A combination of geological interpretations and thermal-orbital evolution models imply that Pluto’s large moon, Charon, had a subsurface water (and possibly ammonia) ocean that eventually froze. Ocean freezing generates large tensile stresses in the upper part of the ice shell and pressurizes the ocean below, perhaps leading to the formation of Charon’s large canyons and putative cryovolcanic flows. Here, we identify the conditions in which a freezing ocean could create fractures that fully penetrate its ice shell, linking Charon’s surface with its ocean and facilitating ocean-sourced cryovolcanism. We find that current models of Charon’s interior evolution predict ice shells that are far too thick to be fully cracked by the stresses associated with ocean freezing. Either Charon’s ice shell was <10 km thick when the flows occurred (as opposed to >100 km) or the surface was not in direct communication with the ocean as part of the eruptive process. If Charon’s ice shell had been thin enough to be fully cracked, it would imply substantially more ocean freezing than is indicated by the canyons, Serenity and Mandjet Chasma. Due to the low radiogenic heating within Charon and the loss of tidal heating early in its history, a thin ice shell should have been short-lived, implying that ocean-sourced cryovolcanic flows would have ceased relatively early in Charon’s history, consistent with interpretations of its surface geology. An additional (and perhaps implausibly large) heat source would be required to generate the substantially larger ocean implied by through-going fractures. We also find that ocean freezing can easily generate deep fractures that do not fully penetrate to the ocean, which may be the foundation of Charon’s canyons. Plain language summary: When ocean-bearing moons begin to cool down, their oceans can freeze. As new ice accretes to the bottom of the existing ice shell, the added volume of the ice can stress the shell. Pluto’s largest moon, Charon, has canyons and cryovolcanic flows that may have formed in response to a freezing ocean. Here, we model the formation of fractures within Charon’s ice shell as the ocean underneath it freezes to explore the evolution of Charon’s interior and surface. We find that an ocean source for cryovolcanic flows is unlikely because the ice shell would have had to be much thinner than current thermal evolution models imply. However, freezing the ocean may have produced the stresses that formed canyons later in Charon’s history.

1. Icarus 392 (2023) 115391
Available online 5 December 2022
0019-1035/© 2022 Elsevier Inc. All rights reserved.
The challenges of driving Charon’s cryovolcanism from a freezing ocean
Alyssa Rose Rhoden a,*,1
, Maxwell L. Rudolph b
, Michael Manga c
a
Southwest Research Institute, Boulder, CO, United States of America
b
Department of Earth and Planetary Sciences, University of California, Davis, United States of America
c
Department of Earth and Planetary Science, University of California, Berkeley, United States of America
A R T I C L E I N F O
Keywords:
Tectonics
Icy satellites
Charon
Cryovolcanism
A B S T R A C T
A combination of geological interpretations and thermal-orbital evolution models imply that Pluto’s large moon,
Charon, had a subsurface water (and possibly ammonia) ocean that eventually froze. Ocean freezing generates
large tensile stresses in the upper part of the ice shell and pressurizes the ocean below, perhaps leading to the
formation of Charon’s large canyons and putative cryovolcanic flows. Here, we identify the conditions in which a
freezing ocean could create fractures that fully penetrate its ice shell, linking Charon’s surface with its ocean and
facilitating ocean-sourced cryovolcanism. We find that current models of Charon’s interior evolution predict ice
shells that are far too thick to be fully cracked by the stresses associated with ocean freezing. Either Charon’s ice
shell was <10 km thick when the flows occurred (as opposed to >100 km) or the surface was not in direct
communication with the ocean as part of the eruptive process. If Charon’s ice shell had been thin enough to be
fully cracked, it would imply substantially more ocean freezing than is indicated by the canyons, Serenity and
Mandjet Chasma. Due to the low radiogenic heating within Charon and the loss of tidal heating early in its
history, a thin ice shell should have been short-lived, implying that ocean-sourced cryovolcanic flows would have
ceased relatively early in Charon’s history, consistent with interpretations of its surface geology. An additional
(and perhaps implausibly large) heat source would be required to generate the substantially larger ocean implied
by through-going fractures. We also find that ocean freezing can easily generate deep fractures that do not fully
penetrate to the ocean, which may be the foundation of Charon’s canyons.
Plain language summary: When ocean-bearing moons begin to cool down, their oceans can freeze. As new ice
accretes to the bottom of the existing ice shell, the added volume of the ice can stress the shell. Pluto’s largest
moon, Charon, has canyons and cryovolcanic flows that may have formed in response to a freezing ocean. Here,
we model the formation of fractures within Charon’s ice shell as the ocean underneath it freezes to explore the
evolution of Charon’s interior and surface. We find that an ocean source for cryovolcanic flows is unlikely
because the ice shell would have had to be much thinner than current thermal evolution models imply. However,
freezing the ocean may have produced the stresses that formed canyons later in Charon’s history.
