Diving deep into Mimas’ ocean: interior structure, evolution, and detection using heat flow

Introduction: Mimas is a small moon of Saturn with a heavily cratered surface and high eccentricity, suggesting an inactive past. It was, thus, surprising when Cassini measurements of Mimas’ libration and tracking of its pericenter precession revealed that Mimas maintains an ocean under an ice shell 20-30 km thick [5,12]. Subsequent investigations into how an ocean-bearing Mimas could have avoided developing tidally-driven fractures [7], its tidal heating budget  [8], constraints on shell thickness from the formation of the Herschel impact basin [3], and thermal-orbital evolution models [5,9] all point to a young ocean that has emerged within the past 10-15 Myr. These results suggest that Mimas may possess the youngest ocean in the Solar System, making it an important target for understanding the early stages of ocean development – such as for Enceladus’ ocean – and the habitability of ocean worlds through time. Uranus’ moon, Miranda, may also have developed an ocean relatively late in its history (e.g., [2]); understanding the evolutionary and geophysical processes at Mimas may help prepare us for a future mission to the Uranian system.

Here, we expand upon past work [8,9], in which we relied on globally-averaged tidal heating and constant surface temperature, to develop a map of plausible ice shell thicknesses and surface heat flows on Mimas assuming a present-day ocean. Our goals are to determine the variability in heat flow and ice shell thickness that result from spatial differences in surface temperature and strength of the tide and to quantify requirements that would enable ocean detection via heat flow measurements. Our results also provide estimates of tidal power, which affect the circularization timescale and ocean lifetime within thermal-orbital evolution models.

Methods: We utilize the numerical toolkit MATH [13] to compute tidal heating within Mimas’ ice shell and identify the equilibrium ice shell thickness and surface heat flux at a suite of locations across Mimas. These calculations depend on the surface temperature and the basal heat flux. Here, we develop a surface temperature map based on models of solar insolation, and informed by Cassini measurements (e.g., [4]), to obtain robust temperatures. We then vary the basal heat flux across a range that encompasses minimal heating from only radiogenic decay to high heat fluxes associated with dissipation in Mimas’ rocky interior. We use the inferred ice shell thickness of 20-30 km [5,12] to determine the basal heating cases that provide consistent results. From these maps, we can deduce the precision needed to use heat flow measurements to differentiate between a fully frozen Mimas, which likely produces endogenic heat flows of ~1 to several mW/m² (e.g., [9]), and an ocean-bearing Mimas.

The ice shell thickness maps can also be used to compute the tidal dissipation associated with Mimas’ present-day orbit and interior structure. We will input these values into the numerical toolkit PISTES [11] to assess the extent to which Mimas’ ice shell evolution can occur over a longer timescale and/or begin at a higher eccentricity than in past models. These results are particularly important for understanding how Mimas came to possess an ocean. While we expect that Mimas’ ocean emerged due to a recent eccentricity-pumping event that increased its eccentricity to the point of melting, the cause and details are not well-understood. A gap in Saturn’s rings, known as the Cassini Division, appears to record Mimas’ phase of inward migration and increasing eccentricity [1,6]. However, models of this process require Mimas to reach a much higher eccentricity than the thermal-orbital evolution models predict; Mimas’ entire ice shell would have melted in that case, which is inconsistent with its geologic record (see discussion in [5]). In addition, the timescales for Mimas’ subsequent outward migration are in conflict. These discrepancies motivate further investigation into Mimas’ thermal-orbital evolution to determine whether the initial conditions and lifetime of the ocean can be extended.

Anticipated results: In Figure 1, we show maps of surface heat flow and ice shell thickness for Europa, assuming different basal heating values [10], which we created using the same tools and approach we are now applying to Mimas. We will present similar maps of ice shell thickness and heat flow across Mimas at its present-day eccentricity that are consistent with the inferred average ice shell thickness. We will also present the precision required for future heat flow measurements to detect the ocean and constrain the thickness of the ice shell, which we will compare to our recent Europa results. Finally, we will present revised thermal-orbital evolution models that account for differences in tidal dissipation between the globally-averaged and spatially-variable models of Mimas and discuss the implications of our findings on the development and age of Mimas’ ocean.

Figure 1: We show equilibrium ice shell thicknesses (left) and surface heat flows (right) for Europa assuming different values of the basal heat flux (rows) and applying surface temperatures from model fits to Galileo data (see [10]). Variations in tidal strength exert a strong control on the pattern of heat flow while surface temperature creates deviations in the shell thickness map from the purely tidal pattern. We are conducting a similar investigation of Mimas to better understand the current state of its ocean and ice shell, develop measurement requirements, and explore implications for the ocean’s evolution.

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