Analytical model for solidification of the Earth's core

Abstract

THE Earth's solid inner core is generally thought to have formed by gradual solidification of the liquid core as the Earth cooled^1–3. To elucidate the relative importance of the various physical effects on the thermal evolution of the core, we have developed an analytical model based on global heat conservation, which describes the cooling of the vigorously convecting, fluid outer core and the concomitant growth of the inner core. We obtain a simple form for the evolution of the inner-core radius which allows the consequences of changes to the model's input parameters to be readily assessed. For most of this evolution, inner-core growth is controlled primarily by the heat capacity of the outer core and the history of the heat flux into the base of the mantle. Heat sources associated with solidification of the inner core, including the release of latent heat and gravitational energy, have a secondary role but become more important towards the end of solidification. Using current seismic estimates of compositional changes at the surface of the inner core, we conclude that the compositional and thermal buoyancy fluxes in the outer core are comparable.