Ganymede is the only known moon with an active dynamo. No mission has discovered intrinsic magnetism at the other Galilean satellites: Io, Europa, and Callisto. A dynamo requires a large magnetic Reynolds number, which in turn demands, for these moons, a large metallic core that is cooling fast enough for convection. Here we quantify these requirements to construct a regime diagram for the Galilean satellites. We compute the internal heat fluxes that would sustain a dynamo over the wide ranges of plausible radii for their metallic cores. Below a critical radius, no plausible heat flux will sustain a dynamo. Europa likely sits on the opposite side of this limit than Ganymede and Io. We predict that future missions may confirm a small (or absent) core, meaning that Europa could not sustain a dynamo even if its interior were cooling as quickly as Ganymede's core.

Key Points

Dynamos in the Galilean moons would require both a dynamo-producing region thicker than ∼250 km and core heat fluxes above ∼3 mW m⁻²
Ganymede and Io probably have larger metallic cores than Europa and Callisto, but all satellites likely have similar core compositions
A small core could explain the absence of a strong dynamo at Europa even if Europa and Ganymede have similar core heat fluxes

Plain Language Summary

In the late 1990s, the NASA Galileo spacecraft visited the four largest moons of Jupiter: Io, Europa, Ganymede, and Callisto. Many studies interpret the Galileo gravity and magnetic field data to mean that: (a) Ganymede's intrinsic magnetic field arises from convection in a liquid metal core (i.e., a “dynamo” that converts mechanical energy into electromagnetic energy), (b) Europa has a metal core that is somehow incapable of generating a detectable magnetic field, and (c) Callisto may not have a metal core at all. Indeed, Ganymede is the only moon in our solar system known to sustain an active dynamo. Confirming the presence (or absence) of core convection provides us with valuable insight into the moons' structural and thermal history. In this study, we show that Europa's and Callisto's metal core (if they exist) may be too small to produce a dynamo, even if they convect. Crucially, no celestial body is known to have a convecting metal core without sustaining a dynamo too, but Europa might be an exception. Recently launched missions such as NASA's Europa Clipper and ESA's JUICE may test whether a small core size can explain the absence of dynamos at Europa and Callisto.

1 Introduction

The Galilean moons of Jupiter—Io, Europa, Ganymede, and Callisto—are diverse. Io is the most volcanically active body in our solar system due to intense tidal heating (e.g., Keane et al., 2023). Europa is the smallest of the Galilean moons with a thin ocean-ice shell (Anderson et al., 1998b; Kronrod & Kuskov, 2006; Kuskov & Kronrod, 2005). Ganymede and Callisto are comparably large, ice-rich, and old in terms of surface age (e.g., Gregg & Byrne, 2022; Vance et al., 2018). Many traits of the Galilean moons correlate with orbital distance from Jupiter (Figure 1a). In this respect, Ganymede is intermediate: neither the closest nor the farthest from Jupiter, neither the least nor most tidally heated, and neither the least nor most dense. Nevertheless, Ganymede hosts a dipolar dynamo with a strength of >700 nT on the surface at the equator (Kivelson et al., 2002), which makes Ganymede the only moon known to sustain an active dynamo (e.g., Stevenson, 2003, 2010). The other Galilean moons either possess dynamos that are too weak to have been detected, or they lack dynamos entirely.

Details are in the caption following the image — **Figure 1**
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Dynamos in planetary bodies require a large fluid region that is electrically conductive and moving vigorously. (a) An overview of the Galilean satellites and physical characteristics trending with orbital distance from Jupiter. Satellites are shown to scale (Table S1 in Supporting Information S1). (b) A regime diagram for different planetary bodies based on Figure 1 from Stevenson (2003). In the upper region, Re_m is sub-critical because high thermal conductivity makes conduction the sole heat transport mechanism. In the lower region, Re_m is also too low for a dynamo because the convecting region is not sufficiently large or electrically conductive. The Galilean moons likely fall near the “triple point” where fluid conductivity and size may prevent dynamo action. (c) A regime diagram focused on bodies with metallic cores. If core composition (and thus conductivity) is similar across the Galilean satellites, then dynamo action may ultimately depend on heat flux and core radii.

