Interior structures of planets and their core masses

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Interior structures of planets and their core
masses

• Yasunori Hori
• PAP Group seminar on June, 12th

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Abstract

• Research motivation
• Schematic structures of our giants
• Basic equations equation of states
• H-He phase separation
• Relation between core masses and EOS
• Numerical calculations of interior structures
• EOS experiments in ILE

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1. Research motivation

• To know interior structures of our giants
• by using an accurate EOS for hydrogen

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2. Schematic picture of our giants
Jupiter
Saturn
Fig.1 Schematic picture of jovian and
Saturn interior Guillot 99, Science
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3-1. Basis equations equation of states

• Hydrostatic equilibrium
• Mass conservation
• Thermodynamic equation
• Energy conservation

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1. Hydrostatic equilibrium
Spherical symmetry Without rotation
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2. Mass conservation
spherical symmetry t constant
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3. Heat transport
ltRadiationgt
Energy density of photon
Energy flux
Mean free path
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3. Heat transport
ltConvectiongt
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4. Energy conservation
Neutrino radiation
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Basic equations
1. Hydrostatic equilibrium 3.
Thermodynamic equation 2. Mass conservation
4. Energy conservation
we need three more supplemental eqs. to solve
eqs.(1) (4).
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5. Three more supplemental eqs.
(e.g.) P-P chain, CNO cycle etc.
(cf.) If the structure changes with time,
we need to solve the additional eq. of chemical
composition.
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3-2. The case of giant planets
1. No nuclear reaction
2. Convection dominant in almost region
Basic equations EOS
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4-1. Observational properties
atmosphere
ltprotosolar nebulagt
X H mass mixing ratio Y He mass mixing ratio
(ref.) Guillot, 2005, ApJ
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4-2. H-He phase separation

• He abundance protosolar nebula gt Jupiter gt
  Saturn

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4-3. Evidence of the presence of a H-He phase
separation
depletion of neon
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5-1. EOS and compressibility of H

• Laser-shock compressed experiments
• ltFor fluid deuteriumgt
• 1. Collins et al., 1998 Nova laser beam _at_
  LLNL
• 2. Mostovych et al., 2000 Nike laser _at_ NRL
• 3. Boehly et al.,2004 OMEGA laser _at_ Rochester
• Other compression techniques
• (1) Two-stage gas gun experiment
• (2) Z-pinch Belov et al. 02, Boriskov et
  al.03,Knudson et al. 01,03,04

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5-2. Relation between EOS and core masses
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5-3. The range of possible indicated by
each hydrogen EOS
Fig.2 Jupiters case
Fig.3 Saturns case

• Saumon Guillot,2004, ApJ

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5-4 .What can jovian core mass have an effect on?

• Which formation scenario of our planets is right ?

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5-5.1. Kyoto model
1. Protosolar nebula appears dust (1µm
heavier elements) gas (H2,He)
2. Planetesimals grow up to 1km 10km
3. Cores arise from accumulation collision of
planetesimals
4. Giant proto-planets capture gas around their
cores
5. Disk dissipation
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5-5.2. Disk instability
1. Heavier protosolar nebula dust gas
2. Gravitational instability ? proto-planets
occur disk dissipation
3. proto-planets grow up
4. Giant proto-planets capture gas around their
cores
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6-1. My numerical calculation
ltAssumptiongt
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6-2. Polytrope model with N1.5, Psurface 1bar,
MJ RJ
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6-3. Polytropic solution with Mcore, MJ and RJ
Calculation scheme with respect to each ? and
Mcore
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6 4.1 . Results Mcore-?- ?boundary picture
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6-4 2. Top view of the previous drawing
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6 - 4 .3. Top view(2)
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6-5. Suggestion problems
Despite a simple model,
Results suggest low-compressibility should lead
to the prediction of a small Mcore.

• However, my numerical calculation remains to be
  corrected.

1. To deal with more realistic model including L
and T 2. To use an accurate EOS date based on
EOS experiments
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7. EOS experiment in ILE

• In June,2006,
• laser-shocked compression experiment of H2

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7-1 . Acknowledgement
ltLaboratory systemgt
Hugoniot relations

Energy conservation EOS
Streak transmission radiograph with X-ray
backlight (Collins et al., 98)
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Thank you for your attention !

• End