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).

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?

This

That

Some multidimensional space

Initial condition

Present state

Evolutionary path

EARTH HISTORY

This

That

Some multidimensional space

Initial condition

Present state

Evolutionary path

EARTH HISTORY

GeophysicsFocus of this talk

Astronomy, geochemistry, physical modeling

Geochemistry,

geology,

geobiology

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

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

106 yr 107 108 109 1010 yr

Phanerozoic

Earth accretion

Nucleosynthesis in massive stars (supernovae for the heaviest elements)

Interstellar medium

Solar nebula

Sun & planets

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

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?)

Rapid formation ofkilometer bodies from dust

Rapid Formation of Moonsized bodies by runaway accretion

Slow (~10 Ma) Formation of Earthlike Planets

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)

Mars mass embryo -hot & differentiated

Solar nebula

Gas density enhancement

~exp[GM/Rc2]

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

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

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

Some Important Numbers

• GM/RCp~ 4 x 104K where M is Earth mass, R is

Earth radius, Cp is specific heat

• GM/RL ~1 where 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 Eradio where Egrav is the energy released by Earth

formation and Eradio is the total radioactive heat release over geologic time

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

Core Formation requires…

• Immiscible components (iron & silicate)

• Macrosegregation of components: At least one was mostly molten

• Substantial Difference in densityOther kinds of differentiation (ocean &

atmosphere formation, continental crust) are not conceptually that different although the details differ a lot.

Core Formation

Stevenson, 1989

Wood et al, 2006

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

Core

Unequilibrated blob

The Importance of Hf-W

182Hf 182W 1/2 ~ 9 MaCore-loving

“early”

“late”

Excess 182W observed

No excess

Early differentiation event in Moon sized bodies collision

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

Early differentiation event in Moon sized bodies collision

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

Quantitative Interpretation of

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?)

CHUR

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

depth

Core Superheat

Early core

Present mantle and core

Adiabat of core alloy

The “Inevitability” of a Magma Ocean

• 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

Frozen (but very hot!)

~500km

Steam atmosphere

Differentiation in the Mantle?

CORE

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?

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

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

Early Earth* Environment?• 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.

*4.4 to 3.8Ga

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.

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!

The End….of the beginning

(but not the beginning of the end)

Geology, 2002

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

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

T(t=0)=Ti T(t=) depends only weakly on Ti if T, Ti differ significantly

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

Some Specific issues with Earth1. 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?

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

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

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

6. What about life?

Rayleigh-Taylor Instabilities & Convective Stirring?

Uncompressed Density

Height

Uncompressed Density

Height

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

Bulge could arise from melt migration in transition zone

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

Core-Mantle EquilibrationSignificant (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?

Fundamental Principles of Magma Oceans

• 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

Adiabat (convective)

melting curveT

P

Liquid (magma ocean)

solid

Rheological boundary

T (K)

P(Mbar)0.01 0.1 1

2000

4000

6000

Approximate conditions in present Earth

Magma ocean base

Precursor bodies

Most of Earth history

Realistic Consequence

Contributing regions of last equilibration

Halliday, 2003

Core Formation; Mantle

Oxidation State

• General idea may still work even with giant impacts

Wood et al, 2006

Core-Forming Process

es• Rainfall & ponding• Percolation• Diapirism (Rayleigh-

Taylor)includes l=1 and self-heating as special cases

• Cracks

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

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

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

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”

Liquid silicate disk

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

Has ~0.8 before processing

Core is isolated

0.1

Volcanism & Volatile Release

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

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

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