Stagnant Lid Convection Research Articles

Unlocking planetesimal magnetic field histories: A refined, versatile model for thermal evolution and dynamo generation

The thermal and magnetic histories of planetesimals provide unique insights into the formation and evolution of Earth’s building blocks. These histories can be gleaned from meteorites by using numerical models to translate measured properties into planetesimal behaviour. In this paper, we present a new 1D planetesimal thermal evolution and dynamo generation model. This magnetic field generation model is the first of a differentiated, mantled planetesimal that includes both mantle convection and sub-eutectic core solidification. We have improved fundamental aspects of mantle heat transport by including a more detailed viscosity model and stagnant lid convection parametrisations consistent with internal heating. We have also added radiogenic heating from 60Fe in the metallic Fe-FeS core. Additionally, we implement a combined thermal and compositional buoyancy flux, as well as the latest magnetic field scaling laws to predict magnetic field strengths during the planetesimal’s thermal evolution until core solidification is complete. We illustrate the consequences of our model changes with an example run for a 500km radius planetesimal. These effects include more rapid erosion of core thermal stratification and longer duration of mantle convection compared to previous studies. The additional buoyancy from core solidification has a marginal effect on dynamo strength, but for some initial core sulfur contents it can prevent cessation of the dynamo when mantle convection ends. Our model can be used to investigate the effects of individual parameters on dynamo generation and constrain properties of specific meteorite parent bodies. Combined, these updates mean this model can predict the most reliable and complete magnetic field history for a planetesimal to date, so is a valuable tool for deciphering planetesimal behaviour from meteorite properties.

Stress regime analysis for the transition to a stagnant-lid convection regime in the terrestrial mantle

A series of numerical simulations of terrestrial mantle convection with temperature-dependent viscosity in a three-dimensional spherical geometry was performed to investigate the thermal structure of the mantle interior and the mechanical condition of the lithosphere. The common “sluggish-lid” convection regime has the thermal structure of the mantle interior with a slowly mobile lid under a moderately temperature-dependent viscosity of mantle rocks, whereas the “stagnant-lid” convection regime has a convection pattern in which the entire surface is covered by a highly viscous lid due to the strongly temperature-dependent viscosity. This study focused not only on the thermal structure of the mantle but also on the mechanical conditions in the lithosphere on an intermediate, transitional convection regime between these end-member convections both under the standard- and the extended-Boussinesq approximations. In this “quasi-stagnant-lid” convection regime, the entire surface of the planet is covered by a highly viscous stagnant-lid that moves slowly, whereas the mantle interior is dominated by a long-wavelength (i.e., degree-one) thermal structure. The stress regime analyses revealed that the strike-slip regime is highly restricted spatially in the lid. If the constitutive laws allow the formation of faults in the future numerical model, the time-dependent formation of weak faults that can initiate plate tectonics may differ among the three convection regimes (i.e., degree-one, quasi-stagnant-lid, and stagnant-lid convection regimes). The range of viscosity contrast of the lid required to realize the “quasi-stagnant-lid” convection regime in the model under the extended-Boussinesq approximation was wider than under the standard Boussinesq approximation, because the adiabatic heating of the mantle increased the mantle temperature with the depth and enhanced the formation of stagnant-lid owing to the strong mechanical decoupling between the cold lid and the underlying hot mantle.

Stagnant-lid convection: comparison of viscosity laws and uniform scaling approach for temperature and heat flux prediction

SUMMARY Numerical simulations of stagnant-lid convection in a 2-D Cartesian fluid heated from below are carried out in order to study how the temperature dependence of the viscosity affects the vertical profile of temperature in the model. I test different viscosity laws, including the Arrhenius law with realistic parameters for the Earth’s mantle or for icy bodies. No approximation is made, which leads to extremely high viscosity contrasts. Results are compared to different approximations, in particular the Frank–Kamenetskii (FK) one. I propose a new approach for the scaling of the temperature drop across the convective part of the layer beneath the stagnant lid. The vertical profile of temperature as a function of the viscosity law is predicted, with a uniform scaling approach for all formulations of the temperature-dependent viscosity. The predicted profiles are in very good agreement with results of 2-D numerical simulations in Cartesian geometry. The complete scaling given here provides a rapid way to compare viscosity laws and to check how approximations affect the results, in terms of interior temperature, stagnant lid thickness and heat flux, compared to the real Arrhenius law for rocky mantles and for the icy outer shells of satellites. In particular, in the context of 2-D Cartesian convection heated from below, in the stagnant-lid regime, I propose a new approach to properly scale the FK formulation when it is used as an approximation of the Arrhenius law.

