Cooling of Earthʼs core andmantle - With or Without amysterious structure below thecore-mantle boundary
Takashi Nakagawa (MAT, JAMSTEC)

Earth system dynamics modelingand target of this talk…

Target area of this talk
The long-term thermal and chemical evolution of Earth could be described as coremantle-plate-environmental system connected in terms of heat transfer caused bymantle dynamics (the slowest dynamics)

Earth as a cooling system
Radiogenic heat producing element (HPE)
Geochemical analysis as well as ʻgeoneutrinoʼ
observations
311

Mantle geo-neutrino rate (TNU)

S.T. Dye et al. / Physics Procedia 61 (2015) 310 – 318

Radial Symmetric Mantle

25Pcc= 6.8 +1.4/-1.1 TW
Homogeneous
20
DMM + Sunken Layer

15

KamLAND + Borexino-1Exposure = 5.3 TNU

10FCMB~10 TW; FS~40 TW; QR~10 to30 TW - Cooling rate ~ 125 to 200
K/GyrsRate = 7.7±6.2 TNU

57 - 29 TW
0051015202530
BSE Radiogenic Power (TW)

Melting Model in the upper mantle- Cooling rate ~ 75 K/Gyrs [Abbottet al., 1994]

Dye et al. [2015]

enic power of bulk silicate Earth (BSE) is constrained between 7 and 29 TW by the combined measurement of geo-neutrinos

However, the amount of HPE would
not matter with thermal evolution

Not very diﬀerent for theamount of HPE in the mantle- Cooling rate ~ 70 to 80 K /Gyrs
Nakagawa and Tackley [2012]

2790.07
0.02
0.10

&2.12
&1.91
&1.77

&2.09
&1.94
&1.85

HPE in the metallic core - Tiny partitioncoeﬃcient: Mainly partitioning into themantle

de and Wood (2005).
t in silicate [wt%] in each study.

Major HPE source in the core Potassium
DK~O(0.01) - only few 10s ppm
could be partitioned into the molten
iron: Very small contribution of coreheat budget - HPE would not belikely to be found in the mantle
rather than metallic core.
Also suggested from partitioning oflight elements in the metallic core
[Hirose et al., 2013].

Watanabe[2014]
4. Temperature dependencyof log DKetat al.
1, 27,
and 60 GPa. DK has a positive
perature dependence and negative pressure dependence. The black dashed, blueRecent hot topic on structure in the core-mantleboundary region - A weird (mysterious) feature foundin seismological and geomagnetic secular variation
analyses

Helﬀrich and Kaneshima [2010] Buﬀett [2014] - Geomagnetic secular variations
MAC wave in the stable region could be explained.
- Seismology

Goal of this talk•

Formulate thermo-chemical evolution ofEarthʼs core•

Implement it into numerical mantle convection
simulations•

How does it work in core-mantle evolution
system.

•Implications and conclusions.

The origin of stable region below theCMB - Thermal or chemical or both?

Buﬀett and Seagle [2010]- Core-mantle chemical coupling

Labrosse [2015] - sub-adiabatic region
occurred by high core thermal
conductivity

Core-mantle
thermo-chemical coupling?
Buﬀett et al. [2001]- Sediment caused by inner core growth?

Two types of stable region
beneath the CMB

Sub-adiabatic shell allows growing beneath the compositionally-stable region only if
the heat ﬂow across the CMB is sub-adiabatic - Assume that the heat ﬂow in thestable region would be equivalent to the CMB heat ﬂow.

First - Compositional evolution
Based on Buﬀett and Seagle [2010 in JGR]
Assumptions
1. Two diﬀusion processes are
assumed in the stable region Simple chemical diﬀusion andbaro-diﬀusion.
2. Fe(mw)→Fe(m)+O(m): Oxygenis the light element of Earthʼscore; This oxygen is supplied
from core-mantle equilibrium
chemical reaction (Frost et al.,2010); Chemical boundary
condition at CMB is as afunction of CMB temperature.
3. At the interface, the neutral
buoyancy state is assumed.

From the mass balance at the interface,02202

Core-mantle chemical coupling FROST ET AL.: CORE-MANTLE OXYGEN PARTITIONING
Thermodynamics
model developed
phisticated methods. Accounting forfrom high P-T experiments

Frost et al. [2010]

volume of mixing between Fe andamount of O required to satisfying thapproximately 0.5 wt%.
[25] At low pressures, Fe-FeO imm
in large positive deviations from ideliquids. The negative excess volum
activities toward ideal mixing with ibut by core-mantle boundary (CMB)
mw→Fem+Om
negative
fromideality toFeOdeviations
cannot assess
the effectsreactionof pressure on
Equilibrium
partitioning
we note that such negative deviations iordered intermediate liquid species suchEarthʼsbecore- Under-saturated
for light
an indicationthat corresponding
soli
stoichiometries
may also become stabl
elements
although to date none have been identi[26] By extrapolating the model t
But not
assumedfor partitioning
ofrelapresent-day
CMB(136 GPa), theHPE
in thecontent
metallic
here.and th
oxygenofcore
the coremagnesiowüstite at the CMB can be dfor the temperature at the CMB rang

Next, thermal evolution
Modiﬁed from Lister and Buﬀett [1998]
If the stable region can be found in the system, two temperatures can be also
computed as following global heat balance equations.

