F. Nimmo ESS298 Fall 2004 Francis Nimmo ESS 298: OUTER SOLAR SYSTEM Io against Jupiter, Hubble image, July 1997

F. Nimmo ESS298 Fall 2004

Francis Nimmo

ESS 298: OUTER SOLAR SYSTEM

Io against Jupiter,Hubble image,July 1997


Giant Planets• Interiors

– Composition and phase diagrams

– Gravimetry / interior structure

– Heating and energy budget

– Magnetic fields

– Formation

• Rings• Atmospheres

– Structure

– Dynamics

• Extra-solar planets will be discussed in Week 10


Image not to scale!

Giant Planets


Basic Parameters

Data from Lodders and Fegley 1998. Surface temperature Ts and radius R are measured at 1 bar level. Magnetic moment is given in 10-4 Tesla x R3.

a (AU)

Porb

(yrs)

Prot

(hrs)

R

(km)

M

(1026 kg)

Obli-quity

Mag. moment

Ts

K

Jupiter 5.2 11.8 9.9 71492 19.0 3.1o 4.3 165

Saturn 9.6 29.4 10.6 60268 5.7 26.7o 0.21 134

Uranus 19.2 84.1 17.2R 24973 0.86 97.9o 0.23 76

Neptune 30.1 165 16.1 24764 1.02 29.6o 0.13 72


Compositions (1)• We’ll discuss in more detail later, but briefly:

– (Surface) compositions based mainly on spectroscopy

– Interior composition relies on a combination of models and inferences of density structure from observations

– We expect the basic starting materials to be similar to the composition of the original solar nebula

• Surface atmospheres dominated by H2 or He:

(Lodders and Fegley 1998)

Solar Jupiter Saturn Uranus Neptune

H283.3% 86.2% 96.3% 82.5% 80%

He 16.7% 13.6% 3.3% 15.2%

(2.3% CH4)

19%

(1% CH4)


Interior Structures again• Same approach as for Galilean satellites

• Potential V at a distance r for axisymmetric body is given by

)()(1 4

4

42

2

2 Pr

RJP

r

RJ

r

GMV

• So the coefficients J2, J4 etc. can be determined from spacecraft observations

• We can relate J2,J4 . . . to the internal structure of the planet


Interior Structure (cont’d)• Recall how J2 is defined:

C

A

R22 MR

ACJ

• What we would really like is C/MR2

• If we assume that the planet has no strength (hydrostatic), we can use theory to infer C from J2 directly

• For some of the Galilean satellites (which ones?) the hydrostatic assumption may not be OK

• Is the hydrostatic assumption likely to be OK for the giant planets?

• J4,J6 . . . give us additional information about the distribution of mass within the interior


Results• Densities are low enough that bulk of planets must be ices or

compressed gases, not silicates or iron (see later slide)

• Values of C/MR2 are significantly smaller than values for a uniform sphere (0.4) and the terrestrial planets

• So the giant planets must have most of their mass concentrated towards their centres (is this reasonable?)

Jupiter Saturn Uranus Neptune Earth

105 J2 1470 1633 352 354 108

106 J4 -584 -919 -32 -38 -.02

C/MR2 0.254 0.210 0.225 0.240 0.331

(g/cc) 1.33 0.69 1.32 1.64 5.52

2R3/GM .089 .155 .027 .026 .003


Pressure• Hydrostatic approximation• Mass-density relation• These two can be combined (how?) to get the

pressure at the centre of a uniform body Pc:

)()( rgrdrdP

2)( )(4 rrdrrdM

4

2

4 R

GMPc

• Jupiter Pc=7 Mbar, Saturn Pc=1.3 Mbar, U/N Pc=0.9 Mbar

• This expression is only approximate (why?) (estimated true central pressures are 70 Mbar, 42 Mbar, 7 Mbar)

