© European Physical Society, EDP Sciences, 2025

Focus on Ganymede’s mysterious magnetic field

The Earth magnetic field, a vital element for our planet’s habitability, is generated by fluid motions inside Earth’s core, which largely depend on the structure of the Earth and the history of its formation. While a wide range of measurements can be performed to improve our understanding of this magnetic field, probing remote planets is much more challenging. In 1996, the Galileo mission revealed the unexpected existence of a magnetic field originating from the interior of Ganymede, an icy moon of Jupiter [1–3]. This puzzling observation raised the question of the mechanism nourishing this magnetic field. A remanent magnetisation from a paleomagnetic field was considered unlikely, as it would require implausibly large amounts of magnetic minerals to record a very intense paleomagnetic field of unclear origin. Induction by the magnetic field of Jupiter, of order 100 nT in the vicinity of Ganymede, could explain some features of Ganymede’s field. Yet, it could not sustain the strong magnetic dipole of the icy moon, of 719 nT near the equator. Dynamo in Ganymede’s iron-rich liquid core therefore became the preferred candidate for magnetic field generation: the coupling between magnetism and the motion of a conducting fluid, such as liquid iron, generates electrical currents that feed the magnetic field. These currents sustain dynamo as long as the inertia of the flow dominates over ohmic dissipation, i.e. as long as the magnetic Reynolds number verifies Re_m = UL/η_m ≫ 1, where U is the typical iron velocity, L the size of the zone of fluid motion and η_m is the magnetic diffusivity.

Iron snow, a candidate for Ganymede’s core convection

The Earth informs us that large-scale fluid motions in a core can be driven by mechanical forcing (tides, libration) or thermo-compositional convection [4]. The latter is the focus of our work, albeit in a completely new configuration compared to that of Earth. Although the heat accumulated during the formation of Ganymede is released from its centre outward, models of Ganymede’s thermal evolution reveal that thermal convection cannot operate in its core because it is thermally stratified. On the opposite, compositional convection can feed core convection: like other small rocky ‘planets’ [5], Ganymede is sufficiently small for its liquid metal core to solidify where it is the coldest, i.e. at the core periphery, due to a low pressure in the core (6-10 GPa). The liquid can be approximated as a mixture of a dense element, iron (Fe), and a light element, sulphur (S). Upon solidification, the pure iron crystals that form are denser than the liquid mixture, so they settle towards the centre of the core: this is iron snow (figure 2). Snow flakes keep growing and settling until the bottom of the snow zone, where the core temperature is equal to the liquidus. Below this depth, temperatures are so large that snow flakes remelt. They produce a ‘molten snow’ that is concentrated in iron and denser than the Fe-S mixture, so it sinks even deeper and nourishes compositional convection. The latter is believed to feed dynamo [6, 7]. Unfortunately, models of Ganymede’s evolution over billions of years cannot resolve the timescales and length scales of crystal formation, settling and remelting. Hence, iron crystals are usually modelled as a dense liquid. We combine laboratory experiments, simulations and analytical models to actually resolve the properties and the particulate dynamics of snow flakes, and determine how they constrain the velocity (U) and length (L) scales of convection.

Fig. 1 Compositional convection driven by the settling and dissolving sugar grains.

Fig. 2 Core convection driven by iron snow in Ganymede’s core. Proportions are not to scale to emphasize the core.

Dispersal of iron flakes in the snow zone

Recent experiments [8] suggest that snow flakes in an iron snow zone might be generated as sudden bursts of a large number of crystals settling collectively. We investigated the dynamics of such particle clouds with laboratory experiments [9]. When releasing a fixed mass of glass spheres with orange dye in a water tank (figure 3a), the dynamics of the falling cloud crucially depends on the particle size. Clouds of tiny particles linearly grow with depth as they entrain ambient fluid (black and white image in figure 3b), leading to their dilution and deceleration, exactly as their purely fluid counterpart, e.g. when a cloud a saltwater with the same density anomaly falls in fresh water. But the influence of particles kicks in as we increase the particle size: the clouds’ growth rate increases by up to 75% (dark measurements in figure 3b), and the larger the particles, the faster they manage to rain out of the ever-decelerating clouds because they settle faster (colour images in figure 3b). Both observations are due to the relative migration of particles with respect to fluid motions, caused by one simple ingredient: settling. Fortunately enough, both phenomena can be replicated at low cost in geophysical models [10], by modelling particles as a field of concentration and quantifying settling as the ratio between the particle settling velocity and the characteristic cloud velocity – the so-called Rouse number ℜ (red diamonds in figure 3b). Planetary rotation is also mimicked in the lab by spinning the whole experiment on a rotating table. Rotation inhibits the clouds’ growth. In this context, the Rouse number affects the dispersal of particles as a stem behind the clouds [11]. All these observations stress the importance of settling. It determines the concentration of snow flakes and the time they take to reach the bottom of the snow zone, and since snow flakes continuously grow in the snow zone, particle settling controls both the size and mass flux of snow flakes nourishing compositional convection deeper in the core.

Fig. 3 (a) Sketch of the particle clouds setup. (b) Growth rate of clouds having different particle sizes, hence corresponding to different settling velocities (the larger the faster) and Rouse numbers. Yellow hatchings are uncertainties on the reference growth rate of purely fluid, saltwater clouds. Dark and red symbols respectively correspond to experimental and numerical data. The black and white image is the superposition of all images from a single experiment without dye, while colored images are snapshots showing particles in white and dye in orange. Details about symbols can be found in [9].

