ESS 298: OUTER SOLAR SYSTEM

Io against Jupiter, Hubble image, July 1997 F. Nimmo ES290Q Winter 2006

Francis Nimmo

Giant Planets

• Interiors – Composition and phase diagrams – Gravimetry / interior structure – Heating and energy budget – Magnetic fields – Formation • Rings • Atmospheric dynamics – not covered • Extra-solar planets will be discussed in Week 10 F. Nimmo ES290Q Winter 2006

F. Nimmo ES290Q Winter 2006

Giant Planets

Image not to scale!

Basic Parameters

Jupiter

a

(AU) 5.2

P orb

(yrs) 11.8

P rot

(hrs) 9.9

R

(km) 71492

M

(10 26 kg) 19.0

Obli quity 3.1

o Mag. moment 4.3

T s

K 165 Saturn Uranus Neptune 9.6

19.2

30.1

29.4

84.1

165 10.6

17.2R

16.1

60268 24973 24764 5.7

0.86

1.02

26.7

o 0.21

97.9

o 0.23

29.6

o 0.13

134 76 72 Data from Lodders and Fegley 1998. Surface temperature

T s

at 1 bar level. Magnetic moment is given in 10 -4 Tesla x and radius

R

3 .

R

are measured F. Nimmo ES290Q Winter 2006

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 H 2 or He: Solar Jupiter Saturn Uranus Neptune H 2 He 83.3% 86.2% 96.3% 82.5% 16.7% 13.6% 3.3% F. Nimmo ES290Q Winter 2006 80% 15.2% (2.3% CH 4 ) 19% (1% CH 4 ) (Lodders and Fegley 1998)

Interior Structures again

• Same approach as for Galilean satellites • Potential

V

at a distance

r

for axisymmetric body is given by

V

 

GM r

1 

J

2

R r

2

P

2 (  ) 

J

4

R r

4

P

4 (  )    • So the coefficients

J 2 , J 4

observations etc. can be determined from spacecraft • We can relate

J 2 ,J 4

. . . to the internal structure of the planet F. Nimmo ES290Q Winter 2006

Interior Structure (cont’d)

• Recall how

J 2

is defined:

J

2 

C



MR

2

A

C

R

• What we would really like is

C/MR 2

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

C

from

J 2

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?

•

J 4 ,J 6

. . . give us additional information about the distribution of mass within the interior F. Nimmo ES290Q Winter 2006

A

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/MR 2

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 10 5

J 2

10 6

J 4 C/MR 2

r (g/cc) w

2 R 3 /GM

1470 -584 0.254

1.33

.089

1633 -919 0.210

0.69

.155

352 -32 0.225

1.32

.027

Neptune Earth 354 108 -38 0.240

1.64

.026

-.02

0.331

5.52

.003

F. Nimmo ES290Q Winter 2006

Pressure

• Hydrostatic approximation

dP

 

dr

• Mass-density relation

dM

(

r

)  4 r

dr

• These two can be combined (how?) ( r

r

(

r

)

r

) 2

g

(

r

) to get the pressure at the centre of a uniform body

P c

: 2

P c

 3

GM

4 8 

R

• Jupiter

P c

=7 Mbar, Saturn

P c

=1.3 Mbar, U/N

P c

=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 F. Nimmo ES290Q Winter 2006

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: Always true

P

 r

RT

 Here

P

is pressure, r is density,

R

the mass of one mole of the gas, 

P



c

r  Adiabatic only is gas constant (8.3 J mol -1 K -1 ),

T

is temperature,  is a constant (ratio of specific heats, ~ 3/2) is • We can also define the specific heat capacity of the gas at constant pressure

C p :

F. Nimmo ES290Q Winter 2006 r

C dT dz p dT

 

C



g p



dP

Temperature (2)

• At 1 bar level on Jupiter,

T

=165 K,

g

=23 ms -2 ,

C p

~3

R,



=

0.002kg (H 2 ), 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

T



T

0  ( 1

c

 1 / 1   ) 

C p



P

1   1 

P

0 1  1   (Here

T 0 ,P 0

are reference temp. and pressure, and

c

is constant defined on previous slide) 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  F. Nimmo ES290Q Winter 2006

Hydrogen phase diagram

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 • Jupiter – interior mostly metallic hydrogen • Saturn – some metallic hydrogen • Uranus/Neptune – molecular hydrogen only F. Nimmo ES290Q Winter 2006

radius

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 F. Nimmo ES290Q Winter 2006

Summary

• Jupiter - mainly metallic hydrogen. Low

C/MR 2

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

M E

.

• 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/MR 2

require large rock-ice cores in the interior.

