Observational constraints on the generation process of the Earth's magnetic field

Abstract

Summary The most likely origin of the Earth's magnetic field is a dynamo process acting in the liquid core, with motions of the fluid driven by thermal convection. This hypothesis is examined in relation t o the constraints imposed by a knowledge of the surface magnetic field, the surface heat flux, and also to some extent the properties of the core. Assuming the Weidemann—Franz relation between the electrical and thermal conductivities for the core, it is possible to obtain lower bounds on the heat flux through the base of the mantle. The minimum heat flux from the core is found to be 2.1010W, independent of either the electrical conductivity or the temperature gradient. By requiring that these bounds be less than the surface heat flux, the product of the electrical conductivity and the temperature gradient may be bounded both from above and from below. The heat flux estimates are improved by considering ohmic heating from the toroidal magnetic field, which cannot be observed directly, and the convected heat flux. An expression is obtained for a bound of the ohmic heating of the toroidal field in terms of the radial fluid velocity. A comparison with existing dynamo models reveals that the true value of the ohmic heating is much larger than the ideal bound. This is evidence against the existence of a toroidal field as large as, say, 10 mT. The heat fluxes are larger for heating by uniformly distributed heat sources than for latent heat from growth of the inner core. Unless the adiabatic gradient is below about 0.1 K km−1, it is not possible to generate the magnetic field by distributed heat sources. The latent heat case does not suffer the same difficulty, but then it is possible for the outer regions of the core to be density-stratified. Gravitational energy released by accretion of the inner core may also be an appreciable or even dominant factor.