Magnetohydrodynamic scaling of geogynamo and a planetary protocore concept

S. V. Starchenko¹ - Y. D. Pushkarev²

¹ IZMIRAN, Troitsk, Moscow region, 142190 Russia
² IPGG RAN, St.-Petersburg, 199034 Russia

Abstract
For fast rotating planets/moons, we derive magnetohydrodynamic (MHD hereafter) scaling laws in the limit of negligible molecular diffusivity, viscosity and magnetic diffusivity effects. Our new scaling law equates the typical magnetic/kinetic energy ratio to the square of a corresponding scales' ratio. In the Earth's core, magnetic energy dominates over kinetic one and a typical magnetic field is proportional to the third root of the buoyancy flux, which initiates convection, while the field is independent on conductivity and angular rotation rate. The same scaling has been obtained recently via compilation of numerical simulations. Besides, here we present new scaling laws for typical velocity, buoyancy acceleration, sinus of the angle between magnetic and velocity vectors, electromagnetic and hydrodynamic scales. The established scaling laws allow to estimate typical geodynamo values and long-term geomagnetic consequences for different evolution scenarios of a core-mantle system. The currently accepted scenario with the inner solid core crystallizing from the liquid core provides a too small value of the geomagnetic field for more than 3 billion years after the formation of the liquid core. Since this is inconsistent with the available paleomagnetic records, we suggest another scenario with a solid protocore, which occupies almost the whole core of the just formatted Earth. This protocore is being slowly melted under the surface influence of the overheated liquid core, which grows up to its contemporary size, while the solid core is a small relic of the protocore. Such protocore concept resolves the problem of energy source for geodynamo and for plume activity in the mantle. In case of validity of this concept, the mantle should be supplemented with the silicate material from the protocore with a primitive isotope composition of lead, but which cannot be the result of the liquid core crystallization. An additional argument to the concept validity could be the primitive isotope composition of lead in combination with primary helium enriched by isotope ³He. Applications of the protocore concept to the terrestrial planets are discussed. Figs 2, Refs 12.