1. Introduction
With the new data sets delivered by the New Horizons mission, more
informed and refined models of Charon’s coupled orbital-interior evo­
lution have been produced (Desch and Neveu, 2017; Malamud et al.,
2017; Bierson et al., 2018; Spencer et al., 2021; Bagheri et al., 2022 and
references therein). While they differ in underlying assumptions and
model complexity, most of these studies find similar results: Charon’s
orbit rapidly circularizes and synchronizes, and a relatively thin (~50
km) ocean forms under >100 km of ice before freezing out entirely.
Thermal evolution models can be affected by the orbital evolution of
Pluto and Charon, as well as the chemical and physical properties of
their interiors, for which there is substantial uncertainty. While the
models generally support a past ocean within Charon during its evolu­
tion, Charon’s geology can offer additional constraints on the true
extent, both in longevity and volume, of Charon’s ocean. For example,
Charon has multiple large chasmata – elongated, steep-sided depressions
– that are visible within the encounter hemisphere (Fig. 1), which are
indicative of global extension (Spencer et al., 2021). The strain inferred
from the observed features is consistent with the volume change
* Corresponding author at: Southwest Research Institute, 1050 Walnut St. #300, Boulder, CO 80302, United States of America.
E-mail address: Alyssa@boulder.swri.edu (A.R. Rhoden).
1
Previously published under the surname Sarid.
Contents lists available at ScienceDirect
Icarus
journal homepage: www.elsevier.com/locate/icarus
https://doi.org/10.1016/j.icarus.2022.115391
Received 15 August 2022; Received in revised form 22 November 2022; Accepted 2 December 2022

2. Icarus 392 (2023) 115391
2
associated with freezing of a ~ 35 km thick ocean (Beyer et al., 2017;
Spencer et al., 2021). Given the limited resolution of images on the non-
encounter hemisphere, it is possible that additional canyon features
exist elsewhere on Charon’s surface, so this constraint provides a lower
bound on the extent of ocean freezing.
A freezing ocean will generate large tensile stresses that can produce
radial fractures many kms deep (Hillier and Squyres, 1991; Nimmo,
2004; Manga and Wang, 2007). In some cases, the fractures can pene­
trate the entire ice shell and tap the subsurface ocean (Rudolph and
Manga, 2009; Hemingway et al., 2020; Rudolph et al., 2022). Because
the ocean is also pressurized by the increase in volume of the newly
frozen ice, water can enter through-going fractures and erupt onto the
surface (Manga and Wang, 2007). Hence, ocean freezing can facilitate
cryovolcanism by both creating conduits in response to cooling stress
and helping to overcome the challenge of erupting higher density liquid
onto lower density ice. Charon’s surface shows evidence of cryovolcanic
flows in the form of smooth plains (Fig. 1) and even a mountain that
appears surrounded by lower viscosity material (Spencer et al., 2021,
and references therein). If the smooth material is cryolava that came
from the subsurface ocean, its composition may be indicative of the
(past) ocean’s composition.
While it has been shown that the extent of ocean freezing in thermal
evolution models should provide sufficient ocean pressure to drive
eruptions (Desch and Neveu, 2017), the viability of generating conduits
through the ice shell from ocean freezing has not been assessed. Here,
we build upon the model of Rudolph et al. (2022) to calculate the
cooling stresses and eruptive potential of a freezing ocean within
Charon. We consider the penetration depth of fractures to be the initial
limiting factor for ocean-sourced eruptions. Hence, we evaluate the
response of the ice shell to the ice-ocean configurations implied by
thermal models and then identify the maximum ice shell thickness for
which through-going fractures can form. We find that, in order to create
conduits between the ocean and surface of Charon, the ice shell would
need to have been substantially thinner than current thermal models
predict, which requires a previously unidentified source of internal heat.
In that case, the additional volume change must have been accommo­
dated by canyons that we have not yet observed, accommodated by
some other geologic process, or somehow erased from Charon’s geologic
record. In all cases in which fractures penetrate to the ocean, liquid
water can be brought close to the surface, although ocean overpressure
alone is insufficient to extrude material onto the surface. Thus, there are
additional challenges that must be overcome for a global ocean to be the
source of Charon’s cryovolcanic material. In contrast, cooling stresses
can easily make deep fractures within the ice shell throughout the
freezing process, perhaps providing the initiation point of Charon’s
canyons.
2. Background
Thermal-orbital models of the co-evolution of Pluto and Charon
provide a framework in which to interpret Charon’s geologic features.
Although most models produce a subsurface ocean 10s of km thick (e.g.,
Desch and Neveu, 2017; Bierson et al., 2018; Bagheri et al., 2022), they
differ in the expected lifetime of the ocean and how recently it froze.
