Surface-To-Ocean Exchange by the Sinking of Impact Generated Melt Chambers on Europa

1. 1. Introduction Many icy moons in the outer Solar System host large subsurface oceans maintained by tidal heating (Nimmo & Pappalardo, 2016), and are considered the most likely bodies in our Solar System to host habitable environments (Domagal-Goldman et al., 2016; Gaidos et al., 1999). The upcoming JUICE and Europa Clipper missions will specifically target the habitability of Jupiter's moon Europa (Grasset et al., 2013; Howell & Pappalardo, 2020). One major unknown is the source of oxidants that are necessary to generate and maintain redox gradients within its ocean (Chyba & Phillips, 2001; Hesse et al., 2022; Pasek & Greenberg, 2012; Russell et al., 2017; Vance et al., 2016). Oxidants are produced by irradiation at Europa's surface, and need to be transported through the ice shell into the ocean to increase its habitability (Carlson et al., 1999; Hand et al., 2007). Vertical transport processes through the ice shell include subduction, brine drainage, and penetrating impacts. While Kattenhorn and Prockter (2014) provide some observational evidence for subduction, the process does not appear to be wide spread, which is consistent with theoretical counter arguments (Howell & Pappalardo, 2019; Johnson et al., 2017). Another mechanism for oxidant transport is the drainage of near-surface brines (Barr et al., 2002; Hesse et al., 2022; Kalousová et al., 2014; Sotin et al., 2002). While many surface features have been interpreted as requiring the presence of near-surface melts (Barr et al., 2002; Chivers et al., 2021; Collins et al., 2000; Cox et al., 2008; Head & Pappalardo, 1999; Manga & Michaut, 2017; Pappalardo & Barr, 2004; Abstract Impacts into icy bodies often generate near-surface melt chambers and thermal perturbations that soften the ice. We explore the post-impact evolution of non-penetrating impacts into Europa's ice shell. Simulations of viscous ice deformation show that dense impact melts founder before refreezing. If the transient cavity depth exceeds half the ice shell thickness, over 40% of the impact melt drains into the underlying ocean. Drainage of impact melts from the near-surface to the ocean occurs on timescales of 103 –104 years. The drainage of melts to the ocean occurs for all plausible ice shell thicknesses and ice viscosities, suggesting that melt foundering is a natural consequence of impacts on icy worlds. Post-impact viscous deformation is an important process on icy worlds that affects cryovolcanism, likely modifies crater morphology, creates porous columns through the ice for surface-to-ocean exchange, and may supply the oxidants required for habitability to subsurface oceans. Plain Language Summary Europa is an ocean world with an outer ice shell in our Solar System. Outer ice shells on ocean worlds serve as both a barrier and facilitator for internal ocean habitability and the detectability of its potential inhabitants. A prominent feature we observe on the surface of ice shells is highly variable craters from impacts that indent but do not penetrate the ice shell. Here, we find that many of the impacts into Europa's ice shell would have generated large near-surface melt chambers, which rapidly drain into the underlying ocean and form a continuous surface-to-ocean melt column. This melt drainage occurs with any entrained surface materials and provides a consistent means of exchange between the surface and ocean, which likely increases the habitability of internal oceans. Furthermore, this drainage displaces large volumes of water from below impact craters, on the order of 10's of cubic kilometers. This large scale drainage may help to explain the wide range of collapsed, enigmatic crater morphologies observed on Europa, and other ocean worlds. CARNAHAN ET AL. © 2022. The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Surface-To-Ocean Exchange by the Sinking of Impact Generated Melt Chambers on Europa Evan Carnahan1,2,3,4 , Steven D. Vance5 , Rónadh Cox6 , and Marc A. Hesse1,2,4 1 Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA, 2 Center for Planetary Systems Habitability, The University of Texas at Austin, Austin, TX, USA, 3 Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA, 4 Department of Geological Sciences, The University of Texas at Austin, Austin, TX, USA, 5 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 6 Geosciences Department, Williams College, Williamstown, MA, USA Key Points: • Impacts into ice shells generate melt chambers that viciously deform and sink through the ice shell, likely modifying crater morphologies • If transient cavity depth exceeds half the ice thickness, impact melts drain to the ocean and may deliver oxidants needed for habitability • Draining impact melts form a stable porous channel that connects the ocean to near-surface and may allow for the escape of ocean fluids Correspondence to: E. Carnahan, evan.carnahan@utexas.edu Citation: Carnahan, E., Vance, S. D., Cox, R., Hesse, M. A. (2022). Surface-to-ocean exchange by the sinking of impact generated melt chambers on Europa. Geophysical Research Letters, 49, e2022GL100287. https://doi. org/10.1029/2022GL100287 Received 1 JUL 2022 Accepted 23 NOV 2022 10.1029/2022GL100287 RESEARCH LETTER 1 of 12 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

2. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 2 of 12 Schmidt et al., 2011), it is currently not clear where the energy to form these melts comes from (Nimmo Giese, 2005). Finally, impacts that penetrate the ice shell provide a direct connection between the surface and internal oceans and may allow rapid transport of large quantities of surface oxidants and other biorelevant materials into the ocean (Cox Bauer, 2015; Schenk Turtle, 2009). Impacts are common throughout Europa's history (Moore et al., 2001; Schenk, 2002; Zahnle et al., 1998), however, despite varied crater morphologies, it is currently not clear if any of the observed impact structures represent penetrating impacts. We propose a new transport mechanism, which focuses on the smaller non-penetrating impacts that dominate the crater record of Europa (Schenk, 2002; Turtle Pierazzo, 2001). Many non-penetrating impacts generate large melt chambers, which are presently thought to sustain long-lived cryovolcanism, for example, Manan- nán Crater on Europa (Steinbrügge et al., 2020) or Occator Crater on Ceres (Bowling et al., 2018; Hesse Castillo-Rogez, 2019; Quick et al., 2019; Raymond et al., 2020). Models for the evolution of such impact-induced melt chambers assume that they freeze in place, which implicitly assumes the surrounding ice is rigid (Bowling et al., 2018; Fagents, 2003; Fagents et al., 2000; Hedgepeth et al., 2022; Hesse Castillo-Rogez, 2019; Lesage et al., 2020; Quick et al., 2019; Steinbrügge et al., 2020). However, impacts that generate melt chambers also significantly warm and soften the surrounding ice making it susceptible to viscous deformation. Furthermore, although not explored here, the impact may generate fractures that allow for transport of melts short distances away from the crater melt pond, for example, Elder et al. (2012). Importantly, the crater record of icy moons includes craters of varying complexities (Schenk, 2002; Turtle Pierazzo, 2001) with anomalous features such as collapsed pits, domes, and central Massifs that imply post-impact modifications (Bray et al., 2012; Elder et al., 2012; Korycansky, 2020; Moore et al., 2017; Silber Johnson, 2017; Steinbrügge et al., 2020). These observed crater features suggest that both impact structures and the generated melts experience significant post-impact evolution that has so far received little attention. Here, we use numerical simulations to determine the long-term evolution of impact-induced melt chambers on Europa. We explore the foundering of impact generated melt chambers and the conditions that result in the transfer of dense melts from the surface into internal oceans. Due to the higher frequency of smaller non-penetrating impacts, foundering provides a potential avenue for sustained delivery of oxidants into the ocean. Our simulations also provide constraints on the longevity of impact-induced cryovolcanism and more broadly the persistence of near-surface melts that are often invoked to explain surface features, such as chaotic terrains. Similar to impact melting, melt below chaotic terrains is often assumed to remain in place at the near-surface of the ice shell throughout the large scale thermal perturbation that cause the melting (Schmidt et al., 2011; Sotin et al., 2002). Thus, our results for the stability of near-surface impact melts inform the presumed persistence and formation mechanisms of these near-surface melts that are thought to provide targets for sampling in future missions (Howell Pappalardo, 2020). 2. Mathematical Model Here, we model the long-term evolution of the impact structure, using the output of a shock-physics cratering simulation as an initial condition (Cox Bauer, 2015). The evolution of impact melt chambers over time are governed by a competition between viscous sinking of dense melt and refreezing of melt within the ice shell. Modeling this competition requires treating both the energy and viscous deformation of the ice-water system after the impact. 2.1. Enthalpy Method We assume a single component two-phase system comprised of ice and water (melt). Phase properties are denoted with subscripts i for ice and w for water. For simplicity, we denote the volume fractions of the melt and ice as ϕw = ϕ and ϕi = 1 − ϕ. In this model the volume fraction of melt, ϕ is equal to the porosity, because no gas phase exists. Phase densities, specific heat capacities, and thermal conductivities are ρα, cp,α, and kα, respectively, where 𝐴𝐴 𝐴𝐴 ∈ [𝑖𝑖𝑖 𝑖𝑖]. The phase change between ice and water at the melting temperature of ice, Tm, requires a latent heat, L. In the presence of phase change the temperature, T, does not fully describe the state of the system. Instead, we use an enthalpy method to describe the phase change (Alexiades Solomon, 1993; Aschwanden et al., 2012; Jordan Hesse, 2015; Katz, 2008). The overall enthalpy of the system, H, is given by 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

3. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 3 of 12 𝐻𝐻 = (1 − 𝜙𝜙)𝜌𝜌𝑖𝑖ℎ𝑖𝑖(𝑇𝑇 ) + 𝜙𝜙𝜙𝜙𝑤𝑤ℎ𝑤𝑤(𝑇𝑇 ), (1) where the specific enthalpies of ice and water are defined as ℎ𝑖 = 𝑐𝑝,𝑖(𝑇 − 𝑇𝑚) and ℎ𝑤 = 𝐿 + 𝑐𝑝,𝑤(𝑇 − 𝑇𝑚) , (2) and we have chosen hi(Tm) = 0, and assumed physical properties of each phase to be constant. With these defini- tions (1) becomes a function of melt fraction and temperature, defined step-wise as 𝐻(𝑇 , 𝜙) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 𝜌𝑖𝑐𝑝,𝑖(𝑇 − 𝑇𝑚) , for 𝑇 𝑇𝑚, 𝜙 = 0, 𝜌𝑤𝐿𝜙, for 𝑇 = 𝑇𝑚, 𝜌𝑤(𝐿 + 𝑐𝑝,𝑤 (𝑇 − 𝑇𝑚)) , for 𝑇 𝑇𝑚, 𝜙 = 0. (3) Here, H depends on either T or ϕ, but never on both simultaneously. Therefore both T and ϕ can be determined uniquely if H is known. 2.2. Governing Equations The governing equations for the ice-water system arise from the balance of momentum, mass, and energy. We assume that both the ice and melt deform as a viscous fluid and we neglect the porous flow of melt within the ice. We write the energy balance in terms of enthalpy, so that we have the following set of governing equations. ∇ ⋅ [ 𝜂𝜂 ( ∇𝐮𝐮 + ∇𝐮𝐮𝑇𝑇 )] − ∇𝑝𝑝 = 𝜌𝜌𝜌𝜌̂ 𝐳𝐳, (4) ∇ ⋅ 𝐮𝐮 = 0, (5) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 + ∇ ⋅ [ 𝐮𝐮𝐻𝐻 − ̄ 𝑘𝑘∇𝑇𝑇 ] = 0. (6) Here, u and p are the velocity and pressure of the ice, respectively. Gravitational acceleration, g, is assumed to be constant across the ice shell. The effective thermal conductivity of the medium is phase-averaged, 𝐴𝐴 ̄ 𝑘𝑘 = (1 − 𝜙𝜙)𝑘𝑘𝑖𝑖 + 𝜙𝜙𝜙𝜙𝑤𝑤, where ki = 3.3 and kw = 0.5 W m−1 K−1 . Similar to previous work, we assume the ice deforms by Newtonian diffusion creep (Goldsby Kohlstedt, 2001; Hussmann Spohn, 2004; Kalousová et al., 2017; Mitri Showman, 2005; Tobie et al., 2003) and that the temperature dependence is given by the Arrhenius relation 𝜂𝜂 = 𝜂𝜂𝑏𝑏 exp [ 𝐴𝐴 ( 𝑇𝑇𝑚𝑚 𝑇𝑇 − 1 ) + 𝜙𝜙𝜙𝜙 ] for 𝜂𝜂 ≥ 𝜂𝜂𝑏𝑏∕100, (7) where 𝐴𝐴 𝐴𝐴 = 𝐸𝐸𝑎𝑎 𝑅𝑅𝑅𝑅𝑚𝑚 , Ea is the viscosity activation energy, R is the universal gas constant, ηb is the viscosity at Tm, and γ = −45 describes the weakening of the ice due to melting (De La Chapelle et al., 1999). Due to high homologous temperatures and low stresses in the post-impact ice shell, deformation likely occurs by Newtonian diffusion creep (Durham et al., 2010; Howell Pappalardo, 2018). However, temperatures are colder in the near-surface region where the impact melts are initially located, and we therefore explore the potential for non-Newtonian creep by lowering the viscosity activation energy following Kalousová et al. (2017) (Section 4). 2.3. Numerical Simulations We use the ice shell convection model developed by Carnahan et al. (2021), based on conservative finite differ- ences and flux limiters. This model has been extended to cylindrical coordinates, following the approach of Hesse and Castillo-Rogez (2019), to match the geometry of the impact simulations. All simulations are two-dimensional in a plane through the central axis of the impacts. Simulations are initiated using output of impact simulations reported by Cox and Bauer (2015) for Europa. To match our rectangular domain, surface topography was filled with ice at near surface temperatures and basal topography was filled with ice at the melting point. The addition of a cold ice layer at the surface of the crater provides a potential insulator for the melt chamber, however, we find 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

4. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 4 of 12 the addition of the layer increases melt drainage by at most 2%. The initial temperature inside the impact melt chambers was assumed constant at Tm. Melt-dominated regions have very low viscosity and fast convective heat transfer. Given the long timescales, ∼104 years, it is not possible to accurately resolve motion of the low viscosity water within the melt chamber or ocean. Similar to previous work, for example, Peddinti and McNamara (2019), our model approximates the low viscosity by setting water viscosity to ηw = ηb/102 . This ensures that the foundering of the melt chamber is governed by the resistance of the ambient ice. We approximate the effects of convective heat transfer in the underlying ocean by increasing the thermal conductivity of water there to kw = 102 ki. This allows the model to recover the long-term steady-state of a conductive ice shell overlying a well mixed ocean with T ≈ Tm. Unless mentioned otherwise, the basal viscosity of the ice in our simulations is ηb = 1014 Pa s and the activation energy is Ea = 50 kJ mol−1 . All simulations assume that the thermal conductivity of the ice is constant at 3.3 W m−1 K−1 , to be consistent with the conductive ice shells of Cox and Bauer (2015). To determine the conditions that allow melt to drain into the underlying ocean, we explore nine impacts into conductive ice shells. We use the suite of impact models for the Europan crust generated by Cox and Bauer (2015), using the iSALE impact software (Collins et al., 2011), as initial conditions for our long-term viscous evolution models. Impactors are assumed to have a bulk density of 600 kg m3 (Weissman Lowry, 2008) and a velocity of 26.5 km s−1 (Turtle Pierazzo, 2001; Zahnle et al., 1998). Diameters of cometary impactors in our simulations are given by Pi-group gravity scaling (Holsapple, 1993; Schmidt Housen, 1987) and range from 560 to 4,258 m (Cox Bauer, 2015), consistent with Jupiter Family Comet sizes (Cox et al., 2008; Fernández et al., 2013; Zahnle et al., 2003). The impacts are into ice shells ranging from 10 to 40 km thick with impact kinetic energies between 20 and 1,334 EJ. For more details on the impact simulations, used herein as initial conditions, see Cox and Bauer (2015). 