Long term evolution of the deep Earth as a window on its initial state

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1 Long term evolution of the deep Earth as a window on its initial state Stéphane Labrosse École Normale Supérieure de Lyon Universtité Claude Bernard Lyon-1 Point Reyes May 2016 Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

Constraints on the thermal evolution of the Earth Energetics of the Earth 180 0 60W 120W 60E 120E 180 60N 30N I Total surface heat flow QS = 46 ± 3TW I Heat production (mantle+crust) H = 18

2 Constraints on the thermal evolution of the Earth Energetics of the Earth W 120W 60E 120E N 30N I Total surface heat flow QS = 46 ± 3TW I Heat production (mantle+crust) H = 18 ± 5TW I Present Urey number Ur = 100 H/QS = 30 ± 19 < S 60S (Jaupart et al, ToG 2015) Stéphane Labrosse (Lyon) mw m Core evolution CIDER workshop / 27

Mantle temperature 200 K above the present value.

3 Constraints on the thermal evolution of the Earth Constraints on the cooling of the mantle in 4.5Gyr Transition from magma ocean to solid state convection when 40% melt is left. Mantle temperature 200 K above the present value. Time to reach that state from an entirely molten mantle 10 Myr. Total mantle cooling in the solid state < 200 K. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

4 Magnetic field evolution Constraints on the thermal evolution of the Earth (Tarduno et al, 2015) Field strength (microtesla) Recent field Detection limit 0 Mesoarchean Paleoarchean Eoarchean LHB Hadean Age (Ma) A dipole field has apparently existed for at least Gyr. An increase of the dipole intensity 1.5 Gyr ago? Can this be attributed to inner core nucleation (Biggin et al, 2015)? Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

5 Core-mantle coupled evolution Classical models for the thermal evolution Principle for thermal evolution models Q Global energy balance MC P dt dt = Q(T ) + H(t) The Urey number (time dependent) Ur = 100 H Q T controls the direction of evolution. Evolution time scale Present value: τ 10Gyr τ = MC PT Q(T ) Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

6 Core-mantle coupled evolution Classical models for the thermal evolution Application in thermal evolution model Boundary layer scaling with Rayleigh number Ra = ρα Tgd 3 /κη(t i ) and internal temperature T i q = C k T ( ) 4/3 Ti d Ra1/3 T Assuming the scaling applies to mantle convection, hence to the present time (t = 0): Q 0, T 0 Scaling of surface heat flow: ( ) 4/3 ( ) 1/3 T η(t ) Q(T ) = Q 0 T 0 η 0 Given the present Urey number: Ur = 100 H/Q [20 50]. Solve the energy equation backward from the present time: MC dt dt = H(t) Q(T ) Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

7 Core-mantle coupled evolution Classical models for the thermal evolution Feedback with temperature-dependent viscosity 400 Temperature (K) Ur=43 Q surf H rad Radiogenic Power, Q surf (TW) Age, Gyr Age, Gyr Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

8 Core-mantle coupled evolution Classical models for the thermal evolution Feedback with temperature-dependent viscosity 400 Temperature (K) Ur=43 Ur= Ur= Q surf H rad Radiogenic Power, Q surf (TW) Age, Gyr Age, Gyr Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

9 Core-mantle coupled evolution Classical models for the thermal evolution Proposed solutions Layered mantle convection = lower cooling efficiency (McKenzie & Richter, 1981). But the inferred lower mantle temperature is too large to keep it solid (Spohn & Schubert, 1982). A hint on the potential importance of a basal magma ocean! A smaller exponent β in the q = ARa β scaling law (e.g. Christensen, 1985; Conrad & Hager, 1999; Sleep, 2000; Korenaga, 2003; Labrosse & Jaupart, 2007). Differential core-mantle cooling. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

10 Core-mantle coupled evolution Classical models for the thermal evolution Proposed solutions Layered mantle convection = lower cooling efficiency (McKenzie & Richter, 1981). But the inferred lower mantle temperature is too large to keep it solid (Spohn & Schubert, 1982). A hint on the potential importance of a basal magma ocean! A smaller exponent β in the q = ARa β scaling law (e.g. Christensen, 1985; Conrad & Hager, 1999; Sleep, 2000; Korenaga, 2003; Labrosse & Jaupart, 2007). Differential core-mantle cooling. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

