Dynamics of the young Solar system

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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
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Overview

• Solar system architecture
• Planet migration
• Two unsolved problems
• - orbits of the giant planets
• - Late Heavy Bombardment (LHB)
• A new migration model
• Results
• Conclusions

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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 ...

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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

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• Planet migration (late stages)
• Gravitational interaction between planets and
  the disc of planetesimals

Fernandez and Ip (1984)
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Oort Cloud(15)
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Ejected!
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Standard migration model - Semi-major axes of
the planets - Kuiper-belt structure -
constrains the size of the initial disc
(lt30-35 AU , m35-50 M?)
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Problem 1 The final orbits of the planets are
circular Problem 2 If everything ended lt108
yr, what caused the
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Late Heavy Bombardment
A brief but intense bombardment of the inner
solar system, presumably by asteroids and comets
(3.90.1) 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

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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!
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• N-body simulations
• Sun 4 giant planets Disc of planetesimals
• 43 simulations t100 My
• ( e , sin? ) 0.001
• aJ5.45 AU , aSaJ22/3 - ?a , ?a lt
  0.5 AU
• U and N initially with a lt 17 AU ( ?a gt 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

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Evolution of the planetary system

• A slow migration phase with (e,sinI) lt 0.01,
  followed by
• Jupiter and Saturn crossing the 12 resonance ?
  eccentricities are increased ? chaotic scattering
  of U,N and S (2 My) ? inclinations are
  increased ?
• Rapid migration phase 5-30 My for 90 ?a

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Crossing the 12 resonance
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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

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Jupiter Trojans

• Trojans asteroids that share Jupiters orbit
  but librate around the Lagrangian points, d?
  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?

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No! ? Chaotic capture in the 11 resonance

• The total mass of captured Trojans depends on
  migration speed
• For 10 My lt Tmig lt 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 )
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The timing of the instability

• What was the initial
• distribution of
• planetesimals like ?

1 My lt ?inst lt 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
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1 Gyr simulation of the young solar system
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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 !

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Conclusions

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