Modelling the magnetic fields of Uranus and Neptune

The ice giants Uranus and Neptune are the only planets in the solar system with an unusual magnetic field morphology that deviates significantly from a dipole-dominated field observed on all other planets in the solar system. Their magnetic fields were measured only once directly during the Voyager II flybys in 1986 and 1989. The flybys provided only brief, distant observations, capturing limited spatial and temporal coverage of each planet’s magnetic environment. As a result, the magnetic field structures of Uranus and Neptune remain poorly constrained and their temporal variations are entirely unknown.

We analyse to which extent these measurements enable accurate determination of the magnetic fields. In particular we assess how well a classical regularized least-square inversion constrains individual Gauss coefficients and other global field properties. To this end, we simulate a variety of multipolar-dominated magnetic fields using MagIC, an open-access pseudo-spectral magnetohydrodynamic code. We then evaluate how effectively the measurements along the Voyager II trajectories allow us to determine the simulated magnetic fields using a statistical analysis to account for the high time dependency of the simulations. Finally, we quantify the similarity to Uranus and Neptune’s field models by comparing the well-constrained Gauss ceofficients.

Additionally, we investigate whether different physically motivated interior structures can reproduce the observed magnetic field morphology of Uranus and Neptune. We implement two representative interior models based on recent literature.

The first model is based on compositionally stratified interiors that include a stably stratified layer above the dynamo region due to a phase separation process (H-H₂O immiscibility) [1]. In this scenario, convection and dynamo action are confined to a relatively thick shell beneath the stable layer above a deeper, highly viscous, electrically superionic layer. The stable stratification suppresses radial motions and promotes more laterally varying flow patterns, which can lead to complex, non-axisymmetric magnetic field structures.

The second model follows a thin-shell dynamo configuration, where the magnetic field is generated in a comparatively shallow convective region located below the envelope and above a superionic layer [2]. In contrast to the stratified model, this setup lacks a strong overlying stable layer and instead confines dynamo action geometrically to a thin shell. This configuration tends to favor shorter convective length scales and enhances the influence of boundary conditions on the flow and magnetic field generation. We explore a broad range of control parameters, including the degree of stratification, the electrical conductivity profile, and the density stratification. This allows us to assess the robustness of the resulting magnetic field morphologies across different dynamical regimes.

The two different setups produce distinct magnetic field morphologies and temporal behaviors, both being capable of generating multipolar fields.
Our results show that the presence and strength of stably stratified layers strongly control the magnetic morphology, enabling transitions between multipolar and more dipole-dominated states. 

To assess the relevance of our models for Uranus and Neptune, we introduce a working criterion for “ice-giant-like” magnetic behavior. Rather than relying on instantaneous agreement with observed spectra, we define ice-giant-like fields as those that (i) are not dominated by the dipole component, (ii) show significant non-axisymmetric and hemispherically asymmetric contributions at low spherical harmonic degrees (l ≤ 3), and (iii) remain consistent with the range of Gauss coefficients that can be robustly recovered under Voyager-like sampling conditions.

We find that apparent agreement with observed ice-giant spectra can depend sensitively on temporal sampling and inversion limitations. Models may transiently reproduce Uranus- or Neptune-like spectra, while their long-term behavior differs significantly. This highlights the importance of considering temporal variability and observational filtering when interpreting spacecraft data.

These results demonstrate that different interior structures can produce qualitatively similar magnetic field morphologies under limited observational constraints, but arise from fundamentally different dynamical regimes. They highlight both the diagnostic power and the inherent limitations of single-flyby magnetic field measurements and provide new insights into how interior structure may shape the dynamo processes of Uranus and Neptune.

[1] Cano Amoros, M., et al. (2024), Astronomy & Astrophysics, 692, A152
[2] Militzer, B. (2024), Proceedings of the National  Academy of Sciences, 121, e2403981121