Dynamos require vigorous motion of electrically conductive material to generate magnetic fields. Core convection can provide this motion, powered by thermal or chemical buoyancy. Thermal convection requires temperature-induced density gradients to drive warm metal upwards as relatively cool metal sinks. In chemically homogenous cores, thermal convection occurs when the core-mantle boundary (CMB) heat flux (Q_cmb) exceeds the adiabatic heat flux (Q_ad). Likewise, chemical convection occurs when crystallization of dense solids (or precipitation of light solids) provides the appropriate buoyancy to the residual fluid. Ganymede's dynamo could be powered by either mechanism or both (e.g., Bland et al., 2008; Breuer et al., 2015; Christensen, 2015; Hauck et al., 2006; Rückriemen et al., 2018). For many bodies, convecting metal cores will host a dynamo (e.g., Stevenson, 2003). However, a small metallic core might not host a dynamo even if it convects.

Scientists typically use two dimensionless parameters—the Rossby number (Ro) and magnetic Reynolds number (Re_m)—to determine whether a planetary dynamo exists (e.g., Stevenson, 2003, 2010). First, Ro is the ratio of inertial and Coriolis forces:

\begin{array}{c}\text{Ro}=\frac{v}{{\Omega }D}.\end{array}

(1)

Here, v is the fluid flow velocity (m s⁻¹), Ω is the angular rotation rate (rad s⁻¹), and D is the thickness of the dynamo source region (m). Dynamos require that Ro << 1 (e.g., Stevenson, 2003, 2010). The Rossby number criterion is satisfied even for Callisto, the slowest rotating Galilean moon, which has Ro < 10⁻³ if its core has a radius of D > 10 km and typical convective velocities of v ∼10⁻⁵ m s⁻². Therefore, the critical parameter is Re_m, which is the ratio of magnetic induction and diffusion:

\mathrm{R}{\mathrm{e}}_{m}=\frac{vD}{\eta }.

(2)

Here, η = 1/(σ₀μ₀) is the magnetic diffusivity (m² s⁻¹), where electrical conductivity is σ₀ (S m⁻¹) and μ₀ is the vacuum permeability (N A⁻²). Dynamo action occurs when Re_m exceeds ∼40 (e.g., Christensen & Aubert, 2006; Stevenson, 2003, 2010).

Planetary bodies can host dynamos in myriad fluids (Figure 1b). Metallic hydrogen fuels Jupiter's and Saturn's dynamo (e.g., Helled et al., 2020). A cocktail of ionic fluid ices (e.g., H₂O, CH₄, and NH₃) powers Uranus' and Neptune's dynamo (e.g., Hubbard et al., 1991). Metallic cores host dynamos in Earth, Mercury, and ancient Mars (Figure 1c; e.g., Christensen, 2006, 2015; Schubert et al., 1996; Weiss et al., 2002). Our Moon probably had a core-hosted dynamo, too (e.g., Jung et al., 2024; Tikoo et al., 2017; Weiss & Tikoo, 2014), as did some early-accreted planetesimals at early times (e.g., Sanderson, Bryson, & Nichols, 2024, Sanderson, Bryson, Nichols, & Davies, 2024; Weiss et al., 2010). Molten silicates could have hosted ancient dynamos in the Moon (e.g., Hamid et al., 2023; Scheinberg et al., 2018), Venus (O’Rourke, 2020), and Earth (e.g., Blanc et al., 2020; Stixrude et al., 2020). The Galilean satellites are small enough that metallic cores are the most plausible reservoirs of electrically conductive fluid that could sustain a dynamo.

A stagnant, liquid core will not produce a dynamo, as is likely the case for Io. The NASA Galileo spacecraft returned gravity data that is consistent with a metal core (e.g., Anderson, Lau, et al., 1996, Anderson, Scholgren, & Schubert, 1996). Widespread silicate volcanism on the surface implies high temperatures in Io's interior (e.g., McEwen et al., 1998). Recent measurements of ³⁴S/³²S ratios from Io's volcanic plumes indicate that ∼80%–97% of Io's initial sulfur content remains in the core (de Kleer et al., 2024), which lowers the core's melting point with respect to pure Fe. Since Io's core is likely hotter than the mantle but has lower melting temperatures than anhydrous silicates, we expect Io's core to be partially (if not completely) molten (e.g., Breuer et al., 2022). Wienbruch and Spohn (1995) argue that Io's hot mantle thermally insulates the core. The low temperature gradient across Io's CMB yields a low core heat flux that inhibits thermal convection, thereby preventing dynamo action.

