Thermal history of the Earth’s core

Thermal history of the Earth’s core

COME-IN meeting

Royal Observatory of Belgium Marie-Hélène Deproost 18 March 2016

Introduction

Introduction

Study thermal evolution of the Earth’s core and apply model to Mercury at a later time

Thermal evolution of the Earth’s core from the energy and entropy budgets

Model based on Gubbins (2003,2004) and Davies 2015

Introduction

What we know about Earth’s core...

Outer core radius rCMB = 3480 km Inner core radius r_ICB = 1221 km Density jump at the ICB ∆ρ = 0.8 g.cm⁻³

⇒ light elements in the core:

outer core 13 at.% O, 4 at.% S, 4 at.% Si inner core 0.1 at.% O, 3 at.% S, 4 at.% Si Geodynamo at least for the last 3.5 Gyr Problem: new higher (3x) thermal conductivity

⇒ enhances the heat conducted along the adiabat

⇒ less power available to generate dynamo

likely stable stratification below the CMB ⇒ influence on the magnetic field at the surface and on convection

alternative energy source needed

One solution: light element exsolution (O’Rourke and Stevenson, 2016 )

Energy and entropy budgets Energy balance

Energy budget

QCMB = Qs + QL+ Qg + QP + QPL+ Qr

CMB heat flux:

QCMB = − I

k ~∇T · ~n dS

Secular cooling:

Qs = fs(Cp, T )dT_CMB dt Latent heat:

Q_L= f_L(L)dT_CMB dt Gravitational energy:

Q_g = f_g(α_c, ∆c_ICB)dT_CMB dt

Energy and entropy budgets Energy balance

Energy budget

QCMB =Qs +QL+Qg + QP + QPL+ Qr

CMB heat flux:

QCMB = − I

k ~∇T · ~n dS Secular cooling:

Qs = fs(Cp, T )dT_CMB dt Latent heat:

Q_L= f_L(L)dT_CMB dt Gravitational energy:

Q_g = f_g(α_c, ∆c_ICB)dT_CMB dt

Energy and entropy budgets Entropy balance

Entropy budget

EJ+ Ek + Ea= Es+ EL+ Eg + EP + EPL+ Eh+ Er

Entropy of thermal conduction: E_k =

Z

k ∇T_a T_a

2

dV Secular cooling:

E_s = g_s(C_p, T , ρ)dT_CMB

dT + Q_s TCMB

Latent heat:

E_L= Q_LT_CMB− T_ICB T_ICBT_CMB Gravitational energy:

Eg = Qg

T_CMB

Energy and entropy budgets Entropy balance

Entropy budget

EJ+Ek + Ea=Es+EL+Eg + EP + EPL+ Eh+ Er

Entropy of thermal conduction:

E_k = Z

k ∇Ta

T_a

2

dV Secular cooling:

E_s = g_s(C_p, T , ρ)dT_CMB

dT + Qs

T_CMB Latent heat:

EL= QL

TCMB− T_ICB T_ICBT_CMB Gravitational energy:

Eg = Q_g TCMB

Marginal dynamo CMB heat flux and cooling rate

Marginal dynamo

Marginal dynamo: E_J = 0

⇒

 QCMB = Qs+ QL+ Qg

E_k = Es+ E_L+ Eg

-2.0 -1.5 -1.0 -0.5 0.0

0.

2.

4.

6.

8.

10.

12.

14.

16.

0 50 100 150 200 250 300

time from today (Gyr)

CMBheatflow(TW) Coolingrate(K.Gyr-1)

Marginal dynamo Energy and entropy contributions

Heat flow and entropy contributions

Secular cooling Latent heat Gravitational energy

-2.0 -1.5 -1.0 -0.5 0.0

0 20 40 60 80 100

time from today (Gy)

%

Contribution to the CMB heat flow

Secular cooling Latent heat Gravitational Energy

-2.0 -1.5 -1.0 -0.5 0.0

0 20 40 60 80 100

time from today (Gyr)

%

Contribution to the entropy of thermal conduction Ek

IC age: ∼ 850 Myr

Without IC: Q_CMB = Q_s and E_k = E_s

With IC: Q_s and E_g most important contributions

Magnesium precipitation One solution to the high thermal conductivity

Magnesium precipitation

Problem: new higher thermal conductivity

⇒ enhances the heat conducted along the adiabat

⇒ alternative energy source is needed

One solution: light element exsolution (O’Rourke and Stevenson, 2016 )

Magnesium precipitation Energy released

Energy balances

Marginal dynamo: E_J = 0

⇒

 Q_CMB = Q_s+ Q_L+ Q_g +Q_{g ,Mg} E_k = E_s + E_L+ E_g +E_{g ,Mg} with:

Qg ,Mg = fg ,Mg(αc, Cm)dT_CMB dt Eg ,Mg = Q_{g ,Mg}

T_CMB

O’Rourke and Stevenson, 2016

Magnesium precipitation Results

CMB heat flux and rate of cooling

-2.0 -1.5 -1.0 -0.5 0.0

0.

5.

10.

15.

0 50 100 150 200 250 300

time from today (Gyr)

CMBheatflow(TW) Coolingrate(K.Gyr-1)

With Mg exsolution:

IC age: ∼ 1.6 Gyr Very little variation Eg ,Mg  E_s

With IC Without IC Larger contribution to Q_CMB (%)

with Mg Qs∼ 50% Qs∼ 65%

without Mg Q_s∼ 55% Q_s= 100%

Larger contribution to E_k(%)

with Mg E_{g ,Mg}∼ 55% E_{g ,Mg}∼ 80%

without Mg Eg∼ 50% Es= 100%

Conclusion

Conclusion

Without Mg:

rate of cooling at the CMB ∼ 300 K.Gyr⁻¹

inner core age ∼ 850 Myr temperature at the CMB ∼ 4400 K (mantle melting) QCMB ∼ 15TW

With Mg:

rate of cooling at the CMB ∼ 65 K.Gyr⁻¹

inner core age doubled temperature at the CMB

decreased by 300 K at t = 2 Gyr QCMB ∼ 5TW

And Mercury?

Mg exsolution unlikely...