Moving beyond the Earth: What use is mineral physics to planetary scientists?

1. Moving beyond the Earth:What use is mineral physics to planetary scientists? Francis Nimmo (U. C. Santa Cruz)

2. Talk Outline • What do we care about? • What do we know? • Earth, solar system, extra-solar planets • What would we like to know (and why)? • Static properties • EOS • Melt behaviour • Dynamic properties • Rheology • Dissipation • Conductivity • Partitioning

3. What do planetary scientists care about? • Present-day interior structure • Formation • Evolution What do mineral physicists care about? • Measuring things (preferably under extreme circumstances) • Here are some justifications for doing so . . .

4. Solar nebula and planets . . . • Nebular material can be divided into “gas” (mainly H/He), “ice” (CH4,H2O,NH3 etc.) and “rock” (including metals) • In our solar system, the proportions of gas/ice/rock are roughly 100/1/0.1 • Planets will contain variable mixtures of these • The compounds which actually condense will depend on the local nebular conditions (temperature) • E.g. volatile species will only be stable beyond a “snow line” (distance depends on stellar luminosity) • But planets can (and do) migrate subsequent to their formation! (e.g. “hot Jupiters”)

5. Other solar systems will certainly contain planets very different from ours (super-Earths, mini-Jupiters, iron planets . . .) GJ876d HD149026b Classes of planetary bodies “Rock” 1 Me 300 GPa ~6000 K Ice + H,He ~15 Me 800 GPa ~8000 K Mainly H,He ~300 Me 7000 GPa ~20,000 K “Rock”+ice ~0.1 Me ~10 GPa ~1500 K

6. What do we know?

7. What are we going to know? • Jupiter/Saturn internal structure (JUNO,Cassini) • Extra-solar planet atmospheric compositions • Extra-solar planet flattening?! (MoI) • Earth-like planets’ mass/radii (COROT, Kepler) • Mars seismology (don’t hold your breath)

8. 1. Static properties • Equations of state • Hydrogen & Helium • Everything else • (Silicate) Melting

9. Hydrogen EOS • Why do we care? • Fundamental to deducing structure of gas giants • “A 5% error in the EOS for hydrogen translates into a factor of six uncertainty in the abundance of ices”* • Different EOS lead to different conclusions! Laser (high compression) Pulse-shock (low comp.) Guillot, Ann. Rev. 2005 *Podalak and Hubbard 1998

10. Hydrogen - Experiments DAC Hubbard et al. Ann. Rev. 2002

11. He EOS • He makes up ~20% by mass of giant planets • He EOS only measured to ~50 GPa (less than 5% of depth within Jupiter) • Extent to which He and H are miscible is important (energy balance) • Ne only 0.1 x solar in Jupiter envelope – is this because it dissolves in He?

12. H/He - Summary • H EOS/compressibility • Size of Jupiter’s core, envelope composition • H molecular/metallic transition • Convective barrier, chemistry, temperature • H/He miscibility • Internal structure, energy budget • He EOS and noble gas solubility • Experiments only up to ~50 GPa

13. H/He -A Caution! HD149026b (1.25 g/cc) 1g/cc 1g/cc 20 g/cc 7 g/cc GJ436b (2.02 g/cc) 3 g/cc 10 g/cc Mixing ratios can be more important than EOS accuracy Gillon et al. 2007

14. EOS – “Everything else” • “Super-Earths” e.g. GJ876d (7.5 Me), Gl581c (5 Me), OGLE-2005-BLG-390Lb (5.5 Me), more to come! • Need for EOS data up to several TPa (Valencia et al. 2007) • Incompressible oxides e.g. Gd3Ga5O12 (Mashimo et al. 2006) • Carbon-rich planets (?) (Kuchner and Seager, submitted) Super Earths (P ~ few TPa) Fortney et al. 2005 parameterization

15. (Silicate) melt behaviour • Why do we care? • Mass transfer (chemistry, differentiation) • Heat transfer (e.g. Io) • Rheology • Many other reasons! • What things to measure? • Liquidus • Density

16. Liquidus/Density • Deep mantle liquidus controls whether magma ocean solidifies from top or bottom – important! • Melt-solid density contrast controls whether magma can move upwards or not – affects e.g. CMB heat flux Mosenfelder et al. JGR in press

17. Summary: Static properties • Equations of state • Hydrogen metallic transition & He miscibility • Helium high pressure EOS, noble gas solubility • Super-Earths imply pressures up to few TPa • (Silicate) Melting • Solidification from top or bottom? • Density compared with solid

18. 2. Dynamic Properties • Rheology • Dissipation • Conductivity • Partitioning

19. Rheology (viscosity) • Why does it matter? • Heat transfer • Mixing/stirring rates (chemistry) • Dissipation (see later) • What would we like to know? • Deep earth • Ices Convection inside Enceladus (image courtesy James Roberts)

20. What would we like to know? • Deep Earth • Perovskite • Post-perovskite . . . • Influence of water . . . • Ices (outer solar system sats.) • Ice I diffusion creep! • Higher pressure ice rheology not well known Ice II Kubo et al. Science 2006 Ice I 5mm Forte and Mitrovica Nature 2001

21. Dissipation • Deforming real materials results in dissipation • Tidal dissipation very important to planets • How do we define dissipation? e Gribb and Cooper 1998 Apples vs. oranges?

