Ohmic heating within the Galilean satellites

The Galileo spacecraft discovered that electromagnetic induction occurs within the electrically conductive interior of Europa and Ganymede and possibly also within Io and Callisto, primarily caused by the tilt of Jupiter’s magnetic dipole axis relative to the orbital plane of the satellites. The analysis of magnetic field data provides insights into the satellites’ internal electrical conductivity structure and reveals that the icy moons probably possess a global subsurface layer of saline water. The existence of a global magma layer in the rocky moon Io is also debated. Using the analytical solution of the Helmholtz equation in an electrically conductive body with radially symmetric conductivity distribution, the magnetic field, the induced electric currents, and the resulting Ohmic heating in the interior are determined. Initially, a sphere of constant conductivity featuring an insulating surface layer in the presence of a linearly polarized time-varying external magnetic field is assumed. Using this simplified model, the total heating rate and the spatial and temporal structure of resulting Ohmic heating as functions of the conductivity of the sphere and the period of the inducing field are investigated. It is found that Ohmic heating does not occur on the axis of the inducing field, while it has a maximum on the equatorial plane of the inducing field directly beneath the surface. The electrical conductivity and the period of the inducing field dominate the radial structure of Ohmic heating. High conductivities and low periods lead to large heating rates near the surface, while the attenuation with depth is stronger as in relatively low-conductive materials or for long periods. The total Ohmic heating rate within the homogeneous sphere does not necessarily increase with rising electrical conductivity. Furthermore, the spatial structure of Ohmic heating and total heating rates for multiple interior models of the Galilean satellites is determined. It is found that Ohmic heating does not play a role in Io, neither for a magma ocean model nor for a rigid model. For Europa, it is also possible to conclude that Ohmic heating is not important neither in the global heat budget nor locally within the subsurface ocean