Hadaean to Palaeoarchaean stagnant-lid tectonics revealed by zircon magnetism

Plate tectonics is a fundamental factor in the sustained habitability of Earth, but its time of onset is unknown, with ages ranging from the Hadaean to Proterozoic eons1–3. Plate motion is a key diagnostic to distinguish between plate and stagnant-lid tectonics, but palaeomagnetic tests have been thwarted because the planet’s oldest extant rocks have been metamorphosed and/or deformed4. Herein, we report palaeointensity data from Hadaean-age to Mesoarchaean-age single detrital zircons bearing primary magnetite inclusions from the Barberton Greenstone Belt of South Africa5. These reveal a pattern of palaeointensities from the Eoarchaean (about 3.9 billion years ago (Ga)) to Mesoarchaean (about 3.3 Ga) eras that is nearly identical to that defined by primary magnetizations from the Jack Hills (JH; Western Australia)6,7, further demonstrating the recording fidelity of select detrital zircons. Moreover, palaeofield values are nearly constant between about 3.9 Ga and about 3.4 Ga. This indicates unvarying latitudes, an observation distinct from plate tectonics of the past 600 million years (Myr) but predicted by stagnant-lid convection. If life originated by the Eoarchaean8, and persisted to the occurrence of stromatolites half a billion years later9, it did so when Earth was in a stagnant-lid regime, without plate-tectonics-driven geochemical cycling.

Early asymmetric growth of planetary stagnant lids

Convection within planetary bodies is often modelled using a temperature-dependent rheology which, when cooled from the surface, naturally leads to the formation of a so-called stagnant lid at the cold outer surface. However, for sufficiently large planets the phase diagram describing the partially molten system may depend significantly on pressure in addition to temperature, leading to significant variations in solid fraction. The aggregate rheology may therefore exhibit significant dependence on both the temperature and pressure, and hence may exhibit marked dependence on depth in addition to the dependence on the thermal structure due to convection. Here, we consider the growth and stability of a planetary stagnant lid. We first characterise the effect of a pressure- and temperature-dependent rheology on the evolution of a symmetric, planetary stagnant lid. This analysis further suggests that the pressure dependence of the rheology may lead to an instability of the growing stagnant lid which, importantly, may lead to asymmetric lid growth. We find that the most unstable mode is at the longest wavelengths, and discuss the implications for stagnant-lid convection and the growth of asymmetric surfaces of planetary bodies. In particular, we discuss the possibility that this instability has implications for the formation of the crustal dichotomy found on the Moon.

Onset of convection in internally heated fluids with strongly temperature-dependent viscosity

We investigate the onset of convection in internally heated fluids with strongly temperature-dependent viscosity by solving numerically a non-linearized system of thermal convection equations in two dimensions for viscosity contrasts up to ∼1035. As the viscosity contrast increases, a high-viscosity stagnant lid develops at the upper surface and convection occurs in a sublayer beneath it. The transition to stagnant-lid convection occurs at about the same viscosity contrast as in Rayleigh–Bénard convection. We obtain asymptotic scaling relationships for the critical Rayleigh number and other parameters in the stagnant-lid regime. We also investigated the possibility of subcritical convection. In contrast to the Rayleigh–Bénard problem, we did not detect a subcritical region for internally heated convection in two-dimensional simulations. The results of this study can help improve our understanding of the conditions under which convection occurs in planetary interiors.

Inefficient Water Degassing Inhibits Ocean Formation on Rocky Planets: An Insight from Self-Consistent Mantle Degassing Models.

