ESS 298: OUTER SOLAR SYSTEM Francis Nimmo Io against Jupiter, Hubble image, July 1997
Last Week • Solar system characteristics and formation – Hill sphere, “snow line”, timescales • Kepler’s laws and Newtonian orbits • Tides • Synchronous rotation • Dissipation / heating • Circularization and outwards migration
Galilean Satellites • This week • Preliminaries, common themes • Io • Callisto • Next week • Ganymede • Europa Callisto Europa Ganymede Io
Why are they important? • Life (!?) – or sub-surface oceans, at any rate • Relatively large (~2000 km), geologically active • Very complicated orbital relationships • Some processes look familiar e.g. plate tectonics (?) • Future exploration target (maybe) • Why “Galilean”? He discovered them (telescope, 1610) • Subsequent exploration – Voyagers & Pioneers (1970’s), Galileo (ended 2003), JIMO??
Voyagers 1 and 2 • A brilliantly successful series of fly-bys spanning more than a decade • Close-up views of all four giant planets and their moons • Both are still operating, and collecting data on solar/galactic particles and magnetic fields Voyagers 1 and 2 are currently at 90 and 75 AU, and receding at 3.5 and 3.1 AU/yr; Pioneers 10 and 11 at 87 and 67 AU and receding at 2.6 and 2.5 AU/yr The Death Star (Mimas)
Galileo antenna • More modern (launched 1989) but the high-gain antenna failed (!) leaving it crippled • Venus-Earth-Earth gravity assist • En route, it observed the SL9 comet impact into Jupiter • Arrived at Jupiter in 1995 and deployed probe into Jupiter’s atmosphere • Very complex series of fly-bys of all major Galilean satellites • Deliberately crashed into Jupiter Sept 2003(why?) • Main source of results
25 15 Distance (Rj) 5 30 20 10 Where are they?
J G I E Laplace Resonance (1) • Periods of Io:Europa:Ganymede are in ratio 1:2:4 • This means that successive conjunctions occur at the same point on the orbit • So the eccentricities get pumped up to much higher values than if the satellites were not in a resonance One of the conjunctions occurring due to the Laplace resonance. Note that there is never a triple conjunction. • High eccentricities mean higher dissipation in the satellites and a tendency for the orbits to contract (see earlier) • This tendency is counteracted by dissipation in Jupiter, which tends to cause the orbits to expand (like the Moon) • The system is currently (roughly) in equilibrium
Compositions/Formation • Surface compositions – mainly water ice (except for Io), plus “contaminants” (spectroscopy) • Io’s surface is silicates + sulphur • Interiors – discussed in detail later, but roughly equal mix of water ice, silicates and iron (how do we know?) • How did they form? • Presumably accreted while Jupiter was forming • Lateral temperature gradient in nebula • May have been earlier satellites that didn’t survive (why?) • Energy of accretion ~0.6 Gms/Rs per unit mass ~2 MJ/kg – this is enough to heat ice through ~1000 K. Why might this present a problem? • Satellites subsequently evolved to their present-day positions
Composition (cont’d) • Callisto has lower reflectivity and shallower absorption bands, indicating a higher non-ice component • Ganymede and Callisto show slight differences between leading and trailing hemispheres (why?) • Non-ice materials are probably hydrated minerals (clays) Earth-based reflectance spectra, from Johnson, in New Solar System
Differentiation • Potential energy of a homogeneous satellite is reduced if the densest components sink to the centre – differentiation is energetically favoured • Differentiation is opposed by rigidity of body, so differentiation is favoured at higher temperatures • As differentiation proceeds, energy is released, driving further differentiation – potential runaway • Heat released may generate thermal expansion and form a source of stress • Sinking materials may undergo phase changes leading to volume changes and either expansion or contraction • Not all Galilean satellites appear to have differentiated
Ice phase diagram Ice I • The key point is that because of the densities involved, we would expect to find liquid water around the ice I – ice V interface (~200 km depth). Why is this important? Water Ice V
Internal Structures (1) • Because the satellites are rotating, they are flattened (oblate) • This means that they do not act as a point mass; the perturbations to the gravity field can be identified by tracking spacecraft on a close approach • Potential V at a distance r for axisymmetric body is given by • So the coefficients J2, J4 etc. can be determined from spacecraft observations (higher order terms require closer approaches – why?) • We can relate J2,J4 . . . to the internal structure of the satellite