Bierson et al. (2018) suggests the ocean was lost billions of years ago,
while Bagheri et al. (2022) found that the ocean persists until ~500 Myr
ago. Desch and Neveu (2017) suggest there was a second period in
which a thin, deep subsurface ocean formed and refroze. In all of these
cases, despinning and orbit circularization are so rapid that evidence of
these processes is unlikely to be present in the geologic record, and the
ocean’s longevity is related to the availability of radiogenic heating, as
opposed to tidal heating. For example, Bagheri et al. (2022) find that
Charon’s ocean is long-lived (~3.5 Gyr) because the heat generated
within the silicate interior is balanced by transport into and through the
shell, thereby avoiding freezing. By 500 Myr ago, the internal heating
sources had decayed sufficiently that the ocean would have completely
frozen.
Studies of “cooling cracks”, which form in response to the tensile
stresses produced by ice shell expansion and ocean pressurization, have
found that the largest controls on the penetration depth of the cracks –
and thus, the propensity to generate conduits for cryovolcanism – are the
gravity of the body and the failure strength assumed for the ice (e.g.,
Rudolph et al., 2022). The cooling cracks initiate within the cold, elastic
ice near the surface and propagate bidirectionally upward and down­
ward. The cracks, which are not filled with water, are hindered from
propagating through the warmer basal portion of an ice shell by the lack
of deviatoric stresses in warmer, viscous ice and by lithostatic
compression. At Europa, the relatively high gravity makes it challenging
to crack through even a 1 km thick ice shell because the overburden
pressure at depth overcomes the cooling stress driving failure. Although
deep fractures can be made via this process, and may be important for
initiating other types of tectonic activity on Europa, eruptions of ocean
water from through-going cooling cracks are unlikely. At Enceladus, on
the other hand, the low gravity enables cooling cracks to reach the ocean
even when the ice shell is of order 10 km thick (Rudolph and Manga,
2009; Rudolph et al., 2022), which may be the mechanism by which the
Tiger Stripe fractures originated (Hemingway et al., 2020). Charon’s
gravity is intermediate between Enceladus and Europa, suggesting that
through-going cracks might be possible but perhaps limited to thinner
shells than at Enceladus.
Past work on cooling cracks adopted failure strengths for the ice shell
of either 1 MPa or 3 MPa (Rudolph and Manga, 2009; Rudolph et al.,
2022), which are consistent with range of tensile failure strengths of
pure, intact ice in laboratory experiments (Schulson, 2006; Collins et al.,
2009). The orientations of surface fractures on both Enceladus and
Europa are consistent with failure when tidal stresses reach 100s of kPa,
or less (e.g., Rhoden et al., 2020; Rhoden et al., 2021), but it is not clear
whether the ice is actually weaker than the laboratory studies suggest (e.
g., due to scale or fatigue) or that cooling stresses also contribute to
failure (as in Nimmo, 2004). If the tensile failure strength of ice shells is
substantially lower than 1 MPa, it becomes easier to form fractures via
Fig. 1. Charon’s encounter hemisphere displays a vast region of smooth plains,
interpreted as cryovolcanic flows, south of its large canyon systems, within the
region labelled Vulcan Planum. Serenity Chasma runs toward the right of the
image while Mandjet Chasma spans the left side. Both Charon’s cryovolcanism
and its chasmata have been attributed to an epoch of ocean freezing. (Image
credit: We have labelled features of note atop PIA19968.)
A.R. Rhoden et al.

3. Icarus 392 (2023) 115391
3
cooling, but they will not penetrate as deeply and eruptions will be less
likely. Given that eruptions occur on Enceladus, it seems likely that the
ice, at least at depth, fails at high stress.
3. Methods
We adopt an interior structure for Charon that is consistent with New
Horizons measurements and recent modeling studies, in which Charon is
differentiated into a rocky interior and outer ice shell (Spencer et al.,
2021). Parameters that characterize the interior and remain constant
throughout the simulations are listed in Table 1. As a preliminary test,
we explored a range of initial ice shell thicknesses and found that the ice
shell thickness at the beginning of our simulation did not have a strong
effect on the properties of cracks that form as the ice shell thickens and
cools. For a variety of material parameters (see Table 2), we identify the
maximum thickness for through-going cracks and assess the ability for
ocean material to reach the surface through the cracks. We then compare
the ice shell thicknesses with the conditions predicted by thermal
models (e.g., Desch and Neveu, 2017; Bierson et al., 2018; Bagheri et al.,
2022).
We apply the model of Rudolph et al. (2022), which tracks the
thermal evolution of an ice shell and the resulting cooling stresses and
ocean pressurization as the ocean freezes. A major component of
Rudolph et al. (2022) was assessing the effects of a periodically-varying
eccentricity on the thermal state of an ice shell. Here, we model ocean
freezing after orbit circularization, in which tidal heating is no longer
significant. Hence, we can focus solely on secular cooling, which leads to
monotonic ice shell thickening. The model solves the coupled equations
for heat transport by conduction through a cooling ice shell, latent heat
release by freezing, thermo-visco-elastic deformation of the ice, and
couples deformation of the ice shell to pressure in the ocean. We include
strongly temperature-dependent viscosity, which leads to rapid relaxa­
tion of deviatoric stresses in the warmer ice in the lower portion of the
ice shell. Cold ice near the surface can support deviatoric elastic stresses
over the 108
yr timescale of ocean solidification. Appendix A summa­
rizes the governing equations. The penetration of cracks, once the tensile
strength of ice is exceeded, is determined by balancing depth integrated
tensile loading and lithostatic compression.
