Dynamics of the global meridional ice flow of Europa’s icy shell

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. 1Department of Solar Energy and Environmental Physics, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion, Israel. 2Department of Earth and Planetary Sciences and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. *e-mail: [email protected] Europa is one of the most probable places in the solar system to find extra-terrestrial life1,2, motivating the study of its deep (~100 km) ocean3–6 and thick icy shell3,7–11. The chaotic terrain patterns on Europa’s surface12–15 have been associated with vertical convective motions within the ice8,10. Horizontal gradients of ice thickness16,17 are expected due to the large equator-to-pole gradient of surface temperature and can drive a global horizontal ice flow, yet such a flow and its observable implications have not been studied. We present a global ice flow model for Europa composed of warm, soft ice flowing beneath a cold brittle rigid ice crust3. The model is coupled to an underlying (diffusive) ocean and includes the effect of tidal heating and convection within the ice. We show that Europa’s ice can flow meridionally due to pressure gradients associated with equator-to-pole ice thickness differences, which can be up to a few km and can be reduced both by ice flow and due to ocean heat transport. The ice thickness and meridional flow direction depend on whether the ice convects or not; multiple (convecting and non-convecting) equilibria are found. Measurements of the ice thickness and surface temperature from future Europa missions18,19 can be used with our model to deduce whether Europa’s icy shell convects and to constrain the effectiveness of ocean heat transport. The surface properties of Europa and its tidal forcing are well known, yet its inner structure and properties are less certain7,12. The known surface properties include the incoming solar radiation16 (~16 W m−2 year-round at the equator and between 0 and ~4 W m−2 at the poles) and the tidal forcing that is expected to lead to a triaxial ellipsoid structure17 at a period of 3.55 Earth days16. Among the less certain interior properties are the thickness of the outer ice layer20,21 (estimated as a few km to more than 30 km), depth of the subsurface ocean3 (~100 km), and rates of heating at the ocean bottom due to tidal heating within the core22 (33–230 mW m−2) and of radiogenic heating (~8 mW m−2) due to the assumed chondritic abundance of U, K and Th in the solid iron core23 (oceanic tidal heating is negligible22). Our focus here is the global-scale horizontal ice flow on Europa. The polar surface of Europa is colder by tens of degrees than the equatorial regions16,24, which could lead to meridional ice thickness gradients and therefore to pressure gradients that may drive ice flow from high to low latitudes. This is reminiscent of Snowball Earth events over 580 million years ago, when the ocean was covered by a ~1-km-thick ice layer25. Ice tidal movements result in a strain rate and heating within the ice that varies in both the zonal and meridional directions16,17 and can also lead to a large-scale lateral ice flow. Europa’s ice thickness is significantly smaller than the horizontal scales of global ice flow, justifying the use of the ‘shallow ice approximation’, which is commonly used to represent soft land ice flow over the solid Earth surface26. Our two-dimensional (latitude-depth) ice flow model for Europa is therefore based on an ‘upside-down’ shallow ice approximation, representing soft, flowing ice under a cold rigid external ice crust3, separated by a ductile-to-brittle transition zone. The model is coupled with a simple (one layer) ocean model whose meridional heat transport is parameterized via effective diffusivity, which is meant to represent the transport by both ocean circulation and eddies. The model’s variables are the ice flux q, ice thickness hI, and ocean temperature To and salinity So (see Methods). The model includes the role of geothermal heating at the ocean bottom and the ice-tidal heating, and parameterizes vertical convection within the ice. The annual mean surface temperature, Ts, is calculated based on the energy balance between the incoming solar radiation, internal heating and outgoing longwave radiation16. Below, we first show that when the roles of ocean and ice convection are ignored the ice flow effectively homogenizes observable horizontal ice thickness gradients. We then show that meridional ocean heat transport can lead to the homogenization of ice thickness as well. Finally, we show that ice convection can lead to reversed equator-to-pole ice flow in which the enhanced polar tidal heating plays a major role. Starting with the simplest case, Fig. 1 shows the model’s equilibrium solution when taking into account the tidal heating, but disabling ice convection and meridional ocean heat transport, such that the heat flux into the ice base is locally equal to the geothermal heating rate at the ocean bottom, Qg = 0.05 W m−2 (ref. 22). Given the uncertainties in grain size, and therefore ice viscosity27, we calculated the model’s solution for a range of melting viscosity values, η0. Figure 1b shows that the ice is thicker at the poles, where the surface temperature is colder. It also shows that a global pole-toequator ice flow develops (Fig. 1d,f). The equator-to-pole thickness difference is dramatically reduced when ice flow is present for the lower values of the specified melting viscosity, from 3.2 km for the stiffer ice to only 350 m for the softer ice. The maximum meridional ice flux occurs where thickness gradients are maximal (Fig. 1d), and the ice velocity is maximal at the bottom of the ice where it is softest and decreases rapidly upward as the ice becomes stiffer. The ice stiffness is exponential in terms of ice temperature, which (Fig. 1c) varies nearly linearly with depth in this case, not being affected by the presence of weak ice tidal heating. Smaller viscosity also leads to smaller mean ice thickness because the softer ice allows for more tidal heating within the ice (see equation (11); ref. 9). The freezing at high latitudes and melting at low latitudes imply an equatorward flow (Fig. 1e). The maximal melting in the cases corresponding to mid-range and softer ice viscosity (blue and red curves) is at mid-latitude due to the value of the vertical temperature gradient at the ice bottom as a function of latitude (see equation (9)). Dynamics of the global meridional ice flow of Europa’s icy shell