The absence of a dynamo at Europa remains a mystery. Conventional explanations involve the lack of a metal core, its total solidification, or stagnation of any liquid (e.g., Kimura, 2024). Scientists infer the size and existence of Europa's metal core using models constrained by the normalized moment of inertia (MoI), which describes the extent to which mass is concentrated toward the planetary center. Multiple analyses of the Galileo gravity data yield different MoI estimates that do not overlap within their formal 1-sigma uncertainties (Gomez-Casajus et al., 2021). These clashing constraints allow for models with a metal core (e.g., Anderson et al., 1998a, 1998b; Kronrod & Kuskov, 2006; Kuskov & Kronrod, 2005; Schubert et al., 2009; Sohl et al., 2002; Vance et al., 2018) and without a metal core (Gomez-Casajus et al., 2021; Petricca et al., 2023). Core formation in Europa, if it occurred, could be a slow process if Europa had a cold start (e.g., Trinh et al., 2023). In this scenario, Europa's core (if it exists) could be young and small.

Callisto is perhaps the least understood (and least studied) of the Galilean satellites. Anderson et al. (1998a, 2001) used Galileo radio tracking data to estimate Callisto's MoI (0.3549 ± 0.0042) using the Radau-Darwin Approximation (RDA), which assumes hydrostatic equilibrium. Past studies argue that Callisto does not have a metallic core using the aforementioned MoI. However, Gao and Stevenson (2013) show that the RDA overestimates the true MoI of slow rotators like Callisto when nonhydrostatic effects are present, so a metal core inside Callisto cannot be ruled out with available data.

Why is Ganymede the only moon with an active dynamo? Here we construct a regime diagram for dynamos in the Galilean satellites by calculating the heat fluxes required to exceed the critical magnetic Reynolds number (Re_m,crit). First, we use geochemical models to estimate the composition of their metallic cores, if they exist. Second, we use Markov Chain Monte Carlo (MCMC) models to estimate the radii of the metallic cores and the associated uncertainty. Third, we quantify the prospect for dynamo action using metal core radius (r_c) and Q_cmb, assuming that thermal convection would be the primary power source of any dynamo. We identify a critical radius (r_crit) below which convection would not produce a dynamo for any plausible heat flux. Europa and Callisto could have r_c < r_crit while Ganymede and Io could have r_c > r_crit.

2 Methods

2.1 Geochemical Modeling

Composition affects parameters that govern Re_m: thermal conductivity, magnetic diffusivity, thermal expansivity, and specific heat capacity of metal-sulfides. Therefore, we use geochemical models to determine likely core compositions for the Galilean moons. Text S1–S2 in Supporting Information S1 describes our modeling approach in detail.

We use the Perple_X Gibbs free energy minimization software (Connolly, 2005, 2009; Connolly & Galvez, 2018) to model the evolving mineralogy of a moon based on temperature, pressure, and bulk composition. We also use RCrust, a wrapper that allows for phase extractions between Perple_X calculations (Mayne et al., 2016). We model the isobaric chemical evolution of unit cells at P = 1–10 GPa, where each cell warms across T = 0–1000°C. As temperature increases, we extract volatile phases (e.g., H₂O, CO₂, CO, etc.) from the mineral assemblage and update the composition for the next temperature step. Our models do not capture the kinetics of chemical reactions, as we focus on phase equilibrium. We test a range of initial compositions assuming a carbonaceous chondrite (CC) precursor (Text S1 in Supporting Information S1). Table S2 in Supporting Information S1 presents the lists of elemental abundances that we tested.

We assume the core is an iron-sulfur alloy, as done in many past studies on the Galilean satellites (e.g., Anderson et al., 1998b; Anderson, Scholgren, & Schubert, 1996; Kronrod & Kuskov, 2006; Kuskov & Kronrod, 2005; Schubert et al., 1996, 2009; Sohl et al., 2002). The abundance of sulfur in the core-forming metal could be higher or lower than the eutectic composition for a Fe-FeS alloy (Figure 2b). Some studies also consider alloying elements such as C, Si, and O (e.g., Dasgupta et al., 2009; Hirose et al., 2021; Vander Kaaden et al., 2020), but we emphasize the Fe-FeS system because it is well-studied and S is cosmochemically abundant.

