Icarus 221 (2012) 53–62
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Icarus
journal homepage: www.elsevier.com/locate/icarus
Enceladus: A hypothesis for bringing both heat and chemicals to the surface
Dennis L. Matson ⇑, Julie C. Castillo-Rogez, Ashley Gerard Davies, Torrence V. Johnson
Jet Propulsion Laboratory, California Institute of Technology, Mail Code 183-301, 4800 Oak Grove Drive, Pasadena, CA 91101, United States
a r t i c l e
i n f o
Article history:
Received 20 January 2011
Revised 19 May 2012
Accepted 23 May 2012
Available online 6 July 2012
Keywords:
Enceladus
Geological processes
Geophysics
Interiors
a b s t r a c t
The eruptive plumes and large heat flow (15 GW) observed by Cassini in the South Polar Region of Enceladus may be expressions of hydrothermal activity inside Enceladus. We hypothesize that a subsurface
ocean is the heat reservoir for thermal anomalies on the surface and the source of heat and chemicals
necessary for the plumes. The ocean is believed to contain dissolved gases, mostly CO2 and is found to
be relatively warm (0 °C). Regular tidal forces open cracks in the icy crust above the ocean. Ocean water
fills these fissures. There, the conditions are met for the upward movement of water and the dissolved
gases to exsolve and form bubbles, lowering the bulk density of the water column and making the pressure at its bottom less than that at the top of the ocean. This pressure difference drives ocean water into
and up the conduits toward the surface. This transportation mechanism supports the thermal anomalies
and delivers heat and chemicals to the chambers from which the plumes erupt. Water enters these chambers and there its bubbles pop and loft an aerosol mist into the ullage. The exiting plume gas entrains
some of these small droplets. Thus, nonvolatile chemical species in ocean water can be present in the
plume particles. A CO2 equivalent-gas molar fraction of 4 104 for the ocean is sufficient to support
the circulation. A source of heat is needed to keep the ocean warm at 0 °C (about two degrees above
its freezing point). The source of heat is unknown, but our hypothesis is not dependent on any particular
mechanism for producing the heat.
Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction
2. Geologic setting
The Cassini–Huygens spacecraft discovered eruptive plumes and
an anomalous and large heat flow in Enceladus’ South Polar Region
(Helfenstein et al., 2006; Porco et al., 2006; Spencer et al., 2006).
The plumes consist of small ice particles and water vapor together
with a variety of gases. Analysis of some of the ice particles found
that salts are present, leading to the hypothesis that Enceladus has
a salty ocean underneath its icy crust (Postberg et al., 2009).
The purpose of this paper is to advance the hypothesis that the
observed heat flow and all of the materials erupted by the plumes
could have been brought up from a subsurface ocean, whose existence has been suggested based on various geological and chemical
observations (e.g., Nimmo et al., 2007; Postberg et al., 2009).
In the following we review the geologic context of the South Polar Region. Next we present the observational constraints and their
interpretations. We then state our hypothesis for the delivery of
heat and materials to the surface by means of ocean water circulating from below the icy crust. The hypothesis is then quantified by
numerical model estimates. Finally, we discuss questions and
implications raised by that hypothesis, our assumptions on certain
input parameters, and our analysis and modeling.
Our model is based on the geological description of Enceladus
by Spencer et al. (2009) and Crow-Willard and Pappalardo
(2010). The area of most importance to the circulation model presented here is the South Polar Region (SPR), which has a radius of
50 km. In mapping the geology of Enceladus, 11 distinct geological terrains were identified by Crow-Willard and Pappalardo
(2010). The outstanding feature of the South Polar Region is the
south polar terrain (SPT). It is geologically active. The SPT is the
youngest terrain, and the focus of our study because it is intensely
faulted and has deep troughs, known as ‘‘tiger stripes’’ (Helfenstein
et al., 2006; Crow-Willard and Pappalardo, 2010). Vents along
these fissures emit plumes of vapor and particles. As discussed in
more detail below, fissures such as these are needed to initiate
the water circulation by the process described in this paper.
Other terrains on Enceladus bear evidence of similar activity
that may have occurred in the past. These include regions of ridged
terrain (such as Cufa Dorsa and Ebony Dorsum), characterized by
bulbous, branching ridges, and the central leading hemisphere terrain, whose anastomosing and interwoven troughs are very similar
to the south polar terrain (Crow-Willard and Pappalardo, 2010).