A sufficient amount of water is required at the surface to develop water oceans. A significant fraction of water, however, remains in the mantle during magma ocean solidification, and thus the existence of water oceans is not guaranteed even for exoplanets located in the habitable zone. To discuss the likelihood of ocean formation, we built two models to predict the rate of mantle degassing during the magma ocean stage and the subsequent solid-state convection stage. We find that planets with low H2O/CO2 ratios would not have a sufficient amount of surface water to develop water oceans immediately after magma ocean solidification, and the majority of the water inventory would be retained in the mantle during their subsequent evolution regardless of planetary size. This is because oceanless planets are likely to operate under stagnant lid convection, and for such planets, dehydration stiffening of the depleted lithospheric mantle would limit the rate of mantle degassing. In contrast, a significant fraction of CO2 would already be degassed during magma ocean solidification. With a strong greenhouse effect, all surface water would exist as vapor, and water oceans may be absent throughout planetary evolution. Volatile concentrations in the bulk silicate Earth are close to the threshold amount for ocean formation, so if Venus shared similar concentrations, small differences in solar radiation may explain the divergent evolutionary paths of Earth and Venus.

LLSVPs of primordial origin: Implications for the evolution of plate tectonics

Today's large low shear velocity provinces (LLSVPs) are assumed to be compositionally dense leftovers from the magma-ocean phase that are formed to dense accumulations (piles) by mantle flow. Due to the stabilising effect of dense material on mantle convection, LLSVPs could be of major importance for the evolution of plate tectonics.Here, we examine the influence of dense primordial material using thermochemical mantle convection models with self-consistent plate generation. Our results show that the general evolutionary path from a stagnant lid to an episodic to a permanently mobile stage is almost unaffected by dense LLSVP-like structures. The stabilising effect of a dense basal layer, however, leads to delayed surface mobilisation events. In particular, we find a prolonged episodic stage and a later emergence of continuously moving surface plates. Mobilisation episodes occur when the rigid surface breaks in either a top-down (by downwellings), a bottom-up (by upwellings) or a mixed, push-pull manner. As dense material is constantly entrained by rising currents, the stabilising effect decreases with time. Consequently, we observe a change of the mechanism which triggers a surface mobilisation from top-down to late push-pull, then bottom-up and finally push-pull if the stabilising effect is decreased.Our results suggest that, for LLSVP-like volumes and density contrasts, plate mobilisation is triggered by mantle upwellings, either directly in a bottom-up manner or delayed after a long phase of stagnant lid convection (late push-pull). Generally, a primordial dense layer has a profound impact: continuous plate motion as known today is strongly delayed and early Earth plate tectonics most likely acted in an episodic manner.

Scaling laws for stagnant-lid convection with a buoyant crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Linear analysis on the onset of thermal convection of highly compressible fluids with variable viscosity and thermal conductivity in spherical geometry: implications for the mantle convection of super-Earths

In this paper, we carried out a series of linear analyses on the onset of thermal convection of highly compressible fluids whose physical properties strongly vary in space in convecting vessels either of a three-dimensional spherical shell or a two-dimensional spherical annulus geometry. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with ten times the Earth’s mass, while the thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively. Our analysis showed that, for the cases with strong temperature dependence in viscosity and strong depth dependence in thermal conductivity, the critical Rayleigh number is on the order of 108–109, implying that the mantle convection of massive super-Earths is most likely to fall in the stagnant-lid regime very close to the critical condition, if the properties of their mantle materials are quite similar to the Earth’s. Our analysis also demonstrated that the structures of incipient flows of stagnant-lid convection in the presence of strong adiabatic compression are significantly affected by the depth dependence in thermal conductivity and the geometries of convecting vessels, through the changes in the static stability of thermal stratification of the reference state. When the increase in thermal conductivity with depth is sufficiently large, the thermal stratification can be greatly stabilized at depth, further inducing regions of insignificant fluid motions above the bottom hot boundaries in addition to the stagnant lids along the top cold surfaces. We can therefore speculate that the stagnant-lid convection in the mantles of massive super-Earths is accompanied by another motionless regions at the base of the mantles if the thermal conductivity strongly increases with depth (or pressure), even though their occurrence is hindered by the effects the spherical geometries of convecting vessels.

Did the cessation of convection in Mercury's mantle allow for a dynamo supporting increase in heat loss from its core?

