Melt-solid Segregation and Fractional Magma Ocean Solidification with Implications for the Evolution Of

Introduction: Large planetary bodies are likely to have been significantly melted during their accretion, simply as a consequence of the potential energy of accretion if accretion occurs rapidly enough or possibly due to giant impacts [1]. Since the solidus and liquidus temperatures of mantle mineral assemblages increase with pressure more rapidly than temperature along an adiabat, solidification of a thermally wellmixed magma ocean (MO) is expected to occur from the bottom up. If the surface temperature is below the liquidus, crystallization may also occur in the cool thermal boundary layer at the planetary surface. Ideal fractional solidification of a MO results in an unstable stratigraphy primarily due to increasing Fe/Mg of residual liquid as solidification proceeds. Highly incompatible elements, including heat producing U, Th, and K, would be progressively enriched in the residual liquid. The unstable solid stratigraphy resulting from fractional solidification, with both density and incompatible elements increasing upward, would overturn on relatively short time scales with significant implications for subsequent planetary evolution. Overturn results in a stably stratified mantle that would resist solid-state thermal convection and in which incompatible heat producing elements are concentrated at the bottom of the mantle. During rapid solidification, the temperature of the solid will follow the solidus. Solid state overturn driven by unstable compositional stratification will then bring cold material to the bottom of the mantle that may cool a metallic core fast enough to generate an early magnetic field [2,3]. On longer time scales this radiogenic elementrich material at the bottom of the mantle will heat the overlying stably stratified mantle and provide a geochemical reservoir that remains partially isolated during planetary evolution as seem to be the case for both the Moon and Mars [4]. Fractional solidification requires the separation of solid from the liquid in which it forms. The rate of this separation may thus control how ideally fractional the MO solidification can be. Cooling of the MO is expected to be controlled by the radiative cooling of the planetary surface, thus depending on the pressure and composition of the atmosphere [5,6]. The rapidity of early planetary evolution is indicated by the presence of significant fractionations in the daughter products of isotopic decay that must have occurred during the earliest evolution, including variation in W [7] and Nd [8,9] that are produced from decay with halflives of approximately 10 and 100 Myr, respectively. Solid-melt segregation during MO solidification: Crystallization will occur in cool sinking plumes and thermals that develop from instability of the surface thermal boundary layer and in the thermal boundary layer itself if the surface temperature is below the liquidus. Figure 1 illustrates the case with solidification occurring only in downwelling plumes. Due to turbulent entrainment the plume radius increases as about 0.1 x depth [10,11]. Solids forming in the cool central region of the plume will impinge on the solidified floor of the MO and spread laterally to form a layer of solid containing interstitial melt with a melt fraction that increases upward. The top of this mostly solid layer will occur at a height where the melt fraction reached about 50%, corresponding to fraction of the radius of the plume. For a MO depth of 500 km this layer should be about 100 km thick. Much like atmospheric, convective upwelling resulting from heating of the earth’s surface, cool, turbulent plumes in a MO are expected to be highly time dependent. Deposition of partially molten material in layers beneath plumes will thus be episodic at an average deposition rate determined by the overall cooling at the surface. For an average solidification velocity V and a layer thickness H, the average time between depositions and the time for each layer to lose its melt before being buried beneath the next layer would be simply H/V.