Modeling the Core Porosity on Enceladus

Introduction: The Cassini mission revealed gas plumes at the south pole of Enceladus that are considered in the context of hydrothermal circulation in the rocky core. We model the internal evolution and differentiation of Enceladus heated by radioactive nuclides and tidal dissipation and investigate core compaction by modeling the evolution of porosity, thereby varying the rock rheology based on different assumptions on the composition.

Model: The model^[2] calculates heating by short- and long-lived radionuclides, latent heat, compaction of porous rock, continuous water-rock separation, redistribution of radionuclides, tidal heating, and water ocean convection. A crucial aspect is the calculation of the core porosity. The core forms by the redistribution of water and silicate particles in a two-phase system after melting of ice. An initial particle agglomerate with interstitial water grows along with an overlying water layer during Enceladus' bottom-up melting. Deformation of the core can lead to a reduction of the pores. The water displaced from them supplies the water layer, while the rock is displaced downward according to the evolution of the porosity. With time it can deform further by creep processes on a geologic timescale. This is modeled by calculating the evolution of the porosity from the change of the strain rate. Here, we use the creep law from [3] that can describe diffusion creep of both “dry” (models A1-A4) and “wet” (models B1-B4) olivine for different values of water fugacity. For a phyllosilicate-rich composition (models C1-C2) supported by plume and E-ring spectral analyses^[4], we use the creep law from [5].

Results: Figure 1 shows the evolution of the structural layers over 4,5 Ga for the model A2 (accretion time of 1,7 Ma), representing successful calculations with the dry olivine rheology. A strong initial temperature increase leads to the onset of melting. The ocean formation starts at ≈3 Ma, with a significant differentiation phase from ≈4 Ma resulting in the formation of an ocean atop a core, finalized by ≈5 Ma after CAIs. During this process, compacting proto-core squeezes a part of the interstitial water through the porous rock into the water layer. The radionuclides are concentrated in the central part of the moon, bringing the central temperature to ≈800 K.

Figure 1: Evolution of the core (dark blue), ocean (yellow), and crust (light blue) shown through the evolution of the heat capacity, since this parameter has considerably different values for all structural layers.

The initial porosity in the ice-rock mixture decreases at ≈2.6 Ma after CAIs throughout the deeper interior at ≈450 K. The displaced water forms an ocean atop of the core. After ≈4 Ma after CAIs the water amount in the central core decreases to 0%. This defines a compact core region upon which a few km thick layer with some interstitial water forms that defines a porous outer core. It is retained because the compaction is not efficient enough to close the pores completely.

Although a liquid layer is retained until present, gradually extincting radionuclides cannot prevent a progressing solidification of the ocean on a global timescale. Additional models (A1-A4, B1-B4, C1-C2) confirm that Enceladus could be far off from a state with a solidified mantle, since a global ocean at present occurs for a variety of parameters. A slowly solidifying ocean shows that, assuming constant orbital conditions, a period of time longer than the age of the solar system must pass until a complete solidification can occur.

Figure 2 shows the water fraction profiles at 4,5 Ga (i.e., at present) in the upper 130 km of Enceladus. A porous outer core is obtained only for wet and dry olivine cores while for an antigorite rheology no porosity is retained.

Figure 2: Final profiles of the water fraction in the upper 130 km for models A1-A4 (dry olivine), B1-B4 (wet olivine), and C1-C2 (antigorite). Note that subduction of a top thin undifferentiated layer, is not modeled.

Conclusions: We modeled the formation and the evolution of an initially porous core and demonstrated the importance of the rheology for its final structure. For both dry and wet olivine core, we could obtain models satisfying conditions for a successful one, in particular, a porous outer core. Compared with different concepts of the core structure discussed in the literature^[6-9], a non-rubble-pile solid but porous structure obtained resembles that derived by [7-9].

A porous outer core obtained for both olivine rheologies supports the hypothesis of hydrothermal circulation of oceanic water. Differing from a sandpile-like structure assumed by [10], a fully consolidated inner core and partially consolidated outer core would result in less tidal heating than suggested by [10]. The assumption of a rubble-pile core made by [11] is inherently closer to our results. However, our calculations show that at least a rubble-pile inner part would be impermanent and a fast consolidation is the ultimate outcome if the core is heated to ≈700 K.

While a porous core layer can generate additional tidal heating^[10,11], this excess heating could catalyze core consolidation, reducing, in turn, the influence of this mechanism. Our results indicate that the amount of heat generated in an unconsolidated core^[10] is an overestimate. From successful models that fit the current understanding of Enceladus’ structure, we constrain the accretion time to 1.3-2.3 Ma. Since an antigorite rheology did not produce successful models with core porosity, it is rather unlikely that the outer core is dominated by this mineral, and the inner core should be dry due to the thermal conditions that facilitate dehydration.

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