Prsentation PowerPoint

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COMETS AND THEIR RESERVOIRS CURRENT DYNAMICS
AND PRIMORDIAL EVOLUTION

• Morbidelli

O.C.A.- Nice

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Overview
Lecture I The Kuiper Belt and the Scattered
Disk Lecture II Dynamics of Short Period
Long Period comets Lecture III The Formation
of the Oort Cloud Lecture IVPrimordial
sculpting of the Kuiper Belt Lecture V The Late
Heavy Bombardment of the terrestrial planets
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Preliminaries orbital elements
a semi major axis eeccentricity ftrue
anomaly Eeccentric anomaly Mean anomaly ME-e
sin E n t with n(GM)1/2/a3/2 (orbital
frequency)
Sun
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Preliminaries orbital elements
iinclination ?longitude of the node ? argument
of the pericenter Longitude of pericenter ? ?
? Mean longitude ?M?
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1930 first object discovered Pluto 1992 second
object discovered (1992 QB1) 2005 1000
Trans-Neptunian Objects discovered
400 of which have orbits computed from
observation over at least 3 oppositions
OUTLINE PART I Orbital structure of the
Trans-Neptunian population PART II Main
dynamical properties of the TNOs in the framework
of the current planet config.
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PART I
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ORBITAL DISTRIBUTION OF MULTI-OPPOSITION BODIES
Sedna
Trujillo et al. (2001) The Scattered Disk and
the Kuiper belt constitute roughly equal
populations
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NOMENCLATURE
Trans Neptunian Population all objects with agt
30 AU TNOKBSDESD Centaurs all objects with
5.2ltalt30 AU
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ORBITAL DISTRIBUTION OF MULTI-OPPOSITION BODIES
Trujillo et al. (2001) The resonant population
constitutes 10 of the classical population
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(No Transcript)
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ORBITAL DISTRIBUTION OF MULTI-OPPOSITION BODIES
Trujillo et al. (2001) The resonant population
constitutes 10 of the classical population
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Evidence for an outer edge of the Kuiper belt at
50 AU
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Modeling by Trujillo and Brown (2001)
Targeted observations by Allen et al. (2001) rule
out with 95 CL the existence in the 50-60 AU
range of a belt of Dgt200km bodies comparable to
that in the 40-50 AU range.
II
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THE INCLINATION DISTRIBUTION
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Inclination bias
Orbital arc
Observed ecliptic band
?
l?/sin i
i
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Inclination bias
Orbital arc
Observed ecliptic band
?
l?/sin i
i
l/lsin i / sin i
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Evidence for a bimodal de-biased inclination
distribution Brown (2001)
COLD POPULATION ilt4o HOT POPULATION igt4o
The cold and hot populations are roughly equal in
number
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PHYSICAL DIFFERENCES BETWEEN THE HOT AND COLD
POPULATIONS OF THE CLASSICAL BELT
I) THE COLOR DISTRIBUTION
Trujillo and Brown (2002), Tegler and Romanishin
(2000), Doressoundiram et al. (2001)
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PHYSICAL DIFFERENCES BETWEEN THE HOT AND COLD
POPULATIONS OF THE CLASSICAL BELT
II) THE SIZE DISTRIBUTION
Levison and Stern (2001)
All of the biggest objects (Pluto, Quaoar, Ixion,
Varuna, Chaos) are in the HOT population
big
small
All bodies with Hlt5 have igt5o and have imed19.7o
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TNO magnitude (size) distribution
q exponent cumulative size distribution
q1.7
Turnover detected _at_ D50km ! (Yoshida et al.
Bernstein et al.)
q3.2
q5.7
Total mass estimate few 0.01 M?
Bernstein et al. (2004)
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THE MISSING MASS PROBLEM
10 -30 Earth masses are expected to exist in the
primordial 30-50 AU region because of

• Extrapolation of the surface density of solids
  incorporated in the giant planets

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• II. Necessity to grow the KBOs in a reasonable
  timescale
• (Stern, 1996 Stern and Colwell, 1999
  Kenyon and Luu 1998, 1999 Weidenshilling, 2003)

Stern and Colwell, 1999
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Summary of the striking properties of the TNO
population

• Coexistence of a KB SD roughly equal
  populations
• Existence of an ESD
• Low order MMRs with Neptune populated up to
  e0.35
• Classical belt quite excited in e and i
• Coexistence of Cold and Hot subpopulations in
  the classical belt
• Correlations between physical properties and
  orbital distribution
• Outer edge of the classical belt _at_ 50 AU
• Mass deficit