11 Core-mantle coupled evolution Classical models for the thermal evolution Proposed solutions Layered mantle convection = lower cooling efficiency (McKenzie & Richter, 1981). But the inferred lower mantle temperature is too large to keep it solid (Spohn & Schubert, 1982). A hint on the potential importance of a basal magma ocean! A smaller exponent β in the q = ARa β scaling law (e.g. Christensen, 1985; Conrad & Hager, 1999; Sleep, 2000; Korenaga, 2003; Labrosse & Jaupart, 2007). Differential core-mantle cooling. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

12 Core-mantle coupled evolution Core-mantle thermal coupling Alternative scenario Standard approach: MC dt = H(t) Q(T ) dt parameterised by the mantle potential temperature only. Core and mantle assumed to cool at the same pace. Assume instead that the core is cooling and not the mantle: No feedback from temperature dependence of the mantle viscosity! M M C M dt M dt M C C C dt C dt = H(t) Q(T M ) + Q CMB = Q CMB Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

13 Core-mantle coupled evolution Core-mantle thermal coupling Alternative scenario Standard approach: MC dt = H(t) Q(T ) dt parameterised by the mantle potential temperature only. Core and mantle assumed to cool at the same pace. Past Slightly warmer Present Assume instead that the core is cooling and not the mantle: No feedback from temperature dependence of the mantle viscosity! Much Hotter M M C M dt M dt M C C C dt C dt = H(t) Q(T M ) + Q CMB = Q CMB Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

14 Core-mantle coupled evolution Core-mantle thermal coupling A modified Urey number Consider the mantle and core with different evolution rates. Count the CMB heat flow as a heat source for the mantle, in addition to internal heating a modified Urey number: Ur = Q CMB + H Q S 100 Ur = 80 requires Q CMB = 16TW What are the constraints on the CMB heat flow? Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

15 Thermodynamics of the dynamo Conditions for a convective dynamo - the classical scenario Minimum necessary conditions for the geodynamo: Q CMB either an inner core crystallising fast enough. Compositional convection driven by the release of light elements upon inner core growth. or a heat flow larger than that conducted along core s isentrope. Thermal convection. Quantitatively: the energy and entropy balances relate the growth rate of the inner core, the CMB heat flow, and the total dissipation (Ohmic, viscous, diffusion). Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

16 Thermodynamics of the dynamo Conditions for a convective dynamo - the classical scenario Minimum necessary conditions for the geodynamo: Q CMB either an inner core crystallising fast enough. Compositional convection driven by the release of light elements upon inner core growth. or a heat flow larger than that conducted along core s isentrope. Thermal convection. Quantitatively: the energy and entropy balances relate the growth rate of the inner core, the CMB heat flow, and the total dissipation (Ohmic, viscous, diffusion). Q CMB Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

17 Thermodynamics of the dynamo Conditions for a convective dynamo - the classical scenario Minimum necessary conditions for the geodynamo: Q CMB either an inner core crystallising fast enough. Compositional convection driven by the release of light elements upon inner core growth. or a heat flow larger than that conducted along core s isentrope. Thermal convection. Quantitatively: the energy and entropy balances relate the growth rate of the inner core, the CMB heat flow, and the total dissipation (Ohmic, viscous, diffusion). Q CMB Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

18 Thermodynamics of the dynamo Conditions for a convective dynamo - the classical scenario Minimum necessary conditions for the geodynamo: Q CMB either an inner core crystallising fast enough. Compositional convection driven by the release of light elements upon inner core growth. or a heat flow larger than that conducted along core s isentrope. Thermal convection. Quantitatively: the energy and entropy balances relate the growth rate of the inner core, the CMB heat flow, and the total dissipation (Ohmic, viscous, diffusion). Q CMB (Alternatively: light element (Mg) exsolution at the CMB (O Rourke & Stevenson, 2016; Badro et al, in review), more later) Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

