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

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
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CARNAHAN ET AL.
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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 mate-
rials 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 trans-
fer 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
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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
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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 rela-
tive 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.
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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 cham-
ber 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 gener-
ated 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 cool-
ing 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.
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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 morphol-
ogies 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 approxi-
mates 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 founder-
ing 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
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Titan is distinct amongst ocean worlds in our Solar System as it has liquid hydrocarbons at the surface and meth-
ane 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 tempera-
ture of ice and prolong the presence of melt, for example, Hesse et al. (2022). Finally, ocean worlds have differ-
ent 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)).
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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
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final crater diameter that results in surface-to-ocean exchange for a given conductive ice thickness: (a) the crite-
rion 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 trans-
fer 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 habita-
bility 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.
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Acknowledgments
E.C. acknowledges the Student Research
Award in Planetary Habitability by the
UT Center for Planetary Systems Habit-
ability and a NASA/Texas Space Grant
Consortium Fellowship. M.A.H acknowl-
edges funding for the development of the
Enthalpy method from NASA-EW Grant
80NSSC19K0505 and NSF-DMS Grant
1720349. Part of the research was carried
out at the Jet Propulsion Laboratory,
California Institute of Technology,
under a contract with the National
Aeronautics and Space Administration
(80NM0018D0004). Work by EC and
SDV was supported by the NASA Astro-
biology Institute's Hydrocarbon Worlds
project (17-NAI8-0017).
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