2.2 Interior Structure Modeling

We use the emcee Python package (Foreman-Mackey et al., 2013) to model interior structures using the MCMC method. Our goal is to estimate the plausible ranges of r_c. We simplify the icy Galilean moons to consist of three layers: a metallic core, silicate mantle, and ocean-ice shell. For Io, we remove the ocean-ice shell. We assume that each layer has constant density with depth. This presents us with six unknowns (four for Io): the thickness and density of each compositional layer. We fix Europa's ocean-ice shell density to 1,000 kg m⁻³. For Ganymede and Callisto, we use 1,200 kg m⁻³ to account for high-pressure ice phases (e.g., Anderson, Lau, et al., 1996, Anderson, Scholgren, & Schubert, 1996).

We use three observational constraints for each moon: the mass, radius, and MoI (see Text S3 and Table S1 in Supporting Information S1). Since the mass error is small, we use satellite mass to calculate the mantle density given the thickness and density of all other layers. This leaves four model unknowns (three for Io) that our MCMC algorithm retrieves: core density, core radius, mantle thickness, and ocean-ice shell thickness. These model parameters are used to calculate the total radius and MoI, which are compared to the observed values to calculate the log-likelihood of each model. Ultimately, emcee returns the posterior probability density functions for each model parameter.

2.3 Dynamo Modeling

We compute the conditions necessary for a dynamo at each Galilean satellite. We first calculate the adiabatic heat flux:

{Q}_{ad}=-k{\left(\frac{dT}{dr}\right)}_{ad}.

(3)

Here, k is the thermal conductivity of the metal-sulfide (W m⁻¹ K⁻¹) and (dT/dr)_ad is the adiabatic temperature gradient (K m⁻¹). We estimate k from recent experimental results (Littleton et al., 2021), which reported the electrical resistivity (b) of FeS at P = 2–5 GPa and T < 1873 K. They used the Wiedemann-Franz “Law” (WFL) to obtain the electrical component of thermal conductivity: k = ŁT/b, where Ł takes on the Lorentz number (2.44 × 10⁻⁸ W Ω K⁻²). This k may underestimate the alloy's thermal conductivity because it does not include contributions from lattice vibrations and phonons. However, electron-electron interactions are the dominant contributor to thermal conductivity in metals and metal alloys (Klemens & Williams, 1986).

The adiabatic temperature gradient is given by

{\left(\frac{dT}{dr}\right)}_{ad}=\frac{-\alpha gT}{{C}_{P}}.

(4)

Here, thermal expansivity is α (K⁻¹), gravity is g (m s⁻²), and specific heat capacity is C_P (J kg⁻¹ K⁻¹). Morard et al. (2018) provides an equation of state for iron-sulfur alloys as functions of temperature, pressure, and sulfur content. We assume a nominal value of 36.47 wt.% S (equal to FeS; Figure S1 in Supporting Information S1). We use the CMB pressure (P_cmb) and average core temperature (T_core) for Equation 4 and estimating b (Text S4 in Supporting Information S1). Since we do not need a precise value for P_cmb (Figure S2 in Supporting Information S1), we use the analytical solution for a constant-density sphere:

{P}_{\text{cmb}}\left({r}_{c}\right)=\frac{2}{3}\pi {\rho }_{\text{avg}}^{2}G\left({R}^{2}-{r}_{c}^{2}\right).

(5)

Here, r_c is the core radius (m), ρ_avg is the bulk density (kg m⁻³), G is the gravitational constant (N m² kg⁻²), and R is the total radius (m). Equations 4 and 5 thus define the transport properties of Fe-FeS as functions of core radius.

Next, we calculate Re_m assuming the upper bound of D = r_c (i.e., the characteristic length scale is the size of the core). The presence of an inner core or (thermally or chemically) stratified layer would lead to D < r_c. We use the scaling law from Olson and Christensen (2006) to calculate convective velocities:

v=1.3{\left(\frac{{r}_{c}}{{\Omega }}\right)}^{\tfrac{1}{5}}{F}^{\tfrac{2}{5}}.

