A perturbation method for evaluating the magnetic field induced 1 from an arbitrary, asymmetric ocean world analytically

ble confirming the presence of subsurface, liquid water oceans. In the exploration of ocean 14 moons, especially Europa, there is a need formathematicalmodels capable of predicting themag- 15 netic fields induced under a variety of conditions, including in the case of asymmetric oceans. 16 Existing models are limited to either spherical symmetry or assume an ocean with infinite con- 17 ductivity. In this work, we use a perturbation method to derive a semi-analytic result capable of 18 determining the induced magnetic moments for an arbitrary layered body, provided each layer 19 is nearly spherical. Crucially, we find that degree-2 tidal deformation results in changes to the 20 induced dipolemoments. We demonstrate application of our results tomodels of plausible asym- 21 metry from the literature within the oceans of Europa and Miranda and the ionospheres of Cal- 22 listo and Triton. For the models we consider, we find that in the asymmetric case, the induced 23 magnetic field differs by more than 2 nT near the surface of Europa, 0:25–0:5 nT at 1R above 24 Miranda and Triton, and is essentially unchanged for Callisto. For Miranda and Triton, this dif- 25 ference is as much as 20–30% of the induced field magnitude. If measurements near the moons 26 can be made precisely to better than a few tenths of a nT, these values may be used by future 27 spacecraft investigations to characterize asymmetry within the interior of icy moons.