If the initial ocean within Charon contained ammonia, ocean water
that freezes and accretes to the base of the ice shell would still be pure
water, and the ammonia concentration in the ocean would increase as it
thins (e.g., discussion in Spencer et al., 2021). Adding ammonia to the
system will depress the melting temperature and slow down the shell
thickening process. It may also affect the depths to which cracks can
penetrate by changing the temperature, and hence, viscosity within the
ice shell. Ammonia in the ocean can also help overcome the density
challenge inherent to erupting liquid water onto overlying water ice.
The content of non-water ices within Charon is presently unknown, so
we test the ability of ocean material to erupt on to the surface using
initial ammonia concentrations up to 10%.
We account for the influence of ammonia on ocean density,
compressibility, and thermal expansivity using the equation of state of
Croft et al. (1988). For ammonia concentrations <32.9%, the ammonia-
water mixture in the ocean is in equilibrium with pure water ice. The
evolution of ammonia concentration (X) in the ocean is described by
dX
dz
= − 4π(ri − z)2X
V
(1)
where ri is the initial radius of the ocean-ice interface, z is the amount of
ice shell thickening relative to ri (in units of distance, with positive
numbers indicating increasing ice shell thickness), and V is the current
ocean volume. Our model is similar to that used by Martin and Binzel
(2021) for a water+ammonia ocean on Pluto, but we account for the
thermal structure and evolution of the ice shell and their impacts on
stresses and crack propagation.
The presence of ammonia modifies the freezing temperature of the
ocean (TM), which sets the temperature at the ocean-ice interface. Pure
water freezes at 273.15 K, and a mixture with 32.9% ammonia solidifies
at 165.6 K. Thus, if ice shell thickness increases, the ammonia concen­
tration in the ocean increases, and the ocean temperature decreases.
This temperature decrease requires the removal of sensible heat from the
ocean by upward conduction through the ice shell. We account for the
change in ocean temperature associated with the effect of changing
ammonia concentration on the melting temperature through an effective
latent heat of fusion, Leff, using:
Leff =
dU
dT
dTM
dX
dX
dz
(2)
where dU/dT = Vρcp /A is the change in internal energy of the entire
ocean per unit change in temperature per unit area at the ocean-ice
interface, V is ocean volume, A is area of ocean-ice-interface, ρ is the
ammonia-water density, and cp is the ammonia-water specific heat ca­
pacity. The second term of Eq. (2) accounts for the change in melting
temperature with respect to ammonia concentration, and the last term
accounts for the change in ammonia concentration with respect to a
change in ice shell thickness. Leff is an effective latent heat capacity that
is combined with the latent heat of fusion when solving the coupled
Table 1
Parameters held constant across all simulations.
Interior structure & global parameters
Charon’s radius R 606 km
Silicate interior thickness rc 376 km
Hydrosphere thickness R-rc 230 km
Surface gravity g 0.279 m/s2
Ice shell properties
Temperature at ice shell base (H2O ocean) TM 273 K
Young’s modulus E 5 × 109
Pa
Poisson ratio ν 0.3
Density of ice ρi 900 kg/m3
Freezing/melting parameters
Coefficient of linear thermal expansion αl 3 × 10− 5
K− 1
Compressibility of water β 4 × 10− 10
Pa− 1
Activation energy Q 40 kJ/mol
Heat capacity of ice Cp 2100 J kg− 1
K− 1
Latent heat of fusion L 3.34 × 10− 5
J kg− 1
Table 2
Test cases and outcomes.
Surface
temp (K)
Ice viscosity μb
(Pa-s)
Failure
strength
(MPa)
Cutoff for
conduits (km)
Charon
100%
H2O
40 1.00E+13 1 2.9
60 1.00E+13 1 2.5
40 1.00E+14 1 3.3
60 1.00E+14 1 3.0
40 1.00E+13 3 8.5
60 1.00E+13 3 7.3
40 1.00E+14 3 9.3
60 1.00E+14 3 8.4
Surface
temp (K)
Ice viscosity
μb (Pa-s)
Failure
strength
(MPa)
Cutoff for
conduits (km)
Charon 90%
H2O 10%
NH3
40 1.00E+13 1 3.0
60 1.00E+13 1 2.5
40 1.00E+14 1 3.2
60 1.00E+14 1 3.0
40 1.00E+13 3 8.2
60 1.00E+13 3 6.5
40 1.00E+14 3 9.1
60 1.00E+14 3 8.0
A.R. Rhoden et al.

