaction between planets and the disc of planetesimals Fernandez and Ip (1984)

Oort Cloud (15%)

~1%

Ejected!

Standard migration model: - Semi-major axes of the planets - ~ Kuiper-belt structure - constrains the size of the initial disc (<30-35 AU, m~35-50 M Ε )

Problem #1: The final orbits of the planets are circular Problem #2: If everything ended <10 8 yr, what caused the …

 We need a huge source of small bodies, which stayed intact for ~600 My and some sort of instability, leading to the bombardment of the inner solar system Late Heavy Bombardment Petrological data (Apollo, etc.) show: Same age for 12 different impact sites Total projectile mass ~ 6x10 21 g Duration of ~ 50 My A brief but intense bombardment of the inner solar system, presumably by asteroids and comets ~ (3.9±0.1) Gyrs ago, i.e. ~ 600 My after the formation of the planets

A new migration model An initially extended SS (Neptune at ~20 AU) undergoes a smooth migration  A more compact system can become unstable due to resonances (and not close encounters) among the planets!

N-body simulations: Sun + 4 giant planets + Disc of planetesimals 43 simulations t~100 My: ( e, sinΙ ) ~ a J =5.45 AU, a S =a J 2 2/3 - Δa, Δa < 0.5 AU U and N initially with a 2 AU ) Disc: M E, edge at AU (1,000 – 5,000 bodies) 8 simulations for 8 simulations for t ~ 1 Gy with a S = AU

Evolution of the planetary system A slow migration phase with (e,sinI) < 0.01, followed by Jupiter and Saturn crossing the 1:2 resonance  eccentricities are increased  chaotic scattering of U,N and S (~2 My)  inclinations are increased  Rapid migration phase: 5-30 My for 90% Δa

Crossing the 1:2 resonance

The final planetary orbits Statistics: 14/43 simulations (~33%) failed (one of the planets left the system) 29/43  67% successful simulations: all 4 planets end up on stable orbits, very close to the observed ones Red (15/29)  U – N scatter Blue (14/29)  S-U-N scatter  Better match to real solar system data

Jupiter Trojans Trojans = asteroids that share Jupiter’s orbit but librate around the Lagrangian points, δλ ~ 60 o Trojans = asteroids that share Jupiter’s orbit but librate around the Lagrangian points, δλ ~ ± 60 o We assume a population of Trojans with the same age as the planet A simulation of 1.3 x 10 6 Trojans  all escape from the system when J and S cross the resonance !!! Is this a problem for our new migration model?

… No!  Chaotic capture in the 1:1 resonance The total mass of captured Trojans depends on migration speed For 10 My < T mig < 30 My  we trap M Tro This is the first model that explains the distribution of Trojans in the space of proper elements ( D, e, I )

The timing of the instability 1 My < Τ inst < 1 Gyr Depending on the density (or inner edge) of the disc LHB timing suggests an external disc of planetesimals in agreement with the short dynamical lifetimes of particles in the proto-solar nebula What was the initial distribution of planetesimals like ?

1 Gyr simulation of the young solar system

The Lunar Bombardment Two types of projectiles : asteroids / comets ~ 9x10 21 g comets ~ 8x10 21 g asteroids (crater records  6x10 21 g) The Earth is bombarded by ~1.8x10 22 g comets (water)  6% of the oceans  Compatible with D/H measurements !

Conclusions Our model assumes: An initially compact and cold planetary system with P S / P J < 2 and an external disc of planetesimals  3 distinct periods of evolution for the young solar system: 1. Slow migration on circular orbits 2. Violent destabilization 3. Calming (damping) phase Main observables reproduced: 1. The orbits of the four outer planets (a,e,i) 2. Time delay, duration and intensity of the LHB 3. The orbits and the total mass of Jupiter Trojans