The Likely Thickness of Europa&#8217;s Icy Shell
Authors: Howell Samuel 
Published: October 2020

AbstractWhile the thickness of Europa&#8217;s ice shell is underconstrained by the current knowledge of the body, it is not unconstrained. That is, while there are many possible ice shell thicknesses, not all are equally plausible. In this study, I survey the current knowledge of Europa and quantify distributions in the parameters and processes that control ice shell thickness. I then create a Monte Carlo simulation of 107 plausible Europa&#8217;s with ice shells in thermodynamic equilibrium, and condition the result into a probability distribution for ice shell thickness. I predict a best estimate thickness of 22.0 km, but &#160;with great uncertainty. These results may inform future planning and inferences from NASA&#8217;s Europa Clipper mission and ESA&#8217;s JUICE mission later this decade [1].&#160;IntroductionWithin its predominantly water-ice shell, Jupiter&#8217;s moon Europa likely harbors a global saltwater ocean, placing it among an emerging class of celestial objects known as Ocean Worlds. The ice shell is thought to consist of a brittle upper lithosphere, where heat transfer occurs by thermal conduction, and a ductile interior asthenosphere that may be convecting in solid-state. The icy surface of this shell exhibits one of the youngest average ages in the solar system (~40 &#8211; 90 Myr) [2], requiring the recent or current geologic resurfacing.The geologic processes within the ice shell responsible for the young surface may convey material between the surface and interior ocean, critically influencing chemical disequilibria within the watery interior and the habitability of Europa&#8217;s ocean [3], [4]. However, the thickness of the ice shell and therefore the potential for geologic material exchange is unknown, and estimates span three order of magnitude.Following discoveries at Europa by the Galileo mission, a summary of ice shell thickness predictions was made by Billings and Kattenhorn [5], providing a name to the &#8220;Great Thickness Debate.&#8221; That study catalogued dozens of previous publications, collating estimates for icy thicknesses from a few hundred meters to many tens of kilometers.In order to estimate a probability distribution for Europa&#8217;s ice shell thickness using the Monte Carlo method, several parameters must be estimated. Therefore, I first identify current best estimate (CBE) values and construct distributions that capture the uncertainty in those values for several key parameters. In each instance, I determine both the range of values for the parameter of interest and the form of the probability distribution for that parameter.&#160;MethodAssuming an ice shell in thermodynamic equilibrium, the heat flux out of the icy lithosphere radiated to space is equal to the heat flux into the base of the lithosphere from the silicate interior plus the internal heat generated by tidal dissipation within a ductile convecting asthenosphere, integrated over the depth of the asthenosphere.For each of these terms, I identify the underlaying uncertainties associated with their calculation. For Europa as a whole, I include uncertainties in total H2O layer and iron core thickness. In the silicate interior, I consider uncertainties in radiogenic heating associated with the material Europa accreted from, as well as the potential for silicate tidal dissipation based on mechanical constraints. For the ice shell, I consider uncertainties in convective and melting temperatures, grain size, empirical diffusion creep constants, non-ice composition, porosity, mechanical properties, and tidal response.The thickness of the conductive and convective layer are then sampled according to the governing equations for heat transfer and tidal heat dissipation (Figure 1).&#160;Results and DiscussionThe CBE ice shell thickness for Europa is 22.0 km (Figure 2), though the spread in potential thicknesses is great. Only ~1% of possible configurations are thinner than 15 km, and the median thickness is ~40 km. Further, ice shells are primarily dominated by heat transfer through thermal conduction (Figure 3), with thermal convection being relegated most commonly to the bottom 1/3rd or less of the ice shell.I will address several surprising results in the underlaying distributions, and their affect on the overall solution. Additionally, there are many key sensitivities built in to this model that may be retired through future laboratory analysis and spacecraft observation. In parallel, some unresolvable issues will persist until the ice shell is explored in situ.&#160;Figures&#160;Figure 1. Differential and cumulative probability distributions for Europa&#8217;s ice shell thickness. The steep rise is attributed to the inverse relationship between minimum ice shell thickness and total heat flux, and the tail to the right is controlled by silicate heat flux and H2O thickness.&#160;&#160;Figure 2. Probability heat map showing conductive and convective thicknesses. Warmer colors denote higher probability. White dashed lines show lines of constant ice shell thickness. Note, for example, that the red line showing a constant thickness of 15 km falls outside the majority of solutions, while the line showing 20 km thickness passes through regions of high probability.&#160;AcknowledgementsThis work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.&#160;References[1]&#160; S. M. Howell and R. T. Pappalardo, &#8220;NASA&#8217;s Europa Clipper&#8212;a mission to a potentially habitable ocean world,&#8221; Nat. Commun., vol. 11, no. 1, Art. no. 1, Mar. 2020, doi: 10.1038/s41467-020-15160-9.[2]&#160; E. B. Bierhaus, K. Zahnle, C. R. Chapman, R. T. Pappalardo, W. R. McKinnon, and K. K. Khurana, &#8220;Europa&#8217;s crater distributions and surface ages,&#8221; Europa, pp. 161&#8211;180, 2009.[3]&#160; K. P. Hand, C. F. Chyba, J. C. Priscu, R. W. Carlson, and K. H. Nealson, &#8220;Astrobiology and the Potential for Life on Europa,&#8221; in Europa, R. T. Pappalardo, W. B. McKinnon, and K. Khurana, Eds. Tucson: University of Arizona Press, 2009, p. 589.[4]&#160; S. M. Howell and R. T. Pappalardo, &#8220;Can Earth-like plate tectonics occur in ocean world ice shells?,&#8221; Icarus, 2019, doi: 10.1016/j.icarus.2019.01.011.[5]&#160; S. E. Billings and S. A. Kattenhorn, &#8220;The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges,&#8221; Icarus, vol. 177, no. 2, pp. 397&#8211;412, Oct. 2005, doi: 10.1016/j.icarus.2005.03.013.&#160;