(6)

Here, F is the buoyancy flux (m² s⁻³). Since the Galilean satellites are tidally locked, the rotation rate is Ω = 2π/t_period, where t_period is the orbital period (s). Other scaling laws may shift r_crit by ∼100 km (Text S5 in Supporting Information S1; Figure S3 in Supporting Information S1). In general, F = F_T + F_C, where F_T and F_C are the thermal and chemical buoyancy fluxes, respectively. In Figure 3e, we assume that any convection is purely thermal (F_C ∼ 0) for simplicity. We can thus calculate (Olson & Christensen, 2006):

{F}_{T}=\frac{\alpha g}{\rho {C}_{P}}\left({Q}_{\text{cmb}}-{Q}_{ad}\right).

(7)

We combine Equations 2-7 to plot the required value of Q_cmb and F as a function of r_c for each of the Galilean satellites, which reveals r_crit. Past studies modeled how the thermal evolution of the rocky mantle controls Q_cmb (e.g., given radiogenic heat production in the silicates and heat transport by conduction or convection) (see Section 3.3).

3 Results

3.1 Composition of the Metallic Core

Our chemical modeling predicts that, if the Galilean moons accreted from carbonaceous chondrite (CC) material, they would have super-eutectic metal-sulfide compositions, which could lead to a super-eutectic core. If CC-like material is the primary building block for the non-ice portions of the Galilean moons, then the metal-sulfides in the Galilean moons may be as S-rich as pyrrhotite (Fe_1-xS, x = 0–0.125), which is 36.47–39.62 wt.% S.

Figure 2c presents our “nominal model,” an example that demonstrates common processes in most of our results. The nominal model assumes that P = 3 GPa, near that of Europa's center. The initial composition matches CI chondrites with half of the water removed (Table S2 in Supporting Information S1), resulting in a mineral assemblage with Europa's bulk water content (∼9 wt.% H₂O). This adjustment of initial water inventory does not affect our Fe-FeS composition (Figure S4 in Supporting Information S1).

Our models assume that temperature increases with time, but slowly enough for the mineral phases to always exist at equilibria. We assume that ice melts during accretion, so the initial temperature is near the melting temperature of water ice. At ∼0°C, the phases consist of water, hydrated minerals (antigorite, lizardite, chlorite, talc, deerite, and goethite), carbonates (magnesite and ankerite), diamond, and pyrite. At higher temperatures (∼370–670°C), silicate dehydration alters the structure and composition of the interior. The first products of silicate dehydration are pyroxene and magnetite. However, magnetite destabilizes with the release of more volatiles, which liberates Fe to join the metal-sulfides. Olivine and garnet appear as the final few wt.% of hydrated silicates destabilize. Carbonates remain stable because pressures are high (Scott et al., 2002). After silicate dehydration and up to the eutectic temperature, the iron-sulfide has a bulk composition of ∼38 wt.% S. Core formation may begin once metal starts melting (∼1000°C). If metallic core formation were self-sustaining (Text S6 in Supporting Information S1), then the core would have that same composition. Otherwise, incomplete melting results in a composition between the Fe-FeS eutectic and ∼38 wt.% S. Our models produce the same result when varying the following variables in isolation with respect to Figure 2c: accreted water (Figure S4 in Supporting Information S1), pressure (Figure S5 in Supporting Information S1), and CC chondrite analog (Figure S6 in Supporting Information S1). Hence, our result is independent of these parameters.

Our result is most sensitive to the assumption that CC chondrites are the primary building blocks of the Galilean satellites. The Galilean satellites could have accreted some non-carbonaceous (NC) material, which is S-poor. If the Galilean satellites form from L chondrite material, the final iron-sulfide has a bulk composition of ∼5 wt.% S and ∼6 wt.% C (Figure 2d). However, if the moons accreted primarily from L chondrites but incorporated at least ∼3 wt.% of CI chondrite-like material, then the metal-sulfides would have a super-eutectic composition (Figure S7 in Supporting Information S1).

3.2 Size of the Metallic Core

Figures 3a–3d shows probability distributions of metallic core radii for the Galilean moons. According to the MCMC samples for Fe-FeS cores with super-eutectic compositions (solid lines), r_c has a 75% probability of being smaller than ∼1,240, 825, 1,160, and 852 km for Io, Europa, Ganymede, and Callisto, respectively. Europa, Io, and Ganymede might have core radii that increase with satellite size. However, our models predict that Callisto's core is relatively small or non-existent because we use the RDA-derived MoI.

