Presentation #201.05 in the session “Planet and Satellite Dynamics”.
Two forms of ohmic heating of astrophysical objects have received particular attention. The first, viewed in the frame of a rotating primary, is homopolar-generator heating due to Lorentz force-driven current flow from the primary through a flux tube to the moving secondary, through the secondary and back to the primary. The second, viewed in the frame of the secondary, is magnetic induction heating, treating the secondary as sitting in the spatially constant but temporally oscillating magnetic field of the primary. Neither mechanism appears to cause significant heating in the contemporary solar system. But these discussions have overlooked an additional electromagnetic heating mechanism that derives from the spatial variation of the primary's field across the interior of the secondary. This leads to Lorentz force-driven currents around conducting paths entirely internal to the secondary, with resulting ohmic heating. We examine three ways to drive such currents, by the cross product of: (1) the secondary’s azimuthal orbital velocity with the non-axially symmetric field of the primary; (2) the radial velocity (due to non-zero eccentricity) of the secondary with any of the components of the primary’s field; or (3) the out-of-plane velocity (due to non-zero inclination) of the secondary with the primary’s field. The first of these operates even for orbits of the secondary that have zero eccentricity and inclination, in strong contrast to tidal dissipation. We consider conductors within the secondary that are spherical (as for metallic cores) or spherical shells (as for magma or liquid water oceans). As an illustration, we show that Jupiter’s moon Io today could experience 2,000 GW of heating in the outer hundred meters of its Fe-FeS core by mechanism (1) above, and likely more in the past. We should expect analogous dissipation to occur in objects in extrasolar systems.