Moving beyond the Earth:What use is mineral physics to

planetary scientists?Francis Nimmo

(U. C. Santa Cruz)

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

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 . . .

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”)

Classes of planetary bodies

“Rock”

1 Me

300 GPa~6000 K

“Rock”+ice

~0.1 Me

~10 GPa~1500 K

Ice + H,He

~15 Me

800 GPa~8000 K

Mainly H,He

~300 Me

7000 GPa~20,000 K

HD149026b

Other solar systems will certainly contain planets very different from ours (super-Earths, mini-Jupiters, iron planets . . .)

GJ876d

What do we know?Earth Moon Mars Ganymede Jupiter KBO ESP

Density Y Y Y Y Y (Y) (Y)

Radius Y Y Y Y Y (Y) (Y)

Surface Composition?

Y Y Y (Y) Y (Y) N

MoI Y Y Y Y? Y N N

Core detected? Y Y? Y Y N N N

Samples? Y Y Y N (Y) N N

Density profile? Y Y? N N Y? N N

Sample size 1 1 1 few 2 ~10 ~200+

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)

1. Static properties

• Equations of state– Hydrogen & Helium– Everything else

• (Silicate) Melting

Hydrogen EOS

*Podalak and Hubbard 1998

Laser (highcompression)

Pulse-shock(low comp.)

Guillot, Ann. Rev. 2005

• 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!

Hydrogen - Experiments

Hubbard et al. Ann. Rev. 2002

DAC

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?

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

H/He -A Caution!

Gillon et al. 2007

HD149026b (1.25 g/cc)

GJ436b (2.02 g/cc)

1g/cc

7 g/cc

1g/cc

20 g/cc

3 g/cc 10 g/cc

Mixing ratios can be more important than EOS accuracy

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)

Fortney et al. 2005parameterization

Super Earths (P ~ few TPa)

(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

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

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

2. Dynamic Properties

• Rheology

• Dissipation

• Conductivity

• Partitioning

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)

• Deep Earth– Perovskite– Post-perovskite . . .– Influence of water . . .

• Ices (outer solar system sats.)– Ice I diffusion creep!– Higher pressure ice rheology not

well known

Forte and Mitrovica Nature 2001

What would we like to know?

5m

Ice II

Ice I

Kubo et al. Science 2006

Dissipation• Deforming real materials results in dissipation

• Tidal dissipation very important to planets

• How do we define dissipation?

Gribb and Cooper 1998

Q

EE

2

1sin Q

Apples vs. oranges?

Dissipation measurements

Increasingdissipation

Maxwell model

Andrade model (~0.3)

Andrade model (~0.2)

0 -1 -2 -3 -4 -5 -6 -7 -8 -9

Apples vs. oranges?

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)

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

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)

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

Questions?

Dihedral angle• Controls melt separation and movement

• Important for core formation, magma transport

Terasaki et al. 2005, 5-20 GPa

• Results depend on O content of liquid Fe (P,T dependent)

• Inefficient Fe separation in lower mantle?• Hard experiments – very large T

gradients

Extra-solar planets

• “Hot Jupiters” have more heating (radiative, tidal)

• Larger core masses? (close-in means less easy to scatter planetesimals)

How do we calculate Q?• For solid bodies, we assume a viscoelastic rheology• Such a body has a rigidity , a viscosity and a

characteristic relaxation (Maxwell) timescale m=• The body behaves elastically at timescales <<m and in a

viscous fashion at timescales >> m

21

)(1 n

nQ

m

m

Tobie et al. JGR 2003

• Dissipation is maximized when timescale ~ m:

Interior Structure of GJ 876d

20,000

12,000

4,000

2,000 6,000 10,000

RADIUS (km)

DE

NS

ITY

(k

g/m

3)

Va

len

cia

, Sa

sse

lov,

O’C

on

nell

(200

6)

7.5 ME

Partitioning

Walter et al. 2000Kegler et al. 2005

Can siderophile element abundances be explained by high P,T partition coefficients?

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

Con

stan

t den

sity

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.

