Heat partitioning in metal-silicate plumes during Earth differentiation

We present an analytical model for core formation that includes both metal diapirs and liquid conduits and produces a superheated core. We start from the standard model of Earth formation consisting of accretion by planetesimal or planetary embryo impacts large enough to create global or local magma oceans. Our model consists of two main fluid dynamical structures: 1) large liquid metal diapirs and 2) narrow conduits with liquid silicate and small liquid metal droplets. We assume that transport of metal from a near-surface magma ocean to the growing core occurs within these structures. The release of gravitational potential energy from the descent of the metal is converted to heat through viscous dissipation, which is broadly distributed around the large liquid metal diapirs but localized in the conduit around the smaller metal droplets. This model gives an average core temperature during accretion and a post-accretion average core temperature for a broad range of impact histories and chemical quilibration assumptions. We consider three types of Earth accretion histories with impacts that are evenly spaced over 30 Ma. These include: 1) equal-sized impacts, 2) equal-sized impacts with a final Mars-sized impact, and 3) exponentially decreasing impact sizes with a final Mars-sized impact. Our preferred model is based on core–mantle chemical equilibrium estimates that correspond to a fractionation, f, the ratio of metal in the diapir to the total metal content in each impact of f = 0.64 and accretion history type 3. This model produces a post-accretion average core temperature that ranges from 5930 K to 5700 K for 8 to 90 impacts, respectively. The efficiency of the metal-silicate conduits, defined as the ratio of the heating of the core by the conduits to their potential energy released has an approximate value of 0.59 for our preferred model. The residual post-accretion structures include a basal magma ocean and a network of mantle conduits that may dictate the style of Hadean tectonics.