Dynamics of the young Solar systemDynamics of the young Solar system

Kleomenis TsiganisKleomenis Tsiganis

Dept. of Physics - A.U.Th.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. 462Gomes et al. (2005), Nature 435, p. 466

Institut fur Astronomie - Universitats Wien, Vienna 27/4/2006

OverviewOverview

Solar system architectureSolar system architecture

Planet migrationPlanet migration

Two unsolved problemsTwo unsolved problems: :

- - orbits of the giant planetsorbits of the giant planets

- - Late Heavy BombardmentLate Heavy Bombardment (LHB)(LHB)

A new migration modelA new migration model

ResultsResults

ConclusionsConclusions

• 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 BeltThe 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 MΕ)

Problem #1: The final orbits of the planets are circular

Problem #2: If everything ended <108 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 ~ 6x1021 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 ) ~ 0.001aJ=5.45 AU , aS=aJ22/3 - Δa , Δa < 0.5 AU

U and N initially with a < 17 AU ( Δa > 2 AU )Disc: 30-50 ME , edge at 30-35 AU (1,000 – 5,000 bodies)

88 simulations for simulations for t ~ 1 Gy with aS= 8.1-8.3 AU

Evolution of the planetary systemEvolution 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 resonanceCrossing the 1:2 resonance

The final planetary orbitsThe final planetary orbitsStatistics:

• 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 TrojansJupiter Trojans

Trojans = asteroids that share Trojans = asteroids that share Jupiter’s orbit but librate around the Jupiter’s orbit but librate around the Lagrangian points, Lagrangian points, δλδλ ~~ ± 6060oo

We assume a population of Trojans We assume a population of Trojans with the same age as the planetwith the same age as the planet

A simulation of 1.3 x 10A simulation of 1.3 x 1066 Trojans Trojans all escape from the system when J all escape from the system when J and S cross the resonance !!!and S cross the resonance !!!

Is this a problem for our new Is this a problem for our new migration model?migration model?

… … No!No! Chaotic capture in the Chaotic capture in the 1 1::11 resonance resonance

• The total mass of captured Trojans depends on migration speed

• For 10 My < Tmig < 30 My we trap 0.3 - 2 MTro

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 < Τinst < 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 BombardmentThe Lunar Bombardment

Two types of projectiles: asteroids / comets

~ 9x1021 g comets ~ 8x1021 g asteroids

(crater records 6x1021 g)

The Earth is bombarded by ~1.8x1022 g comets (water)6% of the oceans

Compatible with D/H measurements !

ConclusionsConclusionsOur model assumesOur model assumes::

An initially compact and cold planetary An initially compact and cold planetary system with system with PPS S / P/ PJ J < 2< 2 and an and an external disc of planetesimalsexternal disc of planetesimals

3 3 distinct periods of evolution for the distinct periods of evolution for the young solar system:young solar system:

1.1. Slow migration on circular orbits Slow migration on circular orbits 2.2. Violent destabilizationViolent destabilization3.3. Calming (damping) phaseCalming (damping) phase

Main observables reproducedMain observables reproduced::1.1. The orbits of the four outer planets The orbits of the four outer planets

(a,e,i)(a,e,i)2.2. Time delay, duration and intensity Time delay, duration and intensity

of the LHB of the LHB 3.3. The orbits and the total mass of The orbits and the total mass of

Jupiter TrojansJupiter Trojans