Figures S8–S15 in Supporting Information S1 show the probability distributions for our other model parameters: core and mantle densities, mantle thickness, and ocean-ice shell density (if applicable). Core size must change with mantle thickness and ocean-ice shell thickness since the thickness of all layers must add to a satellite's radius. However, we find that variations in mantle density allow for a wide range of core radius and density combinations. Therefore, we need chemical models to predict the core density. Using the equation of state from Morard et al. (2018) and assuming 1600 K, Europa's core (P_core ∼ 4 GPa) could have a density between ∼7,477 (pure Fe) and 4,237 kg m⁻³ (pyrrhotite). For pressures relevant to Ganymede (P_core ∼ 8 GPa), estimated densities range from ∼7,711 to 4,594 kg m⁻³. However, assuming a specific composition hardly constrains the size of the metal core, given the model degeneracies inherent in interpreting available gravity data.

Our interior structure models do not rule out the existence of a metal core at Callisto. Assuming the RDA-derived MoI, the presence of a large core (r_c > ∼400 km) at Callisto requires low mantle densities (ρ_mantle ∼ 1,500–2,700 kg m⁻³) that are difficult to justify (Figure S11 in Supporting Information S1). If Callisto has a small core (r_c < ∼400 km), then the average mantle density ranges between ∼2,100 and 2,700 (Figure S11 in Supporting Information S1), which is consistent with hydrated silicates and ice-rock mixtures composing Callisto's upper mantle. Alternatively, our models would make a stronger argument for a metallic core at Callisto if the true MoI is lower than the RDA-derived estimate. If Callisto does have a metal core, then our study suggests that the metal core is small or stagnant.

3.3 Prospects for Dynamo Activity

Figure 3e shows the required heat flux for driving a dynamo with thermal convection at the Galilean satellites as a function of core radius. We assume nominal values of Re_m,crit = 40 and T_core = 1600 K, which are intermediate within the plausible ranges of Re_m,crit = 10–100 and T_core = 1250–2000 K (i.e., the melting points of the Fe-FeS eutectic composition and pure Fe). For large cores (r_c > ∼600 km), thermal convection results in dynamo action. For medium-sized cores (200 < r_c < 600 km), the required Q_cmb begins diverging from Q_ad, so thermal convection in the metal core may not produce a magnetic field. For small cores (r_c < ∼200 km), the required Q_cmb for dynamo action increases rapidly to tens and hundreds of mW m⁻² (Figure S16 in Supporting Information S1), so even vigorous core convection likely does not produce a magnetic field. Such intense Q_cmb values are attainable for planetesimals at early times (e.g., Weiss et al., 2010) but beyond what we expect for the Galilean satellites today. Small metal cores alone may kill the potential for dynamo action at the Galilean moons. This general result remains true when varying Re_m,crit (Figures S17 and S18 in Supporting Information S1) and T_core (Figure S19 in Supporting Information S1).

We plot Io, Europa, and Ganymede at plausible places in this regime diagram (Figure 3e). Io could have a large but stagnant metal core, which implies no dynamo action. Indeed, Wienbruch and Spohn (1995) predict that Io experiences a meager Q_cmb = ∼0.1 mW m⁻², which is too low for convection. Europa may lack a dynamo because of a low Q_cmb and/or r_c. Assuming that Europa's core formed soon after it accreted, Kimura (2024) predicts Q_cmb = ∼0.5–1.2 mW m⁻², which may be sufficient for convection but not dynamo action. The temperature contrast across the CMB should be highest immediately after core formation, leading to rapid core cooling (e.g., Breuer et al., 2015; Kimura, 2024; Kimura et al., 2009; Rückriemen et al., 2018). Trinh et al. (2023) argue that Europa could have formed its core recently. Even if Europa had the same or higher Q_cmb than Ganymede, Europa may not have a dynamo (Figures S10–S12 in Supporting Information S1). Ganymede has a large-enough core for convection to produce a dynamo. Several studies predict Q_cmb = ∼2–4 mW m⁻² for Ganymede today (e.g., Bland et al., 2008; Breuer et al., 2015; Hauck et al., 2006; Rückriemen et al., 2018), which may be sufficient for a thermal dynamo. Callisto's lack of dynamo is consistent with a metal core that is small or non-existent.

