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Accretion and Differentiation of Earth. Dave Stevenson Caltech Neutrino Sciences 2007 Deep Ocean Anti-Neutrino Observatory Workshop Honolulu, Hawaii March 23-25, 2007. Definitions. Accretion means the assembly of Earth from smaller bits

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Accretion and differentiation of earth l.jpg

Accretion and Differentiation of Earth

Dave Stevenson

Caltech

Neutrino Sciences 2007 Deep Ocean Anti-Neutrino Observatory Workshop Honolulu, Hawaii March 23-25, 2007


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Definitions

  • Accretion means the assembly of Earth from smaller bits

  • Differentiation means the separation of components within Earth during or after assembly - in this talk it will be primarily the “initial” differentiation (~4.4Ga or earlier).


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The Big Questions

  • What is the radiogenic heat production inside Earth both now and in the past?

  • How is this related to other reservoirs we know about (Sun & meteorites)?

  • How is that heat production distributed spatially now and in the past?

  • How is heat production related to heat output now and in the past?

  • Are there any important unconventional heat sources (radiogenic or otherwise)?

  • What was the initial condition?


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EARTH HISTORY

This

Some multidimensional space

Initial condition

Evolutionary path

Present state

That


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EARTH HISTORY

This

Some multidimensional space

Initial condition

Focus of this talk

Astronomy, geochemistry, physical modeling

Geophysics

Evolutionary path

Geochemistry, geology, geobiology

Present state

That


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How to think about a Planet (e.g., Earth)?

  • Could discuss provenance- the properties of an apple depend on the environment in which the tree grows

  • Or could discuss it as a machine (cf. Hero[n], 1st century AD)

  • Need to do both


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The (logarithmic) way one should think about time if you want to understand processes and their outcome

Phanerozoic

106 yr

107

108

109

1010 yr

Earth accretion


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Nucleosynthesis in massive stars (supernovae for the heaviest elements)

Interstellar medium

Solar nebula

Sun & planets


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Interstellar medium contains gas & dust that undergoes gravitational collapse

A “solar nebula” forms: A disk of gas and dust from which solid material can aggregate


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Terrestrial Planet formation

  • Rapid collapse from ISM; recondensation of dust; high energy processing

  • Small (km) bodies form quickly (<106yr)[observation]. Some of these bodies differentiate ( 26Al heating)

  • Moon & Mars sized bodies may also form as quickly[theory] -will also therefore differentiate (perhaps imperfectly)

  • Orbit crossing limits growth of big bodies: Time ~ 107- 108 yr.

  • Last stages in absence of solar nebula [astronomical obs.]

  • Mixing across ~1AU likely (chemical disequilibrium?)


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In current terrestrial accretion models, the material that goes into making Earth comes from many different regions

Volatile depletion in the terrestrial planet forming materials (affects potassium; not U & Th)

Zonation of composition in terrestrial zone is unlikely

Results from Chambers, 2003 (Similar results from Morbidelli)


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Solar nebula

Gas density enhancement

~exp[GM/Rc2]

Mars mass embryo -hot & differentiated

This predicts only modest ingassing (even assuming the embryo has an accessible magma ocean)


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The Importance of Giant Impacts

  • Simulations indicate that Mars-sized bodies probably impacted Earth during it’s accumulation.

  • These events are extraordinary… for a thousand years after one, Earth will radiate like a low-mass star!

  • A large oblique impact places material in Earth orbit: Origin of the Moon


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Formation of the Moon

  • Impact “splashes” material into Earth orbit

  • The Moon forms from a disk in perhaps a few 100 years

  • One Moon, nearly equatorial orbit, near Roche limit- tidally evolves outward


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Some Important Numbers

  • GM/RCp~ 4 x 104Kwhere M is Earth mass, R is Earth radius, Cp is specific heat

  • GM/RL ~1where L is the latent heat of vaporization of rock

  • Equilibrium temp. to eliminate accretional heat ~400K

    (but misleading because of infrequent large impacts and steam atmosphere)

  • Egrav~10 Eradiowhere Egrav is the energy released by Earth formation and Eradio is the total radioactive heat release over geologic time


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What Memory does Earth have of Accretion?

