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

F. Nimmo ESS298 Fall 2004 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

F. Nimmo ESS298 Fall 2004 Image not to scale! Giant Planets

F. Nimmo ESS298 Fall 2004 Basic Parameters Data from Lodders and Fegley Surface temperature T s and radius R are measured at 1 bar level. Magnetic moment is given in Tesla x R 3. a (AU) P orb (yrs) P rot (hrs) R (km) M (10 26 kg) Obli- quity Mag. moment TsKTsK Jupiter o Saturn o Uranus R o Neptune o

F. Nimmo ESS298 Fall 2004 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: (Lodders and Fegley 1998) SolarJupiterSaturnUranusNeptune H2H2 83.3%86.2%96.3%82.5%80% He 16.7%13.6%3.3%15.2% (2.3% CH 4 ) 19% (1% CH 4 )

F. Nimmo ESS298 Fall 2004 Interior Structures again Same approach as for Galilean satellites Potential V at a distance r for axisymmetric body is given by So the coefficients J 2, J 4 etc. can be determined from spacecraft observations We can relate J 2,J 4... to the internal structure of the planet

F. Nimmo ESS298 Fall 2004 Interior Structure (cont’d) Recall how J 2 is defined: C A 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 ESS298 Fall 2004 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?) JupiterSaturnUranusNeptuneEarth 10 5 J J C/MR   (g/cc)  2 R 3 /GM

F. Nimmo ESS298 Fall 2004 Pressure Hydrostatic approximation Mass-density relation These two can be combined (how?) to get the pressure at the centre of a uniform body P c : 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 ESS298 Fall 2004 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 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 C p : Combining this equation with the hydrostatic assumption, we get:

F. Nimmo ESS298 Fall 2004 Temperature (2) At 1 bar level on Jupiter, T=165 K, g=23 ms -2, C p ~3R,  =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 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 T 0,P 0 are reference temp. and pressure, and c is constant defined on previous slide)

F. Nimmo ESS298 Fall 2004 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

F. Nimmo ESS298 Fall 2004 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 Constant density

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 2004 From Guillot, 2004

F. Nimmo ESS298 Fall 2004 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 EarthJupiterSaturnUranusNeptune Spin period, hrs Mean eq. field, Gauss Dipole tilt+11.3 o -9.6 o ~0 o -59 o -47 o Distance to upstream magnetosphere “nose”, R p

F. Nimmo ESS298 Fall 2004 Magnetic fields

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 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? incident reflected After Hubbard, in New Solar System (1999) All units in W/m 2 Jupiter Saturn Uranus Neptune

F. Nimmo ESS298 Fall 2004 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 3.5x10 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 ESS298 Fall 2004 Puzzles Why is Uranus’ heat budget so different? –Perhaps due to compositional density differences inhibiting convection at levels deeper than ~0.6R 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 ESS298 Fall 2004 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 ESS298 Fall 2004 Roche Limit The satellite experiences a mean gravitational acceleration of GM p /a 2 But the point closest to the planet experiences a bigger acceleration, because it’s closer by a distance R s (i.e. tides) a RpRp RsRs MpMp MsMs 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: ss pp

F. Nimmo ESS298 Fall 2004 Ring locations (1) Roche limits Roche limits Jupiter Saturn

F. Nimmo ESS298 Fall 2004 Ring locations (2) Roche limits Roche limits Uranus Neptune

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 2004 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

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 2004 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. 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. ~100,000 km Main rings Enceladus E Ring

F. Nimmo ESS298 Fall 2004 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 Keplerian shear Ring particle Satellite

F. Nimmo ESS298 Fall 2004 Pandora and Prometheus shepherding Saturn’s F ring Pan opening the Encke division in Saturn’s rings Ring/Satellite Interactions

F. Nimmo ESS298 Fall 2004 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)

F. Nimmo ESS298 Fall 2004 End of Lecture Thursday’s lecture will be given by Ashwin Vasavada (JPL) Next week will be the start of the computer project

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 2004 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 C p : We can combine these two equations to get: or equivalently Why? Here R is the gas constant, m m is the mass of one mole, and RT/gm m is the scale height of the atmosphere (~10 km) which tells you how rapidly pressure increases with depth

F. Nimmo ESS298 Fall 2004 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 Temperature (schematic) tropopause troposphere stratosphere mesosphere ~0.1 bar radiation adiabat CH 4 (U,N only) NH 3 NH 3 +H 2 S H2OH2O 80 K 140 K 230 K 270 K Theoretical cloud distribution clouds

F. Nimmo ESS298 Fall 2004

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

F. Nimmo ESS298 Fall 2004 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 is a measure of its importance e.g. Jupiter v~100 m/s, L~10,000km we get ~35 so important

F. Nimmo ESS298 Fall 2004 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 ESS298 Fall 2004