Induction in the Subsurface Oceans of Europa and Ganymede

Because of Jupiter’s rotation and the orbital motion, the subsurface oceans of the Galilean moons experience a time varying background magnetic field. This gives rise to induction and the detection of the related magnetic fields lead to the discovery of the subsurface oceans. We numerically study the induction, concentrating on a background field that consist of Jupiter’s potential field and the field of the current disc but ignores the interaction of the moon with the surrounding plasma.

The complex orbital motions yield magnetic field variations of different frequencies, with different amplitudes and phases that change over time. Analyzing the orbital evolution, we provide a catalogue of these important parameters, which are crucial for interpreting the measured induced magnetic. The most important parameter for the induction problem is the magnetic Reynolds number, Rm. Rm is the ratio of the magnetic dissipation time, which scales with the electrical conductivity, and the induction period. The second parameter, which the system is less sensitive to, is the relative ocean depth. We compare different methods of calculating induction, ranging from classical methods to full 3d dynamical simulations. The Matlab code PlanetInd, which is freely available on GitHub, allows choosing the most appropriate method for the induction problem of interest. We find that the classical analytical solutions based on Bessel functions become problematic for larger Rm values.  PlanetInd therefore uses a pseudo-spectral numerical method in radius for these cases.

Using PlanetInd, we explore the dependence of induction effects on Rm and the relative ocean depth for Europa and Ganymede and predict the expected measurements at different space craft altitudes. PlanetInd allows including radial profiles in electric conductivity and calculates the effects of zonal ocean flows. Assuming a conductivity profile caused by salinity variations in Europa’s ocean, we show that this will be very difficult to detect. The magnetic signal from zonal flows will likely be tiny at Europa but could just be detectable at Ganymede because of the presence of an inner dynamo.