Diapositive 1

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FORMATION OF PLANETESIMALS BY GRAVITATIONAL
INSTABILITIES IN TURBULENT STRUCTURES EVIDENCE
FROM ASTEROID BELT CONSTRAINTS

• Morbidelli (OCA, Nice)
• D. Nesvorny, W.F. Bottke, H.F. Levison (SWRI,
  Boulder)

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THE CLASSICAL VIEW ON PLANET FORMATION
1) Dust settles on the disks mid-plane and
coagulates in pebbles
2) A miracle occurs pebbles manage to form
km-size planetesimals, somehow avoiding the
so-called meter-size barrier
3) By pair-wise collisions, km-size planetesimals
grow into larger bodies
4) This triggers a runaway/oligarchic growth
process that leads to the formation of planetary
embryos and cores of giant planets
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However, recent work showed that planetesimals
might have formed big
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However, recent work showed that planetesimals
might have formed big
1. The Heidelberg model
Johansen et al., 2007
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However, recent work showed that planetesimals
might have formed big
1. The NASA-Ames model
Cuzzi et al., 2008
Cuzzi et al., 2001
D100km
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WORK PLAN

• We have developed and tested a classical
  coagulation/fragmentation code
• This code accounts for viscous stirring,
  dynamical friction, gas drag, collisional damping
  and (optionally) turbulent stirring
• We simulate the process of classical collisional
  growth starting from a population planetesimals
  whose initial SFD is a free input of the
  simulation, and check the resulting SFD against
  those of small body reservoirs
• Here we focus on the asteroid belt, for which we
  have many information and constraints on the
  primordial size distribution resulting from the
  accretion process (see next slides)

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ASTEROID BELT CONSTRAINTS
Primordial bump
Primordial slope
Bottke et al. (2005)
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ASTEROID BELT CONSTRAINTS
Bottke et al. (2005)
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ASTEROID BELT CONSTRAINTS
x1,000
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ASTEROID BELT CONSTRAINTS
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Result of classical collisional growth from small
(km-size) planetesimals
(1.5 Earth masses total)
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Starting from 100km planetesimals
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Case-A set-up
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Case-A set-up
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Case-A set-up
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Case-A set-up
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Starting from 100km planetesimals
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Case-B set-up
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Case-B set-up
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Case-B set-up
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Case-B set-up
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Starting from 100km planetesimals
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Effect of turbulent stirring

• Laughlin et al. (2004) from MHD simulations
  derived a recipe to model the stochastic surface
  density fluctuations of the disk
• Ogihara, Ida and Morbidelli (2006) used this
  recipe in N-body simulations and derived a
  formula for the turbulent stirring of
  eccentricities.

de/dt is mass independent de/dt ? f ?
strength of turbulence f density in MMSN
f1, ?10-3
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Starting from 100km planetesimals
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Starting from 100-500km planetesimals
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Starting from 100-500km planetesimals
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Starting from 100-1,000km planetesimals
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Starting from 100-1,000km planetesimals
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Starting from 100-1,000km planetesimals
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CONCLUSIONS

• Asteroids have to have been born big
• The initial planetesimals in the asteroid belt
  had to span the 100-1,000km size
  range
• This favors the Heidelberg model over the
  NASA-Ames model because the latter can only
  produce D100km objects
• The current SFD slope in the 100-1,000km range is
  essentially the primordial slope new challange
  for the Heidelberg model
• Classical collisional coagulation played only a
  minor role in asteroid belt accretion, maybe just
  that of forming Lunar-Martian mass embryos from a
  population of 4,000 Ceres-size bodies.
• If the planetesimals formed in a sea of small
  boulders, runaway growth may be terrifically
  efficient new hope to form the giant planets
  cores?

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IMPLICATION

• The original asteroid belt was deficient in small
  bodies (10km or less) by orders of magnitude with
  respect to the extrapolation of the SFD of the
  big guys
• Thus, despite it was massive, its collisional
  activity was small
• Consistent with one basin on Vesta, lack of shock
  ages of meteorites prior to the LHB, absence of
  pre-LHB families

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SPECULATION I
Why arent all asteroids melted? Need for a
delayed start of the gravitational instability
process
Scott, 2007
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SPECULATION II

• What about the same happened in the Kuiper belt?
• The observed knee in the SFD at D100km would be
  a primordial feature and not the consequence of
  collisional grinding, unlike what is usually
  accepted (from Kenyon Bromleys work)
• Then most of the initial mass would have been in
  large bodies 30 Earth masses implies 1,000
  Pluto-size bodies, consistent with the Nice
  model, formation of the Kuiper belt and Oort
  cloud etc.
• A new mechanism to form binary TNOs?

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Kuiper Belt Binaries

• here we focus on 100-km-class binaries with
  equal size components and wide separations
• 30 binary fraction among ilt5 deg classical
  KBOs (Noll et al. 2008 gt0.06 separations,
  lt2 mag contrast)
• Large angular momentum and stability of binaries
  in the current KB environment suggest early
  formation by capture
• Different capture models make different
  assumptions
• E.g., Goldreich et al. (2002) favored
  bimodal size distribution with ?/?1000.
  Dynamical friction from s assures minimal
  encounter speeds of 100-km bodies and facilitates
  capture

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Coagulation Code Applied to KB
Initially bimodalsize distributions/S1000, v2
cm/s
Initial conditions and setup from Goldreich et
al. (strong dynamical friction from small bodies
promotes runaway growth)
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Coagulation Code Applied to KB
Size distribution after 1 Myr
Reference slope with -5 index
Like Kenyon Luu (1999), we also obtain a very
shallow size distribution slope for Dgt100 km.
Inconsistent with observations.
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Different possibility Binaries formed during
gravitational collapse in eddies of turbulent
disk. Excess of angular momentum prevents
formation of a single object. Fragmentation and
formation of a binary with high angular momentum

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N-body simulations of gravitational collapse with
PKDGRAV (Richardson et al.) Quarter of Million
2.5-km bodies with 1 g/cm3 density distributed in
200,000-km wide region initial rotation mimics
turbulence-induced motion highly idealized no
gas
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• triple system with 120-km-radius
  gravitationally-bound bodies
• subsequent ejection of the outer body or
  collision of the inner pair leads to binary

105 km
104 km
size of objects scaled for visibility
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Formation of KB Binaries
Similar to formation of binary stars in
massive fragmenting disks (e.g., Alexander et
al. 2008) Can explain why components of KB
binaries have identical colors (Benecchi et al.,
38.11) because they would form from the same
local mixture of materials More work is needed
to test this idea and make testable predictions
(angular momentum budget, gas/solids interaction,
realistic initial conditions, etc.)
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• If you know a good student who is interested in
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• Thanks
• morby_at_oca.eu