The role of thermal density currents in the generation of planetary magnetic fields

In this study, we propose a conjecture regarding generating magnetic fields in the interior of planets. Specifically, we investigate the potential contribution of a thermal density current, which is generated by the Seebeck effect, to the intensity of the planetary magnetic field. Our analysis reveals that the scale of the magnetic field associated with the thermal density current is of comparable magnitude to the observed magnetic fields on planets within our solar system. To assess this hypothesis, we leverage degenerate Fermi gas approximation for the fluid internal cores of the planets, enabling us to evaluate the magnitude of thermal contribution to the planetary magnetic field for Mercury, Earth, Jupiter, Saturn, Uranus, and Neptune. Finally, we validate our results by comparing them with the magnetic fields measured by several spatial missions. We will not solve the magnetohydrodynamic equations; instead, our discussion will focus on the order of magnitude of the magnetic field and its associated physics. At this level, we will not consider the specific mechanisms, such as dynamo conversion, responsible for generating the observable magnetic field. Our goal is to provide a scaling that aligns with astronomical observations.