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PART II
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Goal discuss the dynamical behaviours of the
various TNO sub-classes undertand which
structures are due to the current dynamics and
which need to be explained in the framework of a
scenario for solar system formation and
primordial evolution
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The Duncan Levison Budd (1995) numerical survey
Stability map _at_ i0
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The Duncan Levison Budd (1995) numerical survey
Stability map _at_ i0
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The Duncan Levison Budd (1995) numerical survey
Stable orbits at large e in low order MMRs
Stability map _at_ i0
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Mean motion resonance collision protection
mechanism
Restoring Torque
23 MMR (Neptune corotating frame)
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Mean motion resonance collision protection
mechanism
?/2
Restoring Torque
23 MMR (Neptune corotating frame)
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Resonance width
Planet collision line
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MMR widths in the a,e plane
Resonance width
q30
Morbidelli et al., 1995
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Detailed dynamical structure of the 23 MMR
(a,e) plane _at_ i0
Nesvorny and Roig (2000)
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Detailed dynamical structure of the 23 MMR
(e,i) plane _at_ ??
Kozai resonance
Nesvorny and Roig (2000)
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Particularity of the 12 MMR (same for 13, 14,
15 )
Axis-symmetric islands
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Detailed dynamical structure of the 12 MMR
(a,e) plane _at_ i0
Nesvorny and Roig (2000)
Observations show 11 objects 2 low-e symmetric
librators, 7 in the leading island and 2 in the
trailing one (Chiang and Murray-Clay, 2005)
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Unstable but long lived zones?
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High-order, diffusive MMRs
Nesvorny and Roig (2001)
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A misterious hole in the distribution?
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It corresponds to this big unstable region,
caused by secular resonances
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SECULAR RESONANCES
Resonance ggn (perihelion affects e) ssn
(nodal affects i)
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SECULAR RESONANCES IN THE KUIPER BELT
Stability _at_ all i !
ss8
gg8
Stability map _at_ e0
Duncan Levison and Budd, 1995
Resonances from Knezevic et al. (1991)
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HOW A PERIHELION SECULAR RESONANCE WORKS

• Precessing eccentric orbits in a fixed frame.
  Black planets Grey small body
• The same in a frame rotating with the precession
  rate of the small body. If the precession rates
  of the planets are different, on average the
  planet mass distribution remains axisymmetric.
• The inner planet is in a 11 secular resonance
  with the small body, so that its orbit is also
  fixed in the rotating frame. The mass
  distribution is no longer axysimmetric. A torque
  is exerted on the small body

Torque change in angular momentum angular
momentum GMa(1-e2)1/2 Torque change e
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HOW A PERIHELION SECULAR RESONANCE WORKS

• Precessing eccentric orbits in a fixed frame.
  Black planets Grey small body
• The same in a frame rotating with the precession
  rate of the small body. If the precession rates
  of the planets are different, on average the
  planet mass distribution remains axisymmetric.
• The inner planet is in a 11 secular resonance
  with the small body, so that its orbit is also
  fixed in the rotating frame. The mass
  distribution is no longer axysimmetric. A torque
  is exerted on the small body

Torque change in angular momentum angular
momentum GMa(1-e2)1/2 Torque change e
?
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Dynamics of the gg8 resonance at 41 AU
Morbidelli et al., 1995
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Simulation of the evolution of a body in the gg8
resonance by Holman and Wisdom, 1993
Enters in SD
Secular resonance driven slow oscillations
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• Definition of Scattered Disk
• High-e orbits with agt50 AU (MPC)
• Region where the semi major axis undergoes
  macroscopic changes
• Region that can be visited by bodies starting on
  Neptune crossing orbit within 4.5Gy assuming the
  current planet architecture (mine)

The SD embraces the Neptune crossing region and
the region where MMRs deeply overlap.
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Example of evolution of two SD bodies
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Lifetime of SD bodies (from Duncan and Levison,
1997)
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• Origin of the SD
• Sustained by bodies escaping from the KB
  (diffusion, collisions)?
• Remnant of a 100x more populated primordial
  structure?

Populations equation for case I NKB fesc LSD
NSD LSD 100 My (Duncan, Levison 1997) NKB NSD
(Trujillo et al., 2001) fesc 1/100 My
(ABSURD!)
Answer II must be the correct one
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Scattered disk formation simulation
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Is the SD orbital distribution expected in this
scenario consistent with the observed one?
M. Browns method for compareing models to
observations Consider object k, discovered at a
latitude ? and magnitude R
Probability to be at latitude ? and magnitude R
(B)
P
Model probability distribution (M)
Orbital elements, H
Distribution MxB, NORMALIZED (mk)
Repeat the procedure for all objects k1,N and
sum m?k mk Compare m with the orbital
distribution of the k1,,N objects
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Observed distribution
Biased model m
1? uncertitutde on m
Morbidelli, Emelyanenko, Levison, 2004
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Evidence for an ESD
Mismatch !
Morbidelli, Emelyanenko, Levison, 2004
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Numerical integrations of ESD bodies
Emel'yanenko, V. V. Asher, D. J. Bailey, M. ,
2003
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Numerical integrations of ESD bodies
Emel'yanenko, V. V. Asher, D. J. Bailey, M. ,
2003
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Numerical integrations of ESD bodies
Emel'yanenko, V. V. Asher, D. J. Bailey, M. ,
2003
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SUMMARY OF INTRIGUING ASPECTS THAT NEED TO BE
EXPLAINED IN THE FRAMEWORK OF A PRIMORDIAL
EVOLUTION SCENARIO (4th lecture)

• Existence of the resonant Kuiper belt population
• Co-existence of HOT and COLD classical
  populations with different physical properties
• Outer edge of the classical belt
• Origin of the extended scattered disk (2000 CR105
  and Sedna)
• The mass deficit of the Kuiper Belt