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

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

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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 . . .

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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)

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Classes of planetary bodies
Ice H,He 15 Me 800 GPa 8000 K
Mainly H,He 300 Me 7000 GPa 20,000 K

• Rock
• 1 Me
• 300 GPa
• 6000 K

Rockice 0.1 Me 10 GPa 1500 K
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What do we know?
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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 (dont hold your breath)

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1. Static properties

• Equations of state
• Hydrogen Helium
• Everything else
• (Silicate) Melting

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

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H/He - Summary

• H EOS/compressibility
• Size of Jupiters 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

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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
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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
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(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

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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
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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

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2. Dynamic Properties

• Rheology
• Dissipation
• Conductivity
• Partitioning

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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)
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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
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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?
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Dissipation measurements
0 -1 -2 -3 -4 -5 -6
-7 -8 -9
Increasing dissipation
Maxwell model
Andrade model (a0.3)
Andrade model (a0.2)
Apples vs. oranges?
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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)

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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

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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 gtgt 1
• Major growth areas (e.g. extra-solar planets)
• Funding possibilities? (e.g. NASA PIDDP)

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Conclusion a shopping list

• H molecular-metallic transition and He
  miscibility
• He EOS (gt 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

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Questions?
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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
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Extra-solar planets

• Hot Jupiters have more heating (radiative,
  tidal)
• Larger core masses? (close-in means less easy to
  scatter planetesimals)

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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) timescale
  tmh/m
• The body behaves elastically at timescales ltlttm
  and in a viscous fashion at timescales gtgt tm

• Dissipation is maximized when timescale tm

Tobie et al. JGR 2003
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Interior Structure of GJ 876d
20,000
7.5 ME
DENSITY (kg/m3)
12,000
Valencia, Sasselov, OConnell (2006)
4,000
2,000
6,000
10,000
RADIUS (km)
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Partitioning
Can siderophile element abundances be explained
by high P,T partition coefficients?
Walter et al. 2000
Kegler et al. 2005
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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 HHe (J,S) or H/Heice (U,N)

radius
Constant density
mass
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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.

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Compositions (1)

• Well 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)
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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

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Interior Structure (contd)

• Recall how J2 is defined

C
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

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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?)

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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 Pc7 Mbar, Saturn Pc1.3 Mbar, U/N Pc0.9
  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

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Temperature (1)

• If parcel of gas moves up/down fast enough that
  it doesnt 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, 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

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Temperature (2)

• At 1 bar level on Jupiter, T165 K, g23 ms-2,
  Cp3R, m0.002kg (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 g1.5 Note that density
increases more rapidly than temperature why?
Slope determined by g
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Heavy elements
Guillot 2005

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

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He miscibility
Hubbard et al. 2002
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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 110.90.45)

Data from Lodders and Fegley, Planetary
Scientists Companion, CUP, 1998 This is for all
elements with relative abundances gt 105 atoms.
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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, DAlessio et al., A.J. 1998
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Where is everything?
Note logarithmic scales!
Ma
V
E
J
S
U
KB
Me
N
P
1 AU is the mean Sun-Earth distance 150 million
km Nearest star (Proxima Centauri) is 4.2
LY265,000 AU
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Basic data
See e.g. Lodders and Fegley, Planetary
Scientists Companion
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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)

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From Guillot, 2004
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Magnetic fields
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Giant Impacts and Temperature
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Siderophile Elements

• Earth deep magma ocean required
• Mars shallow magma ocean (?)

2250K, 270 kbar
Righter AREPS 2003
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Hf-W system

• Core formation indicates an at least partially
  molten silicate mantle (Stevenson 1990)
• 182Hf decays to 182W, half-life 9 Myrs

Kleine et al. 2002