Rapidly rotating early-Earth dynamos in a full-sphere geometry

SUMMARY While the Earth’s magnetic field has existed for 4 Gyr or more, most recent estimates for the age of the inner core nucleation date no further back than 1.5 Gyr. As a consequence, the relevant geometry for the Earth’s dynamo has been a full sphere for much of its life, fundamentally different from the present-day dynamo operating in a spherical shell. We therefore systematically study magnetic field generation in a rapidly rotating full sphere where convection is driven by heat sources uniformly distributed throughout the fluid. We observe a rich diversity of behaviour in our solutions, including dipolar and multipolar dominated fields, together with vacillating and chaotically reversing magnetic fields. At Prandtl number of unity, we construct regime diagrams as a function of three control parameters, namely the Rayleigh, Ekman and magnetic Prandtl number, which show some similarities with the corresponding diagrams for spherical shell dynamos. This study comprehensively demonstrates the feasibility of early-Earth dynamos that operate based on secular cooling of the core.