Gravitational energy of core evolution: implications for thermal history and geodynamo power

Using density-pressure relationships for mantle silicate and core alloy closely matching PREM we have constructed six models of the Earth in different evolutionary states. Gravitational energies and elastic strain energies are calculated for models with homogeneous composition, separated mantle and liquid core, separated inner and outer cores with the inner core either liquid or solid and models with increased densities, representing cooling of either the mantle or core. In this way we have isolated the gravitational energy released by each of several evolutionary processes and subtracted the consequent increase in strain energy to obtain the net energy released as heat or geodynamo power. Radiogenic heat (∼7.8×10 ³⁰ J) is found to contribute only about 25% of the total heat budget, the balance originating as residual gravitational energy from the original accretion and from core separation (14×10 ³⁰ J). The total energy of compositional convection, driven by inner core formation, is 3.68×10 ²⁸ J and this is the most important (or even the only) energy source for the dynamo for the most recent 2 billion years. It appears unlikely that the inner core existed much before that time. The total net (gravitational minus strain) energy released in the core by the process of inner core formation, 11.92×10 ²⁸ J, is not much less than the thermal energy released in this process, 15.1×10 ²⁸ J. In the mantle the net (gravitational minus strain) energy released by thermal contraction is about 20% of the heat release. All of the numerical results are presented in a manner that allows simple rescaling to any revised density estimates.