1. thermal evolution and Geoneutrino studies
Models of the Earth:
thermal evolution and Geoneutrino studies
Bill McDonough, Yu Huang and Ondřej Šrámek
Geology, U Maryland
Steve Dye, Natural Science,
Hawaii Pacific U and Physics, U Hawaii
Shijie Zhong, Physics, U Colorado
Fabio Mantovani, Physics, U Ferrara, Italy

2. Earth Models Update: …just the last 6 months!
Campbell and O’Neill (March , Nature): “Evidence against a chondritic Earth”
Murakami et al (May , Nature): “…the lower mantle is enriched in silicon … consistent with the [CI] chondritic Earth model.”
Warren (Nov , EPSL): “Among known chondrite groups, EH yields a relatively close fit to the stable-isotopic composition of Earth.”
Zhang et al (March , Nature Geoscience): The Ti isotopic composition of the Earth and Moon overlaps that of enstatite chondrites.
Fitoussi and Bourdon (March , Science): “Si isotopes support the conclusion that Earth was not built solely from enstatite chondrites.”
- Compositional models differ widely, implying a factor of two difference in the U & Th content of the Earth

3. Geoneutrino studies Nature & amount of Earth’s thermal power
radiogenic heating vs secular cooling
- abundance of heat producing elements (K, Th, U) in the Earth
- clues to planet formation processes
- amount of radiogenic power to drive mantle convection & plate tectonics
- is the mantle compositionally layered or have large structures?
estimates of BSE from 9TW to 36TW
constrains chondritic Earth models
estimates of mantle 1TW to 28TW
layers, LLSVP, superplume piles
Geoneutrino studies

4. U content of BSE models
Nucelosynthesis: U/Si and Th/Si production probability
Solar photosphere: matches C1 carbonaceous chondrites
Estimate from Chondrites: ~11ppb planet (16 ppb in BSE)
Heat flow: secular cooling vs radiogenic contribution… ?
Modeling composition: which chondrite should we use?
A brief (albeit biased) history of U estimates in BSE:
Urey (56) 16 ppb Turcotte & Schubert (82; 03) 31 ppb
Wasserburg et al (63) 33 ppb Hart & Zindler (86) 20.8 ppb
Ganapathy & Anders (74) 18 ppb McDonough & Sun (95) 20 ppb ± 20%
Ringwood (75) 20 ppb Allegre et al (95) 21 ppb
Jagoutz et al (79) 26 ppb Palme & O’Neill (03) 22 ppb ± 15%
Schubert et al (80) 31 ppb Lyubetskaya & Korenaga (05) 17 ppb ± 17%
Davies (80) ppb O’Neill & Palme (08) 10 ppb
Wanke (81) 21 ppb Javoy et al (10) 12 ppb

5. Nebula Meteorite Planet: mix of metal, silicate, volatiles
What is the composition of the Earth?
and where did this stuff come from?
Nebula
Meteorite
Heterogeneous mixtures of components with different formation temperatures and conditions
Planet:
mix of metal, silicate, volatiles

6. “Standard” Planetary Model
Orbital and seismic (if available) constraints
Chondrites, primitive meteorites, are key
So too, the composition of the solar photosphere
Refractory elements (RE) in chondritic proportions
Absolute abundances of RE – model dependent
Mg, Fe, Si & O are non-refractory elements
Chemical gradient in solar system
Non-refractory elements: model dependent
U & Th are RE, whereas K is moderately volatile

8. Most studied meteorites
fell to the Earth ≤0.5 Ma ago

9. Mg/Si variation in the SS
Forsterite
-high temperature
-early crystallization
-high Mg/Si
-fewer volatile elements
Enstatite
-lower temperature
-later crystallization
-low Mg/Si
-more volatile elements

10. Inner nebular regions of dust to be highly crystallized,
Outer region of one star has
- equal amounts of pyroxene and olivine
- while the inner regions are dominated by olivine.
Boekel et al (2004; Nature)
Olivine-rich
Ol & Pyx