A sugary analogue for the deep convection of molten snow

Let us take a step back, and return to the assumptions behind models of Ganymede’s thermal evolution. The zone of compositional convection is nourished by a uniform steady flux of buoyancy – effectively acting like a dense liquid (see figure 2). We reproduce these conditions in the lab by sieving sugar grains with a steady uniform mass flux above a water tank (figure 4a): sugar grains stand for snow flakes, and their dissolution is physically analogous to melting [12, 13]. This approach enables to observe and quantify the finite time and distance necessary for snow flakes to remelt, which up-to-now, are not included in geophysical models. To observe the dense sugary water which mimics molten snow, we home-made fluorescent caramel and crushed it into grains. Different regimes of convection were revealed (figure 4b), mainly controlled by the grain size. Large grains rain out of fluid motions, are too distant to interact with neighbouring grains and are slowly dissolved, resulting in a laminar flow that is inefficiently driven by the cumulative forcing of successive grains over time (figure 4b-1). On the opposite, small grains barely decouple from fluid motions (ℜ ≪ 1), interact with neighbouring grains, are quickly dissolved and trigger a Rayleigh-Taylor instability, leading to a turbulent plume that effectively behaves as a fluid (figure 4b-2). As long as grains have not fully dissolved, their disperse nature strongly constrains the heterogeneous forcing of the flow, since grains only drag fluid locally and the sugary water is only deposited in their localised wakes. More surprisingly, the particulate nature of the buoyant material imprints a persistent trace on the flow even below the region of dissolution.

Fig. 4 (a) Experiment of sugar-driven convection, with a snapshot of a fluorescent streak of dyed sugary water behind a grain. (b) Snapshots of experiments with dyed sugar. (1) Grains of radius 363 μm (mass rate 0.05 g/s) result in a particle-constrained, settling-driven regime of convection, whereas (2) grains of radius 45 μm (mass rate 0.12 g/s) feed a turbulent plume that behaves as negatively buoyant liquid; (3) intermediate grains (101 μm, 0.12 g/s) combine observations from both regimes.

Implications for Ganymede and perspectives

Coupled data from past studies of Ganymede’s evolution [6, 7] with our sugar experiments enable to model plumes of melting snow flakes in Ganymede [12]. The size of such plumes is unconstrained and therefore varied. As an example, a 10 m-wide plume transports snow flakes of size 10 μm down to a few centimeters with a fluid velocity U ≃ 10⁻⁴ m/s, whereas meter-large snow flakes are transported down to several tens of kilometers with a velocity U ≃ 10⁻⁶ m/s. The smaller the plume width and the larger the grains, the smaller the size L of the convective zone and the smaller the convective velocity U. This impedes the emergence of dynamo for a wide range of scenarios because Re_m is too low. Importantly, all snow flakes larger than 50 − 100 μm nourish the regime of particle-constrained, settling-driven flow (figure 4b-1).

These conclusions call for additional efforts to refine the model and constrain the size of snow flakes which is the key quantity controlling most of the dynamics. The canonical model of iron snow assumes that snow flakes nucleate in the whole snow zone. An inevitable consequence would be that snow flakes are polydisperse, complexifying the modelling of phase change which hugely depends on particle size. But major uncertainties remain about the process of nucleation. Another plausible scenario is the nucleation of iron flakes at the Core-Mantle Boundary (CMB). This might lead to the growth of much larger, possibly mushy grains. Constraints are yet to be determined about their maximum size before a possible detachment from the CMB.

About the Authors

Quentin Kriaa is a former PhD student at Aix-Marseille Université (France), now postdoctoral researcher at the University of Twente (Netherlands), with a broad interest in environmental and geophysical flows, with a particular emphasis on understanding the microphysical processes that govern their dynamics.

Benjamin Favier is a CNRS Research in the French laboratory IRPHE (Aix-Marseille Université), with special interest in rotating and stratified flows, magneto-hydrodynamics, turbulence, phase changes and thermal convection.

Michael Le Bars is a CNRS Research Director in IRPHE. His research spans the boundaries between traditional disciplines, focusing on a wide range of geophysical and astrophysical flows by combining experimental, theoretical and numerical approaches.

References

All Figures

	Fig. 1 Compositional convection driven by the settling and dissolving sugar grains.
In the text

	Fig. 2 Core convection driven by iron snow in Ganymede’s core. Proportions are not to scale to emphasize the core.
In the text

Fig. 3 (a) Sketch of the particle clouds setup. (b) Growth rate of clouds having different particle sizes, hence corresponding to different settling velocities (the larger the faster) and Rouse numbers. Yellow hatchings are uncertainties on the reference growth rate of purely fluid, saltwater clouds. Dark and red symbols respectively correspond to experimental and numerical data. The black and white image is the superposition of all images from a single experiment without dye, while colored images are snapshots showing particles in white and dye in orange. Details about symbols can be found in [9].

In the text

Fig. 4 (a) Experiment of sugar-driven convection, with a snapshot of a fluorescent streak of dyed sugary water behind a grain. (b) Snapshots of experiments with dyed sugar. (1) Grains of radius 363 μm (mass rate 0.05 g/s) result in a particle-constrained, settling-driven regime of convection, whereas (2) grains of radius 45 μm (mass rate 0.12 g/s) feed a turbulent plume that behaves as negatively buoyant liquid; (3) intermediate grains (101 μm, 0.12 g/s) combine observations from both regimes.

In the text