4. Icarus 392 (2023) 115391
4
thermal-mechanical equations numerically.
An initial set of sensitivity tests revealed that the depth and fre­
quency of cooling cracks are affected by the surface temperature and the
melting point viscosity at the base of the ice shell. A colder surface leads
to steeper temperature gradients that drive more rapid ice shell thick­
ening, as well as a thicker elastic layer of ice, causing stresses to accu­
mulate faster. More viscous ice slows stress relaxation and leads to a
thicker elastic layer and larger stresses. We use surface temperatures of
40 K and 60 K, which are within the range of surface temperatures
predicted for Charon (e.g., Grundy and 33 Colleagues, 2016). We test
values for the melting point viscosity of 1013
and 1014
Pa s and,
following previous work (Rudolph et al., 2022), test failure strengths of
1 MPa and 3 MPa.
These simulations are most applicable to the freezing that occurs
once the orbit is circular and tidal heating is no longer contributing to
Charon’s heat budget. In that case, the timescale of ocean freezing is
controlled by the heat generation within Charon’s silicate interior and
its ability to be transported to and through the ice shell. For our main
suite of simulations, we do not add any heat to the base of the ice shell
(equivalent to assuming zero radiogenic heating), so ocean freezing is
maximized. As a result, the ocean fully freezes within the 250 Myr
timescale of the simulation rather than happening within 500 Myr (as in
Bagheri et al., 2022) or longer (1 Gyr, Spencer et al., 2021). Sensitivity
tests with a basal heat flux of 3 mW/m2
revealed no substantive changes
in our results (see SOM).
4. Results
Table 2 lists the parameters tested for Charon and reports the thickest
shells that can be fully breached by a cooling crack in each case. Here,
we show results using either a pure water ocean or a mixed water-
ammonia ocean with initial ammonia contents of up to 10%. We find
that the ice shell must be no thicker than ~9 km (with a 3 MPa failure
strength) or ~ 3 km (with a 1 MPa failure strength) to create through-
going fractures from ice shell thickening. In general, cracks can pene­
trate deeper into an ice shell with a higher tensile failure strength or a
lower surface temperature; a higher ice viscosity only slightly increases
the depths of cracks. For all other parameters being equal, changing the
tensile failure strength from 1 MPa to 3 MPa increases the maximum
thickness at which an ice shell can be fully breached by a cooling crack
Fig. 2. A) For an initial ice shell thickness of 2 km, fractures can connect the
ocean to the surface. Vertical red lines are plotted at times when failure is
predicted, and the vertical extent of the lines shows the depths over which
fractures would extend. B) The time evolution of ocean overpressure is shown,
with red and green symbols indicating the pressure immediately before and
after cracks form. Blue vertical dashed lines indicate times at which cracks
connect the ocean to the surface. The black curve indicates the critical excess
pressure needed to extrude water onto the surface. C, D) In a thicker shell (here,
initially 30 km), fractures are never able to penetrate the entire thickness of the
shell, but deep fractures can form throughout the simulation. (For interpreta­
tion of the references to colour in this figure legend, the reader is referred to the
web version of this article.)
Fig. 3. As in Fig. 2, but with 10% ammonia in the initial ocean and an initial ice
thickness of 2 km. The presence of ammonia extends the lifetime of the ocean,
but it does not enable eruptions of ocean material or extend the range of ice
shell thicknesses that can be fully cracked. A) Fractures can connect the ocean
to the surface at early times. Vertical red lines are plotted at times when failure
is predicted, and the vertical extent of the lines shows the depths over which
fractures would extend. B) The time evolution of ocean overpressure is shown,
with red and green symbols indicating the pressure immediately before and
after cracks form. Blue vertical dashed lines indicate times at which cracks
connect the ocean to the surface. The black curve indicates the critical excess
pressure needed to extrude water onto the surface. Although there are times in
which the ocean pressure would exceed this limit, there are no through-going
conduits because the ice shell has become too thick. C) Evolution of
ammonia mass fraction. Simulations are truncated when the ammonia content
exceeds 32.9%. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
A.R. Rhoden et al.

5. Icarus 392 (2023) 115391
5
by roughly a factor of 3, which is the most substantial effect. In contrast,
higher surface temperature, lower failure stress, and lower melt vis­
cosity reduce the depth of fractures, requiring thinner ice shells in order
to connect the surface with the ocean.