Internal Structures (2) C R • Mean density and J2 are especially useful • It turns out that we can rewrite J2 in terms of the differences in moments of inertia of the planet (look at the diagram ): A • What we would really like is C/MR2 (why?) • If we can observe the precession of the planet, that gives us (C-A)/C and thus C given J2(where can we do this?) • Otherwise, we can assume that the planet has no strength (hydrostatic) and use theory to infer C from J2 (is this OK?) • In practice, flybys of the Galilean satellites were usually equatorial (why?), so we determine the equivalent equatorial term to J2which is called C22 – the analysis is similar
Internal Structures (3) Fe core • How do we know? • Mean density • Moment of inertia, derived from J2=(C-A)/MR2 and hydrostatic assumption (is this likely?) • Other observations (magnetometer) • Expectations of likely components (silicates, ices, iron) • Tradeoffs – we only have two observations (J2 and r) and have more than two unknowns.Means the results are non-unique Fe-FeS core Contours of Europa ice shell thickness giving correct mean density for indicated core radius and rock density. Bold line is MoI constraint. From Anderson et al., Science, 1998
Khurana et al. 2002 Magnetometer (1) • Jupiter’s magnetic pole is offset from its rotation pole • So as Jupiter rotates (10 hour period), satellites experience a time-varying magnetic field • A time varying magnetic field induces eddy currents in a conductor • These currents generate a secondary (induced) magnetic field • The amplitude of the secondary magnetic field tells us about the conductor, in particular its conductivity and thickness
Magnetometer (2) • Strong induced signatures have been detected at Europa, Ganymede and Callisto, indicating a layer of high conductivity • A relatively near-surface ocean at least a few km thick satisfies these observations • The direction of the induced signal depends on the orbital geometry; but permanent (static) signals have also been detected at Ganymede and (possibly) Io • These static fields are presumably generated by convection within an iron core, just like the Earth • We can combine the magnetometer constraints with the geodetic constraints to infer internal structures . . .
Io – liquid iron core (dynamo), silicate mantle (partially molten?). No volatiles – why not? Ganymede – liquid iron core (dynamo), silicate mantle and ~800 km thick ice shell containing an ocean (presumably at the I-III/V boundary) Europa – core and mantle similar to Ganymede, but ice shell much thinner (~100-200 km) and mostly liquid (magnetic induction signature) Callisto – has not differentiated completely (?). An ice layer ~300km thick, containing an ocean and overlying a mixture of rock-ice. NB the hydrostatic assumption is particularly dodgy here – why?
Ice Rheology (1) stress brittle • Under applied stress, ice will deform: • At low stresses and strains, elastically (recoverable) • At low temperature and/or high strain rate, brittle • At high temperature and/or low strain rate, ductile elastic depth ductile • A good measure of its tendency to deform in a ductile fashion is the homologous temperature (Th=T/Tmelt) (in K) • Rock at Earth surface Th~0.2 • Ice at Galilean satellite surface Th~0.4 • Ice in Antarctica/Mars Th~0.8 • So ice at the surface of the Galilean satellites behaves more like rock than ice on Earth
Ice Rheology (2) • Ductile deformation is important because it controls convection, topographic relaxation and tidal dissipation (see later) • But ice deformation is complicated and involves multiple mechanisms (see Goldsby and Kohlstedt JGR 2001) • Each mechanism obeys the same equation: Here is strain rate, A is a constant, s is stress, gs is grain size, T is temperature, Q is activation energy, R is the gas constant and n and p are constants. A Newtonian rheology has n=1 and a grain-size independent rheology has p=0. Increasing stress / strain rate Grain-boundary sliding (n>1, grain-size dependent) Actually two mechanisms, slower one dominates Diffusion creep (n=1, grain-size dependent) Dislocation creep (n>1,p=0)
Orbital Evolution • Recall dissipation in primary drives satellite outwards • Dissipation in satellite drives satellite inwards and circularizes orbit • Possible scenario: • Io causes dissipation in Jupiter, moves outwards until . . . • It encounters the 2:1 resonance with Europa; the two bodies then move outwards in step until . . . • They encounter the 2:1 resonance with Ganymede • There are alternative scenarios • The present-day configuration involves a balance between dissipation in primary (outwards) and dissipation in satellites (inwards)
Europa Io Ganymede 2:1 Europa:Ganymede time 2:1 Io:Europa distance (schematic) Hypothetical orbital history from Peale, Celest. Mech. Dyn. Ast. 2003 Note that we don’t actually know whether the orbits are currently expanding or contracting Also note that during capture into resonance, eccentricities are transiently excited to high values – so what?