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

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)

Solar Jupiter Saturn Uranus Neptune

H283.3% 86.2% 96.3% 82.5% 80%

He 16.7% 13.6% 3.3% 15.2%

(2.3% CH4)

19%

(1% CH4)

Interior Structures again• Same approach as for Galilean satellites

• Potential V at a distance r for axisymmetric body is given by

)()(1 4

4

42

2

2 Pr

RJP

r

RJ

r

GMV

• So the coefficients J2, J4 etc. can be determined from spacecraft observations

• We can relate J2,J4 . . . to the internal structure of the planet

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

C

A

R22 MR

ACJ

• 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

• 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

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

(g/cc) 1.33 0.69 1.32 1.64 5.52

2R3/GM .089 .155 .027 .026 .003

Pressure• Hydrostatic approximation• Mass-density relation• These two can be combined (how?) to get the

pressure at the centre of a uniform body Pc:

)()( rgrdrdP

2)( )(4 rrdrrdM

4

2

8

3

R

GMPc

• 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

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:

RT

P cP 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 Cp:

• Combining this equation with the hydrostatic assumption, we get:

dPdTC p

pdzdT

C

g

Temperature (2)• At 1 bar level on Jupiter, T=165 K, g=23 ms-2, Cp~3R,

=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

11 10

1

1

/1

0 )1(

PP

C

cTT

p

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 T0,P0 are reference temp. and pressure, and c is constant defined on previous slide)

Heavy elements

• He subsolar – sedimentation?• Ne depleted – dissolves in He?• Others supersolar – delivery by cold bodies (comets)?

Guillot 2005

He miscibility

Hubbard et al. 2002

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):

Data from Lodders and Fegley, Planetary Scientist’s Companion, CUP, 1998This is for all elements with relative abundances > 105 atoms.

Element H He C N O Ne Mg Si S Ar Fe

Log10 (No. Atoms)

10.44 9.44 7.00 6.42 7.32 6.52 6.0 6.0 5.65 5.05 5.95

Condens.

Temp (K)

180 -- 78 120 -- -- 1340 1529 674 40 1337

• Blue are volatile, red are refractory• Most important refractory elements are Mg, Si, Fe, S (in the

ratio 1:1:0.9:0.45)

Temperature and Condensation

Temperature profiles in a young (T Tauri) stellar nebula, D’Alessio et al., A.J. 1998

Nebular conditions can be used to predict what components of the solar nebula will be present as gases or solids:

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

Mid-plane

Photosphere

Earth Saturn

Where is everything?

J S U N P

1 AU is the mean Sun-Earth distance = 150 million kmNearest star (Proxima Centauri) is 4.2 LY=265,000 AU

KB

Me V E Ma

Note log scales!

Inner solar system

5 AU1.5 AU

Outer solar system

30 AU

Note logarithmic scales!Me V MaE

Gas giants Ice giants Terrestrial planets

Basic dataDistance (AU)

Porbital (yrs)

Protation

(days)

Mass (1024kg)

Radius (km)

(g cm-3)

Sun - - 24.7 2x106 695950 1.41

Mercury 0.38 0.24 58.6 0.33 2437 5.43

Venus 0.72 0.62 243.0R 4.87 6052 5.24

Earth 1.00 1.00 1.00 5.97 6371 5.52

Mars 1.52 1.88 1.03 0.64 3390 3.93

Jupiter 5.20 11.86 0.41 1899 71492 1.33

Saturn 9.57 29.60 0.44 568 60268 0.68

Uranus 19.19 84.06 0.72R 86.6 24973 1.32

Neptune 30.07 165.9 0.67 102.4 24764 1.64

Pluto 39.54 248.6 6.39R 0.013 1152 2.05See e.g. Lodders and Fegley, Planetary Scientist’s Companion

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)

From Guillot, 2004

Magnetic fields

Giant Impacts and Temperature

Siderophile Elements

2250K, 270 kbar

Righter AREPS 2003

• Earth – deep magma ocean required

• Mars – shallow magma ocean (?)

Hf-W system

Kleine et al. 2002

• Core formation indicates an at least partially molten silicate mantle (Stevenson 1990)

• 182Hf decays to 182W, half-life 9 Myrs

182Hf (lithophile)

182W (siderophile)

Late core formation – no excess 182W

Core forms

Undiff. planetDifferentiatedmantle

Early core formation – excess 182W in mantle

Core forms