Magnetism and convection scaling laws in planets

Starchenko Sergey, sstarchenko@mail.ru, IZMIRAN, Troitsk, Moscow region, Russian Fed

Abstract
Scaling laws for planetary convection and magnetism relate the characteristic magnetic field strength, characteristic flow velocity and other properties to primary quantities such as size of dynamo region, rotation rate, electrical conductivity, and available heat and/or composition power. The advent of direct numerical simulations of planetary dynamos and the ability to perform them for a wide range of control parameters predict a field strength that is independent of rotation rate and electrical conductivity and proportional to the cubic root of the available power. However, rotation rate controls whether the magnetic field is dipolar or multipolar. The predictions of this power-based scaling law agree well with the observed field strength of the Earth and Jupiter, but not so well for the other planets with known magnetic fields and estimated dynamo powers. It seems for the first time in the World practice I analytically from the first principals derive those power-based and all the other possible scaling laws for planetary magnetism, velocity, scales, magnetic-velocity vector relations and turbulent transports. My scaling laws work perfectly for the Solar system planets and could be extended on exoplanets. Those laws could also be applied to some stars helping to understand the link between planetary and stellar dynamos.