3. Results The energy deposition from the impact locally warms the ice shell and the melt formed sinks due to the relative density of the melt. Sinking of melt chambers below impacts is facilitated by the viscosity reduction in the surrounding ice due to the impact-induced temperature increase (Figure 1a). In our simulations, both phases move together as a viscous fluid that sinks due to the increased density of the partially molten region. First, we discuss two simulations that illustrate the range of modeled behaviors, and then we describe, based on nine simulations for ice shells of different thickness, a criterion for predicting when melt drainage to the ocean occurs. Figure 1. Evolution of temperature and melt fraction for two non-penetrating impacts into a 10 km thick ice shell. Top row is for an impact with a cometary diameter of 756 m, an impact energy of 64 EJ, and a transient cavity depth of 6.87 km (043.04 in Cox and Bauer (2015)). Bottom row is for an impact with a cometary diameter of 560 m, an impact energy of 21 EJ, and a transient cavity depth of 4.98 km (038.00 in Cox and Bauer (2015)). Both impact melt chambers go through substantial post-impact viscous evolution, however only the melt from impact 043.04 sinks to the ocean. The viscous evolution of 043.04 forms a continuous near-surface to ocean melt column, draining around 40% of the initial melt chamber into the ocean. 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

5. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 5 of 12 Figures 1a–1e show the evolution of temperature and porosity following a 64 EJ impact into a 10 km thick ice shell that generates an impact melt chamber with a volume of approximately 17 km3 . The impact-induced thermal perturbation in the surrounding ice raises the temperature of the ice beneath the crater close to its melting point and leaves it correspondingly soft. This configuration allows the dense melt chamber to sink, displacing the ice side- ways. The melt chamber is initially confined to the top 4 km of the ice shell, but sinks rapidly enough to avoid refreezing. Over several thousand years, the melt forms a continuous vertical porous column through the ice shell. Approximately 7,000 years after impact, the melt column pierces the base of the ice shell, and impact melt begins to drain into the ocean. In this case, approximately 40% of the original impact melt chamber drains into the ocean within 11,000 years of the impact. Not all melt chambers will evolve to communicate with the ocean. Figures 1f–1j show the evolution of a smaller 20 EJ impact. Although it generated significant amounts of melt (7 km3 ), the thermal effects of the impact do not sufficiently reduce the viscosity of the underlying ice. The dense melt begins to sink but migrates more slowly due to high viscous resistance. This slow sinking allows sufficient time (about 20,000 years) for conductive cooling to refreeze the melt before it reaches the ocean. However, significant vertical material transport has already occurred and the melt chamber sinks over a kilometer through the ice shell before refreezing. To assess the prevalence of impact drainage induced material transport into the ocean, we conducted nine simulations spanning a range of ice shell and impactor conditions. Figure 2 shows the fraction of the initial impact melt chamber that drains into the ocean as a function of the ratio between the depth of the transient cavity, C, and the ice shell thickness, D. Impacts with C/D 0.9 result in breaching of the ice shell and direct communication between the surface melts and ocean (Cox Bauer, 2015). However, we find that non-breaching impacts with C/D 0.5, that is, a transient cavity depth greater than half the ice shell thickness, sufficiently modify the underlying ice such that impact melt chambers sink into the ocean, with 40% of impact-generated melt draining into the ocean in our simulations. 4. Discussion Our results show that impacts into the ice shell of Europa cause significant post-impact viscous deformation due to the softening of ice around the impact site and the negative buoyancy of melt. This leads to downward vertical transport, which may affect local composition and the thermal structure of the ice shell. In some cases, melt foundering can reach the underlying ocean, providing a mechanism to transport surface derived materials to the ocean. Our model includes several assumptions, but in general these tend toward making our results more conservative, and do not affect the overall robustness of our conclusions. First, all simulations assume a conductive ice shell to match the impact simulations of Cox and Bauer (2015). Although it is possible that there is convection in the lower parts of Europa's ice shell, using a conductive model provides a more rigorous test of impact induced