F.Nimmo EART162 Spring 10 Francis Nimmo EART162: PLANETARY INTERIORS

F.Nimmo EART162 Spring 10 Last Week Tidal bulge amplitude depends on mass, position, rigidity of body, and whether it is in synchronous orbit Love numbers measure how much the body is deformed (e.g. by rotation or tides) Love numbers are reduced by central mass concentration and/or rigidity We can use the observed shape of a body to infer the fluid Love number and thus its moment of inertia – as long as it is behaving like a fluid Tidal torques are responsible for orbital evolution e.g. orbit circularization, Moon moving away from Earth etc. Tidal strains cause dissipation and heating

F.Nimmo EART162 Spring 10 This Week Case Study – we will do a whole series of calculations, which give you an idea of roughly what planetary scientists actually do We may not be as precise or sophisticated as the real thing, but the point is that you can get a very long way with order of magnitude / back of the envelope calculations! This should also serve as a useful reminder of many of the techniques you’ve encountered before

F.Nimmo EART162 Spring 10 Case Study: Europa

F.Nimmo EART162 Spring 10 Galilean Satellites Large satellites orbiting Jupiter Europa is roughly Moon-size (~1500 km radius) 3 inner satellites are in a Laplace resonance (periods in the ratio 1:2:4) (what about their orbital radii?) Orbital eccentricities are higher than expected due to this resonance (tidal heating) Io Europa Ganymede Callisto

F.Nimmo EART162 Spring 10 Basic parameters Note higher eccentricity and greater degree of mass concentration than the Moon MoonEuropa a (R p ) Period (days) Eccentricity Radius (km) Mean density (g/cc) g (m s -2 ) C/MR

F.Nimmo EART162 Spring 10 ~100km Surface Observations Only lightly cratered (surface age ~60 Myr) Surface heavily deformed ridges lenticulae bands chaos

F.Nimmo EART162 Spring 10 What is it like? Cold ( ~120K on average) Rough – heavily tectonized Young – surface age ~60 Myrs Icy, plus reddish “non-ice” component, possibly salts? Trailing side darker and redder, probably due preferential implantation of S from Io Interesting – it has an ocean, maybe within a few km of the surface, and possibly occasionally reaching the surface

F.Nimmo EART162 Spring 10 Bulk Properties Europa Io Radius = 1560 km Flyby (schematic) Earth r M=5x10 22 kg So bulk density = 3 g/cc What does this tell us? What’s the surface gravity? What’s the pressure at the centre?

F.Nimmo EART162 Spring 10 Shape Planet Synch. Sat. Quantity Only true for fluid bodies! For Europa, a= km, b= km, c= km Thus (b-c)/(a-c)=0.26. So what? We can use (a-c)/R to obtain h 2f =1.99. Now what? Only true for fluid bodies! Plug in the values, we get C/MR 2 =0.34. So what?

F.Nimmo EART162 Spring 10 Interior Structure Let’s assume a very simple two-layer model R fR mm  g  m  Mass constraint: MoI constraint: Combining the two: We know R (1560 km), M (5x10 22 kg) and C/MR 2 (0.34) Assuming a value for  m, we can solve for f,g...

F.Nimmo EART162 Spring 10 Interior structure (cont’d) Assuming  m =1000 kg m -3, we get f=0.87 and g=3.26 (see diagram) The implied density of the interior (4260 kg m -3 ) is greater than low-pressure mantle silicates. Could the density simply be due to high pressures? 1565   1362 Remember the simple equation of state (Week 3): Where does this come from? Use K=200 GPa, g=1.3ms -2,   =3300 kgm -3, this gives  ~3400 kgm -3 at the centre What do we conclude from this?

F.Nimmo EART162 Spring 10 Summary Radius, mass give us bulk density and some constraint on the bulk structure (mostly rock/metal, not ice) Shape tells us that body is hydrostatic For a hydrostatic body, we can use the observed flattening to derive h 2f and hence C/MR 2 C/MR 2 allows us to make further inferences e.g. how thick the outer ice shell is, presence of an iron core Rather than use the shape, we could also use the observed gravity (e.g. J 2 ) and the hydrostatic assumption. This gives us the same answer (as it should)

F.Nimmo EART162 Spring 10 Interior Structure Probably similar to Io, but with a layer of ice (~100 km) on top We can’t tell the difference between ice and water due to density alone Magnetometer data strongly suggest ocean at least a few km thick (see later) Thickness of solid ice shell not well known (see later) Ocean Silicate mantle ~120km Ice shell

F.Nimmo EART162 Spring 10 Why do we think there’s an ocean? Khurana et al Jupiter’s varying field induces a current and a secondary magnetic field inside Europa Galileo detected this secondary field The amplitude of the secondary field depends on how conductive Europa’s interior is The results are consistent with a shallow salty ocean > a few km thick Why couldn’t the conductive layer be deeper?

F.Nimmo EART162 Spring 10 So What? Astrobiology (groan) Interesting physical problem – why hasn’t the ocean frozen?

