Crystallization of a compositionally stratified basal magma ocean

https://doi.org/10.1016/j.pepi.2017.07.007Get rights and content

Highlights

  • A dense, iron-rich silicate melt is a byproduct of early differentiation.

  • Core cooling through a chemically stratified layer allow long term heat retention.

  • A chemically stratified basal magma ocean helps sustain the geodynamo longer.

Abstract

Earth’s ∼3.45 billion year old magnetic field is regenerated by dynamo action in its convecting liquid metal outer core. However, convection induces an isentropic thermal gradient which, coupled with a high core thermal conductivity, results in rapid conducted heat loss. In the absence of implausibly high radioactivity or alternate sources of motion to drive the geodynamo, the Earth’s early core had to be significantly hotter than the melting point of the lower mantle. While the existence of a dense convecting basal magma ocean (BMO) has been proposed to account for high early core temperatures, the requisite physical and chemical properties for a BMO remain controversial. Here we relax the assumption of a well-mixed convecting BMO and instead consider a BMO that is initially gravitationally stratified owing to processes such as mixing between metals and silicates at high temperatures in the core-mantle boundary region during Earth’s accretion. Using coupled models of crystallization and heat transfer through a stratified BMO, we show that very high temperatures could have been trapped inside the early core, sequestering enough heat energy to run an ancient geodynamo on cooling power alone.

Introduction

Conducted heat loss is thought to be one of the greatest hurdles for a terrestrial planet to overcome in the long-term sustenance of a magnetic field by dynamo action (Stevenson, 2003). To avoid thermal stratification and cessation of convection currents that sustain the dynamo, this conducted heat must either be taken up into the overlying sluggishly convecting solid mantle or returned into the deeper core under the influence of a stronger buoyancy source (Badro et al., 2016, O’Rourke et al., 2017, O’Rourke and Stevenson, 2016, Hirose et al., 2017) or strong mechanical stirring (Cébron et al., 2010, Le Bars et al., 2015). Heat loss to the mantle results in core cooling, while re-ingestion of conducted heat can partly delay core cooling. While crystallization of Earth’s solid inner core may provide a significant composition-induced buoyancy source for re-ingesting heat at the present day, the inner core itself has likely existed for only a fraction of the age of the geomagnetic field. Unless there is another buoyancy source to help drive convection prior to inner core crystallization (O’Rourke and Stevenson, 2016, Badro et al., 2016, O’Rourke et al., 2017, Hirose et al., 2017), heat loss from the core to the mantle implies a minimum of 500–1000 K of core cooling since 3.5 Ga (Gomi et al., 2013, Labrosse, 2015). The actual cooling would be significantly higher if one accounted for fluctuations in heat flow. The ∼7–14 TW of core-mantle boundary (CMB) heat flow that is compatible with recent estimates (Lay et al., 2008, Hernlund and McNamara, 2014) may be insufficient to account for this degree of secular cooling.

Recent estimates of Earth’s core conductivity are roughly twice to thrice as high as some earlier estimates (de Koker et al., 2012, Pozzo et al., 2012, Gomi et al., 2013), which contributes to the high degree of estimated core cooling. The precise value of the core conductivity is still highly debated but studies performed before that debate and using values of conductivity in the lower end of the current debate or even smaller already recognized that the requisite core cooling prior to the birth of the inner core meant that the ancient core-mantle boundary (CMB) may have been hotter than the solidus temperature of rocks in the deep mantle (Buffett, 2002, Labrosse et al., 2007). Combined with observations of ultra-low velocity zones at the bottom of the mantle that have often been ascribed to the presence of partial melt (e.g. Williams and Garnero, 1996, Labrosse et al., 2015), even modest cooling rates of the core imply a larger amount of melt in the past, leading to the idea of an extensive “basal magma ocean” (BMO) of up to ∼1000 km thickness that may have existed at the bottom of the early Earth’s mantle (Labrosse et al., 2007).

Earlier models of BMO evolution were relatively simplistic, utilizing an idealized phase diagram and assuming a homogeneous magma existed at the end of Earth’s accretion. However, accretion itself was probably a messy process, and is unlikely to have produced the kind of neat conditions we have assumed in past models. It is therefore worth relaxing previous assumptions to explore whether the evolution model can permit a wider range of core secular cooling histories.

Here we consider the possibility that a dense iron-rich silicate melt could have formed in the core-mantle boundary region of the early Earth via silicate-metal mixing between liquids at high temperatures, for example following a giant impact event. During silicate-metal mixing, we expect a chemical reaction of the following kind:SiO2Sil+2FeMetSiMet+2FeOMet+Sil.

The superscripts Sil and Met denote the silicate and metal liquids, respectively. Higher temperatures are known to shift reactions of this kind to the right (Tsuno et al., 2013, Fischer et al., 2016, Hernlund, 2016). Dissolution of Si from an oxide state into metal at higher temperature is accompanied by production of FeO, some of which may remain in solution in metallic liquid and some of which will be partitioned into the silicate liquid. Fig. 1 illustrates the evolution scenarios considered in previous models compared to the present study.