Estimating Q • Recall that the rate of outwards motion of a satellite depends on planetary dissipation Qp (see Week 1). • If we assume that Io formed 4.5 Gyr B.P., and has been moving outwards ever since, we get a lower bound on Jupiter’s Q of ~105 (why a lower bound?) • This value is typical of gas giants, but is much higher than for silicate bodies (~102) • The Earth’s Q is anomalously high (~12) because the current continental configuration means oceanic tides are close to resonance – lots of dissipation • We’ll calculate the rate of dissipation in a second
Tidal Deformation – Recap. • Satellite in synchronous rotation – period of rotation equals orbital period • Eccentric orbit (due to Laplace resonance) – amplitude and direction of tidal bulge changes, so surface experiences changing stresses and strains • These diurnal tidal strains lead to friction and thus tidal dissipation (heating) Diurnal tides can be large e.g. 30m on Europa Satellite Jupiter Eccentric orbit
Tidal Heating (1) • Recall diurnal tidal amplitude goes as in the limit when rigidity dominates ( ) • So strain goes as • Energy stored per unit volume = stress x strain • In an elastic body, stress = strain xm(rigidity) • So total rate of work goes asme2H2Rs/ • For tide raised on satelliteH=Rs(mp/ms)(Rs/a)3 • From the above, we expect the energy stored E to go as Note that here we have used
Tidal heating (2) • From the definition of Q, we have • We’ve just calculated the energy stored E, so given Qs and n we can thus calculate the heating rate dE/dt • The actual answer (for uniform bodies) is • But the main point is that you should now understand where this equation comes from • Example: Io • We get 80 mW/m2, about the same as for Earth (!) • This is actually an underestimate – why?
How do we calculate Q? • We can get estimates/bounds on Q by considering orbital evolution of some satellites (see Week 1) • For solid bodies, we assume a viscoelastic rheology • Such a body has a rigidity m, a viscosity h and a characteristic relaxation (Maxwell) timescaletm=h/m • The body behaves elastically at timescales <<tm and in a viscous fashion at timescales >> tm • Dissipation is maximized when timescale ~ tm: Tobie et al. JGR 2003
Calculating Q (cont’d) • Ice has rigidity ~109 Pa and viscosity ~1014 Pa s, so the Maxwell time is ~105s which is comparable to the orbital period, so we expect dissipation in the ice shells • Silicates m~1011 Pa, h~1021 Pa s, so less dissipation • But silicate viscosity decreases significantly if melting occurs, which will lead to an increase in dissipation, and thus a feedback effect • This runaway situation was first identified by Peale et al. (1979), who predicted massive volcanism on Io two weeks before it was observed for the first time • A similar feedback effect may also occur in ice (see previous diagram)
Tidal Energy and Stress • Tidal stresses and heating decrease markedly with distance • Radiogenic heating is dominant in Callisto and Ganymede (now), secondary in Europa, and insignificant for Io H is static tidal bulge for a fluid body, 3eH gives peak-to-peak diurnal tidal amplitude, dW/dt is tidal dissipation rate for a uniform body with Jupiter’s mass=1.899x1027 kg, k=3/2 and Q=100, dWR/dt is radiogenic heat production within silicate portion of body assuming a heating rate of 3.5x10-12 W/kg, EeH/Rs gives the approximate stresses due to diurnal tides with E=10 GPa, C/msRs2 gives the normalized moment of inertia (Anderson et al. 1996,1998b,2001a,b) and 3Gms/5Rs gives the energy delived during homogeneous accretion. A uniform body has a normalized MoI of 0.4.