F.Nimmo EART162 Spring 10 How could we check the ocean exists? Equilibrium tide: Tidal amplitude d is reduced by rigidity , depending on the tidal Love number: What is the size of the equilibrium tide for Europa? (m/M=40,000, a/R=430) What is the size of the fluid diurnal tide? How big would the diurnal tide be if there were no ocean? (Note that this assumes a uniform density structure)

F.Nimmo EART162 Spring 10 Europa’s Temperature Structure What’s the surface temperature? If there were only radioactive heat sources, how thick would the conductive ice shell be? Is the ocean convecting? How long would the ocean take to freeze? Are there other heat sources we’ve forgotten about? ocean ice mantle T z

F.Nimmo EART162 Spring 10 Tidal Dissipation Recall from Week 8, dissipation per unit volume: How much power is being dissipated in the ice? What about in the mantle? What is the effect of the dissipation on the ice shell thickness? Jupiter Satellite Eccentric orbit Diurnal tides can be large e.g. ~30m on Europa

F.Nimmo EART162 Spring 10 Equilibrium Shell thickness Let’s put some numbers on this... How reliable is the shell thickness derived? Is the shell really conductive? How might we tell? Shell thickness Heat flow Heat production Heat loss Mantle Equilibrium

F.Nimmo EART162 Spring 10 Convection! Maybe the ice shell is convecting? How thick would the ice shell have to be for convection to occur? Congratulations – you have just written a Nature paper! (Because you have just constrained the ice shell thickness) 150km What kind of topography would you expect to be associated with the convection? If the ice shell is convecting, what happens to the equilibrium shell thickness argument?

F.Nimmo EART162 Spring 10 Equilibrium Shell Thickness conduction convection Equbm. Shell thickness Hussmann et al What would happen if Europa’s mantle was like Io’s? Is the shell actually in steady state? How else might we measure the shell thickness? Why does convective heat transport decrease as shell thickness increases? Obtain equilibrium shell thickness km

F.Nimmo EART162 Spring 10 Flexural models Wavelength of deformation gives rigidity of ice (can be converted to elastic thickness T e – see Week 4) Rigidity can be converted to shell thickness (assuming a conductive temperature structure): t c ~ 2-3 T e What determines the temperature at which the ice ceases to behave elastically? 270 K 100 K elastic viscous 190 K Depth TeTe Temp.

F.Nimmo EART162 Spring 10 Flexure and gravity There seem to be a wide range of elastic thicknesses on Europa, from km. Why? What constraints do these values place on the shell thickness? What sort of gravity anomaly would you see at the surface associated with this feature? What about at 100 km altitude? What if it were compensated?

F.Nimmo EART162 Spring 10 Icebergs “Icebergs” and the edges of chaos regions stand a few 100 m higher than the matrix What does this observation imply about the thickness of the ice blocks? (Another Nature paper in the bag!) Do chaos regions really involve liquid water? Rotation and translation of blocks suggest a liquid matrix From Carr et al., Nature, km iceberg water h tctc t c ~ 10 h

F.Nimmo EART162 Spring 10 What about seismology? What would the velocities of P and S waves be on Europa? What would the potential sources of seismicity be? How would you use them to measure the shell thickness? What other remote-sensing techniques can you think of to constrain the shell thickness?

F.Nimmo EART162 Spring 10 Future Mission - JEO Launch 2020, arrive 2025, end of mission 2029 Will tour other satellites before orbiting Europa Nuclear powered, radiation-shielded orbiter Cassini-like instrument package (+ altimeter) Will get approval from Congress (hopefully!) next year

F.Nimmo EART162 Spring 10 Conclusions Planetary science is not that hard A few observations can go a very long way The uncertainties are so large that simple approaches are perfectly acceptable Combining surface observations with simple calculations is the right way to proceed Although sometimes it can get you into trouble...

F.Nimmo EART162 Spring 10 Planning Ahead... Week 9 –Tues 25 th – Tides pt II –Thurs 27 th – Case study I Week 10 –Tues 1 st – Case study II –Thurs 3 rd – Revision lecture Final Exam – Mon 7 th June 4:00-7:00 p.m.

F.Nimmo EART162 Spring 10

Gravity field MacCullagh’s formula tells us how the acceleration varies with latitude (  ): So what’s the difference between the acceleration at the poles and at the equator? Flyby again Earth r R  Closest approach is 600 km (above the surface) and we measure an acceleration difference between pole and equator of 0.65 mm s -2. What is J 2 ? And (C-A)?

F.Nimmo EART162 Spring 10 Now we have J 2 – what next? We really want C – how do we get it? –Measure the precession rate  (C-A)/C, or... –Assume hydrostatic Is hydrostatic assumption reasonable? Mass deficit at poles Mass excess at equator What causes the flattening? Here a is equatorial radius Plug in the values, we get C/Ma 2 =0.34. So what?

F.Nimmo EART162 Spring 10 Where does all that deformation come from, anyway? How much stress do we need to get deformation? What are the sources of stress we can think of?