Melty Shells: Thermal Evolution of Ice Shells on Ocean Worlds

Icy worlds are abundant in the solar system. Several of these are known to possess subsurface liquid water oceans beneath their ice shells, several more potentially have oceans today or had them in the past, and others have always been frozen. The energy required to sustain liquid water in outer solar system moons can come from tidal dissipation in their interiors. Subsurface oceans can be sustained over geologic timescales through orbital resonances that maintain the eccentricity and obliquity necessary to maintain the tidal heating (e.g., [1-2]).

Resonances are not constant through time, and orbital evolution can cause moons to pass through several over their histories. The changing orbits lead to a variety of interesting thermal interiors, but one key feature is robustness against freezing. Resonances can drive strong dissipation in the ocean layer itself, once it becomes extremely thin (< 1 km) [3–4]. A thickening ice shell may place the ocean into a state that prevents complete freezing. By keeping the ice shell mechanically decoupled from the rocky layers, the ability of the ice shell to deform in response to tidal forces is preserved [5–6] and tidal heating in the solid portion can continue, albeit at a reduced rate. Should the ocean freeze entirely, the deformation of the ice will be sharply restricted by the much more rigid rocky interior and tidal heating will plummet.

Here, we explore methods by which icy worlds could escape from a frozen state, and how new habitable regions might form in the solar system. We focus on two well-known ocean worlds, Enceladus and Europa, along with two candidate ocean worlds, Callisto and Mimas [2,7–8]. These four worlds have been chosen to span wide ranges in key physical characteristics such as radius, hydrosphere thickness, interior structure (Figure 1), and prevalence of surface impacts.

The tidal dissipation rate is a strong function of the eccentricity [9], and dissipation tends to circularize the orbit in the absence of a resonance to maintain it. A completely frozen satellite is much less dissipative than one with an ocean, and can sustain a high eccentricity over much longer timescales, allowing heat to build up. If the basal heat flux and tidal dissipation exceeds the heat lost from the surface, then melting is initiated. Moreover, tidal migration is a notable feature of the Jupiter and Saturn systems [10] and eccentricities of satellites may have been different in the past (e.g., [11]). Here, we identify the eccentricities required to initiate ocean formation in an initially frozen state. As an initial condition, we assume a fully frozen Europa. In Figure 2, we show a series of “stability envelopes,” which plot the heat flux at the ice-rock interface as a function of ice temperature and orbital eccentricity (which control tidal heating). The initial condition is a stable, frozen Europa with a basal temperature of 150K and a heat flux of 1.5 W m^-3 (top). If the orbital eccentricity increases, tidal heating raises the temperature, even if the ice shell is fully frozen and coupled to the silicate layer beneath. At e= 0.003, the ice shell is still stable and grounded at a basal temperature of 150 K. If e continues to increase to 0.004, a grounded ice shell is incompatible with the basal heat flux.

Once the ice shell begins to melt, the shell thickness is no longer constant, and is a free parameter. Instead, the basal temperature is constant and controls the shell thickness. In Figure 3, we show a “zipper,” which plots the basal heat flux as a function of orbital eccentricity and the shell thickness. For e = 0.004 and 6 mW m^-2 basal flux, we find that a 57-km thick shell that is stable.

While this can be achieved under moderate conditions for larger satellites such as Europa, the eccentricity must be relatively high at Mimas for this to occur. In fact, the present-day eccentricity of 0.02 is nearly the upper limit for Mimas to avoid a large melting event. Raising the eccentricity to 0.03 would result in completing melting of Mimas’ ice shell; rapid dissipation and damping of the eccentricity would be needed to prevent this. Similar results are observed for Enceladus. The basal heat flux must have been higher in the past to produce the subsurface ocean, but is inconsistent with the present-day eccentricity is inconsistent with melting, implying the ice shell is thickening today.

The above results assume a purely conductive ice shell. Sufficiently warm and thick ice shells may be able to convect, and have a significant feedback between heat production and removal. The lower viscosity of a warm convective ice shell promotes stronger tidal heating. This low viscosity also increases the vigor of convection, which can remove the heat more quickly. Ongoing models of convection in the ice shells of these moons will quantify the relative effects of viscosity on heat production and removal, to refine the equilibrium shell thicknesses expected.

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