Accretion and
Differentiation of
Earth
Dave Stevenson
Caltech
Neutrino Sciences 2007 Deep Ocean AntiNeutrino 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?
EARTH HISTORY
This
Initial
condition
Some
multidimensional
space
Evolutionary
path
Present
state
That
EARTH HISTORY
This
Initial
condition
Focus of this
talk
Astronomy,
geochemistry,
physical
modeling
Evolutionary
path
Geochemistry,
geology,
geobiology
Some
multidimensional
space
Geophysics
Present
state
That
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
Phanerozoic
106 yr
107
108
Earth accretion
109
1010 yr
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 of
kilometer bodies from dust
Rapid Formation of Moon
sized 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)
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)
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
• GM/RL ~1
where M is Earth mass, R is
Earth radius, Cp is specific heat
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 density
Other 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
Unequilibrated blob
Core
The Importance of Hf-W
182Hf
 182W
1/2 ~ 9 Ma
Core-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 
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?)
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
Early core
Core
Superheat
Adiabat of core alloy
Present mantle
and core
depth
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
Steam
atmosphere
surface
Magma ocean
~500km
Frozen (but very hot!)
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
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?
*4.4 to 3.8Ga
• Ocean and atmosphere in
place.
• Ocean may not have been
very different in volume
from now. Might be icecapped.
• 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.
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
T(t=0)=Ti
Sometimes initial
conditions matter a lot;
e.g., layered system
with compositional
differences comparable
or larger than T
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 Earth
1. 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?
Height
Bulge could arise
from melt migration
in transition zone
Height
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
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
T
melting curve
Adiabat
(convective)
Liquid
(magma
ocean)
solid
Rheological
boundary
P
T (K)
6000
Realistic
Consequence
Contributing
regions of last
equilibration
Magma
ocean base
4000
2000
Most of
Earth
history
Approximate
conditions in
present Earth
Precursor
bodies
0.01
0.1
1
P(Mbar)
Halliday, 2003
Core Formation;
Mantle
Oxidation State
• General idea
may still work
even with giant
impacts
Wood et al, 2006
CoreForming
Process
es
• Rainfall & ponding
• Percolation
• Diapirism (RayleighTaylor)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”
0.1 
Liquid silicate disk
Core is
isolated
Has ~0.8
before
processing
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
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