Scaling laws of convection for cooling planets in a stagnant lid regime

Thiriet, Mélanie; Breuer, D.; Michaut, Chloé; Plesa, Ana‐Catalina

doi:10.1016/j.pepi.2018.11.003

Cited by 32 publications

(60 citation statements)

References 70 publications

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“…It results in a TBL thicker at the top of the mantle, than at the bottom of the mantle. Strictly, the value of Ra crit should be different when considering the upper or lower TBL (Thiriet et al 2019). The value of 450 is adapted for the upper mantle.…”

Section: Tbls Parametrizationmentioning

confidence: 99%

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

Monteux

Andrault

Guitreau

et al. 2020

Geophysical Journal International

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SUMMARY In its early evolution, the Earth mantle likely experienced several episodes of complete melting enhanced by giant impact heating, short-lived radionuclides heating and viscous dissipation during the metal/silicate separation. After a first stage of rapid and significant crystallization (Magma Ocean stage), the mantle cooling is slowed down due to the rheological transition, which occurs at a critical melt fraction of 40–50%. This transition first occurs in the lowermost mantle, before the mushy zone migrates toward the Earth's surface with further mantle cooling. Thick thermal boundary layers form above and below this reservoir. We have developed numerical models to monitor the thermal evolution of a cooling and crystallizing deep mushy mantle. For this purpose, we use a 1-D approach in spherical geometry accounting for turbulent convective heat transfer and integrating recent and solid experimental constraints from mineral physics. Our results show that the last stages of the mushy mantle solidification occur in two separate mantle layers. The lifetime and depth of each layer are strongly dependent on the considered viscosity model and in particular on the viscosity contrast between the solid upper and lower mantle. In any case, the full solidification should occur at the Hadean–Eoarchean boundary 500–800 Myr after Earth's formation. The persistence of molten reservoirs during the Hadean may favor the absence of early reliefs at that time and maintain isolation of the early crust from the underlying mantle dynamics.

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Section: Tbls Parametrizationmentioning

confidence: 99%

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

Monteux

Andrault

Guitreau

et al. 2020

Geophysical Journal International

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“…We write Q cmb using a simple functional form,

Q_{cmb} = Q_{p} + Q_{f} e^{- bold-italict / bold-italicτ}

where t is time, Q p + Q f is the heat flow at t = 0 and τ is a time scale. By varying Q p , Q f , and τ it is possible to closely reproduce previously published time series of Q cmb for Mars (Leone et al, 2014; Thiriet et al, 2019; Williams & Nimmo, 2004). In particular, values of Q p = 0.2 TW, Q f = 1.3 TW, and τ = 0.9 Gyr closely represent the time series of Q cmb from Williams and Nimmo (2004) that was used in Davies and Pommier (2018).…”

Section: Joint Experimental‐modeling Approachmentioning

confidence: 84%

A Joint Experimental‐Modeling Investigation of the Effect of Light Elements on Dynamos in Small Planets and Moons

2020

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We present a joint experimental‐modeling investigation of core cooling in small terrestrial bodies. Significant amounts of light elements (S, O, Mg, Si) may compose the metallic cores of terrestrial planets and moons. However, the effect of multiple light elements on transport properties, in particular, electrical resistivity and thermal conductivity, is not well constrained. Electrical experiments were conducted at 10 GPa and up to 1850 K on high‐purity powder mixtures in the Fe‐S‐O(±Mg, ±Si) systems using the multianvil apparatus and the four‐electrode technique. The sample compositions contained 5 wt.% S, up to 3 wt.% O, up to 2 wt.% Mg, and up to 1 wt.% Si. We observe that above the eutectic temperature, electrical resistivity is significantly sensitive to the nature and amount of light elements. For each composition, thermal conductivity‐temperature equations were estimated using the experimental electrical results and a modified Wiedemann‐Franz law. These equations were implemented in a thermochemical core cooling model to study the evolution of the dynamo. Modeling results suggest that bulk chemistry significantly affects the entropy available to power dynamo action during core cooling. In the case of Mars, the presence of oxygen would delay the dynamo cessation by up to 1 Gyr compared to an O‐free, Fe‐S core. Models with 3 wt% O can be reconciled with the inferred cessation time of the Martian dynamo if the core‐mantle boundary heat flow falls from >2 TW to ~0.1 TW in the first 0.5 Gyr following core formation.

