The Formation of Giant PlanetsEGPs

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The Formation of Giant Planets/EGPs
(Adam Burrows)
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(No Transcript)
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Two Main Models

• Disk Instability (problematic)
• Core Accretion (favored)

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Disk Instability A. Boss major advocate
Quinn et al.
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Requires cool disks How do they cool?
Toomre condition?
Disk temperatures and cooling?
Quinn et al.
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Toomre Condition

• S0 gt cs?k/p G
• r S0 /2H
• H cs/?k
• 2pGr gt ?k2

• Collapse time lt Period!?
• Cooling by convection?
• Mach-1convection?
• Is disk gravitationally unstable?

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( T. Guillot)

• This shows the heavy element abundance in the
  four major planets and estimated uncertainties
• A major source of uncertainty is in the equations
  of state.

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Dust disk lifetimes
From Haisch, Lada Lada 2001, ApJ, 553, 153
Is there enough time for core-accretion mechanism?
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Core-Accretion Model A Tale of Two Instabilities

• Solid core grows first avoids Toomre dilemma
• Nucleates rapid accretion of gas after a critical
  core mass is achieved
• 3 phases of evolution
• 1) planetesimal accretion to depletion embryo
  creation
• 2) Gas and solid accretion (slowest phase?)
• 3) Unstable gas accretion

• Safranov 1969
• Perri Cameron 1974
• Mizuno 1980
• Hayashi et al. 1985
• Bodenheimer Pollack 1986
• Lissauer 1987
• Pollack et al. 1996

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Nucleated Instability/Core Accretion Model
Truncated by gap formation- Final Mass?
Phase 3 Rapid gas accretion
Phase 2 Embryo isolation
Phase 1 Embryo formation (runaway)
Pollack et al. 1996
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First Runaway Phase

• Safranov 1969
• dMp/dt p Rp2Fg S0 ?
• Fg gravitational focusing (vesc/vi)2
• Vi (5e2/8i2)1/2Vk
• (inclination, eccentricity, gravitational
  scattering)
• Hill Sphere Roche/Tidal
• RH a (Mp /M )1/3

• Areal mass density, S0 , of condensates
  (ice/rock) gt1 of total
• MMSN S0 3 g cm-3 at 5.2 AU (need supersolar
  Z?)
• Ice line
• dMp/dt Mp4/3 (early)
• Runaway Core Growth 1st Instability

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Cosmic (Solar) Abundances
Ice versus rock? Factor of ten?
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Phase 1 (cont.)

• Runway growth of core until depletion of heavies
  in feeding zone
• Isolation mass (Miso)
• Miso (a2 S0)3/2
• tph1 Miso1/3/S0?kFg
• Lissauer 1987
• tph1 increases with a

• Does migration maintain planetesimal accretion
  (Alibert et al. 2006) Is there an Isolation
  Mass?

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Phase 2 Longest Phase
What is its duration?
S0
Duration very sensitive to S0
Phase 2 Embryo isolation
Pollack et al. 1996
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Phase 2 Slower Gas and Heavy Element (Z)
Accretion

• Planetesimal accretion by gas drag in envelope
• Dynamic pressure breakup of solids
• Mixing of heavies?
• m and heating (Lp) distribution in envelope

• Luminosity due to planetesimal accretion
• Lp GMp/RpMp Mp2/3
• Duration ( tph2) depends on
• 1) Miso (strongly)
• 2) Opacity (weakly)
• 3) S0 (strongly, mostly through Miso )
• 4) Heating profile

.
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tph2 Total Formation Time

• tph2 GMcMenv/RLp if little or no
  penetration to core of planetesimals (core
  heating)
• Lp Mt4 (radiative zero solution) (Mt near
  (gt) Mc)
• tph2 GMc2/(RcLp) (near crossover mass, if
  luminosity is due to core accretion) Mc5/3/Lp
  Mc-3 (!), Mc Miso
• Distribution of heating by planetesimals (ds in
  Pollack et al. 1996)
• (Recall, tph2 depends on opacity, nebular
  conditions, S0)
• During this phase, the gas accretion rate
  dominates

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Phase 3 Runaway Gas Accretion - Critical Core
Mass Acheived
Phase 3 Runaway Accretion Instability
S0
Pollack et al. 1996
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Second Instability

• Crossover (total) mass,
• Critical core mass runaway gas accretion due to
  rapid contraction of planet and growth of outer
  boundary (min(RH, Ra))
• No hydrostatic solution at Mc Mcrit(Mt)
• Mizuno 1980
• Stevenson 1982

• Crossover/critical mass 2 times Miso
• Approximately when Menv Mc
• Bondi accretion (steeply increasing function of
  Mp)
• Runaway gas accretion
• Growth limited by nebula
• Final planet mass?

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Very approximate derivation of critical core mass
Luminosity from accretion onto core
Unstable No solution
M is total mass Mc is core mass Menv is
envelope mass
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Depend on k, m, and Mc
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Suggested Chronology of Last Phase Final Mass

• Usual gas inflow from nebula, which accelerates
  as mass increases.
• Gas fills the Roche lobe, but then contraction
  cooling lead to proto-Jupiter (700 K)
• Last stages of inflow at much lower fluxes (one
  MMSN 0.02MJ per 106yr)

dM/dt
10-2M?/yr
106 yr
time
Declining accretion as nebula gap develops onset
of satellite formation
Rapid gas accretion
a la Stevenson 2004
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Issues

• Convection (Perri Cameron 1974 Rafikov 2006
  Ikoma et al. 2001)
• Convective in inner nebula, radiative in outer
  nebula
• Entropy when its convective at large a, it is
  unstable by the Toomre condition?
• Core mass versus orbital distance small a, small
  Mc
• Gap opens when width equals scale height H
  subsequent accretion? Lin Papaloizou 1993
• Fragmentation of planetesimals (Inaba et al.
  2003) size distribution?
• Multi-dimensional accretion

• Nebular T, r, and S0 distributions
• Gas drag, planetesimal capture physics and
  dynamics
• Mean molecular weight and heating distributions
  in envelope
• Envelope Opacities
• Relative roles of ice and rock, ice line
• Multiple cores, Oligarchic interference and
  growth
• Accretion shock physics at runaway gas accretion
• Migration (Alibert et al. 2006)
• Neptune and Uranus (cores!)

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Disk Formation Gap Opening
Canup Ward 2002, from Lubow 1999
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Close-in EGPs and Cores??
High-Z Planet
(T. Guillot)
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Approximate Core Mass vs. Stellar Metallicity
Evidence for cores/heavy-element envelopes in
EGPs?
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Larger EGPs Models vs. Data
Higher Metallicity Atmospheres increase radii
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The Hydrogen Phase diagram

• Jupiter Saturn are in the fluid region,
  possibly crossing a PPT phase transition.
• Relevant conditions encountered in reverberation
  shock experiments
• Helium immiscibility suggested by observation
  theory but not well understood.

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Burrows et al. 2001
EOS of H2
Coulomb interactions vs. electron degeneracy
Wigner and Huntington (1935)