Mercury's large core generates a magnetic field and harbors a solidified inner component. These features constrain models of the planet's thermal history. The mantle provides the boundary condition on Mercury's core that determines heat loss. Recent studies suggest Mercury's mantle may have a higher thermal diffusivity than the silicate shells of other rocky bodies due to iron depletion. Considering the role of diffusivity, we model Mercury's mantle starting from a post magma-ocean state by calculating core-mantle boundary heat flow and the ratio of inner-core boundary radius to core-mantle boundary radius, fc, for periods comparable to the age of the solar system. Core-mantle boundary (CMB) heat flow is calculated using 3D mantle convection simulations for thermal diffusivities, κ, ranging from 1.0 - 3.0 ×10−6 m2/s and initial radiogenic uniform mantle heating rates, χ, of 0 - 40 pW/kg (that decay with a 3 Gyr half-life). Several scenarios can unfold for the range of parameters considered: these include cases featuring both the cessation of mantle convection and its continuation at 4.5 Gyr. We map a trend in κ - χ space and find that for some parameters present-day core heat flux and inner-core size estimates are satisfied for a Mercurian mantle that is cooling by conduction. The influence of initial sulfur fraction in the core was examined for a subset of cases. For a sulfur fraction of 0.10, fc falls between 0.1 and 0.55 which corresponds to planetary radius contractions below 7 km (since the Late Heavy Bombardment). However, fc exceeds 0.55 for a lower initial sulfur fraction and results in planetary contraction in excess of 7 km. In general, we find that the mean core heat flux reaches a temporal local minimum when the mantle transitions from a convective to a conductive regime and subsequently climbs before decreasing. The transition to conduction is delayed with increased mantle internal heating rate but the maximum mean heat flux from the core into the conducting and cooling mantle is always greater than the heat flux observed at the cessation of the stagnant-lid convection. We find that for an initially more vigorously convecting mantle the onset of inner-core growth is earlier while the basal heat flux is marginally reduced at present day. In general, we find that current-day conductive cooling of the Mercurian mantle can satisfy estimates on Mercury's core heat loss inferred from the strength of its magnetic field while also satisfying the limits on the present-day size of its inner core.

The Growth of Europa's Icy Shell: Convection and Crystallization

AbstractThe thickness of Europa's icy shell, which controls its thermal and rheological structure, cannot currently be directly measured. However, it can be estimated through indirect methods, including geodynamic modeling. We simulate the crystallization of the ice shell from a liquid water ocean and its subsequent thermal equilibration in the presence of tidal heat. We evaluate the effects of solid‐state stagnant lid convection on the shell's thermal equilibrium thickness and shell formation timing. The thermal equilibrium thickness of the ice shell ranges from 5 to 30 km, depending on the imposed tidal flexure strain rate. The ice lithospheric thickness remains less than 8 km, independently of imposed tidal flexure strain rate, overall shell thickness, and surface temperature, suggesting the Europan ice lithospheric strength is globally uniform. Thermal convection significantly reduces the thermal equilibration time scale, with the Europan ice shell able to fully crystallize out from a liquid water ocean in less than 2 Myr. Heterogeneous thermal equilibrium thickness values across the satellite suggest that widespread crystallization and melting may occur at the base of the shell. Rapid melting and crystallization timing suggest that the young surface age of the Europan ice shell may be the result of rapid catastrophic whole‐shell melting and recrystallization entirely recycling the surface.

Stagnant lid convection with temperature-dependent thermal conductivity and the thermal evolution of icy worlds

