Thermal evolution of the Earth's core

Abstract

The persistence of the magnetic field of the Earth demands a constant energy source for the last three thousand million years, and this provides a constraint on the thermal evolution of the core. The equations of global energy and entropy balance are used to estimate the power source required for a specific magnetic field. The amount of power required depends on the exact nature of the source. Three possibilities are considered here: radioactive heating in the core itself, loss of internal energy due to cooling and freezing of the outer core to form the inner core, and cooling of the whole core with consequent differentiation to form the inner core with release of gravitational energy. The last of these includes all the sources except for radioactive heating, but the introduction of some radioactivity into this calculation would be a simple matter. For radioactive heating alone, 1013W is required for the dynamo. This is just within the limits set by the observed surface heat flux (4 × 1013W) and what some geochemists believe to be the heating due to K40. Cooling itself cannot release enough heat to power the dynamo because the required cooling rate is so high that the inner core would be a very recent feature of the Earth. The release of gravitational energy can produce a magnetic field of 100–200 gauss, with the inner core growing slowly to its present size over 4Ga, and a heat release of 2.5 × 1012W. A lower heat flux is required because of the greater efficiency of conversion of gravitational energy into magnetic fields than heat. When pursuing the calculations backwards in time, the rate of energy release is found to be proportional to the mass of the inner core. A surprising feature of this model, which assumes a constant rate of cooling at the top of the core, is that the useful power available for the dynamo increases with time, so that the field should be stronger now than it was in the past, although only by about 30 per cent.