Non-synchronous rotation (1) • From the satellite’s point of view, the planet travels in the opposite direction round the sky to the satellite itself • The tidal bulge always lags the planet’s motion • In an eccentric orbit the amplitude of the tidal bulge varies and is largest at the periapse • The result of the varying bulge is a varying torque, which turns out to be positive i.e. it should increase the satellite’s rotation rate slightly above synchronous Eccentric orbit satellite Apoapse Periapse planet Torque opposes spin Smaller Torque increases spin Larger
Non-synchronous rotation (2) • For an eccentric satellite, the net tidal torque should lead to non-synchronous rotation • But the torque may be balanced by a frozen-in mass asymmetry, leading to synchronous rotation • A frozen-in mass asymmetry requires a relatively rigid body (See Greenberg and Weidenschilling, Icarus 1984) Mass torque: Tidal torque: • Both the rigidity of the satellite and Q depend on its internal structure, so there are potential feedbacks between orbital evolution and rotation state Internal structure Orbital behaviour
Impact Cratering • Main source of impact craters in outer solar system is comets • Synchronously rotating satellite will be preferentially cratered on its leading hemisphere (think raindrops) • So distribution of impact craters on surface can be used to test whether NSR has occurred • Density of impact craters can be used to infer surface age • Obtaining absolute surface ages requires the impact rate to be derived, from a combination of current and historical astronomical observations, and models. Uncertainties are currently large. • Note that the impact rate will increase for satellites closer to the primary (effect of gravitational focusing)
Furrowed terrain Grooved terrain Cratering Statistics Zahnle et al. Icarus 1997 Expected curves if NSR is not occurring Absolute ages have been revised upwards since (Zahnle et al. Icarus 2003)
Cratering Statistics - Results • Io – no impact craters observed (!) so surface is very young (< 1 Myr) • Europa – few impact craters, surface age ~50 Myr. Not enough craters to detect if NSR is happening • Ganymede – bimodal surface, ages ~2 Gyr and ~4 Gyr (uncertainties large). Spatial distribution flatter than expected, suggests NSR has occurred. • Callisto – very ancient surface, ~4.5 Gyr. Spatial distribution very flat, but may be because crater population is saturated everywhere (i.e. one crater is destroyed for every new one produced)
Thermal & Orbital Evolution • We would like to be able to answer the question: how have the satellites’ orbits and interiors evolved over solar system history? • This is difficult because • Observations are severely limited (e.g. cratering evidence is not much use on Io or Europa) • Important parameters (such as Q) are uncertain • The theoretical problem is difficult. Why? • Feedbacks. Orbital evolution, NSR and tidal dissipation all depend on Q, but Q is dependent on the internal structure of the satellite, which depends on tidal dissipation . . . • Coupling. The satellites can’t be treated as isolated objects, because of the Laplace resonance. So you have to model their evolution simultaneously . . .
Thermal & Orbital Evolution (cont’d) • Nonetheless, progress is being made, both on the observational and the theoretical front. We’ll discuss examples of both later in the course. This is an example of Europa’s shell thickness evolution with time, from Hussmann and Spohn, Europa’s Ice Shell Meeting, LPI, 2004. The periodicity arises because Io and Europa’s eccentricities change over time, which changes the dissipation in Europa’s ice shell and thus the shell thickness. In this model the shell is convecting.