SUMMARY Convection is an efficient process to release heat from planetary interiors, but its efficiency depends on the detailed properties of planetary mantles and materials. A property whose impact has not yet been studied extensively is the temperature dependence of thermal conductivity. Because thermal conductivity controls heat fluxes, its variations with temperature may alter heat transfer. Here, I assess qualitatively and quantitatively the influence of temperature-dependent thermal conductivity on stagnant lid convection. Assuming that thermal conductivity varies as the inverse of temperature $(k \propto 1/T)$, which is the case for ice Ih, the main component of outer shells of solar System large icy bodies, I performed numerical simulations of convection in 3-D-Cartesian geometry with top-to-bottom viscosity and conductivity ratios in the ranges 105 ≤ Δη ≤ 108 and 1 ≤ Rk ≤ 10, respectively. These simulations indicate that with increasing Rk, and for given values of the Rayleigh number and Δη, heat flux is reduced by a factor Rk0.82, while the stagnant lid is thickening. These results have implications for the structures and thermal evolutions of large icy bodies, the impact of temperature-dependent conductivity being more important with decreasing surface temperature, Tsurf. The heat fluxes and thermal evolutions obtained with temperature-dependent conductivity are comparable to those obtained with constant conductivity, provided that the conductivity is fixed to its value at the bottom or in the interior of the ice shell, that is, around 2.0–3.0 W m−1 K−1, depending on the body. By contrast, temperature-dependent conductivity leads to thicker stagnant lids, by about a factor 1.6–1.8 at Pluto (Tsurf = 40 K) and a factor 1.2–1.4 at Europa (Tsurf = 100 K), and smaller interior temperatures. Overall, temperature-dependent thermal conductivity therefore provides more accurate descriptions of the thermal evolutions of icy bodies.

Scaling of heat transfer in stagnant lid convection for the outer shell of icy moons: Influence of rheology

The persistence of subsurface oceans in icy moons primarily depends on the efficiency of heat transfer through the outer ice shell. Scaling laws for heat transfer have already been determined by previous studies. These consider however a simplified rheology assuming a single creep mechanism, often using a linearized version of the temperature-dependent viscosity law (called Frank-Kamenetskii approximation). In the present study, we test the influence of ice rheology on the efficiency of heat transfer by considering a more realistic composite viscosity law, including diffusion creep, grain boundary sliding, basal slip and dislocation creep. We performed a large number of numerical simulations of thermal convection in the stagnant lid regime using a 2-D spherical annulus geometry with different rheology assumptions. Our results show that the dynamics of the ice shell is mainly controlled by the dominant creep mechanism in the rheological sublayer (the unstable lower portion of the cold boundary layer beneath the stagnant lid), which is mostly determined by grain size. For grain sizes lower than 3 mm, diffusion creep is the dominant creep mechanism in the rheological sublayer, while a combination of grain boundary sliding and basal sliding prevails for coarser grains. We derive new simple scaling relationships for the heat transfer suitable for the specific case of thin ice shells that account for the activation energy of the dominant creep mechanisms, thus allowing for a more accurate quantification of the temperature profile in the ice shell and cooling rate of the internal oceans.

Rapid crustal growth and efficient crustal recycling in the early Earth: Implications for Hadean and Archean geodynamics

The geodynamic regime of the early Earth remains elusive, with so far proposed hypotheses ranging from stagnant lid convection to rapid plate tectonics. Available geological data are severely limited for the first two billion years of the Earth's history, and this scarcity of relevant data is often compounded by the nonuniqueness of interpretation. Here we propose that the samarium–neodymium isotope evolution, which has been suggested to be consistent with stagnant lid convection in the early Earth, may be better understood as the result of rapid crustal growth and extensive crustal recycling. We delineate the permissible scenario of crustal evolution through geochemical box modeling with a Monte Carlo sampling of the model parameter space, and our results suggest that the net growth of continental crust was complete by the end of the Hadean and that the rate of crustal recycling could have been as high as 2−4×1022 kg Gyr−1 at that time and has gradually decreased since then. Such crustal evolution yields a specific prediction for the present-day distribution of crustal formation ages, which is shown to be in remarkable agreement with a recent estimate based on the global compilation of zircon age data. The mode of subsolidus mantle convection after the putative magma ocean is probably plate tectonics, but its style could have been very different from that of contemporary plate tectonics, characterized by more voluminous magmatism and more destructive subduction.

