Transcript Orbital excitation of the Giant planets & its relation to the Late Heavy

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
Results
Conclusions
Solar system architecture
• 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 + ...
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 MΕ)
Problem #1: The final orbits of the planets are circular
Problem #2: If everything ended <108 yr, what caused the …
Late Heavy Bombardment
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
Petrological data (Apollo, etc.) show:
• Same age for 12 different impact sites
• Total projectile mass ~ 6x1021 g
• Duration of ~ 50 My
 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
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 ) ~ 0.001
aJ=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)
8 simulations for t ~ 1 Gy with aS= 8.1-8.3 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 ~ ± 60o
We assume a population of Trojans
with the same age as the planet
A simulation of 1.3 x 106 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 < 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
• What
was the initial
distribution of
planetesimals like ?
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
1 Gyr simulation of the young solar system
The 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 !
Conclusions
Our model assumes:
An initially compact and cold planetary
system with PS / PJ < 2 and an
external disc of planetesimals
 3 distinct periods of evolution for the
young solar system:
1.
2.
3.
Slow migration on circular orbits
Violent destabilization
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