Again, using the heat balance at the interface, we also ﬁnd the thermal eﬀects ofdisplacement rate of stable region -Finally, the position of interface between stable and well-mixed regions can becomputed asSimple case - Heat ﬂow across theCMB given as a function of time(a) CMB Temperature(b) Super-adiabatic heat flow
80

5500

Heat flow (TW)

Temperature (K)

6000
5000
4500
4000
Stable region(4850 K)
Stable region(6000 K)
No Stable region

3500
3000
2500

40
200-2000.5

11.5

22.533.544.5

Magnetic dissipation (TW)

01

1.5

22.53(d) Magnetic dissipation

5000.51(c) Inner core size

1000

00.5

Time (Gyrs)

Stable region(4850 K)
Stable region(6000 K)
No Stable region

1500

0Time (Gyrs)

2000

Radius (km)Stable region(4850 K)
Stable region(6000 K)
No Stable region

60

1.5

2

2.5

Time (Gyrs)

3

3.5

4

4.5

3.5

4

4.5

4

4.5

15
Stable region(4850 K)
Stable region(6000 K)
No Stable region1050-500.5

1

1.5

22.5

Time (Gyrs)

33.5

What happens with the stableregion - Preferable origin
TCMB(t=0) = 4850 K
TCMB(t=0) = 6000 K

150
10050011.522.533.544.5150

200

1.522.533.54(c) TCMB(t=0)=4850 K(d) TCMB(t=0)=6000 K(b) Thermo-chemical effects for QCMB=5 TW

5001100

Time (Gyrs)

100

0.550

Distance from CMB (km)T-C effects
T-effectC-effect00

400
350QCMB=15 TW
300QCMB=11 TW=8 TW
Q250 CMBQCMB=5 TW
20015010050000.51Time (Gyrs)

200150

TCMB(t=0) = 4850 K
TCMB(t=0) = 6000 K

1.5

2

2.5

Time (Gyrs)

33.5

4

4.5

200

Distance from CMB (km)

0.5

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04

(a) Sensitivity to the CMB heat flow

Distance from CMB (km)Oxygen in the core (wt. %)2000

Distance from CMB (km)(b) Layer structure

Distance from CMB (km)Distance from CMB (km)(a) Layer thickness

T-C effects
T-effectC-effect

150
100
50
0
0

0.5

1

1.5

2

2.5

Time (Gyrs)

3

3.5

4

4.5

2000

4.5

T-C effectC effect
T effect

10000-1000-2000
00.51

1.5

2

2.5

3

3.5

4

4.5

Time (Gyrs)

Growth rate caused by sub-adiabatic eﬀects - 1500 km for 1.0 billion years: Compositional eﬀects
are required for consistent thickness of stable region.
From some constraint on CMB heat ﬂow (~11 TW), the preferable origin would be purely
compositional eﬀects

Eﬀects on chemical diﬀusivity ofEarthʼs core
CMB heat ﬂow at the present time= 15 TW
Initial CMB T = 4850 K

Distance from CMB (km)(a) Sensitivity to the chemical diffusion
250-9 2
DC = 3x10 m /s-9 2DC = 6x10 m /s
DC = 9x10-9 m2/s
DC = 1.2x10-8 m2/s

200
150
100
50
000.5

11.5

22.5

33.5

44.5

Time (Gyrs)

Distance from CMB (km)-8 2(b) Thermo-chemical effects for DC = 1.2x10 m /s

250
T-C effectC effect
T effect

200
150
100
50
000.5

11.5

22.5

Time (Gyrs)

33.5

44.5

To be consistent with a constraint
on stable layer thickness estimatedfrom geomagnetic secular variation(~140 km) [Buﬀett, 2014], thechemical diﬀusivity would beO(10-8) m2/s - Somewhat consistent
with with theoretical estimates[Pozzo et al., 2013; Ichikawa andTsuchiya, 2015].

CMB heat ﬂow given fromnumerical mantle dynamics modelStable region - The strongest
heat buﬀer

Core evolution diagnostics

Quick view on evolution of stableregion

Inﬂuences of HPE in the mantle

Nothing happened with HPE in the mantle.

HPE eﬀects in the mantle

High HPE - very slow cooling down but rapid cooling down in early Earthcorresponding to the spike of surface heat ﬂow (~initiate the plate-like behavior).

Summary and implications•

Incorporating ʻcore-mantle chemical couplingʼ into numerical mantle convection simulations to check
how the stable region works for core-mantle evolution system•

Reducing the initial CMB temperature from unrealistically high temperature - 4900 K with the stableregion.

•Low CMB heat ﬂow may not explain the possible thickness of stable region - Compositional origin would
be preferable and purely thermal origin may not be allowed (ceasing the geodynamo actions and so on).

•High chemical diﬀusivity would be rather explained for the current constraint on thickness of stableregion inferred from geomagnetic secular variations.

•With realistic mantle dynamics (?), the core-mantle boundary would not be rapidly cooled down because
the stable region works for the much stronger heat buﬀer of heat transport across the core but
keeping high CMB heat ﬂow (~13 TW).

•HPE in the mantle may not aﬀect the core evolution but small eﬀects for mantle evolution. - If HPE in
the mantle would be upper-limit value inferred from ʻgeoneutrino ﬂuxʼ, the mantle would not be rapidly
cooled down over the age of the Earth. Most amount of cooling might be happened in around the ʻearlyEarthʼ = 50 K/Gyr. The heat transport system in a convecting mantle would be almost balanced after
the early Earth stage has been ﬁnished, that is, CMB heat ﬂow + HPE + magmatic heat ﬂow-Surface
heat ﬂow ~ 0 TW. This would be consistent with the recent melting experiments under high P-T
condition and its implications [Andrault et al., 2016].

The END!
Thanks!