Origin of the Solar System

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Origin of the Solar System
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Historical development

• Pre-Newtonian views (Descartes)
• Nebular hypothesis (Kant, Laplace)
• Collisional/tidal hypothesis (Jeans)
• Modern picture
• Solar nebula, accretion disk, turbulence,
  planetesimals, planet-disk interactions

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Elements of modern cosmogony (1)

• Theory
• - Collapse models for molecular clouds
• - Accretion disk models for the solar nebula
• - Grain growth and planetesimal formation models
• - Planetary accretion models including
  planet-disk interactions
• - Migration and gravitational scattering models

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Elements of modern cosmogony (2)

• Observations
• Molecular cloud structure chemistry
• Embedded IR sources
• Pre-Main Sequence stars (T Tauri stars) with and
  without disks
• Circumstellar, protoplanetary dust disks

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Elements of modern cosmogony (3)

• Detective work
• Meteorites and their origin
• Asteroids and comets as preplanetary remnants
• The Main Belt, trojans and transneptunian
  populations
• Planetary satellites

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Cloud collapse

• The Virial Theorem 2? ? 0
• for a system in equilibrium
• T kinetic energy
• ? gravitational potential energy
• Jeans Criterion gives minimum mass for a
  contracting cloud of given radius and temperature

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The Jeans criterion
A cloud with mass Mc, radius Rc and temperature
Tc is at the verge of instability a slight
compression or cooling will make it unstable
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Cloud Contraction

• A cloud may be set in contraction, e.g. by
  external pressure
• Return to virial equilibrium causes contraction
  and heating
• Radiative cooling causes further departure from
  virial equilibrium
• The cloud contracts along the stability line
  while radiating away excess heat

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Onset of instability

• Dust opacity ? no heating by starlight
• Molecule formation on grain surfaces
• UV darkness ? no molecule destruction
• Efficient cooling by molecule radiation
• Loss of kinetic energy ? cloud contracts
• Increased density ? ice condensation on grains
• Increased density ? increased rate of molecule
  formation

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Centrifugal equilibrium

• Conservation of angular momentum in a contracting
  cloud ? increase of angular velocity and
  rotational energy
• Rotational energy Urot increases faster than
  gravitational energy U decreases
• Contraction perpendicular to the spin axis stops
  when the centrifugal force equals the force of
  gravity at the equator of the cloud
• Rlim Rc (centrifugal radius)
• Continued collapse along the spin axis ?
  flattened disk with radius R Rc

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Rotation and Contraction

• Potential energy of a spherical, homogeneous
  cloud
• Moment of inertia
• Energy of rotation
• Centrifugal equilibrium condition

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Estimating a rough value of Rc

• Use L/M ?R2 from observations of molecular
  cloud cores
• R5000 AU and ?2?10-14 s-1 leads to Rc25 AU
• Observations of protoplanetary disks are
  consistent with this estimate

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Protoplanetary disks

• HH 30
  proplyds
• Herbig-Haro object (Orion
  nebula)
• General radii 100 AU
• HST pictures

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Accretion disk

• Differentially rotating disk - angular velocity
  decreases outward SHEAR
• The shear has a physical effect, if elements at
  different radial distances interact
• For a gaseous disk the interaction can be
  described as a VISCOSITY (suppressing relative
  motion)

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Consequences of shear and viscosity

• The energy of relative motion is dissipated ?
  HEATING
• Angular momentum is transported outward
• Local tendency for the disk to break up radially
• Material deprived of angular momentum collects at
  the center of the disk ACCRETION

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Magneto-rotational instability
Initiates turbulence and transports angular
momentum

• Suppose the gas disk is partially ionized and
  penetrated by a frozen-in magnetic field
• If a field line connects two gas parcels at
  somewhat different radial distance, their
  differential rotation will stretch the field
  line, and magnetic tension acts to keep them
  together ? instability against radial break-up

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Viscosity and energy budget

• Sources of viscosity
• - turbulent viscosity
• - magnetic viscosity

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Disk structure

• Viscous energy dissipation rate ? mass flux ?
  effective temperature of the disk Teff
• Grains yield a high opacity
• ? large temperature gradient midplane
  temperature Tc gtgt Teff
• convection maintains turbulence
• A dead zone may develop inside the disk,
  where neither thermal motion nor X-rays are able
  to ionize the gas enough for MRI

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Variable accretion rates (1)

• The dead zone would accumulate material from the
  outside and grow in mass
• There may be bursts of accretion, when such
  clumps fall onto the protostar
• This may explain the FU Orionis phenomenon

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Variable accretion rates (2)

• Observations of T Tauri stars (UV excess
  emission) shows that the accretion rate decreases
  with age
• After about 10 Myr the accretion seems to stop
  entirely (disk lifetime)

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Minimum mass solar nebula (1)
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Minimum mass solar nebula (2)

• The terrestrial planets are dominated by
  refractories
• The gas giants are dominated by gases
• The ice giants are dominated by volatiles gases
• Use the planetary compositions, and estimate
  correction factors to obtain the minimum nebular
  mass to form each planet
• These factors range from 3 (Jupiter) to 300
  (terrestrial planets)

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Minimum mass solar nebula (3)
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MMSN Density Structure
But this picture is inconsistent with current
understanding of the formation of planets!
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Disk masses

• Observing the thermal emission of the dust
  component ? masses 0.01 M? or lower (hence, lt
  MMSN mass)
• But due to uncertainties of dust opacities, the
  real masses could be higher
• With accretion rates 10-8 M?yr-1 for times 2
  Myr, one expects disk masses of at least 0.02 M?
• Much larger masses still could lead to
  gravitational instability

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The snow limit

• Snow limit (or ice limit) the radial distance
  where T corresponds to H2O sublimation
• - Outside the ice limit, the grains retain the
  full inventory of volatiles
• - Inside the ice limit, volatiles can only be
  adsorbed onto the grain surfaces