A Geophysical Perspective on the Bulk Composition of Mars

AbstractWe invert the Martian tidal response and mean mass and moment of inertia for chemical composition, thermal state, and interior structure. The inversion combines phase equilibrium computations with a laboratory‐based viscoelastic dissipation model. The rheological model, which is based on measurements of anhydrous and melt‐free olivine, is both temperature and grain size sensitive and imposes strong constraints on interior structure. The bottom of the lithosphere, defined as the location where the conductive geotherm meets the mantle adiabat, occurs deep within the upper mantle (∼200–400 km depth) resulting in apparent upper mantle low‐velocity zones. Assuming an Fe‐FeS core, our results indicate (1) a mantle with a Mg# (molar Mg/Mg+Fe) of ∼0.75 in agreement with earlier geochemical estimates based on analysis of Martian meteorites; (2) absence of bridgmanite‐ and ferropericlase‐dominated basal layer; (3) core compositions (15–18.5 wt% S), core radii (1,730–1,840 km), and core‐mantle boundary temperatures (1620–1690°C) that, together with the eutectic‐like core compositions, suggest that the core is liquid; and (4) bulk Martian compositions with a Fe/Si (weight ratio) of 1.66–1.81. We show that the inversion results can be used in tandem with geodynamic simulations to identify plausible geodynamic scenarios and parameters. Specifically, we find that the inversion results are largely reproducible by stagnant lid convection models for a range of initial viscosities (∼1018–1020 Pa s) and radioactive element partitioning between crust and mantle around 0.01–0.1. The geodynamic models predict a mean surface heat flow between 15 and 25 mW/m2.

Cratonic basins with reference to the Michigan basin

Abstract Seafloor and passive margins gradually subside as a result of thermal contraction of the underlying lithosphere. Thermal subsidence is also an attractive mechanism for the Michigan basin. For subsidence to occur within this previously stable continental region, some mechanism is needed to heat the lithosphere and to reduce the buoyancy of the continental crust. Mechanical stretching of the lithosphere along with its crust does both at the same time. The ponding of plume material beneath the crust supplies heat, but does not directly thin the crust. The British Isles and the Congo basin provide analogies to the Michigan basin. Continental stretching before subsidence is evident within the British Isles and the Congo basin. Stretching is not obvious in Michigan, but undetected rifts extending from the Iapetus break-up margin may exist. A closed region of thin lithosphere beneath the Irish Sea may have trapped hot buoyant material from the Iceland plume; the Michigan basin may have trapped material from an Iapetus age plume near Montreal. Cratonic basins provide information on the tail of the subsidence curve, unlike more ephemeral oceanic crust and passive margins. The poorly resolved tails in the Michigan and the Congo basins are consistent with the time subsidence constant, c. 280 myr predicted by stagnant lid convection formalism.

Long-term preservation of early formed mantle heterogeneity by mobile lid convection: Importance of grainsize evolution

The style of tectonics on the Hadean and Archean Earth, particularly whether plate tectonics was in operation or not, is debated. One important, albeit indirect, constraint on early Earth tectonics comes from observations of early-formed geochemical heterogeneities: 142Nd and 182W anomalies recorded in Hadean to Phanerozoic rocks from different localities indicate that chemically heterogeneous reservoirs, formed during the first ∼500 Myrs of Earth's history, survived their remixing into the mantle for over 1 Gyrs. Such a long mixing time is difficult to explain because hotter mantle temperatures, expected for the early Earth, act to lower mantle viscosity and increase convective vigor. Previous studies found that mobile lid convection typically erases heterogeneity within ∼100 Myrs under such conditions, leading to the hypothesis that stagnant lid convection on the early Earth was responsible for the observed long mixing times. However, using two-dimensional Cartesian convection models that include grainsize evolution, we find that mobile lid convection can preserve heterogeneity at high mantle temperature conditions for much longer than previously thought, because higher mantle temperatures lead to larger grainsizes in the lithosphere. These larger grainsizes result in stronger plate boundaries that act to slow down surface and interior convective motions, in competition with the direct effect temperature has on mantle viscosity. Our models indicate that mobile lid convection can preserve heterogeneity for ≈0.4–1 Gyrs at early Earth mantle temperatures when the initial heterogeneity has the same viscosity as the background mantle, and ≈1–4 Gyrs when the heterogeneity is ten times more viscous than the background mantle. Thus, stagnant lid convection is not required to explain long-term survival of early formed geochemical heterogeneities, though these heterogeneities having an elevated viscosity compared to the surrounding mantle may be essential for their preservation.