In Fig. 2, we show the evolution of ice shell thickness over time,
starting with a 2 km shell (2A,B) or a 30 km shell (2C,D), using the
parameter values highlighted in green in Table 2. In both cases, the
ocean is fully frozen within the timescale of the simulation. Adding
ammonia increases the freezing timescale, although these simulations
were truncated when the ammonia concentration in the ocean exceeded
the limit of our analytical treatment, so we could not obtain a timescale
for complete freezing of the ocean in these cases. In Fig. 2A and C, the
colored region represents the ice shell, with the colour bar showing the
tensile stresses accumulating within the shell as it thickens. Red, vertical
lines show fractures that form within the ice shell as a result of cooling
stresses. Cracks of varying depths are formed throughout both simula­
tions. With a 70 km thick ocean, consistent with the results of past
thermal models, no conduits are generated by ice shell cooling through
which water could then reach the surface. We can, therefore, conclude
that cooling cracks did not create conduits for ocean-sourced cry­
ovolcanic flows on Charon if the ocean was only 70 km thick (or less), as
indicated by past studies (Desch and Neveu, 2017; Bierson et al., 2018;
Bagheri et al., 2022).
In Fig. 2B and D, we show the corresponding evolution of ocean
pressure. Blue, vertical, dashed lines indicate the times at which
through-going fractures form, linking the ocean with the surface. The
black curve indicates the pressure required to extrude ocean material
onto the surface. Until the ice shell reaches a thickness of ~9 km, with a
3 MPa failure strength, cracks can fully penetrate the shell. In thicker ice
shells, fractures continue to form, but their propagation is arrested
within the shell. In cases that produce through-going fractures, the
ocean pressure is insufficient to drive eruptions all the way to the sur­
face. Even with the addition of ammonia to the ocean (Fig. 3), which
reduces the critical overpressure necessary to erupt water, the pressure
is insufficient to fully erupt at a time when cracks can penetrate through
the entire shell. It is possible that an additional effect enables eruptions
(e.g., exsolution of dissolved gases in the ocean or decompression
boiling) or that the liquid can interact with the existing geologic features
to modify the surface without actually being extruded.
Given that continued geologic activity can obscure the evidence of
eruptions (e.g., through cratering), it is possible that more cryovolcanic
events occurred on Charon than are preserved in the current geologic
record. Achieving numerous eruption events through the freezing pro­
cess would require that the shell was even thinner than the values we
report such that there is sufficient growth of the shell to create multiple
cracking epochs. Hence, if the observed surface flows were created by
extruded ocean material during ocean freezing, nearly the entire ~230
km cryosphere had to have melted and refrozen. Fractures that do not
fully penetrate to the ocean can form even in the thickest shells we tested
(170 km), and throughout the simulations (Figs. 2 and 3 at late times).
When the ice shell is relatively thin, the fractures penetrate nearly the
entire shell thickness. As the shell thickens, the fractures can grow to 10s
of km, but they are generally limited to less than half the total ice shell
thickness. Given the propensity for cooling cracks to form, if an ocean
ever existed within Charon, we would expect that fractures formed as a
result of the ocean freezing. The tensile stresses from cooling may have
facilitated the formation of Charon’s canyon systems.
5. Discussion
We find that cracks formed in response to Charon’s freezing ocean
could only breach its entire ice shell when the shell was thinner than
~10 km, with the limit depending on the exact parameter values used
(Table 2). Thermal-orbital evolution models do not support the high
degree of melting that would be required to create such a thin shell
(Desch and Neveu, 2017; Malamud et al., 2017; Bierson et al., 2018;
Spencer et al., 2021; Bagheri et al., 2022 and references therein). Rather,
published models find an ocean thickness of 30–70 km overlain by
200–160 km of ice, or no ocean in the case of Malamud et al. (2017). To
test parameter sensitivity, Bagheri et al. (2022) included one scenario in
which they set the initial ocean thickness to 170 km (in contrast to their
nominal case of 15 km), but without any specific mechanism to create it.
Even in that case, the ocean solidifies down to ~50 km thickness within
about 500 Myr after Charon’s formation and remains close to that
thickness until it rapidly freezes within the last 500 Myr.
Combined with our findings, these results suggest that ocean-sourced
cryovolcanic activity on Charon requires a mechanism that produces
significantly more internal heating than currently predicted in order to
create the conduits for eruptions, which may not be plausible. Also, such
activity can only occur during the epoch in which the ocean freezes from
an initial thickness of ~220 km (ice shell <10 km thick) because late
freezing of a 30–70 km ocean cannot crack the entire ice shell. In
addition, ocean pressurization can only get material near the surface;
generating surface flows requires an additional mechanism. If an extra
heat source led to an initially thick ocean that rapidly froze, such as in
the example from Bagheri et al. (2022), it would imply that the pur­
ported cryovolcanic features are among the oldest features on Charon.
Based on stratigraphic relationships, combined with crater counts,
Robbins and 28 Colleagues (2019) propose that the smooth plains of
Vulcan Planum were emplaced via some form of cryovolcanism after the
formation of Oz Terra, ~ 4 Gyr ago. Such an interpretation would be
consistent with our finding that ocean-sourced cryovolcanism could
only have occurred in the earliest part of Charon’s history. However,
given the challenges in both producing a thin enough shell to fully crack
and erupting ocean material onto the surface, it is also entirely possible
that cryovolcanism on Charon was not driven by freezing of a global
ocean.
