Systematic parameter study of Ice Giant-like dynamos and magnetic fields

To date, Uranus and Neptune remain largely mysterious planets, with the only direct data available on them having been performed during the Voyager II flybys. The closest approach of the satellite to the two ice giants occurred at distances of 4.2 Uranus radii and 1.2 Neptune radii, respectively, meaning that the collected data was sparse and poorly constrained [1,2]. Nevertheless, magnetic field models have been proposed based on inverse modelling work, although these can only be reliably resolved up to spherical harmonic degree 3 or 4 [3]. This, as well as studies of Uranian auroral emissions [4], and of the ice giants’ rotation periods [5] suggest that the ice giants have a complex magnetic field dominated by higher degree components, as well as retrograde equatorial zonal winds.

Simulations of the magnetic fields of the ice giants have shown that a thin electrically conducting outer dynamo layer provides the best geometry to produce multipolar results [6]. It has also been demonstrated that, provided large supercriticality (above the critical Rayleigh number required for the onset of convection), multipolar dynamos may be obtained for both thick and thin shell geometries [7]. However, these simulations make use of the Boussinesq approximation of the magnetohydrodynamic (MHD) equations, omitting the large density contrasts within the planetary interior, and assume a constant electrical conductivity across the dynamo region, which does not reflect reality.

By contrast, this study models ice giant-like dynamos in the anelastic approximation using MagIC: a pseudospectral numerical code that solves the MHD equations in spherical shell geometry [8]. This allows us to model the large density contrasts between the inner boundary of the dynamo region and the outermost boundary of the planet with a suitable polytrope.  We also incorporate radially variable electrical conductivity to account for the steep drop-off of conductivity in the outer regions of the planets. The model geometry and boundary conditions are based on the latest internal structure models of the ice giants [9]. Chemical compositional gradients are omitted from the system. A systematic control parameter sweep is conducted on the Ekman, Rayleigh, and magnetic Prandtl numbers to determine the parameter configurations which can yield similar characteristic observables to those of Uranus and Neptune.

It is found that, for the parameters Ek = 10^-3, Pm = 10, and density scale height equal to 5, multipolar dynamos and retrograde zonal winds are obtained for Rayleigh numbers which are more than 20 times supercritical. However, as Ek and Pm are decreased, even more turbulent conditions are required to obtain ice giant-like dynamos, which is consistent with previous high-turbulence studies. This paves the way for a more thorough understanding of the dynamics and structure of the ice giant interiors and provides an opportunity to incorporate more complex structural elements to the given successful configurations in future investigations.

References:

[1] N. F. Ness, et al. (1986) Science, 233(4759):85–89.

[2] N. F. Ness, et al. (1989) Science, 246(4936):1473–1478.

[3] R. Holme & J. Bloxham. (1996) JGR: Planets, 101(E1):2177–2200.

[4] F. Herbert. (2009) JGR: Space Physics, 114.

[5] R. Helled, et al. (2010) The Astrophysical Journal, 726.

[6] S. Stanley & J. Bloxham. (2006) Icarus, 184(2), 556-572.

[7] K. Soderlund, et al. (2013) Icarus, 224(1):97–113.

[8]  https://magic-sph.github.io/

[9] B. Militzer. (2024) Proceedings of the National Academy of Sciences, 121.