Heat-pipe planets

Observations of the surfaces of all terrestrial bodies other than Earth reveal remarkable but unexplained similarities: endogenic resurfacing is dominated by plains-forming volcanism with few identifiable centers, magma compositions are highly magnesian (mafic to ultra-mafic), tectonic structures are dominantly contractional, and ancient topographic and gravity anomalies are preserved to the present. Here we show that cooling via volcanic heat pipes may explain these observations and provide a universal model of the way terrestrial bodies transition from a magma-ocean state into subsequent single-plate, stagnant-lid convection or plate tectonic phases. In the heat-pipe cooling mode, magma moves from a high melt-fraction asthenosphere through the lithosphere to erupt and cool at the surface via narrow channels. Despite high surface heat flow, the rapid volcanic resurfacing produces a thick, cold, and strong lithosphere which undergoes contractional strain forced by downward advection of the surface toward smaller radii. We hypothesize that heat-pipe cooling is the last significant endogenic resurfacing process experienced by most terrestrial bodies in the solar system, because subsequent stagnant-lid convection produces only weak tectonic deformation. Terrestrial exoplanets appreciably larger than Earth may remain in heat-pipe mode for much of the lifespan of a Sun-like star.

Earth’s thermal evolution, mantle convection, and Hadean onset of plate tectonics

During Solar System condensation, the early Earth formed through planetesimal accretion, including collision of a Mars-sized asteroid. These processes rapidly increased the overall thermal budget and partial fusion of the planet. Aided by heat supplied by radioactivity and infall of the Fe-Ni core, devolatilization and chemical-density stratification attended planetary growth. After the thermal maximum at ∼4.4Ga, terrestrial temperatures gradually declined as an early Hadean magma ocean solidified. By ∼4.3–4.2Ga, H2O oceans+a dense CO2-rich atmosphere blanketed the terrestrial surface. Near-surface temperatures had fallen well below the low-P solidi of dry peridotite, basalt, and granite, ∼1300, ∼1120, and ∼950°C, respectively. At less than half their melting T, rocky materials existed as thin lithospheric platelets in the surficial Hadean Earth. Upper mantle stagnant-lid convection may have operated locally, but was rapidly overwhelmed by heat build-up-induced asthenospheric circulation, rifting and subduction, because massive heat transfer required vigorous mantle overturn in the early, hot planet. Bottom-up mantle overturn, involving abundant plume ascent, brought deep-seated heat to the surface. It decreased over time as cooling, plate enlargement, and top-down plate descent increased. Thickening, lateral extension, and contraction typified the post-Hadean lithosphere. Geologic evolutionary stages included: (a) ∼4.5–4.4Ga, the magma ocean solidified, generating ephemeral, ductile platelets; (b) ∼4.4–2.7Ga, small oceanic and continental plates were produced, then were destroyed by mantle return flow before ∼4.0Ga; eventually, continental material began to accumulate as largely subsea, sialic crust-capped lithospheric collages; (c) ∼2.7–1.0Ga, progressive suturing of old shields and younger orogenic belts led to cratonal plates typified by emerging continental freeboard, intense sedimentary differentiation, and episodic glaciation during transpolar plate drift; temporally limited stagnant-lid mantle convection occurred beneath growing supercontinents; (d) ∼1.0Ga-present, laminar-flowing mantle cells are capped by giant, stately moving plates. Near-restriction of komatiitic lavas to the Archean, and formation of multicycle sediments, ophiolite complexes±alkaline igneous rocks, and high-pressure/ultrahigh-pressure (HP/UHP) metamorphic belts in youngest Proterozoic and Phanerozoic orogens reflect increasing density of cool oceanic plates, but decreasing subductability of enlarging, more buoyant continental plates. Attending assembly of supercontinents, negative buoyancy of thickening oceanic lithosphere began to control the overturn of suboceanic mantle as cold, top-down convection. The scales and dynamics of hot asthenospheric upwelling versus plate foundering and mantle return flow (bottom-up plume ascent versus top-down plate subduction) evolved gradually, due to planetary cooling. After accretion of the Earth, heat transfer through mantle convection has resulted in the existence of surficial rocky plates or platelets, and vigorous, lithosphere-coupled mantle overturn since ∼4.4Ga. Thus plate-tectonic processes have typified the Earth’s thermal history since Hadean time.