11. Pyrolite-EARTH CO CV CI CM H LL L EL Enstatite-EARTH EH Olivine-rich
Pyroxene-rich

12. SS Gradients EARTH CO CV CI CM H LL L MARS EL EH Mars @ 2.5 AU
1 AU
Olivine-rich
EARTH CO CV CI CM H LL L
MARS EL
SS Gradients
-thermal
-compositional
-redox EH
Pyroxene-rich

13. Moles Fe + Si + Mg + O = ~93% Earth’s mass
weight % elements
Moles Fe + Si + Mg + O = ~93% Earth’s mass
(with Ni, Al and Ca its >98%)

15. Volatiles in Chondrites (alkali metals) Enstatite Chondrites
enriched in volatile elements
High 87Sr/86Sr [c.f. Earth]
40Ar enriched [c.f. Earth]
CI and Si Normalized

16. 142mNd What does this Nd data mean for the Earth? Earth
Solar S heterogeneous
Chondrites are a guide
Planets ≠ chondrites ?
Enstatite
chondrites
Ordinary
chondrites
Carbonaceous
chondrites
Data from:
Gannoun et al (2011, PNAS)
Carlson et al (Science, 2007)
Andreasen & Sharma (Science, 2006)
Boyet and Carlson (2005, Science)
Jacobsen & Wasserburg (EPSL, 1984)

17. Enstatite chondrite vs Earth diagrams from Warren (2011, EPSL)
Carbonaceous
chondrites
diagrams from Warren (2011, EPSL)
Carbonaceous
chondrites
Carbonaceous
chondrites

18. Mg/Si -- is very different
Earth is “like” an Enstatite Chondrite!
Mg/Si -- is very different
shared isotopic: O, Ti, Ni, Cr, Nd,..
shared origins -- unlikely
core composition -- no K, Th, U in core
“Chondritic Earth” -- losing meaning…
6) Javoy’s model – recommend modifications

19. Th & U K
from McDonough & Sun, 1995

20. Chromatographic separation Mantle melting & crust formation
U in the Earth:
~13 ng/g U in the Earth
Metallic sphere (core)
<<<1 ng/g U
Silicate sphere
20* ng/g U
*Javoy et al (2010) predicts 12 ng/g
*Turcotte & Schubert (2002) 31 ng/g
Continental Crust
1300 ng/g U
Mantle
~12 ng/g U
“Differentiation”
Chromatographic separation
Mantle melting & crust formation

21. Parameterized Convection Models
vigor of convection
Thermal evolution of the mantle
Q Rab
Q: heat flux, Ra: Rayleigh number,
: an amplifer - balance between viscosity and heat dissipation
h = viscosity
= density
g = accel. due gravity
a = thermal exp. coeff.
= thermal diffusivity
d = length scale
T = boundary layer To
rogan (T1– T0)d3
h k
Ra =
Ramantle > Racritical
mantle convects!
Some mantle convection model suggests that the radiogenic heat produced should a larger fraction of the total heat flow. So at least one of the following have some problems: the total heat flow measured, the estimated amounts of U, Th or K, or the mantle convection model. So, by measuring the antineutrinos from beta decays of daughter nuclei in the U and Th decay chains, we can maybe serve as a cross-check of the radiogenic heat production rate.
chondritic meteorites -> 19TW, mantle convection model->more
>70% should be from radiogenic heat.
Need to subtract continental crust contribution (6.5TW) -> only ~35% (44TW) or ~51%(31TW).
At what rate does the Earth dissipate its heat?
Models with b ~ Schubert et al ‘80; Davies ‘80; Turcotte et al ‘01
Models with b << Jaupart et al ‘08; Korenaga ‘06; Grigne et al ‘05,’07

22. Convection Urey Ratio and Mantle Models
radioactive heat production
Urey ratio =
heat loss
Mantle convection models typically assume:
mantle Urey ratio: ~0.7
Geochemical models predict:
mantle Urey ratio ~0.3
Factor of 2 discrepancy