mobility. Impacts into convecting ice, for example, Silber and Johnson (2017), likely founder more readily, because once melt reaches the warm convecting ice the rate of refreezing will decline, and the melt pocket will sink more rapidly. Second, melt transport through the ice occurs only by the viscous flow of the water-ice system. The model does not consider drainage of melt by porous or fracture flow. Including such two-phase flows would likely increase the volume of fluid reaching the ocean, because the timescales for porous drainage are compara- ble to those for viscous foundering (Gaidos Nimmo, 2000; Hesse et al., 2022; Kalousová et al., 2014). Third, we neglect convective heat transfer in the melt chamber because heat loss is primarily controlled by conduction through the surrounding ice (Korycansky, 2020; O’Brien et al., 2005). Fourth, we assume constant thermal conductivity in the ice to match the simulations of Cox and Bauer (2015). In contrast to the previous assumptions, Figure 2. Fraction of each impact melt chamber that drains into the ocean versus the dimensionless penetration depth, that is, the ratio of the impact maximum transient cavity depth, C, to the ice shell thickness, D, for a range of ice shell thicknesses. Impacts with a dimensionless penetration depth, C/D, greater than 0.9 result in breaching (Cox Bauer, 2015); we find values greater than 0.5 result in impact melt drainage to the ocean. 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

6. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 6 of 12 this assumption is not conservative because it underestimates the heat loss and hence the refreezing rate of the melt chamber. Including the temperature dependence of thermal conductivity would likely reduce vertical transport and the volume of melt that reaches the ocean, but we expect these effects to be secondary to those that result from uncertainty in the ice viscosity. Our simulations assume a Newtonian viscosity and neglect weakening due to impact damage. To explore uncertainty in the rheology of the ice, we vary both the viscosity at the melting temperature and the viscosity activation energy, see Table 1. We vary viscosity at the base of the ice shell to capture the effects of ice grain size variation; and we change activation energies to approximate the effects of non-Newtonian creep. Despite viscosity variations of several orders in magnitude the cut-off in C/D ∼ 0.5 between impacts that drain into the ocean and those that do not is largely consistent (Table 1). For very coarse grained ice, ηb = 1015 Pa s, our results, Table 1, show a transition region rather than a sharp cut-off when different ice shell thicknesses are compared. At low activation energies, impacts that only penetrate a third of the ice shell still result in vertical transport, that is, a transient cavity depth of 0.35 of the ice shell is sufficient for drainage to the ocean. The cut-off increases to 0.5–0.7 if both activation energy and basal viscosity are high. These small changes in the threshold for drainage for all ice thicknesses occurs due to two orders of magnitude change in basal viscosity and a wide range of activation energies. These results show that the foundering of impact melt chambers and drainage into the ocean is possible even for the thickest and most viscous ice shells. As such, this previously ignored process is highly likely to occur despite the present uncertainties in ice shell thickness and rheology. 4.1. Crater Morphologies Our results suggest that any impact that generates a substantial melt chamber will experience post-impact defor- mations due to the foundering of the melt that may influence its final surface morphology. The interpretation of crater topography should therefore include the deformation caused by melt foundering; this may help to explain features that have proven difficult to reproduce with impact simulations alone. Several authors have already concluded that structures such as central pits, domes and the diverse and inter-mixed crater morphologies observed on Europa indicate post-impact modifications (Elder et al., 2012; Korycansky, 2020; Moore et al., 2017; Silber Johnson, 2017; Steinbrügge et al., 2020). Manannán is a good example of a crater with puzzling topography (Moore et al., 2001; Silber Johnson, 2017). It has a large disrupted central massif and a central pit (Figure 3a), suggesting post-impact modification (Schenk Turtle, 2009; Steinbrügge et al., 2020). Figures 3c–3l shows the post-impact evolution of a simulation from Cox and Bauer (2015) that closely approximates the depth and diameter of Manannán Crater. Our results indicate that the melt chamber beneath Manannán Crater would quickly drain a melt volume of over 28 km3 to the ocean from the near surface within 1,000 years (Figure 3b). Although we do not explicitly model surface evolution, this foundering of a large near-surface melt chamber provides an explanation for the collapsed central features observed at Manannán Crater and around Europa, for example, Moore et al. (2001, 2017). Although Europa is the focus of this study, many ocean worlds exhibit complex impact features (Moore et al., 2017; Neish et