Francis Nimmo

1
ESS 298 OUTER SOLAR SYSTEM

• Francis Nimmo

Io against Jupiter, Hubble image, July 1997
2
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

3
Giant Planets
Image not to scale!
4
Basic Parameters
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

• 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.

5
Compositions (1)

• Well 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

Solar Jupiter Saturn Uranus Neptune
H2 83.3 86.2 96.3 82.5 80
He 16.7 13.6 3.3 15.2 (2.3 CH4) 19 (1 CH4)
(Lodders and Fegley 1998)
6
Interior Structures again

• Same approach as for Galilean satellites
• Potential V at a distance r for axisymmetric body
  is given by

• So the coefficients J2, J4 etc. can be determined
  from spacecraft observations
• We can relate J2,J4 . . . to the internal
  structure of the planet

7
Interior Structure (contd)

• Recall how J2 is defined

C
R

• 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

A

• 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

8
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
r (g/cc) 1.33 0.69 1.32 1.64 5.52
w2R3/GM .089 .155 .027 .026 .003
9
Pressure

• Hydrostatic approximation
• Mass-density relation
• These two can be combined (how?) to get the
  pressure at the centre of a uniform body Pc

• Jupiter Pc7 Mbar, Saturn Pc1.3 Mbar, U/N Pc0.9
  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

10
Temperature (1)

• If parcel of gas moves up/down fast enough that
  it doesnt 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
Adiabatic only
Here P is pressure, r is density, R is gas
constant (8.3 J mol-1 K-1), T is temperature, m
is the mass of one mole of the gas, g 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

11
Temperature (2)

• At 1 bar level on Jupiter, T165 K, g23 ms-2,
  Cp3R, m0.002kg (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

(Here T0,P0 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 g1.5 Note that density
increases more rapidly than temperature why?
Slope determined by g
12
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

13
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 HHe (J,S) or H/Heice (U,N)

radius
Constant density
mass
14
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.

15
From Guillot, 2004
16
Magnetic Fields

• Jupiters originally detected by radio emissions
  (electrons being accelerated in strong magnetic
  field bad for spacecraft!)
• Jupiters field is 10o off the rotation axis
  (useful for detecting subsurface oceans)
• Saturns field is along the rotation axis
• Jupiters and Saturns 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

17
Magnetic fields
18
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)

19
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?

20
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

Where does this come from?
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.

21
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

22
Rings

• Composed of small (mm-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 (Saturns rings
  collected together would make a satellite 100 km
  in radius)

23
Roche Limit

• The satellite experiences a mean gravitational
  acceleration of GMp/a2
• But the point closest to the planet experiences a
  bigger acceleration, because its closer by a
  distance Rs (i.e. tides)

Ms
rs
Mp
rp
a
Rs
Rp

• 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

• 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

24
Ring locations (1)
Jupiter
Saturn
Roche limits
Roche limits
25
Ring locations (2)
Uranus
Neptune
Roche limits
Roche limits
26
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 Jupiters rings
27
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

28
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
29
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?)

E Ring
Hubble image of Saturns 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.
30
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

collision
slower
faster
Satellite

• 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

Keplerian shear
Ring particle
31
Ring/Satellite Interactions
Pan opening the Encke division in Saturns rings
Pandora and Prometheus shepherding Saturns F ring
32
Sharp edges (contd)

• Positions withing the rings which are in
  resonance with moons tend to show gaps why?
• E.g. the Cassini division (outer edge of Saturns
  B ring) is at a 21 resonance with Mimas
• Edge of A ring is at a 76 resonance with
  Janus/Epimetheus
• Resonances can also lead to waves

Waves arising from 53 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)
33
End of Lecture

• Thursdays lecture will be given by Ashwin
  Vasavada (JPL)
• Next week will be the start of the computer
  project

34
Atmospheric Composition

• Escape velocity ve (2 g r)1/2 (wheres this
  from?)
• Mean molecular velocity vm (2kT/m)1/2
• Boltzmann distribution negligible numbers of
  atoms with velocities gt 3 x vm
• Molecular hydrogen, 900 K, 3 x vm 11.8 km/s
• Jupiter ve60 km/s, Earth ve11 km/s
• H has not escaped due to escape velocity (Jeans
  escape)

35
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

Why?
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
36
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
Temperature (schematic)
Theoretical cloud distribution
mesosphere
80 K
CH4 (U,N only)
stratosphere
140 K
0.1 bar
NH3
tropopause
clouds
230 K
NH3H2S
troposphere
adiabat
270 K
H2O
37
(No Transcript)
38
Observations

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

39
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(q)
• How important is the Coriolis effect?

q is latitude
is a measure of its importance
e.g. Jupiter v100 m/s, L10,000km we get 35 so
important
40
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

41
(No Transcript)