• But it gives us a good idea of the orders of magnitude involved


Temperature (1)• If parcel of gas moves up/down fast enough that it doesn’t

exchange energy with surroundings, it is adiabatic

• In this case, the energy required to cause expansion comes from cooling (and possible release of latent heat); and vice versa

• For an ideal, adiabatic gas we have two key relationships:

RT

P cP Always true Adiabatic only

Here P is pressure, is density, R is gas constant (8.3 J mol-1 K-1), T is temperature, is the mass of one mole of the gas, is a constant (ratio of specific heats, ~ 3/2)

• We can also define the specific heat capacity of the gas at constant pressure Cp:

• Combining this equation with the hydrostatic assumption, we get:

dPdTC p

pdzdT

C

g


Temperature (2)• At 1 bar level on Jupiter, T=165 K, g=23 ms-2, Cp~3R,

=0.002kg (H2), so dT/dz = 1.4 K/km (adiabatic)

• We can use the expressions on the previous page to derive how e.g. the adiabatic temperature varies with pressure

11 10

1

1

/1

0 )1(

PP

C

cTT

p

This is an example of adiabatic temperature and density profiles for the upper portion of Jupiter, using the same values as above, keeping g constant and assuming =1.5

Note that density increases more rapidly than temperature – why?

Slope determined by

(Here T0,P0 are reference temp. and pressure, and c is constant defined on previous slide)


Hydrogen phase diagram

• Jupiter – interior mostly metallic hydrogen

Hydrogen undergoes a phase change at ~100 GPa to metallic hydrogen (conductive)

It is also theorized that He may be insoluble in metallic H. This has implications for Saturn.

Interior temperatures are adiabats

• Saturn – some metallic hydrogen

• Uranus/Neptune – molecular hydrogen only


Compressibility & Density• As mass increases, radius

also increases

• But beyond a certain mass, radius decreases as mass increases.

• This is because the increasing pressure compresses the deeper material enough that the overall density increases faster than the mass

• The observed masses and radii are consistent with a mixture of mainly H+He (J,S) or H/He+ice (U,N)

mass

radius

Con

stan

t den

sity


Summary• Jupiter - mainly metallic hydrogen. Low C/MR2 due

to self-compression. Rock-ice core ~10 ME.

• Saturn - mix of metallic and molecular hydrogen; helium may have migrated to centre due to insolubility. Mean density lower than Jupiter because of smaller self-compression effect.

• Uranus/Neptune – pressures too low to generate metallic hydrogen. Densities and C/MR2 require large rock-ice cores in the interior.


From Guillot, 2004


Magnetic Fields • Jupiter’s originally detected by radio emissions (electrons being

accelerated in strong magnetic field – bad for spacecraft!)

• Jupiter’s field is ~10o off the rotation axis (useful for detecting subsurface oceans)

• Saturn’s field is along the rotation axis

• Jupiter’s and Saturn’s fields are mainly dipolar

• Uranus and Neptune both have complicated fields which are not really dipolar; the dipolar component is a long way off-axis

Earth Jupiter Saturn Uranus Neptune

Spin period, hrs 24 9.9 10.7 17.2 16

Mean eq. field, Gauss 0.31 4.28 0.22 0.23 0.14

Dipole tilt +11.3o -9.6o ~0o -59o -47o

Distance to upstream magnetosphere “nose”, Rp

11 50-100 16-22 18 23-26


Magnetic fields


How are they generated?• Dynamos require convection in a conductive medium

• Jupiter/Saturn – metallic hydrogen (deep)

• Uranus/Neptune - near-surface convecting ices (?)• The near-surface convection explains why higher-order terms

are more obvious – how? (see Stanley and Bloxham, Nature 2004)


Energy budget observations• Incident solar radiation much less than that at Earth• So surface temperatures are lower• We can compare the amount of solar energy absorbed

with that emitted. It turns out that there is usually an excess. Why?