Ocean freezing has also been suggested as the source of stress by
which Charon’s chasmata and graben formed. According to Beyer et al.
(2017), Serenity Chasma has a minimum depth of 3 km, and Mandjet
Chasma is 5 km deep; these depths are consistent with normal faults that
penetrate 10s of km (Beyer et al., 2017). Our results show that radial
fractures can form quite readily in response to Charon’s ocean freezing,
and they can penetrate 10s of km deep as the ice shell thickens. How­
ever, the ice shell must be ~50 km or thicker to generate such long
fractures. Models that move beyond one spatial dimension (radial po­
sition, here) are required to ascertain how radial faulting from ice shell
cooling could be related to the formation of Charon’s laterally-extending
chasmata.
The observed chasmata and scarps on Charon indicate areal strain of
1%, which is consistent with the volumetric change caused by a deep,
~35 km ocean freezing (Beyer et al., 2017). If Charon did possess a ~
220 km thick ocean that later froze, it would imply >6% areal strain,
using the same equations and parameter values as Beyer et al. (2017),
which is substantially more than has been identified in the geologic
record to date. Only one side of Charon has been observed in detail (e.g.,
Spencer et al., 2021), so other canyon systems may be present, although
their total extent would need to dwarf those already identified on
Charon. Identifying additional canyons, or other mechanisms by which
strain can be accommodated, may be the best test of Charon’s past ocean
thickness and ability to host ocean-sourced cryovolcanism.
If both the chasmata and cryovolcanism resulted from ocean
freezing, they place some constraints on the relative timing of activity on
Charon. Our simulations suggest that through-going fractures would
form first, enabling eruptions. Later, as the ocean freezes and the ice
shell thickens, fractures would no longer reach the ocean, instead
forming deeper cracks that could become the basis for Charon’s chas­
mata and grabens. Hence, ocean-sourced cryovolcanism should cease
fairly early, followed by the formation of extensional features that
accommodate Charon’s change in volume. Any later cryovolcanism
would have to be sourced from material within the ice shell or reach the
surface through means other than cooling cracks. Additional, detailed
A.R. Rhoden et al.

6. Icarus 392 (2023) 115391
6
investigations of Charon’s geologic history are needed to determine
whether this chronology is consistent with observations.
An additional open question is what controls the diversity and cre­
ation of canyons and chasmata on icy satellites. Like Charon, Tethys
(moon of Saturn) has negligible present-day eccentricity and a large
canyon system, Ithaca Chasma. The two moons are similar in radius, but
Charon’s density is much larger, indicating a higher rock fraction. As
with Charon, it is thought that Tethys went through a period of tidal
dissipation that circularized its orbit and generated a subsurface ocean
that later froze out (Castillo-Rogez et al., 2018, and references therein),
a hypothesis that is supported by Tethys’ relaxed craters (White et al.,
2017). As shown in Beyer et al. (2017), Serenity Chasma and Ithaca
Chasma have similar depths, but Ithaca is about twice the width. In
addition, Ithaca Chasma is centered on Tethys’ sub-Saturn point, sug­
gesting that perhaps tides played a role in determining its initiation
location, whereas Charon’s chasmata are not currently co-located with
its tidal axis.
Saturn’s moons Enceladus and Dione, and Jupiter’s moon Europa, all
possess subsurface oceans that likely experienced some amount of ocean
freezing due to the reduced impact of early heat sources and changes in
their orbital eccentricities (Neveu and Rhoden, 2019 and references
therein; Hussman and Spohn, 2004). Curiously, while these moons
display extensional tectonic features (e.g., Patterson et al., 2018; Schenk
et al., 2018; Kattenhorn and Hurford, 2009), none of them have canyons.
Determining the factors that govern which types of extensional features
form as a result of ocean freezing would be highly valuable in disen­
tangling the different histories and mechanical properties of these
moons.
6. Conclusions
Both Charon’s extensional tectonics, mainly in the form of chasmata
and large graben structures, and its putative cryovolcanic flows have
been attributed to freezing of a past internal ocean. Here, we present a
quantitative assessment of this process on Charon. We find that ocean
freezing can create radial fractures that penetrate from surface to ocean,
early in Charon’s history. However, the ice shell must have been an
order of magnitude thinner than thermal-orbital models have thus far
suggested to create conduits that could facilitate cryovolcanism. While
through-going conduits will partially fill with ocean material, our
models do not yet provide a mechanism to extrude that material onto the
surface. Although the addition of ammonia can prolong the lifetime of
the ocean, it does not enable through-going fractures from the freezing
of a 30–70 km thick ocean or the eruption of ocean material onto
Charon’s surface. Although we consider the generation of upward-
propagating cracks to be mechanically challenging because of the
rapid relaxation of stresses near the ocean-ice interface, upward prop­
agating cracks may, in principle, breach a thicker ice shell.