22. Dissipation measurements 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 Increasing dissipation Maxwell model Andrade model (a~0.3) Andrade model (a~0.2) Apples vs. oranges?

23. Conductivity • High pressure ice conductivities important for Neptune, Uranus mag.fields (Cavazzoni et al. 1999, Lee et al. 2006) • Fe conductivity uncertain by a factor of 2 (Matassov 1977, Bi et al. 2002) • Affects strength of magnetic field • Affects age of inner core (Nimmo et al. 2004)

24. Partitioning • Vital for using geochemical observations to constrain physical processes. Examples • Re/Os/Pt and age of inner core (?) (Brandon et al.) • He/U/Th and mantle layering (Parman) • Siderophile elements and core formation (various) • Experimentally challenging e.g. high temperature gradients can drive diffusion • Affected by many factors e.g. oxygen fugacity, silicate polymerization

25. Summary • Available observational constraints much poorer than for Earth, but . . . • Parameter space much wider! • Higher P,T • Different and exotic compositions (hydrogen, noble gases, carbides etc.) • N >> 1 • Major growth areas (e.g. extra-solar planets) • Funding possibilities? (e.g. NASA PIDDP)

26. Conclusion: a shopping list • H molecular-metallic transition and He miscibility • He EOS (> 50 GPa) • High P silicate melting • Q (at ~1 hr periods; better theoretical understanding) • High P silicate/ice rheology • Fe/high P ice conductivity • High P partition behaviour

27. Questions?

28. Dihedral angle • Controls melt separation and movement • Important for core formation, magma transport • Results depend on O content of liquid Fe (P,T dependent) • Inefficient Fe separation in lower mantle? • Hard experiments – very large T gradients Terasaki et al. 2005, 5-20 GPa

29. Extra-solar planets • “Hot Jupiters” have more heating (radiative, tidal) • Larger core masses? (close-in means less easy to scatter planetesimals)

30. How do we calculate Q? • 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

31. Interior Structure of GJ 876d 20,000 7.5 ME DENSITY (kg/m3) 12,000 Valencia, Sasselov, O’Connell (2006) 4,000 2,000 6,000 10,000 RADIUS (km)

32. Partitioning Can siderophile element abundances be explained by high P,T partition coefficients? Walter et al. 2000 Kegler et al. 2005

33. 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) radius Constant density mass

34. Basic Parameters 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.

35. 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 H2 or He: (Lodders and Fegley 1998)

36. 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

37. Interior Structure (cont’d) C • Recall how J2 is defined: 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

38. 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?)

39. 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 Pc=7 Mbar, Saturn Pc=1.3 Mbar, U/N Pc=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

40. 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: Adiabatic only Always true 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:

41. Temperature (2) • At 1 bar level on Jupiter, T=165 K, g=23 ms-2, Cp~3R, m=0.002kg(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 g=1.5 Note that density increases more rapidly than temperature – why? Slope determined by g

42. Heavy elements Guillot 2005 • He subsolar – sedimentation? • Ne depleted – dissolves in He? • Others supersolar – delivery by cold bodies (comets)?

43. He miscibility Hubbard et al. 2002

44. Nebular Composition • Based on solar photosphere and chondrite compositions, we can come up with a best-guess at the nebular composition (here relative to 106 Si atoms): • Blue are volatile, red are refractory • Most important refractory elements are Mg, Si, Fe, S (in the ratio 1:1:0.9:0.45) Data from Lodders and Fegley, Planetary Scientist’s Companion, CUP, 1998 This is for all elements with relative abundances > 105 atoms.

45. Temperature and Condensation Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids: Mid-plane Photosphere Earth Saturn Condensation behaviour of most abundant elements of solar nebula e.g. C is stable as CO above 1000K, CH4 above 60K, and then condenses to CH4.6H2O. From Lissauer and DePater, Planetary Sciences Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998

46. Terrestrial planets Gas giants Ice giants V E Me Ma Inner solar system 30 AU Note log scales! 1.5 AU 5 AU Outer solar system Where is everything? Note logarithmic scales! Ma V E Me J S U KB N P 1 AU is the mean Sun-Earth distance = 150 million km Nearest star (Proxima Centauri) is 4.2 LY=265,000 AU

47. Basic data See e.g. Lodders and Fegley, Planetary Scientist’s Companion

48. Sequence of events • 1. Nebular disk formation • 2. Initial coagulation (~10km, ~104 yrs) • 3. Orderly growth (to Moon size, ~105 yrs) • 4. Runaway growth (to Mars size, ~106 yrs), gas loss (?) • 5. Late-stage collisions (~107-8 yrs)

49. From Guillot, 2004

50. Magnetic fields