5.4

8.1

13.5

48

2.0

2.6

4.6

14

0.6

0.6

3.5

0.3

0.3

0.6

1.4

incidentreflected

After Hubbard, in New Solar System (1999)All units in W/m2

Jupiter Saturn Uranus Neptune


Sources of Energy • One major one is contraction – gravitational energy

converts to thermal energy. Helium sinking is another.• Gravitational energy of a uniform sphere is

• So the rate of energy release during contraction is

RGMEg /6.0 2 Where does this come from?

dt

dR

R

GM

dt

dEg

2

2

6.0

e.g.Jupiter is radiating 3.5x1017 W in excess of incident solar radiation.This implies it is contracting at a rate of 0.4 km / million years

• Another possibility is tidal dissipation in the interior. This turns out to be small.

• Radioactive decay is a minor contributor.


Puzzles• Why is Uranus’ heat budget so different?

– Perhaps due to compositional density differences inhibiting convection at levels deeper than ~0.6Rp (see Lissauer and

DePater). May explain different abundances in HCN,CO between Uranus and Neptune atmospheres.

– This story is also consistent with generation of magnetic fields in the near-surface region (see earlier slide)

• Why is Uranus tilted on its side?– Nobody really knows, but a possible explanation is an

oblique impact with a large planetesimal (c.f. Earth-Moon)

– This impact might even help to explain the compositional gradients which (possibly) explain Uranus’ heat budget


Rings• Composed of small (m-m) particles• Generally found inwards of large satellites. Why?

– Synchronous point (what happens to satellites inward of here?)– Roche limit (see below)– Gravitational focusing of impactors results in more impacts

closer to the planet

• Why do we care?– Good examples of orbital dynamics– Origin and evolution linked to satellites– Not volumetrically significant (Saturn’s rings collected together

would make a satellite ~100 km in radius)


Roche Limit• The satellite experiences a mean

gravitational acceleration of GMp/a2

• But the point closest to the planet experiences a bigger acceleration, because it’s closer by a distance Rs (i.e. tides)

a

RpRs

Mp

Ms

• The net acceleration of this point is

• If the (fluid) satellite is not to break apart, this acceleration has to be balanced by the gravitational attraction of the satellite itself:

322

2

)1(

11

a

RGM

a

GM sp

aR

p

s

3

3

32

22

a

R

M

M

a

RGM

R

GM s

p

ssp

s

s

• This expression is usually rewritten in terms of the densities of the two bodies, and has a numerical constant in it first determined by Roche:

s

p

3/1

456.2

s

p

pR

a


Ring locations (1)

Roche limits

Roche limits

Jupiter Saturn


Ring locations (2)

Roche limits

Roche limits

Uranus Neptune


Things to notice• Roche limit really does seem a good marker for ring edges• Why are some satellites found inwards of the Roche limit

and the synchronous point?• All the rings have complex structures (gaps)• Ring behaviour at least partly controlled by satellites:

Galileo image of Jupiter’s rings


Ring Particle Size• The rings are made of particles (Maxwell). How do

we estimate their size?– Eclipse cooling rate

– Radar reflectivity

– Forward vs. backscattered light

• The number density of the particles may be estimated by occultation data (see )

• Ring thickness sometimes controlled by satellites (see previous slide). Typically ~ 0.1 km

Starlight being occulted by rings;drop in intensity gives information on particle number density


Ring Composition• Vis/UV spectra indicate rings are predominantly

water ice (could be other ices e.g. methane, but not yet detected)

• Some rings show reddening, due to contamination (e.g. dust) or radiation effects

Cassini colour-coded UV image; blue indicates more water ice present. Note the sharp compositional variations


Ring Lifetimes• Small grains (micron-size)

have lifetimes of ~1 Myr due to drag from plasma and radiated energy

• So something must be continuously re-supplying ring material:– Impacts (on satellites) and

mutual collisions may generate some

– Volcanic activity may also contribute (Io, Enceladus?)

Hubble image of Saturn’s E-ring. Ringis densest and thinnest at Enceladus, and becomes more diffuse further away. This is circumstantial evidence for Enceladus being the source of the ring material. It is also evidence for Enceladus being active.