F. Nimmo ES290Q Winter 2006

From Guillot, 2004 F. Nimmo ES290Q Winter 2006

Magnetic Fields

• Jupiter’s originally detected by radio emissions (electrons being accelerated in strong magnetic field – bad for spacecraft!) • Jupiter’s field is ~10 o 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 Spin period, hrs Mean eq. field, Gauss Dipole tilt Distance to upstream magnetosphere “nose”,

R p

F. Nimmo ES290Q Winter 2006

Earth

24 0.31

+11.3

o 11

Jupiter

9.9

4.28

-9.6

o 50-100

Saturn

10.7

0.22

~0 o 16-22

Uranus Neptune

17.2

16 0.23

-59 o 18 0.14

-47 o 23-26

F. Nimmo ES290Q Winter 2006

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) F. Nimmo ES290Q Winter 2006

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?

All units in W/m 2

48

reflected

14 3.5

After Hubbard, in

New Solar System

1.4

(1999) incident

13.5

4.6

0.6

0.6

8.1

2.6

0.6

0.3

5.4

Jupiter F. Nimmo ES290Q Winter 2006

2.0

Saturn Uranus

0.3

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

E g



0 .

6

GM

2

/

R

Where does this come from?

• So the rate of energy release during contraction is

dE dt g

 

0 .

6

GM

2

R

2

dR dt

e.g.Jupiter is radiating 3.5x10

17 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.

F. Nimmo ES290Q Winter 2006

Puzzles

• Why is Uranus’ heat budget so different? – Perhaps due to compositional density differences inhibiting convection at levels deeper than ~0.6

R p

(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 F. Nimmo ES290Q Winter 2006

Atmospheric Structure (1)

• Atmosphere is hydrostatic: • Gas law gives us: r

RT P

 

dP dz

  r (

z

)

g

(

z

) • Combining these two (and neglecting latent heat):

dP P g



dz

 

RT

Here

R RT/g

 is the gas constant, is the scale height  is the mass of one mole, and of the (isothermal) atmosphere (~10 km) which tells you how rapidly pressure increases with depth F. Nimmo ES290Q Winter 2006

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 atmosphere radiation mesosphere Temperature (schematic) Theoretical cloud distribution 80 K CH 4 ( U,N only ) stratosphere 140 K tropopause ~0.1 bar NH 3 clouds 230 K NH 3 +H 2 S troposphere adiabat 270 K H 2 O F. Nimmo ES290Q Winter 2006

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) F. Nimmo ES290Q Winter 2006

Roche Limit

• The satellite experiences a mean gravitational acceleration of

GM p /a 2

• But the point closest to the planet

M s

r

s

experiences a bigger acceleration, because it’s closer by a distance

R s

(i.e. tides) • The

net

acceleration of this point is • If the (fluid) satellite is not to

GM a

2

p

   1 

R s

( 1  1

R s a

) 2    

a

2

GM p R s a

3

M p

break apart, this acceleration has to be balanced by the gravitational attraction of the satellite itself:

GM s R s

2  2

GM p R s a

3 

M s M p

 2

R s

3

a

3 r

p R p

• 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: F. Nimmo ES290Q Winter 2006

a R p

 2 .

456   r r

s p

  1 / 3

Jupiter

Ring locations (1)

Saturn Roche limits F. Nimmo ES290Q Winter 2006 Roche limits

Roche limits F. Nimmo ES290Q Winter 2006

Ring locations (2)

Uranus Neptune Roche limits

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 F. Nimmo ES290Q Winter 2006

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 Starlight being occulted by rings; drop in intensity gives information on particle number density • 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 F. Nimmo ES290Q Winter 2006

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 F. Nimmo ES290Q Winter 2006

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) Main rings Enceladus Hubble image of Saturn’s E-ring. Ring is 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.

F. Nimmo ES290Q Winter 2006

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 Satellite Ring particle collision faster slower • 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 F. Nimmo ES290Q Winter 2006

Ring/Satellite Interactions

Pan opening the Encke division in Saturn’s rings F. Nimmo ES290Q Winter 2006 Pandora and Prometheus shepherding Saturn’s F ring

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 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) F. Nimmo ES290Q Winter 2006

F. Nimmo ES290Q Winter 2006

End of Lecture

Atmospheric Composition

• Escape velocity

v e

=

(2 g r) 1/2

(where’s this from?) • Mean molecular velocity

v m

=

(2kT/m) 1/2

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

v m

• Molecular hydrogen, 900 K, 3 x

v m

= 11.8 km/s • Jupiter

v e

=60 km/s, Earth

v e

=11 km/s • H has not escaped due to escape velocity (Jeans escape) F. Nimmo ES290Q Winter 2006

F. Nimmo ES290Q Winter 2006

Observations • Surface temperatures • Occultation • IR spectra & doppler effects • Galileo probe and SL9 • Clouds and helium a problem

F. Nimmo ES290Q Winter 2006

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 w decreases (it moves backwards relative to the rotation rate) • Coriolis acceleration =

2

w

sin(



)

 is latitude • How important is the Coriolis effect?

2

L

w sin  is a measure of its importance

v

e.g. Jupiter v~100 m/s, L~10,000km we get ~35 so important F. Nimmo ES290Q Winter 2006

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 F. Nimmo ES290Q Winter 2006

F. Nimmo ES290Q Winter 2006