Summary • Tides are important in determining spin state, orbital evolution and heating of satellite • Ice rheology is complicated: • Near-surface, it will behave like rock on Earth • At depth, it will flow at a geologically rapid rate • Cratering observations can provide us with relative surface ages, but absolute ages are subject to large uncertainties • Satellite internal structures are constrained by a mixture of observations (C/MR2, mean density, magnetometer) and reasonable expectations
Basic Parameters • Note the likely structural similarities with the Moon
What’s it like? • Volcanically very active (see later) • Cold – surface temperature about 130K, but variable (due to volcanism) • Very tenuous atmosphere (volcanic) • Sulphur-rich surface – deduced from ground-based spectroscopic observations (different colours are different sulphur allotropes) • Very hostile environment (for people or spacecraft) – charged particles accelerated by Jupiter’s large magnetic field • Not clear whether Io has an internal magnetic field (Kivelson et al. JGR 2001) – interactions with Jupiter’s field make identification difficult
Landforms • Three main types: Volcanoes, Mountains and Paterae(irregular depressions, similar to calderas) 200km 350km flow patera Low-sun angle; shadow measurements give mountain elevations of up to 4km. Lobate flows are large landslides. Mountains show no signs of volcanic activity and appear to be fault-bounded. volcano
Lava flows Amirani lava flow, Io • Dark flows are the most recent (still too hot for sulphur to condense on them) • Flows appear relatively thin, suggesting low viscosity 500km 500km Comparably-sized lava flow on Venus (Magellan radar image)
Time-Variability Lava flow erupted at Prometheus between Voyager and Galileo missions (Davies JGR 2003) • Changes detected from Voyager to Galileo missions and within Galileo mission April 1997 July 1999 Sept 1997 Pillan Galileo images of overlapping deposits at Pillan and Pele 400km Pele
Volcanic activity (1) • Galileo image of Tvashtar, apparently in the process of erupting • The CCD was overloaded by the eruption, but it has been interpreted as a fire-fountain 1.5 km high Voyager image of eruption plume, approximately 300 km high Fire fountain(?)
Volcanic activity (2) • Images suggest molten magma immediately beneath the surface (at least in some places) • Volcanic activity erupts about 1 tonne / second sulphur into the “atmosphere”, some of which may end up on Europa (contaminants have been detected there) Erta Ale lava lake, Ethiopia. Lake is 100m across. Galieo nightside image of Pele, SSI clear filter. Radebaugh et al. 2004
Ground-based observations • Have the advantage of longer observation periods and better spectral resolution than spacecraft • Spatial resolution is also getting much better thanks to adaptive optics and Hubble • The sequence below shows a hot spot which flares up to equal the brightness of Loki (spot 2) over a few days 1 arcsecond From Macintosh et al., Icarus 2003 July 12 1998 July 28 1998 Aug 4 1998 Keck interferometer
Energetics (1) • We can measure the power output of Io by looking at its infra-red spectrum • Heat flux is appx. 2.5 W m-2 .This is 30 times the Earth’s global heat flux. • Assume low rigidity ( ) – why?. To balance the heat being produced requires Qs=90. Is this reasonable? What does it imply about viscosity? • Where does the power ultimately come from? • A heat loss of 2.5 Wm-2 over 4.5 Gyr is equivalent to 0.03% of Jupiter’s rotational energy
Energetics (2) • How do we get 2.5 Wm-2 out of the ground? • A conductive layer (or convective stagnant lid) would need to be ~1 km thick. Reasonable? • What about magma transport (advection)? • Silicate magma generates ~5 GJ/m3 on cooling 1000K and solidifying • A resurfacing rate of ~1 cm/yr can account for the observed surface heat flux • This resurfacing rate is also consistent with estimates based on impact craters and IR cooling models • So Io is unique among the solar system in that its heat flux is dominated by advection
Interior Structure After Anderson et al., JGR 2001 Silicates 3500 kg m-3 • Lacks outer ice layer (in contrast to other Galilean satellites). Why? • Even though sulphur is abundant at the surface, the bulk of the interior must be silicates/iron from simple cosmochemistry 1821 km 700 km Fe-FeS 5150 kg m-3 Remember these structures are non-unique: the ones shown assume plausible but not necessarily correct densities. • Io likely has a crust, but we can’t detect it with current data • We can’t tell (directly) whether the core or the mantle are partially or completely liquid. • Io’s k2=1.29. What is this telling us? (rigidity or mass concn.)
~50km Solid lid Partially- molten mantle ~500km Solid mantle Interior Structure(?) • Rigid lid is required by high mountains and is a result of rapid burial of cooled surface material • Bulk of dissipation occurs in partially molten mantle • Magma percolates through mantle and ascends through cold lid in discrete fractures i.e. dikes • Erupted material cools by radiation and is re-buried After Moore, Icarus, 2001