23. Earth’s surface heat flow 46 ± 3 (47 ± 2)
Mantle cooling
(18 TW)
Crust R*
(8 ± 1 TW)
Core
(~9 TW) -
(4-15 TW)
Mantle R*
(12 ± 4 TW)
total R*
20 ± 4
*R radiogenic heat
(0.4 TW) Tidal dissipation
Chemical differentiation
after Jaupart et al 2008 Treatise of Geophysics

24. Radioactive decay driving the Earth’s engine!
Plate Tectonics,
Convection,
Geodynamo
Radioactive decay driving the Earth’s engine!

25. 2011
Detecting
Geoneutrinos
from the Earth
2005
2010

26. Terrestrial antineutrinos from uranium and thorium are detectable
40K
νe + p+ → n + e+
1.8 MeV Energy Threshold
212Bi
228Ac
1α, 1β
4α, 2β
208Pb νe
2.3 MeV
2.1 MeV
234Pa
214Bi
5α, 2β
206Pb
2α, 3β
3.3 MeV
40Ca 1β
Terrestrial antineutrinos from
uranium and thorium are detectable
31% 1%
46%
20%
Efforts to detect
K geonus
underway

28. Reactor and Earth Signal
Reactor Background
with oscillation
Geoneutrinos
KamLAND
KamLAND was designed to detect reactor antineutrinos to measure the neutrino oscillation parameters. The picture shows the locations of KamLAND and all the nearby nuclear reactors. Nuclear reactors are indicated by the red-green dots. Naturally, the most significant background for geoneutrino detection is the antineutrinos from these reactors. The right plot shows the expected energy distributions of the geoneutrino spectrum and reactor background.
KamLAND was designed to measure reactor antineutrinos.
Reactor antineutrinos are the most significant contributor to the total signal.

29. Latest results 106 9.9 KamLAND +29 -28 Event rates +4.1 Borexino -3.4
from 2002 to Nov 2009
Event rates
9.9
+4.1
-3.4
from May ‘07 to Dec ‘09
Borexino
under construction

30. Summary of geoneutrino results
Constrainting U & Th in the Earth
MODELS
Cosmochemical: uses meteorites – Javoy et al (2010); Warren (2011)
Geochemical: uses terrestrial rocks – McD & Sun, Palme & O’Neil, Allegre et al
Geophysical: parameterized convection – Schubert et al; Davies; Turcotte et al; Anderson

31. Earth’s geoneutrino flux
U or Th
FX(r0)
Flux of anti-neutrinos from X at detector position r0 AX
Frequency of radioactive decay of X per unit mass NX
Number of anti-neutrinos produced per decay of X R
Earth radius
aX(r)
Concentration of X at position r
r(r)
Density of earth at position r
Interrogating “thermo-mechanical pile” (super-plumes?) in the mantle …

32. Present and future LS-detectors
Borexino, Italy (0.6kt)
KamLAND, Japan (1kt)
SNO+, Canada (1kt)
Europe
Hanohano, US
ocean-based (10kt)
LENA, EU
(50kt)

33. Constructing a 3-D reference model Earth
assigning chemical and physical states to Earth voxels

34. Estimating the geoneutrino flux at SNO+
Geology
Geophysics
seismic
x-section

35. Global to Regional RRM SNO+ Sudbury Canada using only global inputs
improving our flux models
This map shows the decrease of flux from each tile in the refined regional model. The bottom 5 tiles are covered by sedimentary rock and the upper crust is not be able to be refined. Thus, the signals remain the same. The signal from all the 15 tiles and central tile both decrease by about 10%
adding the regional geology

36. Structures in the mantle

37. Testing Earth Models

38. SUMMARY
Earth’s radiogenic (Th & U) power
20 ± 9 TW* (23 ± 10)
Prediction: models range from
11 to 28 TW
Future: -SNO+ online early 2013
…2020…??
- Hanohano
LENA
Neutrino Tomography… 