  • Overall composition (almost a closed system)

  • Isotopic

  • Bulk chemistry (partitioning; provided reservoirs are not fully equilibrated)

  • Thermal if layered


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Core Formation requires…

  • Immiscible components (iron & silicate)

  • Macrosegregation of components: At least one was mostly molten

  • Substantial Difference in density

    Other kinds of differentiation (ocean & atmosphere formation, continental crust) are not conceptually that different although the details differ a lot.


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Wood et al, 2006

Core Formation

Stevenson, 1989


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Core Formation with Giant Impacts

  • Imperfect equilibration no simple connection between the timing of core formation and the timing of last equilibration

  • No simple connection between composition and a particular T and P.

Molten mantle

Unequilibrated blob

Core


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The Importance of Hf-W

182Hf  182W 1/2 ~ 9 Ma

Core-loving

Excess 182W observed

“early”

No excess

“late”


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Early differentiation event in Moon sized bodies

collision

CORE MERGING EVENT (Hf-W timescale  planet formation timescale)


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Early differentiation event in Moon sized bodies

collision

EMULSIFICATION DURING IMPACT (Hf-W timescale  planet formation timescale provided emulsification is sufficiently small scale)


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Quantitative Interpretation of 

CHUR

Chondritic reference (=0)

Very Early core formation  >>1

Late core formation  ~0

Earth observation is =1.9

Many combinations of events can give this value.. but the likely inference is that the last major core forming events occurred ~50 Ma (last giant impact?)


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Core Superheat

Early core

Core Superheat

  • This is the excess entropy of the core relative to the entropy of the same liquid material at melting point & and 1 bar.

  • Corresponds to about 1000K for present Earth, may have been as much as 2000K for early Earth.

  • It is diagnostic of core formation process...it argues against percolation and small diapirs.

T

Adiabat of core alloy

Present mantle and core

depth


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The “Inevitability” of a Magma Ocean

Steam atmosphere

  • Burial of accretional energy prevents immediate re-radiation - a chill crust can form.

  • In presence of sufficient atmosphere (e.g., steam), the magma ocean is protected.

  • Lower mantle can easily freeze because of pressure - this limits magma ocean depth

surface

Magma ocean

~500km

Frozen (but very hot!)


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Differentiation in the Mantle?

Dense suspension, vigorously convecting. May be well mixed Solomatov & Stevenson(1993)

Much higher viscosity, melt percolative regime. Melt/solid differentiation?

High density material may accumulate at the base.Iron-rich melt may descend?

CORE


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A Layered Mantle?

  • Unlikely to arise in the magma ocean (suspended crystal stage)

  • Could arise from percolative redistribution (melt migration near the solidus) after magma ocean phase

  • Might (or might not) be eliminated by RT instabilities & thermal convection

  • Could be relevant to D”, or to a thicker layer.

  • Growing evidence for its existence

Kellogg et al, 1999


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Cooling times …to decrease mean T by ~1000K

  • From a silicate vapor atmosphere: 103yr

  • From a deep magma ocean/steam atmosphere: 106 yr

  • Capped magma ocean: Up to 108 yr [cold surface!]

  • Hot subsolidus convection : Few x108 yr

  • At current rate: >1010 yr


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Early Earth* Environment?

*4.4 to 3.8Ga

  • Ocean and atmosphere in place.

  • Ocean may not have been very different in volume from now. Might be ice-capped.

  • Atmosphere was surely very different… driven to higher CO2 by volcanism, but the recycling is poorly known. When did plate tectonics begin?

  • Uncertain impact flux but consequences of impacts are short lived.


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Conclusions

  • Timing of Earth formation still uncertain but compatible with a few x 107 yr duration. Hf-W constrains but does not clearly provide this timing.

  • High energy origin of Earth extensive melting and magma ocean

  • Legacy expressed in core superheat & composition (siderophiles in the mantle, light elements in the core) -but not yet understood. Maybe also in primordial mantle differentiation.

  • Rapid cooling at surface but a “Hadean” world. Impacts may affect onset time of sustained life.


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Responses to the Big Questions

  • What is the radiogenic heat production inside Earth both now and in the past?Determined by U, Th and K in the source material… maybe some K is lost.

  • How is this related to other reservoirs we know about (Sun & meteorites)?Closely related (U, Th) ; K depleted; but some uncertainty

  • How is that heat production distributed spatially now and in the past? Core formation: Any U, Th or K in the core? Primordial mantle differentiation?

  • How is heat production related to heat output now and in the past? Later speakers

  • Are there any important unconventional heat sources (radiogenic or otherwise)? No compelling evidence or good candidates

  • What was the initial condition? Very hot!


