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Report from the Oort Cloud
Simulations of the Formation of the Comet Reservoir
Luke Dones
Hal Levison
Paul Weissman
Martin Duncan
KBO Workshop, 9/1/2003
Scenario for Oort Cloud Formation
Icy planetesimals formed in the region of the giant planets
Some formed the cores of Jupiter, Saturn, Uranus, and Neptune
Some stayed small and were scattered into big orbits
Most were ejected from the Solar System, but the orbits of some
were lifted from the planetary region by galactic tides and
passing stars and reached the Oort Cloud
This scenario neglects gas, interactions between planetesimals
due to gravity or collisions, …
Tides and stars perturb some comets back into orbits that
approach the Sun within a few AU, making them sublime
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Tremaine, in
Planets Around
Pulsars (1993)
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To determine …
Goals
 where Oort cloud [OC] comets originated
(Conventional wisdom: Uranus-Neptune region, but
compositions are diverse)
 the fraction of comets that end up in the Oort cloud 
the original mass in solids in the giant planets region
 the spatial distribution of comets in the OC
– Does a massive inner OC exist? 
If so, big comet showers are possible
 the temperatures reached by OC comets as their orbits
evolved
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200,000 AU
Outer Oort Cloud
Comets ejected
20,000
2000
50
Long period comets
5
Inner Oort cloud
Kuiper Belt, scattered disk
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Wiegert and Tremaine (1999)
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Fading Problem
Observed
• 109 new long-period comets (a > 10,000 AU)
• 178 returning long-period comets (34 AU < a < 10,000 AU) 
There are 1.6 returning comets for each new comet.
Predicted
57 returning comets for each new comet (gambler’s ruin model)
34 returning comets for each new comet (Paul Wiegert’s thesis)
 We’re still off by a factor of 20.
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Calculations

Direct integrations of 3000 “comets” for up to 4 billion years

Integrations include
– Sun
– Jupiter, Saturn, Uranus, Neptune with current masses and orbits
– Present-day Galactic tides (r and z components)
– Passing stars

Two sets of runs, both with a0 between 4 and 40 AU
– Cold: 2000 particles, root-mean-square e0 = 0.02, i0 = 0.01
– Warm: 1000 particles, root-mean-square e0 = 0.2, i0 = 0.1

Integrate orbit of each comet until it:
– is ejected from the Solar System
– impacts the Sun or a planet
– survives for 4 billion years
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Duncan,
Quinn,
Tremaine
(1987)
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Hale-Bopp
Everhart, Astron. J. 72, 1002 (1967)
Halley
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Mass of the Oort Cloud
 Outer Oort cloud: 0.5 x 1012 comets
with absolute magnitude H10 < 11
 Number in inner Oort cloud ~ Number in outer Oort cloud 
Total of 1012 comets in the entire Oort cloud
 Calibrate to Halley, which has H10 ~ 6 and known size, assume
density of 0.6 g cm-3 and Everhart’s size distribution 
mean mass of a comet ~ 4 x 1016 g = 7 x 10-12 Earth masses
 
Present-day mass of Oort cloud Mnow ~ 7 Earth
masses
 Fraction of comets in the Oort cloud at present: h = 0.046
 
Original mass in planetesimals between 4 and 40 AU:
Mdisk = Mnow/ h ~ 150 Earth masses
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Hahn & Malhotra (1999)
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Science 280, 1250 (1998)
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Cometary Impact Rates
 Impact rates on Earth and galilean satellites
due to active long-period comets are low
at present (Zahnle et al. 1998)
 Two uncertainties:
– Inner Oort cloud: Many or few comets?
– “Fading”
My my, hey hey,
Rock and roll is here to stay
It's better to burn out, than to fade away
My my, hey hey
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57P/du Toit-Neujmin-Delporte
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Levison et al., Science 296, 2212 (2002)
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Oort Cloud “To Do” List
1. Assume the Sun formed in a cluster
2. Let planets grow and migrate
3. Include other perturbers:



planet or brown dwarf in the Oort cloud
molecular clouds
residual gas in solar nebula
4. Model collisions
5. Include fading on the way out
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Icarus 150, 151–162 2001)
°
Adams and
Laughlin, Icarus
150, 151 (2001)
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Ida et al., Ap. J. 528, 351 (2000)
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First 5 Myr
First 50 Myr
Thommes et al., Astron. J. 123, 2862 (2002)
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Nature 409, 589 (2001)
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Conclusions
 The fraction of comets that reach the Oort cloud and
survive to the present is small, < 5%.
 Efficiency is low because most comets evolve inward and
are ejected from the Solar System by Jupiter or Saturn.
 Two-stage formation:
– Early by Jupiter and Saturn
– Late by Uranus and Neptune (peaks at 1 billion years)
 Typical comet evolves inward to ~10 AU (Saturn’s distance
from Sun) before being placed in the Oort cloud.
 Inner Oort cloud does not appear to be the Phantom
Menace
 More observations and modeling are needed to work out
the cosmogonic implications.
KBO Workshop, 9/1/2003