XVI Outer planet interiors 2018 - Cornell...
Transcript of XVI Outer planet interiors 2018 - Cornell...
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Astronomy6570
PhysicsofthePlanets
OuterPlanetInteriors
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GiantPlanets,CommonFeatures
Mass: 15– 317MRadius: 3.9– 11.2RDensity: 0.69– 1.67gcm-3
Rotationperiod: 9.9– 18hoursObliq.: 3° – 98°Vis.Surf.: clouds;zonallybanded(N?)
decreasingcontrast:Jè Sè UAtmos.Comp.: H2 +He(roughlysolar)
+CH4,NH3,H2O,…(enhanced)Atmos.Struct.: adiabaticbelow~1bar
warmstratospheresEnergyoutput: ~2*solarinput(exc.U)Atmos.Circ’n.: Zonalwindsof100– 400msMag.Field: 0.14– 4.2Gauss
tilt=0– 59°Satellites: inner,regularsats(e~i~0)
outer,irreg.satsRingsystem: increasingmass:Jè Nè Uè S
assoc.withsmallsatellitesephemeralstructures?
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Radio Occultation Temperature Profiles
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CondensationLevels
RadioSpectrum
T(°K)
P(bar)
Jupiter
λ
• Microwave emission originates from 0.5 – 10 bar levels
• NH3 absorption v. strong near 1 cm è minimum in TB.
TB(°K)
• Condensation levels correspond to predicted cloud layers
• Only uppermost clouds observed directly
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Planetary insolation patterns
• small obliquity (J)
• large obliquity (U)
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Emitted infrared flux and equivalent brightness temperatures versus latitude for the four outer planets. The radiation is emitted, on average, from the 0.3 to 0.5 bar pressure levels. The equator-to-pole temperature differences are small. The largest temperature gradients occur at the extrema of the zonal velocity profile. (Ingersoll, 1990)
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Zonalwindprofiles(Voyagerdata)
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Sanchez-Lavega (2005) Science 307, 1223.
System III (Voyager)SKR (Cassini)
Cassini ISS
HST (1994-2004)
Voyager ISS
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Internalcirculationmodels:Saturn
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Magnetic field comparison:
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ComparisonofplanetarymagneticfieldsEarth Jupitera Saturna Uranusa Neptunea
Radius,Rplanet (km) 6,373 71,398 60,330 25,559 24,764SpinPeriod(Hours) 24 9.9 10.7 17.2 16.1MagneticMoment/MEarth 1b 20,000 600 50 25SurfaceMagneticField(Gauss)
DipoleEquator,B0 0.31 4.2 0.22 0.23 0.14Minimum 0.24 3.2 0.18 0.08 0.1Maximum 0.68 14.3 0.84 0.96 0.9
DipoleTiltandSensec +11.3°
-9.6° -0.0° -59° -47°
Distance(A.U.) 1d 5.2 9.5 19 30SolarWindDensity(cm-3) 10 0.4 0.1 0.03 0.005RCF 8RE 30RJ 14RS 18RU 18RNSizeofMagnetosphere 11RE 50-100RJ 16- 22RS 18RU 23-26RNa Magnetic field characteristics from Acuna & Ness (1976), Connerney et al. (1982, 1987, 1991).b MEartth = 7.96 × 1025 Gauss cm3 = 7.906 × 1015 Tesla m3.c Note: Earth has a magnetic field of opposite polarity to those of the giant planets.d 1 A.U. = 1.5 × 108 km.
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PlanetaryInteriorModels(generalconsiderations)
Assume spherical symmetry (for simplicity only!)
1. Hydrostatic equilib.: dPdr = −ρg =
−Gm r( )ρr2
2. Mass conservation: dmdr = 4π r 2ρ
3. Equation of state: P = f ρ,T; composition( )
4. Heat transfer: k dT
dr = F! conduction
dTdr =
∂T∂P( )s dP
dr ! convection
%
&'
('
- in approximate treatments (4) may be dropped and (3) replaced by P = f ρ( )3 first-order D.E.'s ⇒ 3 boundary conditions
1. m 0( ) = 0
2. P R( ) = 0
3.T R( ) =Tsurf (solid surface)Teff (jovian planets)
%&'
('
Adjust model parameters (e.g., composition, Mcore, etc.) to fit observables:
M,R,J2 ~ CMR2( ),J4, etc.
Model ⇒ ρ r( ),P r( ), g r( ),T r( )
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Central pressures : dP
dr = −Gmρ
r 2
⇒ roughly Pc −P0
R ! 4π3
GM2
R5
∴ Pc !GM2
R4
Case I : a uniform-density planet:
m r( ) = 4π3 ρr 3 ⇒
g = 4π3 Gρr ⇒
dPdr = −
4π3( )Gρ2 r
∴ P r( ) = Pc −2π3 Gρ2 r 2
Boundary condition ⇒ Pc =2π3 Gρ2R2 = 3
8πGM2
R4
ρ (gcm-3)
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Case II : P = !ρ2 (n = 1 polytrope ~ Jupiter)
⇒Pc =2π 3
9 Gρ2R2 (see Polytrope notes)
Body ρ(gcm-3) R(km) CaseI CaseII(Mb=1011 Nm-2)
Moon 3.34 1738 0.047 0.155
Earth 5.52 6371 1.73 5.68
Uranus 1.32 25,600 1.60 5.25
Jupiter 1.33 71,400 12.6 41.4
Examples
Detailedmodels:Earth=3.5MbJupiter=70MbUranus=8Mb
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Adiabats
HYDROGEN
H-He
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Cassini gravity model (Iess 2018)
Constraints on heavy element content in Jupiter & Saturn.
(Guillot)
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Saturn
Jupiter
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2 3 4 5 6 7 8 9 10 11 12
DHgUHH
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
8nnoUm
DOizH
d Z
onDO H
DUm
onic
CoHff
iciH
ntV
(Jl)
8nifoUm UotDtion2bVHUvHd 9DOuH8ncHUtDinty
Saturn gravity harmonics (Cassini proximal orbits)
Iess, et al. (2108)
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-80 -60 -40 -20 0 20 40 60 80-200
0
200
400U
(m s
-1)
a
ObservedReconstructed
-80 -60 -40 -20 0 20 40 60 80Latitude
-200
0
200
400
U (m
s-1
)
b
ObservedDifferential RotationReconstructed
Observed and reconstructed zonal wind profiles for Saturn, based on Cassini gravity measurements. Dashed curve indicates a symmetric model with rotation on cylinders (Iess, et al. 2018).
Rotation on cylinders.
Winds decay with depth at ~9000 km.
Winds truncated at 60 deg latitude.
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GiantPlanetModels(Stephenson)
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HubbardandMacFarlane
“rock”
“ice”
gas
Density distribution in Uranus, calculated for a model with solar abundances of “ice”and “rock”. The temperature distribution corresponds to the present epoch.
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HubbardandMacFarlane
“rock”
“ice”
gas
Density distribution in Neptune, calculated for a model with solar abundances of “ice” and “rock”. The temperature distribution corresponds to the present epoch.