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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

Accretion and Differentiation of Earth

Dave Stevenson


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

  • 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
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?



Some multidimensional space

Initial condition

Evolutionary path

Present state





Some multidimensional space

Initial condition

Focus of this talk

Astronomy, geochemistry, physical modeling


Evolutionary path

Geochemistry, geology, geobiology

Present state


how to think about a planet e g earth
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




1010 yr

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
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?)

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)


Solar nebula

Gas density enhancement


Mars mass embryo -hot & differentiated

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

the importance of giant impacts
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
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
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
what memory does earth have of accretion
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
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.

core formation with giant impacts
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


the importance of hf w
The Importance of Hf-W

182Hf  182W 1/2 ~ 9 Ma


Excess 182W observed


No excess



Early differentiation event in Moon sized bodies


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


Early differentiation event in Moon sized bodies


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

quantitative interpretation of
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?)

core superheat
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 argues against percolation and small diapirs.


Adiabat of core alloy

Present mantle and core


the inevitability of a magma ocean
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


Magma ocean


Frozen (but very hot!)

differentiation in the mantle
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?


a layered mantle
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
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
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.
  • 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
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)


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


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)

some specific issues with earth
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?
rayleigh taylor instabilities convective stirring
Rayleigh-Taylor Instabilities & Convective Stirring?



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!

core mantle equilibration
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?

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

Fundamental Principles of Magma Oceans

melting curve


Adiabat (convective)

Liquid (magma ocean)



Rheological boundary


T (K)

Realistic Consequence

Most of Earth history


Contributing regions of last equilibration

Magma ocean base


Approximate conditions in present Earth

Precursor bodies






core formation mantle oxidation state
Core Formation; Mantle Oxidation State
  • General idea may still work even with giant impacts

Wood et al, 2006

core forming processes
Core-Forming Processes
  • Rainfall & ponding
  • Percolation
  • Diapirism (Rayleigh-Taylor)includes l=1 and self-heating as special cases
  • Cracks
earth s engine
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
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
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
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”

0.1 

Has ~0.8 before processing

Liquid silicate disk

Core is isolated

Silicate vapor atmosphere


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

volcanism volatile release
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
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