Diapositive 1

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Coupling the dynamical and collisional evolution
of the Kuiper Belt, the Scattered Disk the
Oort Cloud
S. Charnoz A. Morbidelli
Equipe AIM Université Paris 7 / CEA Saclay
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A big mistery of the Kuiper Belt The mass
deficit
A popular scenario to explain the mass deficit
is the Collisional Griding of the KB over the age
of the Solar System We explore here some
consequences of this scenario.
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Collisional Grinding Scenario
Start , dn/dr ?r-4.5
Initial Conditions Steep size distribution
Only a few Plutos
end
Consequences Strong erosion after 4 109 years.

From Kenyon Bromley 2004
Kenyon, Stern, Broomley, Weisman, Davis etc
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The  recipe  of the todays kuiper belt
1- The mass must be contained in small bodies
that are naturally easy to break (? steep
initial distrution (q -4.5) down to R10m)
2- KBO must have a very low material strength (
102 to 103 than usual estimates)
3- In situe formation of the KB Accretion
destruction occurs at the same place
4- The system is described as a statistical set
of particles at thermodynamical
equilibrium (Particle in a Box) gt Collisional
griding occurs over the age of the Solar
System gt Coarse description of the dynamics
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BUT Other scenarios reproduce the KB size
distribution Dynamical depletion of the belt
(see presentation by Morby) gt Need very low
collisonal evolution, initial SD todays SD
In short All models seem to reproduce the
todays size distribution of the Kuiper Belt !!
How to be more discriminent ?
We should broaden the problem and take into
account .
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THE 4th ZONE !!
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Broadening the problem the Oort and the
Scattered Disk
All 3 populations (KB, SD, OC) have their
origin approximately in the same region gt
Similar Starting Size-distribution
SD Objects KB
From Dones et al. 2004
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The origin of the 3 populations cannot be studied
separately
What are the consequences of the KB formation
scenario for the evolution Implication of
steep-size distributions for the evolution of
- Scattered Disk - Oort Cloud
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IDEA Test the collisional griding scenario for
bodies of - Kuiper Belt - Oort Cloud -
Scattered Disk
DIFFICULTY To couple properly both the
DYNAMICAL COLLISIONALevolution of bodies
 Particle in a box  method cannot achieve this
properly
ALGORITHM Use of a new hybrid approach (Charnoz
Morbidelli Icarus 2004) that was used to
compute evolution of bodies ejected by Jupiter
and Saturn.
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COUPLING DYNAMICAL with COLLISIONAL EVOLUTION A
Hybrid approach
Dynamical code Integration of 6000 particles
with J,S,U,N
Compute collision frequencies and velocities
for all pairs of particles, with steps 104
years.
Each of 6000 particles holds a full size
distribution evolved with a Fragmentation code
Fragmentation Craterisation
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• A REALISTIC DYNAMICAL
• EVOLUTION
• 6000 independant size
• distributions evolved conjointly
• same time
• At the end of the Simulation
• 700 particles in the KB

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Investigation of 2 scenarios
1 The initial size distribution is very
steep, consistent with what is needed In the
scenario a few plutos, R_break100m Consistent
with Collisional griding scenario
2 The initial size distribution is today,
but 100 times more massive Consistent with
Dynamical depletion
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CASE 1
Evolution of the Kuiper Belt
Initial conditions mass in small bodies ?
Collisional grinding senario QBenz Asphaug
1999
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Oort Cloud
20 times less massive than expected gt As
argued in Stern Weissman (2001)
Initial conditions mass in small bodies ?
Collisional grinding senario
BUT big observational uncertainties exist for
the Oort Cloud !!

• From Flux of Long period cometsFrancis et al.
  2005

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Scattered Disk
A too severe collisional evolution due to
strong dynamical steering of giant planets
From flux of Jupiter family comets
Initial conditions mass in small bodies ?
Collisional grinding senario
Only 107 bodies with Dgt1Km survive in the
Scattered Disk. 100 times less than Inferred from
the observation of Jupiter Family comets (Duncan
Levison, 1997 )
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CASE 2
The Oort Cloud
Much better mach With the estimated population Of
the Oort Cloud
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The Scattered Disk
Good match to observartions
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The Kuiper Belt
Good shape of the S.D. But to get the right
(low) mass only the scenario of
dynamical Implantation seem to work
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SUMMARY

• Using a new and hybrid approach to couple
  collisional and dynamical evolution, we show
  that

1- In every scenario, the most severly depleted
population is the SCATTERED DISK
2- The collisional griding of the KB has severe
problems - The Oort Cloud is too severly
depleted by a factor of 20 - The Scattered
Disk is too severely depleted by a factor of 100
3- Dynamical depletion, not collisional erosion,
should be responsible for the mass deficit of the
KB
?
? Charnoz Morbidelli 2007, ICARUS In press
Reprints charnoz_at_cea.fr
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SUGGESTIONS FOR NEW HORIZONS

• Observation of the surface moderately big
  objects (gt50 and lt 200 km) Kuiper Belt
• objects may help to determine the Cratering rate
  and the constrain the flux of impactors
• over the age of the Solar System
• Observation of small (lt10 km) Kuiper belt objects
  may help detrmine if they are
• Pristine or not (difficult !!) . scattered
  disk bodies are better here

Such data may be critical to better constrain the
formation scenario of the KB Region and may
help to decide which  story  is the right one
Collisional erosion ? Dynamical Depletion
? (A. Stern may have a preference for the first
!!)
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THE END
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The Oort Cloud population Divided into 2
parts The  visible  or Outer Oort Cloud
with agt 104 au The Inner Oort Cloud with alt104
au Total 4 1011 bodies with Dgt1km
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CLEAR OPPOSITION BETWEEN 2 MODELS OF KUIPER BELT
ORIGIN
Collisional Griding
Dynamical erosion
Mass in big bodies shallow S.D. A few 100
plutos
Mass in small bodies Steep S.D. A few plutos
N
?
How to get out of the dilemna ?
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Other Scenario mass in big bodies ? Dynamical
depletion
The size distribution almost does not evolve
under collisions Reasonable results for Oort
Cloud (4 time less) Scattered Disk (OK)
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The outer edge of the Solar System is occupied
by 3 populations of small bodies whose dynamical
collisional history is coupled

• The Kuiper Belt
• 0.01-0.1 Me
• The Scattered disk
• 109 with Dgt 1km

Gladman et al. 2005
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