lec13_28oct2009

lec13_28oct2009 - Jovian planet formation Core-accretion or...

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Ge/Ay133 Jovian planet formation. Core-accretion or gravitational instability?
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The radius-mass  relationship and M.o.I.  are used to infer the  presence of primordial  cores of 10-30 M earth . Properties of the Jovian Planets in the Solar System   ρ 2 for H 2 -He I/MR 2 =0.4 for a uniform sphere I/MR 2 =0.26 for P    ρ 2 11-13
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[preferred EOS] [envelope]   Caveat! Core mass estimate based on high pressure EOS: OK for Saturn, but…
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dubious EOS? Previously favored. Currently preferred EOS (Boriskov et al. 2005) [envelope]                 (need better high P,T measurements, very difficult)
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Theory of nucleated instability: Cores in Jovian planets are almost certainly primordial, and the fact that all  such objects in the solar system radiate more energy than they receive means  they started hot. This has led to the development of the core-accretion model  in which gas accretes onto cores built along the lines discussed in Lec. #12. Hill Sphere Photosphere Dense core Adiabatic  envelope Ambient  solar nebula ~Isothermal r H
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Theory of nucleated instability: How do we analyze this situation? The extent of the envelope is determined  via hydrostatic equilibrium. Key is the temperature profile, which is  established by the radiative transfer equations below.  L  is the luminosity,  K  is  the mass opacity coefficient. Hill Sphere Photosphere Dense core Adiabatic  envelope Ambient  solar nebula r H
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The minimum luminosity that needs to be radiated is that which balances any  ongoing accretion (equation at left). From this the mass/density properties of the  envelope can be estimated: Hill Sphere Photosphere Dense core Adiabatic  envelope r H Thus we need to solve for the  density structure to get the  envelope mass, which means  we need to know the  temperature profile.
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Solving the radiative transfer equations yields (for the envelope): Hill Sphere Photosphere Dense core Adiabatic  envelope r H Ideal gas  Clearly the value of  K  is  critical. Gas can only  contribute a small fraction of  the overall opacity, and so  the dust grain or ice content  in the envelope must be  known, or assumed. ..
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How massive does the core need to be for the atmosphere to collapse? Photosphere Dense core Adiabatic  envelope Stevenson 1982,  Pl. Sp. Sci.   30 , 755 f~ K  in cm 2 /g Setting dM c /dM t =0 gives ( α ∝ μ 4 29
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The gas/dust ratio in the envelope is also critical for TIME SCALES!                    (determines how rapidly the envelope can cool)
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lec13_28oct2009 - Jovian planet formation Core-accretion or...

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