There are many possible scenarios in which FeO-enriched melts can be produced by silicate-metal mixing at high temperatures in the CMB region. For example, in a scenario where the Moon is formed by a giant impact between a Mars-sized embryo and the proto-Earth (e.g. Canup, 2004, Canup, 2012), extensive turbulent mixing should occur between the in-falling impactor core and the surrounding molten mantle silicates (Deguen et al., 2014). The resultant heavy silicate-metal mixture would be expected to sink to the CMB region, after which metal droplets would separate from the silicate liquid onto the top of the core. Such a process would leave behind a FeO-rich silicate liquid at the bottom of the mantle, and produce a Si- and O-enriched metallic fluid atop the core. Such structures in the core could remain even after crystallization of the molten mantle, so long as they are stable against turbulent entrainment (Landeau et al., 2016). Such a mechanism may be compatible with layering observed by seismological analysis of the shallow core (Helffrich and Kaneshima, 2010).

Production of FeO-rich fluid at the base of the mantle changes two key properties that permit such a liquid to persist long after Earth’s formation. The first is a density increase, allowing the FeO-rich melt to remain gravity-stabilized beneath the overlying relatively FeO-poor mantle. The second is a depression in the freezing temperature (i.e., liquidus) which can allow the melt to persist after the overlying mantle has solidified. The latter property occurs because FeO is slightly (Andrault et al., 2011) to moderately (Nomura et al., 2011, Tateno et al., 2014) incompatible and hence promotes melting. This mechanism for producing a BMO is distinct from previously discussed scenarios involving mid-mantle crystallization from a homogeneous molten mantle at the intersection of the liquid isentrope and liquidus, overturning and remelting of a fractionally crystallized solid mantle, or melting from below of the mantle owing to the initial superheat in the core (Labrosse et al., 2015). The efficacy of this mechanism for initially producing a BMO also does not depend upon the density difference between melt and solid in equilibrium, although such difference would still lead to different evolutionary scenarios.

The silicate-metal mixing scenario is unlikely to produce a homogeneous well-mixed fluid underlying a relatively iron-poor mantle. Owing to variable degrees of chemical interaction, heterogeneous temperature, and partial mixing between the dense liquid and overlying mantle, it is more natural to expect a gradient in density inside the residual silicate liquid, characterized by increasing FeO-content with depth inside the layer. Such a layer would not convect unless the thermal gradient were sufficiently steep to overcome the stratifying effects of FeO.

The goal of this paper is to test the influence of an initially stratified, liquid silicate layer at the core mantle boundary on the thermal evolution of the core. We chose to approach the problem from a parametric perspective, to characterize the importance of a range of parameters on observables. Therefore this model cannot be used to predict the degree of stratification or the size of the layer, but rather provide tools to understand how such a layer would fit in a global view of the early evolution of the Earth.

In the following, we first present equations to compute the erosion of the stratification as the layer crystallizes. We then provide a description of its implementation in an evolution simulation and a discussion of the choice of parameters. In the results section, we first describe the erosion process, irrespective of any particular evolution scenario. Only after do we present typical predicted evolution and discuss its influence on core cooling.

Section snippets

Model

We now consider the evolution of the initially stably stratified liquid silicate layer. The tendency for such a stratified BMO to crystallize from the top is enhanced owing to relative depletion of FeO with height. Fractional crystallization (with solids containing relatively lower concentrations of FeO) leaves behind a magma that is enriched in FeO compared to its initial composition. This triggers compositional convection that erodes the underlying stratification.

We separate the problem into

Results

The strength of the stratification controls the rate at which it can be eroded (Fig. 3, top). A small stratification will be easier to erode, which also means that a lower fraction of the basal magma ocean will need to be crystallized before full erosion (Fig. 3, bottom). On the other hand, a strong stratification is harder to erode. This leads to cases where the convective zone quickly reaches a maximum size at which the rate of crystallization is similar to that of erosion. For instance, for

Discussion

The actual composition of the lower mantle being largely unknown, we chose to consider an artificial mineralogy composed of (Mg,Fe)O. The two end members have a factor two difference in density, and we take the difference in liquidus between the end-members to be 2000 K. This is justified by the fact that we do not try to predict the composition of the layer here, but to understand the general properties of the core mantle boundary heat flow as driven by a stratified layer. Early onset of the

Acknowledgments

ML is grateful for funding from the Itoh Foundation. SL is supported by a public grant overseen by the French National Research Agency (ANR-15-CE31-0018-01, MaCoMaOc). We wish to thank J. Rudge and an anonymous reviewer for comments that helped clarify the manuscript. The complete code and scripts to run the various simulations can be obtained by request to ML ([email protected]).

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