al., 2013), that beggar standard explanations extrapolated from rocky planets (Moore et al., 2017). Our study shows that impacts on Europa are highly susceptible to post-impact viscous deformation that isn't consistent with rocky lithospheres because Europa's icy lithosphere is much closer to the melting temperature than silicate ones and the melt formed from the ice is negatively buoyant. Although, the prevalence of melt foundering on ocean worlds beyond Europa is not evaluated in this study, these aspects of Europa's lithosphere are consistent with other ocean worlds. Ocean worlds exhibit a wide range of characteristics important for determining the prevalence of viscous foundering below impacts including varied ice shell thicknesses, surface temperatures, gravities, material compositions, and ice grain sizes (Tobie et al., 2005; Vance et al., 2018). The effects of changes in surface temperature are not evaluated here, however some ocean worlds including Ganymede and Titan, have similar surface temperatures to Europa, ∼95 K (Ashkenazy, 2019; Jennings et al., 2016). Both Ganymede and Titan have slightly higher gravities than Europa, which will increase the relative negative buoyancy of melt in ice and thus the rate of foundering. Ea = 22 Ea = 50 Ea = 60 ηb = 1013 0.35 0.5 0.5 ηb = 1014 0.35 0.5 0.5 ηb = 1015 0.35–0.5 0.5 0.5–0.69 Note. For coarse grained ice, ηb = 1015 Pa s, the threshold for melt drainage to the underlying ocean shows a transition region rather than a sharp cut-off when different ice shell thicknesses are compared. Table 1 Cut-Off Criterion in Dimensionless Penetration Depth, That Is, Maximum Transient Cavity Depth Divided by Ice Shell Thickness, C/D, for Melt Drainage to the Underlying Ocean (Figure 2), for Different Ice Viscosity Activation Energies, Ea, in kJ mol−1 and Melting Temperature Viscosities of Ice, ηb, in Pa s, Equation 7 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. 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7. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 7 of 12 Titan is distinct amongst ocean worlds in our Solar System as it has liquid hydrocarbons at the surface and methane clathrates that are potentially entrained in the ice shell (Carnahan et al., 2022; Kalousová Sotin, 2020; Tobie et al., 2005). Europa and other Galilean satellites also have oxidants present at the surface and potentially impurities within the ice shell (Buffo et al., 2020; Hand et al., 2006; Trumbo et al., 2019). The foundering of these mixed-component brines are not evaluated here, but in general impurities serve to decrease the melting temperature of ice and prolong the presence of melt, for example, Hesse et al. (2022). Finally, ocean worlds have different ice shell thicknesses, conductive lid thicknesses, and ice grain sizes (viscosities) (Barr Showman, 2009; Vance et al., 2018). These aspects of ocean worlds will likely be paramount in determining the extent of viscous impact melt foundering, due to their large influence on viscous dynamics and heat transfer (McKinnon, 1999). However, for all ice shell thicknesses and ice viscosities, we find that melt founders to the ocean on Europa. These simulations include ones where the conductive portion is 40 km thick, commensurate to the larger conductive lid thickness expected on Titan and Ganymede (Vance et al., 2018). Therefore, we suggest that melt foundering to the ocean likely occurs on ocean worlds similar to Europa, for example, Ganymede and Titan. Importantly, melt foundering occurs for all melt generating impacts investigated here, even if the melt does not reach the ocean, see Figures 1f–1j. Thus, our results suggest that viscous foundering may help to explain complex crater expression on Europa as well as on other, similar, ocean worlds. 4.2. Impact-Induced Cryovolcanism Actively erupting water vapor plumes have been identified on Europa (Huybrighs et al., 2020; Jia et al., 2018; Roth et al., 2014; Sparks et al., 2017), and impact melt chambers beneath Manannán Crater have been proposed as a potential source (Steinbrügge et al., 2020). Previous models of impact-induced cryovolcanism, and post-impact melt chambers more generally, assume that once formed the melt remains static within the ice (Bowling et al., 2018; Fagents, 2003; Fagents et al., 2000; Hedgepeth et al., 2022; Hesse Castillo-Rogez, 2019; Lesage Figure 3. (a) Image of Manannán Crater with visible collapsed and disrupted central massif (Pappalardo, Seeking Europa's Ocean, Proceedings of the International Astronomical Union, 6, S269, 101–114, reproduced with permission) (Pappalardo, 2010). (b) Percentage of initial impact melt chamber that drains into the ocean as well as the volume of the melt drained. Marked are locations of temperature and melt fraction shown in (c–l). Time series of temperature (c–g) and melt fraction (h–l) during the foundering of impact melts to the ocean below. Marked in red is the location of greater than 1% melt. Initial conditions taken from an iSALE simulation closely approximating the crater depth and diameter of Manannán Crater. The impactor has a cometary diameter of 916 m, a transient cavity depth of 8.2 km, and results in a final crater depth and diameter of 0.28 and 23.06 km, respectively (033.21 from Cox and Bauer (2015)). 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

8. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 8 of 12 et al., 2020; Quick et al., 2019; Steinbrügge et al., 2020). Our simulations suggest that in many cases this is a flawed assumption and that viscous deformation is an important aspect of the evolution of impact melts. On one hand, the drainage of impact melts in less than 10,000 years limits the duration of cryovolcanism by reduc- ing the volume of near-surface melt available for eruption (Figure 3b). Although it is possible some near-surface melt remains after the chamber has foundered, for example, the sill seen in Figure 3g, the remnant melt volume is a small fraction of the original, and, in the case of a Manannán-sized crater, freezes within 3,000 years of impact. The likelihood of cryovolcanism is also affected by the availability of near-surface melt due to downward melt percolation and drainage into fractures. The latter has been suggested as a potential mechanism for the formation of central pits (Bray et al., 2012; Elder et al., 2012). On the other hand, melt drainage generates a continuous high porosity column though the ice shell. In the case of a Manannán-sized crater, this channel reaches very close to the surface and remains open for over a thousand years. If the ocean is pressurized (Manga Wang, 2007) or contains gases that can exsolve (Melwani Daswani et al., 2021) this channel can serve as a potential pathway for ocean fluids to the surface. Connection of impact melts to deep fluids may extend cryovolcanism as suggested for Occator on Ceres (Hesse Castillo-Rogez, 2019; Quick et al., 2019; Raymond et al., 2020) and initiate the venting of ocean materials as observed on Enceladus (Porco et al., 2006), where the origin of the Tiger stripes at the south pole region remains enigmatic (Hemingway et al., 2019; Kite Rubin, 2016). Impacts may therefore be suitable sites to sample deep overpressured fluids and search for signs of life by forthcoming missions (Howell Pappalardo, 2020). The drainage of impact melts and the formation of porous columns through the crust of Europa will also influence impacts on other icy bodies and the resulting cryovolcanism there. An interesting counter example to drainage may be Occator Crater on Ceres, where the crust is ice-rich but has a higher density (Park et al., 2020), which may reverse the buoyancy of the brine, potentially increasing the longevity of cryovolcanism (Nathues et al., 2020; Neesemann et al., 2018; Scully et al., 2018). 4.3. Persistence of Near-Surface Melts and Oxidant Transport The viscous foundering of impact melts investigated here and the porous drainage of near-surface melt reser- voirs studied previously (Hesse et al., 2022; Kalousová et al., 2014, 2016) suggests that it is difficult to retain, or even accumulate, fluids in the near-surface of icy worlds. However, large volumes of melt are often invoked in the near surface of Europa to explain surface features such as chaotic terrains, domes, and lenticulae (Manga Michaut, 2017; Pappalardo Barr, 2004; Schmidt et al., 2011). For comparison, the volume of the rapidly foundering melt chamber beneath Manannán Crater in Figure 3a is only 30 km3 , three orders of magnitude less than the melt volumes suggested to be present in the near-surface beneath the chaos terrain Thera Macula (Schmidt et al., 2011). Our results show that maintaining such large melt volumes requires that the underlying ice remains cold and viscous during chaos formation to prevent foundering. Insisting on the stability of near-surface melt would therefore exclude chaos formation mechanisms that invoke hot upwelling in the underlying crust (Pappalardo et al., 1998; Sotin et al., 2002) and point toward formation by brittle processes, such as the injection of a sill (Chivers et al., 2021; Collins et al., 2000; Manga Michaut, 2017; Manga Wang, 2007). While drainage, or foundering, may prevent the accumulation of large near-surface melt pools, it does provide a transport mechanism from the near-surface to the ocean. This is important for the transport of surface-derived oxidants (Carlson et al., 1999; Hand et al., 2006, 2007; Spencer Calvin, 2002) that are required for redox gradients needed to sustain chemotrophic life in the underlying ocean (Chyba Phillips, 2001; Pasek Greenberg, 2012; Russell et al., 2017; Vance et al., 2016). Our results clearly show that even non-penetrating impacts lead to the drainage of impact melts from the surface into the ocean, but whether these melts incorporate surface generated oxidants requires further study. For example, it is not clear whether surface oxidants survive the impact and, if so, what fraction is mixed into the impact melt chamber. If the foundering of impact melts does transport oxidants to the ocean, the oxidant flux is inversely proportional to the ice shell thickness (Figure 2) and will decrease over time with the impactor flux (Zahnle et al., 1998). A rough estimate for the oxidant flux from the sinking of impact melt chambers on Europa can be made by calcu- lating the transient crater depth from the crater record of Europa (Moore et al., 2001) and comparing the transient cavity depths to the cut-off for melt drainage determined here. Several simplifying assumptions are necessary to make an estimate for the oxidant delivery rate. First, we merge three scaling relationships to estimate the 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