19 Energy balance of the core Thermodynamics of the dynamo If an inner core (radius r IC ) is growing CMB heat flow = secular cooling P C(r IC ) r IC + latent heat P L(r IC ) r IC + compositional energy P ξ (r IC ) r IC + radiogenic heat H(t) Q CMB (t) = [ P C(r IC ) + P L(r IC ) + P ξ (r IC ) ] r IC + H If Q CMB (t) is known, the radius of the inner core r IC (t) can be computed from the present value to its onset as well as all the energy terms. Before the IC: only the secular cooling and radiogenic heat balance the CMB heat flow Q CMB (t) = PC(T c) T c + H Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

20 Thermodynamics of the dynamo Entropy Efficiency of the geodynamo ( ) 2 Φ + T D k T OC T dv = T D T ICB T CMB (Q T CMB T ICB + Q L ) ICB + + T D T H T CMB T CMB T H T D T CMB T C T CMB T C T D T CMB E ξ H(t) ρc OC P T ad t Each term on the RHS is also written as F(R IC ) R IC. All heat sources have a Carnot-type efficiency (T D /T CMB )(T X T CMB )/T X. Compositional energy is more efficient (T D /T CMB ). Part of the available power is used to maintain the isentropic temperature gradient in the core. The associated dissipation is proportional to the thermal conductivity k. dv Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

21 Thermodynamics of the dynamo Entropy Efficiency of the geodynamo ( ) 2 Φ + T D k T OC T dv = T D T ICB T CMB (Q T CMB T ICB + Q L ) ICB + + T D T H T CMB T CMB T H T D T CMB T C T CMB T C T D T CMB E ξ H(t) ρc OC P T ad t Each term on the RHS is also written as F(R IC ) R IC. All heat sources have a Carnot-type efficiency (T D /T CMB )(T X T CMB )/T X. Compositional energy is more efficient (T D /T CMB ). Part of the available power is used to maintain the isentropic temperature gradient in the core. The associated dissipation is proportional to the thermal conductivity k. dv Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

22 Thermodynamics of the dynamo Thermal conductivity of the core Until recently (Stacey & Loper, 2007): k = 28W m 1 K 1 Ab initio calculations (de Koker et al, 2012; Pozzo et al, 2012) and experiments (Gomi et al, 2013; Ohta et al, 2016): k > 85W m 1 K 1 Resistivity (Ωm) Fe-Si Fe 300 K DFT calculation (Gomi et al, PEPI, 2013) Pressure (GPa) Room T experiments extrapolated including saturation resistivity effect Electrical resistivity (µωcm) GPa Bloch-Grüneisen Saturation effect (Ohta et al, Nature, in press) Temperature (K) Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

23 Thermodynamics of the dynamo Thermal conductivity of the core k (W m 1 K 1 ) Radius (km) k (present) k (IC onset) Old game, new rules! Minimum value k(p, T ) from Gomi et al (2013) Isentropic temperature gradient q s = k( r T ) s q s (present) q s (IC onset) q S (mw m 2 ) = Isentropic heat flow at the CMB: Q S = 13.3TW Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

24 Thermodynamics of the dynamo Inner core growth and core cooling rate For a given Ohmic + viscous dissipation, what is the required IC growth rate at present and the cooling rate just before the IC onset? IC growth rate and age dr IC /dt, km/ma Age of IC, Ma Total dissipation Φ, TW No radioactivity Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

25 Thermodynamics of the dynamo Inner core growth and core cooling rate For a given Ohmic + viscous dissipation, what is the required IC growth rate at present and the cooling rate just before the IC onset? IC growth rate and age dr IC /dt, km/ma Age of IC, Ma Total dissipation Φ, TW No radioactivity [K]=200ppm Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

26 Thermodynamics of the dynamo Inner core growth and core cooling rate For a given Ohmic + viscous dissipation, what is the required IC growth rate at present and the cooling rate just before the IC onset? IC growth rate and age 700 Cooling rate before IC 800 dr IC /dt, km/ma Age of IC, Ma Total dissipation Φ, TW No radioactivity [K]=200ppm No radioactivity [K]=200ppm Total dissipation Φ, TW dt c /dt, K/Ga Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