4 Discussion

4.1 Core Composition and Chemical Convection

Our prediction that the Galilean moons may have super-eutectic metal-sulfide composition is consistent with previous studies that used a wide range of methods and assumptions. Other thermodynamic models of Europa show that the composition of the core-forming metal remains super-eutectic from low temperatures at the end of accretion to the temperature at which metal first melts, assuming a CM/CI precursor (Kargel et al., 2000; Melwani-Daswani et al., 2021; Scott et al., 2002). Bercovici et al. (2022) showed that planetesimals could form FeS cores if their bulk compositions matched CM/CI material, even if they formed much hotter than we assume. Scott et al. (2002) performed high T-P experiments of synthetic CI chondrites at variable oxygen fugacities, which also led to pyrrhotite formation.

Studies should continue exploring the prospect of core crystallization in the Galilean satellites. The Earth-like model of inner core growth may not apply to the Galilean moons (e.g., Breuer et al., 2015). For Fe-FeS cores at low pressures, Fe snow and FeS crystals may represent the most plausible core crystallization regimes (e.g., Breuer et al., 2015; Christensen, 2015; Hauck et al., 2006; Rückriemen et al., 2015, 2018). We predict that FeS would eventually crystallize from the cooling cores. A layer of FeS would form at the CMB and grow downward, enriching the residual fluid in iron. The relatively dense, Fe-rich fluid sinks, thus driving chemical convection (Rückriemen et al., 2018). This process could enable dynamos for Q_cmb values lower than plotted in Figure 3e. Other core crystallization regimes are possible if there are other light elements in the core. However, Figure 3f and Figure S20 in Supporting Information S1 show that the r_crit below which a dynamo is implausible does not depend on the source of convective buoyancy.

4.2 Implications for Future Spacecraft Missions

Upcoming missions will enable vastly improved estimates of core radii. For example, Cascioli et al. (2024) developed a new modeling approach that incorporates gravity field spectra, which could estimate Europa's r_c within ±50 km using anticipated data from NASA Europa Clipper (Mazarico et al., 2023). Similar methods could be applied to data from the ESA JUICE mission at Ganymede and Callisto. Likewise, joint gravity-magnetic field inversions can reveal the detailed structure of the hydrosphere (e.g., Petricca et al., 2023). Better data will help us construct sophisticated models of interior structure. Beyond our simple 2- and 3-layer models, realistic complexities include considerations of hydrated silicates (e.g., Kargel et al., 2000), high-pressure ices (e.g., Vance et al., 2018), the compressibility of metal-sulfides (e.g., Sohl et al., 2002), ocean chemistry (e.g., Vance et al., 2018), and internal heating (e.g., Howell, 2021).

5 Conclusion

Why is Ganymede the only Galilean moon known to sustain an active dynamo? Core composition alone is unlikely to be the distinguishing factor. If the Galilean moons accreted CC-like material, then they all likely have S-rich cores. Core size is much more likely to vary across the Galilean moons. Alas, fixing the core composition (and thereby core density) in interior structure models does not lead to strong constraints on core size. Crucially, we still cannot rule out small or absent cores in Europa and Callisto. At a critical core radius (∼250 km), the required heat flux for a dynamo skyrockets. Existing thermal models of the Galilean moons predict Q_cmb values that do not exceed several mW m⁻² today, which is far too low for dynamo action in small cores. If Europa and Callisto have small metal cores with the same (or higher!) heat fluxes as Ganymede's metal core, Europa and Callisto could still lack a dynamo. The upcoming NASA Europa Clipper and ESA JUICE missions will conduct gravity and magnetic field investigations that constrain models of the icy Galilean satellites' interior structures, which could test whether a small core size is a sufficient explanation for Europa's and Callisto's absent dynamo. Alternatively, the lack of dynamo results from the moons having no metal core, a stagnant core, or a small convecting region within an otherwise large core.

Acknowledgments

This work is funded by the NASA FINESST program (80NSSC21K1545). We thank two anonymous reviewers for their insightful feedback.

Open Research

Data Availability Statement

The Perple_X software is available at https://perplex.ethz.ch/. The RCrust software is available at https://www.sun.ac.za/english/faculty/science/earthsciences/rcrust. All code and data used for geochemical, structural, and dynamo modeling are available on Zenodo (Trinh et al., 2024).

Supporting Information

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Volume51, Issue22

28 November 2024

e2024GL110680

A Critical Core Size for Dynamo Action at the Galilean Satellites

Abstract

Key Points

Plain Language Summary

1 Introduction