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“…We solve for the a rh values suggested above (see table 5). For all cases the initial temperature of the convection cell is 1214 K. Table 5 continued on next page In order to derive the heat flux into a possible MH-III enriched layer following the onset of convection in the rocky core we adopt the 1-D model from Thiriet et al (2019). The rocky core is divided into three layers, the convection cell, a cold boundary (i.e.…”

Section: Thermal Evolution and The Mh-iii Layermentioning

confidence: 99%

“…The convective heat flow is estimated using the Nusselt number which scales as the Rayleigh number to the power of β. In this work we adopt the best-fit value of β = 0.335 (Thiriet et al 2019). Also as in Thiriet et al (2019) we use a fourth-order Runge-Kutta scheme to advance the convection cell temperature, T c , and the thickness of the stagnant lid with time.…”

Section: Thermal Evolution and The Mh-iii Layermentioning

confidence: 99%

“…In this work we adopt the best-fit value of β = 0.335 (Thiriet et al 2019). Also as in Thiriet et al (2019) we use a fourth-order Runge-Kutta scheme to advance the convection cell temperature, T c , and the thickness of the stagnant lid with time. We solve numerically for the heat conduction within the stagnant lid using an implicit scheme and cartesian coordinates, with 100 spatial levels.…”

Section: Thermal Evolution and The Mh-iii Layermentioning

confidence: 99%

See 1 more Smart Citation

The Equation of State of MH-III: A Possible Deep CH₄ Reservoir in Titan, Super-Titan Exoplanets, and Moons

Levi

Cohen

2019

ApJ

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We investigate the thermal equation of state, bulk modulus, thermal expansion coefficient, and heat capacity of MH-III (CH 4 filled-ice Ih), needed for the study of CH 4 transport and outgassing for the case of Titan and super-Titans. We employ density functional theory and ab initio molecular dynamics simulations in the generalized-gradient approximation with a van der Waals functional. We examine the finite temperature range of 300 K-500 K and pressures between 2 GPa-7 GPa. We find that in this P-T range MH-III is less dense than liquid water.There is uncertainty in the normalized moment of inertia (MOI) of Titan; it is estimated to be in the range of 0.33 − 0.34. If Titan's MOI is 0.34, MH-III is not stable at present in Titan's interior, yielding an easier path for the outgassing of CH 4 . However, for an MOI of 0.33, MH-III is thermodynamically stable at the bottom of a ice-rock internal layer capable of storing CH 4 . For rock mass fractions 0.2 upwelling melt is likely hot enough to dissociate MH-III along its path. For super-Titans considering a mixture of MH-III and ice VII, melt is always positively buoyant if the H 2 O:CH 4 mole fraction is > 5.5. Our thermal evolution model shows that MH-III may be present today in Titan's core, confined to a thin (≈ 10 km) outer shell. We find that the heat capacity of MH-III is higher than measured values for pure water-ice, larger than heat capacity often adopted for ice-rock mixtures with implications for internal heating.

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Scaling laws of convection for cooling planets in a stagnant lid regime

Cited by 32 publications

References 70 publications

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

A Joint Experimental‐Modeling Investigation of the Effect of Light Elements on Dynamos in Small Planets and Moons

The Equation of State of MH-III: A Possible Deep CH₄ Reservoir in Titan, Super-Titan Exoplanets, and Moons

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Scaling laws of convection for cooling planets in a stagnant lid regime

Cited by 32 publications

References 70 publications

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

A Joint Experimental‐Modeling Investigation of the Effect of Light Elements on Dynamos in Small Planets and Moons

The Equation of State of MH-III: A Possible Deep CH4 Reservoir in Titan, Super-Titan Exoplanets, and Moons

Contact Info

Product

Resources

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The Equation of State of MH-III: A Possible Deep CH₄ Reservoir in Titan, Super-Titan Exoplanets, and Moons