.............................................................. Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields Sabine Stanley & Jeremy Bloxham Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, Massachusetts 02138, USA ............................................................................................................................................................................. The discovery of Uranus’ and Neptune’s non-dipolar, non-axi- symmetric magnetic fields 1–4 destroyed the picture—established by Earth, Jupiter and Saturn 5–6 —that planetary magnetic fields are dominated by axial dipoles. Although various explanations for these unusual fields have been proposed 3,7–10 , the cause of such field morphologies remains unexplained. Planetary magnetic fields are generated by complex fluid motions in electrically conducting regions of the planets (a process known as dynamo action), and so are intimately linked to the structure and evolution of planetary interiors. Determining why Uranus and Neptune have different field morphologies is not only critical for studying the interiors of these planets, but also essential for understanding the dynamics of magnetic-field generation in all planets. Here we present three-dimensional numerical dynamo simulations that model the dynamo source region as a convecting thin shell surrounding a stably stratified fluid interior. We show that this convective-region geometry produces magnetic fields similar in morphology to those of Uranus and Neptune. The fields are non-dipolar and non-axisymmetric, and result from a combination of the stable fluid’s response to electromagnetic stress and the small length scales imposed by the thin shell. Uranus’ and Neptune’s magnetic fields are probably generated in their ionically conducting, fluid ‘ice’ (H 2 O, CH 4 , NH 3 and H 2 S, not necessarily in the form of intact molecules 11 ) layers, which extend out to about 0.75 and 0.8 of their total radii, respectively 12 . Podolak et al. 8 and Hubbard et al. 9 examined thermal evolution models that satisfy the present-day observed luminosities of Uranus and Neptune, and found that the interior portion of these planets’ ice layers may be compositionally stably stratified and therefore unable to convect. They proposed that a subtle difference in the stratifica- tion between the two planets could explain the seemingly contra- dictory observation that the two planets have very similar internal composition and structure, yet very different internal heat flows. They also suggested that this geometry of a thin shell dynamo surrounding a stably stratified fluid interior might explain the non- dipolar, non-axisymmetric magnetic fields of Uranus and Neptune. Here we use the numerical dynamo model of refs 13 and 14 to test whether this geometry is favourable for producing non-dipolar, non-axisymmetric magnetic fields. Early models of the Earth’s dynamo were successful at reproducing many of the salient features of its magnetic field, including westward drift, reversals and most notably, the axial dipole dominance of the field 13,15,16 . More recent numerical models (see ref. 17 for a review) that implement different numerical methods or work in different parameter regimes still produce predominantly axially dipolar fields. A handful of non- axial, non-dipolar dynamos have been found 18–22 when working in specific regions of parameter space, but because all numerical models at present cannot operate in the appropriate parameter space for planetary cores, we seek solutions that prevail over a wide range of parameter values. If non-dipolar, non-axisymmetric solu- tions result from changing only the geometry of the problem, then it would seem a more likely and more robust explanation for Uranus’ and Neptune’s magnetic fields. In geodynamo models, the implemented geometry is consistent with the Earth’s internal structure, in which the magnetic field is generated by convection in the fluid-iron outer core of the planet surrounding the small solid-iron inner core (Fig. 1a). In order to study Uranus’ and Neptune’s magnetic fields, we implement the geometry proposed by Podolak et al. 8 and Hubbard et al. 9 in which the magnetic field is generated by convection in a thin shell surrounding a stably stratified fluid core (Fig. 1b). Table 1 lists the control parameters for our model. We find that this geometry produces fields similar in morphology Figure 1 Dynamo model geometries. Interior planetary geometries used in numerical modelling of Earth’s dynamo (a) and Uranus’ and Neptune’s dynamos (b). A radius measure of 1 corresponds to the top of the dynamo source region. Solid regions are in brown, convective fluid regions are in light blue and stably stratified fluid regions are in dark blue. In our numerical dynamo models for Uranus and Neptune, we make the conductivity of the stable shell equal to that of the convecting shell so that the only difference between the two layers is their stability to convection. The method of maintaining stability and instability is similar to that of refs 27(a study of thermal convection in the presence of stable layers) and 28 (in which a thin stable layer near the core–mantle boundary was incorporated in a 2.5D geodynamo model), although our actual stability profiles are different. In the convectively unstable shell, we impose a super- adiabatic background temperature gradient consistent with our fixed heat flux boundary conditions: ›T 0 /›r / 2r 22 . In our stable shell we impose a sub-adiabatic temperature gradient: ›T 0 /›r / c, where c is a positive constant. Table 1 Control parameters of our dynamo model Parameter Value ............................................................................................................................................................................. r io 1/6 r so 2/3 E ¼ n 2Q d 2 2 £ 10 25 Ro ¼ h 2Q d 2 2 £ 10 25 q k ¼ k h 1 Ra ¼ aT g0hT d 2 2Q h 18,000–24,000 ............................................................................................................................................................................. Definitions and values of control parameters in our numerical model. The parameters given in the table are the ratio of the solid inner core to total core radius (r io), the ratio of the stable fluid shell to total core radius (r so), and the Ekman, magnetic Rossby, Prandtl and Rayleigh numbers (E, Ro, q k and Ra, respectively). These non-dimensional numbers depend on the kinematic viscosity (n), magnetic and thermal diffusivities (h and k, respectively), core rotation rate (Q), outer core thickness (d), thermal expansion coefficient (a T), gravity (g 0) and the characteristic heat flux (h T ). The small solid inner core in our models is a numerical necessity, but may also be physically realistic because Uranus and Neptune probably contain small rocky solid cores 26 . Except for the core radius and stability, all other parameters are the same as those in Kuang and Bloxham geodynamo models. As well as the prescribed parameters in the table, we use impenetrable, stress-free boundary conditions on the velocity and fixed heat flux boundary conditions on the temperature. We use the same hyperdiffusivities as ref. 14 on the thermal, viscous and magnetic diffusivities, but we do not believe that our non-dipolar, non-axial solutions result from the use of hyperdiffusivities, because current geodynamo models using similar hyperdiffusivities produce axially dipolar dominated solutions. letters to nature NATURE | VOL 428 | 11 MARCH 2004 | www.nature.com/nature 151 ©2004 Nature Publishing Group