27 Thermodynamics of the dynamo Inner core growth and core cooling rate For a given Ohmic + viscous dissipation, what is the required IC growth rate at present and the cooling rate just before the IC onset? a IC < 1.5Gyr and T > 1200K in 3 Gyr! IC growth rate and age 700 Cooling rate before IC 800 dr IC /dt, km/ma Age of IC, Ma Total dissipation Φ, TW No radioactivity [K]=200ppm No radioactivity [K]=200ppm Total dissipation Φ, TW dt c /dt, K/Ga Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

28 Age of the inner core Thermodynamics of the dynamo Q CMB Q S -a IC Time IC age, Ma Constant Q CMB /Q S Isentropic heat flow CMB heat flow, TW Q CMB < Q S does not allow dynamo action before the IC Minimum Q CMB decreases (here linearly) between Q S at IC onset and a given value for the present time. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

29 Age of the inner core Thermodynamics of the dynamo Q CMB Q S Q CMB Q S -a IC Time IC age, Ma ~900 =max 800 Constant Q CMB /Q S Decreasing Q CMB Isentropic heat flow -a IC Time ~min CMB heat flow, TW Q CMB < Q S does not allow dynamo action before the IC Minimum Q CMB decreases (here linearly) between Q S at IC onset and a given value for the present time. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

7000 6000 5000 4000 Evolution of TCMB for the minimal thermal evolution Liquidus Solid mantle Melting of mantle minerals at CMB pressure

30 Thermodynamics of the dynamo Evolution of the CMB temperature CMB temperature, K 8000 I Even if ULVZs are not partial melt, the lower mantle must have been largely molten in the past: the basal magma ocean Evolution of TCMB for the minimal thermal evolution Liquidus Solid mantle Melting of mantle minerals at CMB pressure Solidus Time BP, Ma 0 ULVZs Core (Labrosse, Hernlund, Coltice, 2007) The evolution of the CMB temperature is rather extreme! An alternative? Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

31 Thermodynamics of the dynamo Precipitation of light elements at the top of the core Buffett et al (2000): sedimentation at the top of core driven by inner core crystallization. O Rourke & Stevenson (2016): Mg precipitation. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

32 Thermodynamics of the dynamo Predictions for Mg precipitation A lower cooling rate can produce the same dissipation Particularly useful before nucleation of the inner core Crucially depends on the initial concentration in Mg core formation processes the temperature dependence of saturation (Badro et al, Nature, in press) Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

33 Thermodynamics of the dynamo Conclusions: a very multi-disciplinary problem 10 years ago we thought the dynamics and evolution of the core was well understood. High thermal conductivity of the core (de Koker et al, 2012; Pozzo et al, 2012; Gomi et al, 2013; Ohta et al, 2016; etc.) changes the game. New scenarios: exsolution (O Rourke & Stevenson 2016; Badro et al, 2016; Hirose et al, 2016), precession or tides (Le Bars, Cébron et al). Related questions on the possibility of stably stratified or snow (slurry) regions, structure of the inner core, as seen by seismology. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

34 Thermodynamics of the dynamo Conclusions: a very multi-disciplinary problem 10 years ago we thought the dynamics and evolution of the core was well understood. High thermal conductivity of the core (de Koker et al, 2012; Pozzo et al, 2012; Gomi et al, 2013; Ohta et al, 2016; etc.) changes the game. New scenarios: exsolution (O Rourke & Stevenson 2016; Badro et al, 2016; Hirose et al, 2016), precession or tides (Le Bars, Cébron et al). Related questions on the possibility of stably stratified or snow (slurry) regions, structure of the inner core, as seen by seismology. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

