Astronomy6570

PhysicsofthePlanets

OuterPlanetInteriors

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?

Radio Occultation Temperature Profiles

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

Planetary insolation patterns

• small obliquity (J)

• large obliquity (U)

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)

Zonalwindprofiles(Voyagerdata)

Sanchez-Lavega (2005) Science 307, 1223.

System III (Voyager)SKR (Cassini)

Cassini ISS

HST (1994-2004)

Voyager ISS

Internalcirculationmodels:Saturn

Magnetic field comparison:

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.

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( )

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)

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

Adiabats

HYDROGEN

H-He

Cassini gravity model (Iess 2018)

Constraints on heavy element content in Jupiter & Saturn.

(Guillot)

Saturn

Jupiter

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)

-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.

GiantPlanetModels(Stephenson)

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.

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.