In cooling ice shells thicker than ~10 km, fractures can continue to
form, but they cannot penetrate to the ocean. These fractures may be the
initiation points of Charon’s chasmata. Further analysis is needed to
understand the evolution of canyons and how extension caused by ocean
freezing manifests across ocean worlds. If additional large extensional
features were identified on Charon’s non-encounter hemisphere, or
compositional analysis could prove that Charon’s cryovolcanism was
sourced from the ocean, it would support the idea that Charon’s ocean
was substantially thicker than currently expected. Ocean freezing also
predicts a sequence of geologic activity, in which ocean-sourced cry­
ovolcanism ceases before strain accommodation via tectonism. More
detailed analysis of Charon’s geologic record could help determine
whether such a scenario is viable.
Declaration of Competing Interest
None.
Data availability
Data will be made available on request.
Acknowledgements
This work was supported by NASA’s Solar System Working program
(80NSSC19K1026 to AR and 80NSSC22K1379 to MM and MR). Source
code and output files related to this work can be found at
https://zenodo.org/record/7336096#.Y3gG3-zMKgk.
Appendix A. Temperature, stress, and rheological evolution models
The evolution of stresses that lead to tensile failure and overpressure in the ocean depend on the thermal evolution of the ice shell, which governs
its rheology and hence the accumulation and relaxation of stresses. Here, we summarize the governing equations, closure models, and approximations.
Charon is approximated as a spherically symmetric body so that we only need to consider thermal and mechanical processes and properties in one
(radial) spatial dimension. We assume that heat transfer within the ice shell occurs by heat conduction so that temperature is determined by the
thermal diffusion equation
ρiCp
∂T
∂t
=
1
r2
∂
∂r
(
r2
k
∂T
∂r
)
+ H (A1)
where T is temperature, t is time, r is radial position, ρi is the density of ice, Cpis the heat capacity of ice, k(T) = 651/T Wm− 1
K− 1
is the thermal
conductivity of ice (Petrenko and Whitworth, 1999), and H is the volumetric heat production, which is assumed to be zero in the simulations shown
here. Eq. (A1) is solved implicitly using a conservative finite different scheme.
The equations for thermo-visco-elastic deformation are presented in Hillier and Squyres (1991) and Nimmo (2004). Here, we derive the governing
equation for the radial stress σr(r). The radial and tangential strains ϵr and ϵt, respectively, are calculated from the displacement u by
ϵr =
dur
dr
=
d
dr
(rϵt) (A2)
and
ϵt =
ur
r
(A3)
Conservation of momentum relates radial and tangential stresses,
A.R. Rhoden et al.

7. Icarus 392 (2023) 115391
7
dσr
dr
=
2
r
(σt − σr) (A4)
For a Maxwell constitutive model, stress and strain-rates are related by
dϵr
dt
=
d
dt
(
1
E
[σr − 2νσt] + α
)
+
σd
r
2μ
(A5)
dϵt
dt
=
d
dt
(
1
E
[σt − ν(σt + σr) ] + α
)
+
σd
t
2μ
(A6)
where E is the Young’s modulus, ν is the Poisson ratio, α = αlΔT where αl is the coefficient of linear expansion and ΔT is the temperature relative to a
reference, and the superscript d indicates the deviatoric value (σd
r = − r
3
dσr
dr and σd
t = r
6
dσr
dr ). The viscosity μ is given by
μ(T) = μbexp
[
Q(Tb − T)
RTbT
]
(A7)
with Q as the activation energy, R as the gas constant and the subscript b indicating values at the base of the ice shell.
Differentiating (A2) with respect to time we obtain
d
dt
(ϵr − ϵt) = r
d
dt
dϵt
dr
(A8)
Substituting the constitutive relations (A5) and (A6) into (A8) we obtain
r
d
dt
dϵt
dr
=
d
dt
[
1 + ν
E
(σr − σt)
]
+
σd
r − σd
t
2μ
(A9)
Combined with momentum conservation (A4), Eq. (A9) provides an equation for the evolution of σr
3(1 − ν)
2E
d
dr
d
dt
(σr) +
(1 − ν)
E
d
dr
(
r
2
d
dr
dσr
dt
)
+
1
4μ
dσr
dr
+
d
dr
(
r
12μ
d
dr
dσr
dt
)
= −
d
dr
dα
dt
(A10)
given the boundary condition at the base of the ice shell σr = Pex, with Pex the overpressure in the ocean. Pex is obtained from ur at the base of the shell,
following Manga and Wang (2007),
Pex =
3r2
i
β
(
r3
i − r3
c
)
[
z(ρw − ρi)
ρw
− ur
]
(A11)
The numerical methods for solving (A10) and verification are summarized in Rudolph et al. (2022).
Appendix B. Supplementary data
Supplementary data to this article can be found online at https://doi.org/10.1016/j.icarus.2022.115391.
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