~100

,000

km

Main rings

Enceladus

E R

ing


Why the sharp edges?• Keplerian shear blurs the rings

– Particles closer in are going faster– Collisions will tend to smear particles out with time – this will destroy

sharp edges and compositional distinctions

faster slower

collision

• Shepherding satellites– Outer satellite is going slower than particles– Gravitational attraction subtracts energy from particles, so they move inwards; reverse true for inner sat.– So rings keep sharp edges– And gaps are cleared around satellites

Kep

leri

an s

hear

Ring particle

Satellite


Pandora and Prometheus shepherding Saturn’s F ring

Pan opening the Encke division in Saturn’s rings

Ring/Satellite Interactions


Sharp edges (cont’d)• Positions withing the rings which are in resonance with

moons tend to show gaps – why?• E.g. the Cassini division (outer edge of Saturn’s B ring) is at

a 2:1 resonance with Mimas• Edge of A ring is at a 7:6 resonance with Janus/Epimetheus• Resonances can also lead to waves

400km

Waves arising from 5:3 resonance with Mimas. The light and dark patterns are due to vertical oscillations in ring height (right-hand structure) and variations in particle density (left-hand structure)


End of Lecture

Thursday’s lecture will be given by Ashwin Vasavada (JPL)

Next week will be the start of the computer project


Atmospheric Composition

• Escape velocity ve= (2 g r)1/2 (where’s this from?)

• Mean molecular velocity vm= (2kT/m)1/2

• Boltzmann distribution – negligible numbers of atoms with velocities > 3 x vm

• Molecular hydrogen, 900 K, 3 x vm= 11.8 km/s

• Jupiter ve=60 km/s, Earth ve=11 km/s

• H has not escaped due to escape velocity (Jeans escape)


Atmospheric Structure (1)• Atmosphere is hydrostatic:• Assume ideal gas, no exchange of heat with the outside

(adiabatic) – work done during expansion as pressure decreases is provided by cooling. Latent heat?

• Specific heat capacity at constant pressure Cp:

• We can combine these two equations to get:

or equivalently

)()( zgzdzdP

dPdTC p Why?

pC

g

dz

dT

RT

gmP

dz

dP m

Here R is the gas constant, mm is the mass of one mole, and RT/gmm is the scale height of the atmosphere (~10 km) which tells you how rapidly pressure increases with depth


Atmospheric Structure (2)• Lower atmosphere (opaque) is dominantly heated from below

and will be conductive or convective (adiabatic)

• Upper atmosphere intercepts solar radiation and re-radiates it

• There will be a temperature minimum where radiative cooling is most efficient; in giant planets, it occurs at ~0.1 bar

• Condensation of species will occur mainly in lower atmosphereTemperature (schematic)

tropopause

troposphere

stratosphere

mesosphere

~0.1 bar

radiation

adiabat

CH4 (U,N only)

NH3

NH3+H2S

H2O

80 K

140 K

230 K

270 K

Theoretical cloud distribution

clouds



Observations• Surface temperatures

• Occultation

• IR spectra & doppler effects

• Galileo probe and SL9

• Clouds and helium a problem


Atmospheric dynamics• Coriolis effect – objects moving on a

rotating planet get deflected (e.g. cyclones)• Why? Angular momentum – as an object

moves further away from the pole, r increases, so to conserve angular momentum decreases (it moves backwards relative to the rotation rate)

• Coriolis acceleration = 2 sin()• How important is the Coriolis effect?

is latitude

v

L sin2 is a measure of its importance

e.g. Jupiter v~100 m/s, L~10,000km we get ~35 so important


Atmospheric dynamics (2)• Coriolis effect is important because the giant planets

rotate so fast• It is this effect which organizes the winds into zones• Diagram of wind bands and velocities


Documents

F. Nimmo ESS298 Fall 2004 Francis Nimmo ESS 298: OUTER SOLAR SYSTEM Io against Jupiter, Hubble image, July 1997