moving beyond the earth: what use is mineral physics to planetary scientists? francis nimmo (u. c....
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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
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