Heat Sources of the Giant Planets

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Heat Sourcesof the Giant Planets

• Sam Williams
• http//www.cs.berkeley.edu/samw/249/

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Outline

• Observations
• Models
• Structure
• Processes
• Radiation and Tidal
• Homogeneous cooling
• He / CNO Separation
• Extrasolar Giants
• Stratification
• Radiative Windows
• Meridional Transport / Seasonal Variation
• Conclusions

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Observations
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Temperature Observations
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Composition Observations

• After Galileo, Voyagers numbers were revised
• Saturn, is now X0.76, Y0.215
• Saturns is slightly more depleted in Helium than
  Jupiter
• Uranus, Neptune are about solar

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Internal Models
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Metallic Hydrogen

• Above 1Mbar, molecular hydrogen transitions to an
  atomic metallic state
• Follows a n1 polytrope PK?11/n
• Most of mass is concentrated in the center
• Vast majority of Jupiters mass is metallic
  hydrogen, but only 2/3 of Saturns
• Not pure hydrogen, but near solar mix.
• Depending on T,P and Y, helium might not be
  miscible

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Phase Diagram immiscibility
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Behavior of Ices

• Scandolo and Jeanloz (2003) suggested methane
  will disassociate at only 200kbar, forming
  hydrocarbons, and even diamond
• Simulations showed rapid changes (5ps)
• Experiments lasted only minutes
• Are species a function of depth?
• Water will also ionize at around 200kbar

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Structure
Jupiter
Saturn
Molecular Envelope
Molecular Envelope
Metallic Hydrogen Helium
Metallic Hydrogen Helium
Uranus Neptune
Uranus Neptune
Molecular Envelope
Molecular Envelope
Ionic Ocean Hydrocarbons ?
Ionic Ocean
disassociated ices?
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Heat Sources
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Heat Sources

• Tidal? No
• Radioactive Decay? Maybe for Uranus
• (chondritic 4x10-8 erg/g/s - 2-13 erg/cm2/s)
• Gravitational? Most likely
• if EGM2/R, HMcv(?Ti/?t)/R2 E/R2 then
• Saturn and Neptune are warmer, Uranus is colder.
  (ignored insolation)

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Cooling

• Hubbard (1977)
• Cooling at constant radius
• age ?(?/2.757)Te-2.75710.41(Teq/Te)4
• ? (22.4/R2?)?Cv?1.64r2dr
• ? 2.8e23 for Jupiter
• With other corrections provides an age 4-5Gyrs

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Scaling for Uranus/Neptune

• Hubbard (1978)
• Tried applying previous method to Uranus and
  Neptune by scaling ?.
• Assuming ?aice 17 ?aH doesnt work
• Guessed at ? to get relative behavior
• ?Neptune should be 20 larger
• Neptunes age should be 20 greater (4.3Gyrs)

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Uranus / Neptune

• But Marley McKay (1999) suggested that
  tropospheric temperature profile necessitates
  60-120 erg/cm2/s
• Hubbard (1981) compared rocky and icy versions of
  Neptune. Icy Neptune formed at 80K?
• Similar scaling totally fails for Saturn

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Homogeneous Cooling

• Fortney Hubbard (2003)
• Numerical Approach
• Saturn cools too quickly

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Heterogeneous Cooling

• Fortney Hubbard (2003)
• HDW/S immiscibility model only increases cooling
  time by 1Gyr
• No He separation in Pfaffenzeller
• Modified (crafted) Pfaffenzeller or CNO
  separation will allow Saturn cool in 4.5Gyrs
• Separation is slow compared to mixing, so
  atmosphere and interior remain well mixed
• Scandolo Jeanloz (2003) believed that
  disassociation of methane could allow for
  differentiation heating in Neptune and Uranus

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Saturns Evolution
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Extrasolar

• Fortney Hubbard (2004) provided analysis of
  Extrasolar gas giants at 5AU and 10AU from a 1L?
  star.
• Only included Helium Separation
• Rocky cores increase temperature by 5K for
  smaller giants.

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_at_5AU
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_at_10AU
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Stratification

• Based on formation theories and cooling models,
  only a fraction of the ice giants internal heat
  is being convected to the surface.
• Inhibited convection inside 0.6RUranus and
  0.5RNeptune
• Slight variation in mean molecular weight can
  inhibit convection
• Could hydrocarbons, diamond, etc have been
  created early in formation of ice giants?

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Radiative Windows

• Guillot (1994) showed only small radiative
  windows in Jupiter, Saturn, and Neptune
• Appears that Uranus is entirely dominated by
  radiation above 1400K
• There must be some convection to generate
  magnetic field?

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Meridional / Seasonal Variation

• Friedson and Ingersol (1987) showed seasonal
  variation in not only the polar heat flux on
  Uranus, but also global.
• Depending on depth at which absorption occurs,
  much of the heat transport is within the
  interior.

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Conclusions
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References

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