35 Thermodynamics of the dynamo Conclusions: a very multi-disciplinary problem 10 years ago we thought the dynamics and evolution of the core was well understood. High thermal conductivity of the core (de Koker et al, 2012; Pozzo et al, 2012; Gomi et al, 2013; Ohta et al, 2016; etc.) changes the game. New scenarios: exsolution (O Rourke & Stevenson 2016; Badro et al, 2016; Hirose et al, 2016), precession or tides (Le Bars, Cébron et al). Related questions on the possibility of stably stratified or snow (slurry) regions, structure of the inner core, as seen by seismology. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

36 Thermodynamics of the dynamo Conclusions: a very multi-disciplinary problem 10 years ago we thought the dynamics and evolution of the core was well understood. High thermal conductivity of the core (de Koker et al, 2012; Pozzo et al, 2012; Gomi et al, 2013; Ohta et al, 2016; etc.) changes the game. New scenarios: exsolution (O Rourke & Stevenson 2016; Badro et al, 2016; Hirose et al, 2016), precession or tides (Le Bars, Cébron et al). Related questions on the possibility of stably stratified or snow (slurry) regions, structure of the inner core, as seen by seismology. Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

37 Thermodynamics of the dynamo Conclusions: a very multi-disciplinary problem 10 years ago we thought the dynamics and evolution of the core was well understood. High thermal conductivity of the core (de Koker et al, 2012; Pozzo et al, 2012; Gomi et al, 2013; Ohta et al, 2016; etc.) changes the game. New scenarios: exsolution (O Rourke & Stevenson 2016; Badro et al, 2016; Hirose et al, 2016), precession or tides (Le Bars, Cébron et al). Related questions on the possibility of stably stratified or snow (slurry) regions, structure of the inner core, as seen by seismology. We need more constraints on thermo-chemical properties (mineral physics), on the actual core structure (seismology, geomagnetism) and evolution (palaeomagnetism) and better geodynamics models, in particular for exotic scenarios such as the snow models for the core, double-diffusive layers, integrated evolution models including a basal magma ocean... Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

38 Thermodynamics of the dynamo Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

39 Lower β exponent to decrease the feedback? ( ) 1+β ( ) β T η(t ) Q(T ) = Q 0 T 0 η 0 But, no self-consistent dynamical model gives such low values of β Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

40 Low exponent β From Christensen (1985): Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

41 Heat flow and plate size Plate "age" Subduction Ridge Ridge Ridge Subduction Subduction Subduction 1/q Surface heat flow q top 50 0 Surface velocity u top 0 Temperature (Grigné et al, 2005 ; Labrosse & Jaupart, 2007) 1.0 λ=1.0 Heat flux coefficient λ=0.5 λ=0.3 Loop model: q top = C(L)Ra 1/3 m T 4/3 m classical β supported by convection models with self-consistent plate tectonics (pseudo-plastic rheology) Stéphane Labrosse Cell (Lyon) width Core evolution CIDER workshop / 27

42 Contributions to energy and efficiency equation Contrib. to Q CMB, TW Contrib. to Φ, TW Present time Isentropic heat flow Total Q CMB (0) 7TW Lost in conduction Compositional E Total Cooling Latent heat Compositional E Latent heat Total dissipation Φ, TW Cooling Contrib. to Φ, TW Contrib. to Q CMB, TW Just before IC onset Cooling Lost in conduction Total Cooling = CMB heat flow Q CMB (-a IC ) 16TW Lost in conduction Total dissipation Φ, TW Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

43 Evolution of energy and efficiency terms A Power, TW Contribs. to Φ, TW CMB heat flow Secular cooling Compositionnal E Latent heat Secular cooling Compositional E Latent H ICB heat flow Flow along isentrope Total Φ Diff. isentrope B Backward time evolution with minimum Q CMB for Φ > 0 at all times (Q CMB = 1.15Q S ). Mantle side: No reason to think Q CMB droped once the IC started to crystallize! Stéphane Labrosse (Lyon) Core evolution CIDER workshop / 27

Nature and origin of what s in the deep mantle

Nature and origin of what s in the deep mantle S. Labrosse 1, B. Bourdon 1, R. Nomura 2, K. Hirose 2 1 École Normale Supérieure de Lyon, Universtité Claude Bernard Lyon-1 2 Earth-Life Science Institute,