9. Geophysical Research Letters CARNAHAN ET AL. 10.1029/2022GL100287 9 of 12 final crater diameter that results in surface-to-ocean exchange for a given conductive ice thickness: (a) the criterion for melt drainage developed here, C/D = 0.5; (b) the ratio between transient cavity depth, C, and transient cavity diameter, θt, that is, C/θt = β (Cox Bauer, 2015; Gault Sonett, 1982; Melosh Ivanov, 1999); (c) the scaling between transient crater diameter and final crater diameter, θf, on Europa, 𝐴𝐴 𝐴𝐴𝑓𝑓 = 0.872(𝜃𝜃𝑡𝑡)1.087 (Cox Bauer, 2015), for which similar relationships that differ by ∼15% exist for other ocean worlds (McKinnon Schenk, 1995). Merging these three simplified relationships gives the minimum final crater diameter that will result in surface to ocean exchange as a function of conductive lid, or ice, thickness, 𝜃𝜃𝑓𝑓 = 0.872 ( 0.5 𝛽𝛽 𝐷𝐷 )1.087 . (8) Reasonable values for β range from 0.25 to 0.49 (Cox Bauer, 2015; Gault Sonett, 1982; Melosh Ivanov, 1999). We choose a conservative value for β of 0.35 (Cox Bauer, 2015). Assuming an upper bound ice shell conductive lid thickness of D = 10 km (Bray et al., 2014; Cox Bauer, 2015; Silber Johnson, 2017), Equation 8 implies that a crater diameter greater than ∼16 km results in surface-to-ocean exchange on Europa. Second, Artemieva and Lunine (2003) find that on Titan during an impact ∼10% of surface organics sustain mini- mal damage and mix with the melt. If we assume that 10% of the oxidants in the surface area of the crater (Hesse et al., 2022) are entrained into the melt chamber and 50% of the melt chamber drains to the ocean (Figure 2), this results in a total oxidant delivery of between 2 ⋅ 108 and 1012 kg from observed craters on Europa. Finally, given a resurfacing time of 40–90 Ma (Zahnle et al., 2003) results in a rate of oxidant delivery between 3 and 2 ⋅ 104 kg yr−1 (102 −6 ⋅ 105 mol yr−1 ). This oxidant delivery rate is four orders of magnitude lower than the amount estimated by melt percolation below chaos terrains (Hesse et al., 2022), reflecting the smaller fraction of Europa's surface area covered by impacts as opposed to chaos (Moore et al., 2001; Senske et al., 2018). Yet, unlike for chaos terrains, the energy source for near-surface melting beneath impacts is not speculative. Even if the impact melts don't transport oxidants, they are likely to entrain salts and other impurities and transfer them from the conductive lid into the underlying convective mantle and ocean. If the conductive lid is not renewed by resurfacing, repeated impacts would strip salts and other soluble materials from the conductive lid over time. If the conductive lid is stable over long timescales, the foundering of impact melts has the potential to significantly modify the composition of the conductive lid and ice shell in comparison to static models of freezing and salt incorporation (Buffo et al., 2020). 5. Conclusions We have investigated the post-impact viscous deformation of non-penetrating impacts into the ice shell of Europa. Our simulations show that impacts that generate significant melt chambers lead to substantial post-impact viscous deformation due to the foundering of the impact melts. If the transient cavity depth of the impact exceeds half the ice shell thickness the impact melt drains into the underling ocean and forms a continuous surface-to-ocean porous column. Foundering of impact melts leads to mixing within the ice shell and the transfer of melt volumes on the order of tens of cubic kilometers from the surface of Europa to the ocean. This foundering of large volumes of melt below craters likely alters crater morphology, affects cryovolcanism, and may contribute to the habitability of oceans within icy worlds. This study shows foundering of impact melts is a viable, robust, and likely widespread transport mechanism for surface materials to the ocean of Europa. Interesting directions for future work include examining the effects of ice shell thermal structure, salts, impurities and melt drainage by porous and fracture flow on this surface-to-ocean exchange process, as well as evaluating the detailed geomorpholgical changes to craters this process likely causes. While this study has focused on Europa, the viscous foundering of impact melts to the ocean occurs for all ice shell thickness and ice viscosites explored here, and is therefore likely to occur on other icy worlds similar to Europa, for example, on Titan. Data Availability Statement The numerical model, initial conditions for the simulations, and code to make figures are available at https://doi.org/10.5281/zenodo.7343693. 19448007, 2022, 24, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2022GL100287 by CAPES, Wiley Online Library on [20/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

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