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The End….of the beginning

(but not the beginning of the end)


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Geology, 2002


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Sometimes initial conditions don’t matter much….e.g., heat flow  Tn with n > 2 or 3

T(t=0)=Ti

T(t=) depends only weakly on Ti if T, Ti differ significantly

Sometimes initial conditions matter a lot; e.g., layered system with compositional differences comparable or larger than T

Some history is preserved in the compositional layering (through imperfect mixing or through heat storage)


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Some Specific issues with Earth

  • How hot was it? (And does any of that “signature” remain?)

    2. How is the starting state expressed in the mantle and core composition and layering?

  • How does this depend on our (imperfect) understanding of planetary accumulation.

  • What do we learn from the Moon, & from other planets.

  • What were conditions like on early Earth? What is the origin of atmosphere and ocean.

  • What about life?


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Rayleigh-Taylor Instabilities & Convective Stirring?

Height

Height

Bulge could arise from melt migration in transition zone

May (or may not) become well mixed after freezing & RT instabilities?

Uncompressed Density

Uncompressed Density

But this all depends on the (as yet unknown) phase diagram!


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Core-Mantle Equilibration

Significant (perhaps unexpected) success in explaining mantle siderophiles through equilibrium at a particular P,T representative of the base of the magma ocean

Problem: Lack of knowledge at higher P,T.. Could still fit the data with a mixing line that includes higher P,T?


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Melting curve steeper than the adiabat (at most depths)

Freezing of most of the deeper part of the ocean is fast (~1000yrs). Processes deep down involve solid silicates.

Freezing of shallow part can be slow (up to 100Ma).

T vs. P in a planet

Fundamental Principles of Magma Oceans

melting curve

T

Adiabat (convective)

Liquid (magma ocean)

solid

P

Rheological boundary


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T (K)

Realistic Consequence

Most of Earth history

6000

Contributing regions of last equilibration

Magma ocean base

4000

Approximate conditions in present Earth

Precursor bodies

2000

0.01

0.1

1

P(Mbar)


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Halliday, 2003


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Core Formation; Mantle Oxidation State

  • General idea may still work even with giant impacts

Wood et al, 2006


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Core-Forming Processes

  • Rainfall & ponding

  • Percolation

  • Diapirism (Rayleigh-Taylor)includes l=1 and self-heating as special cases

  • Cracks


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Earth’s Engine

  • Plate tectonics is not at all obvious! But once in motion, it is a heat engine.

  • But why do plates happen? Mantle convection does not require plates!

Cold slab sinks under the action of gravity


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Plate Tectonics & the Role of Water

  • Water lubricates the asthenosphere

  • Water defines the plates

  • Maintenance of water in the mantle depends on subduction; this may not have been possible except on Earth


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What Happens During a Giant Impact?

  • Most of the material is melted; part is vaporized.

  • Much of the Core of projectile is often intact and crashes into Earth, plunging to the core on a free fall time.

  • Severe distortion (sheets, plumes; not spheres). But SPH does not indicate much direct mixing.

Canup & Asphaug


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Oxygen Isotopes

  • Fundamental origin of the differences between Earth, Mars and meteorites is not understood

  • Still, the “identity” of Earth & Moon is often taken to imply same “source”


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0.1 

Has ~0.8 before processing

Liquid silicate disk

Core is isolated

Silicate vapor atmosphere

IN BETWEEN

A disk exists for 102 103 years. Radiates at ~2500K. Vapor pressure ~10 to 100 bars.

Timescale for exchange between vapor & atmosphere ~10c/(G) ~ week. Aided by “foam”.

Convective timescale in disk or Earth mantle ~week

Convective timescale in atmosphere ~days


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Volcanism & Volatile Release

  • Earth’s atmosphere & ocean came in part through outgassing

  • But volatiles are recycled on Earth- the inside of Earth is “wet”


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Some Conclusions

  • SPH or other large scale codes do not tell you the extent of mixing.

  • There is the possibility of incomplete mixing (i.e., preservation of Hf-W from an earlier core separation event). But the importance of this is not deterministic. Most likely when the iron is in large quasi-spherical blobs.

  • Roughly speaking, this applies to planets independent of size (except that small bodies may suffer higher energy impacts where vimpact >> vescape, which enhances mixing.

  • There is no straightforward connection between the measured W and the timing of Earth core formation


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