On the distribution of volatiles in the Galilean moons&#8217; primordial hydrospheres
Authors: Tenelanda-Osorio Laura Isabel , Mousis Olivier , Bouquet Alexis , Danger Grégoire 
Published: July 2021

The accretion of the Galilean icy moons within the Jovian circumplanetary disk (hereafter CPD) and the subsequent overturn of their cores led to their differentiation and the disposal of the hydrospheres at the top of the denser rocky mantles. In the most extreme cases, when the accretional energy is high enough to sublimate the icy material, volatiles are expected to settle in a liquid&#8211;vapor equilibrium between the ocean and the atmosphere. Here, we present an equilibrium model that investigates the effect of the variation of the initial oceanic compositions on the thermodynamic equilibrium between primordial oceans and their coexisting atmospheres. This model will be applied to ultimately derive links between the current compositions of Europa, Ganymede, and Callisto&#8217;s surfaces and those of their primordial hydrospheres.Given a starting concentration of volatiles in a primordial ocean and the expected temperature of the system, our model outputs the equilibrium composition of the species involved in the vapor and liquid phase, and the atmospheric pressure with the contribution of each species (partial pressure). Using different initial concentrations, we can compare the impact of the initial ratio among the volatiles, in their final distribution in the hydrospheres. Furthermore, the model evaluates the clathrate formation, which is expected depending on the concentration of species such CO2 and CH4, and the high pressure (HP) ices formation.The liquid&#8211;Vapor equilibrium is reached when the fugacities of both phases are equal. This translates into the following expression:where &#934;i is the fugacity coefficient of component i, yiisthe molar fraction of i in the vapor phase, P is the pressure, &#947;i is the activity coefficient of i, xi is the molar fraction of i in the liquid phase and fi0 is the reference state.Fugacity coefficients (&#934;i) are obtained using the approximation from Peng&#8211;Robinson equation of state [1]:Where a is the attraction parameter of the mixture, b is the covolume parameter of the mixture and&#160;bk of component k, P is the pressure,&#160;T the temperature, R the gas constant and&#160;Z the compressibility factor. Activity coefficients (&#947;i) are obtained using the ex-tended UNIQUAC&#8211;Debye&#8211;Huckel model [2], and the reference state is approximated to the saturation pressure in the case of water and to Henry&#8217;s constant for the solutes (Eq. 3):&#160;Some of the dissolved species can self&#8211;dissociate in the liquid phase and change the contribution of other species to the final thermodynamic state [3]. Therefore, we model the ocean as an electrolytic solution taking into account the acid/base equilibrium and the subsequent formation of new ions.The highlights of the model include:&#8226; An extended list of molecules based on cometarycomposition and CPD origin for the starting composition, such CO, CO2, CH4, NH3, H2O, CH3OH, H2S, HCN, SO2, H2O2, Kr, Ar, Xe.&#8226; A precise estimate of clathrates formation conditionsand composition via the use of a thermodynamic statistical model [4,5]. This model provides a description of clathrates properties including structure, density and determination of whether they would sink or float and form a crust.&#8226; Description of the thermodynamic properties of HP ices that might form at the base of the ocean, usingthe SeaFreeze EOS package [6].References[1] Peng, D.-Y., and Robinson, D. B., &#8220;A new two-constantequation of state,&#8221;Industrial &amp; Engineering Chemistry Fun-damentals, Vol. 15, No. 1, 1976, pp. 59&#8211;64.[2] Sander, B., Rasmussen, P., and Fredenslund, A., &#8220;Calculationof vapour-liquid equilibria in nitric acid-water-nitrate saltsystems using an extended UNIQUAC equation,&#8221;Chemicalengineering science, Vol. 41, No. 5, 1986, pp. 1185&#8211;1195.[3] Marounina, N., Grasset, O., Tobie, G., and Carpy, S., &#8220;Roleof the global water ocean on the evolution of Titan&#8217;s primitiveatmosphere,&#8221;Icarus, Vol. 310, 2018, pp. 127&#8211;139.[4] Bouquet, A., Mousis, O., Glein, C. R., Danger, G., and Waite,J. H., &#8220;The role of clathrate formation in Europa&#8217;s oceancomposition,&#8221;The Astrophysical Journal, Vol. 885, No. 1,2019, p. 14.[5] Mousis, O., Lakhlifi, A., Picaud, S., Pasek, M., and Chas-sefiere, E., &#8220;On the abundances of noble and biologicallyrelevant gases in Lake Vostok, Antarctica,&#8221;Astrobiology,Vol. 13, No. 4, 2013, pp. 380&#8211;390.[6] Journaux, B., Brown, J. M., Pakhomova, A., Collings, I. E.,Petitgirard, S., Espinoza, P., Boffa Ballaran, T., Vance, S. D.,Ott, J., Cova, F., et al., &#8220;Holistic approach for studyingplanetary hydrospheres: Gibbs representation of ices thermo-dynamics, elasticity, and the water phase diagram to 2,300MPa,&#8221;Journal of Geophysical Research: Planets, Vol. 125,No. 1, 2020, p. e2019JE006176&#160;