The Impact of the Geophysical Constraints on the Internal Structure of Europa

Introduction 

Missions Galileo and Juno have significantly advanced our understanding of Jovian moons.  Through their measurements, these missions unveiled the possible presence of subsurface water oceans. Building on these discoveries, upcoming missions, JUICE and Europa Clipper, hold the potential to further enhance characterisation of the internal structure by delivering new and/or improved data, including tidal deformation and magnetic induction measurements ([1], [2], [3]).  

Our study aims to characterise the internal structure of Europa. We employed a combination of known material properties ([4], [5], [6], [7]) alongside measured satellite data to assess Europa’s plausible internal structures. Among data we included total mass (M), radius (R_surf), moment of inertia (MOI) [8], as well as amplitude of magnetic induction measured at synodic period (A_syn), obtained from Gallileo [9], new measurement of the ice shell thickness (D_Ih), measured by Juno [10], as well as anticipated tidal Love number k₂ into our statistical analysis, aiming to enhance our understanding of the moons' structural characteristics. 

 

Model 

We numerically evaluate the internal density, pressure, and temperature profiles, assuming known structural parameters, which represent our a priori information about possible structures: the total radius, core and mantle radii, densities of mantle and core, salinity C_w, and surface heat flux.  From these, we derive data values predicted for each assumed structure. 

For the thermal profile, we assume conductive heat transfer in the ice shell, and an adiabatic profile in the liquid ocean. Equations of state (EOS) and parameters describing the hydrosphere’s material properties are adopted from [4], [5], [6],[7], while the core and mantle properties are simplified. 

For each model, we also evaluate tidal deformation, using a library based on [11], as well as magnetic induction response, using code based on [12].  

To determine the interior structures, that are consistent with measured data, such as measured values for M, MOI and R_surf, along with A_syn [9], D_Ih [10], and anticipated k₂, along with their uncertainties, we apply a statistical approach by coupling our model with emcee sampler [13], that uses the Markov chain Monte Carlo method, which samples posterior distributions of internal structure parameters. We test several combinations of measured data and analyse how the used dataset impacts statistical distribution of the parameters. 

 

Results 

We assumed models, where Europa is either fully differentiated into the hydrosphere, mantle, and core, or a model with only the hydrosphere and a silicate-iron inner layer, to assess the structure. We analysed the internal structure for two different salts present in the ocean: MgSO₄ and NaCl.  

We compared the resulting internal structures as additional data information was gradually incorporated. The most significant change was the variation in surface ice shell thickness among tested dataset configurations. Models that incorporated information about A_syn preferred very thin ice shell thicknesses, compared to other models.  

We then studied resulting structures for models, where the inner layer was not fully differentiated for both salts. Our results showed that their structures preferred thicker hydrospheres, when compared with models where we had differentiated mantle and core.  

We then plotted the resulting structures as functions of D_Ih with respect to A_syn, marking the regions where both the measured values of D_Ih and A_syn fall within one-sigma standard deviation range.  The results are depicted in Figure 1, for MgSO₄, and Figure 2, for NaCl. 

Our results showed that, across all models, most of the resulting structures do not fall within the one-sigma interval for D_Ih and A_syn.  For the models where 0-10wt% MgSO₄ was present, to be consistent with both measured data, Europa must have at least a partially differentiated core and mantle. In the case of 0.2-4.2wt% NaCl, we found structures that fall within one-sigma range of both measurements, with or without differentiated mantle and core, due to the higher conductivity of NaCl compared to MgSO₄. It is important to note that, in the presence of NaCl, we worked with a narrower range of concentrations than for MgSO₄, so it is plausible that if higher concentrations had been allowed, it could yield a larger number of compatible models for NaCl. 

Summary 

We modelled the internal structure of Europa, considering the existence of both mantle core, as well as only layer composed of iron-silicate mixture, for compositions of MgSO₄ and NaCl. We employed Markov chain Monte Carlo, using emcee library. In the dataset we also included information about magnetic induction and ice shell thickness. We found if MgSO₄ is present, for models to be compatible with both measurements, Europa’s deep interior must be at least partially differentiated.   

Acknowledgement 

This research was supported by Charles University through project No. 142125 and by the Czech Science Foundation (project No. 26-21877S).  

References 

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