No features recognizable as lava (or cryolava) flows have been
reported. Such effusive activity would fill troughs, and as apparently old troughs remain unfilled, any such effusive activity cannot
⇑ Corresponding author.
E-mail address: dmatson@jpl.nasa.gov (D.L. Matson).
0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.icarus.2012.05.031
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D.L. Matson et al. / Icarus 221 (2012) 53–62
have been widespread. The active area of the SPR, i.e., the actual
vent area, is only a tiny fraction of the area of the SPR, and filling
by fluids even in these areas is not evident
3. Spacecraft data and interpretation
Voyager’s images of Enceladus’ crater-poor, smooth surface and
the apparent correlation between the E-ring maximum brightness
and Enceladus’ orbit suggested the possibility of geologically recent activity (Smith et al., 1982). When the Cassini magnetometer
(MAG) detected distorted field lines during a flyby of Enceladus
in 2005 (Dougherty et al., 2006) suggesting an atmospheric plume
emanating from Enceladus, it became evident that the satellite
might be currently active. The subsequent Cassini follow up campaign to investigate this phenomenon led to a multi-instrument
dataset of the eruptions taking place. A review was published by
Spencer et al. (2009).
Cassini images constrain the plume locations and the overall
distribution and estimates for the amount of particulate matter
in the plumes (Porco et al., 2005, 2006; Albers and Spahn, 2006;
Spahn et al., 2006). Observations of the occultations of stars and
the Sun in the ultraviolet have allowed the Cassini Ultraviolet
Imaging Spectrometer (UVIS) to constrain gas column abundances
and composition for some species. Analyses of these data have
yielded an estimated plume eruption rate of 150–300 kg s1 (Hansen et al., 2006, 2008, 2011).
Cassini’s Composite Infrared Spectrometer (CIRS) measured an
unexpectedly large amount of thermal radiation coming from the
surface in the SPR (Spencer et al., 2006, 2009; Howett et al.,
2011). Many thermal anomalies are present, especially at and in
the vicinity of the tiger stripes. Their total thermal emission
amounts to about 15 GW (Howett et al., 2011).
The erupting plumes consist of gas and small particulate matter
(almost certainly containing frozen volatiles, but called ‘‘dust’’, a
particle-size nomenclature applicable to their size). The chemical
composition of the plume gas and dust has been obtained from
analysis of in situ data obtained as Cassini flew through the plumes
(Waite et al., 2006, 2009, 2010; Postberg et al., 2008, 2009, 2010,
2011; Schmidt et al., 2010). The Cassini Ion and Neutral Mass Spectrometer (INMS) and the UVIS data constrain the gas phase composition (Hansen et al., 2006, 2011; Waite et al., 2006, 2009). Plume
gas composition is 90% water vapor and 10% other gases, with
CO2 making up 50% of these gases in the plume.
The Cassini Cosmic Dust Analyzer (CDA) made in situ measurements of the plume dust. The particles are mostly composed of
water ice, but many of them also contain sodium and potassium
compounds, including salts. Recently small amounts of Si (presumably SiO2) have been detected in that dataset (Hsu et al., 2010). The
salty grains were first discovered in E-ring dust and later were
found in considerably higher proportions in the plume particles
themselves. The discovery of salts and related chemicals led Postberg et al. (2009) to conclude that these particles came from ‘‘sea
water’’. Referring to the model by Zolotov (2007) they wrote:
‘‘. . .we find that the composition of type III E-ring grains agrees with
the modeled Enceladus ocean composition. Our values for the concentrations of NaCl (0.05–0.2 mol kg1) and the Na-carbonates
(0.02–0.1 mol kg1) as well as the inferred alkalinity (pH 8.5–9)
match the model. . . . . .Our measurements imply a ‘soda-ocean’ rich
in bicarbonate and/or carbonate. This is consistent with the abundant CO2 observed in the plume vapour’’ (Postberg et al., 2009).
Schmidt et al. (2008) modeled the gas and dust as escaping from
a subsurface chamber through a nozzle. In this chamber gases
would evaporate from the water and ice. Ice particles could be
formed by condensation from evaporated water vapor. Involatile
species dissolved in the water could be lofted as aerosol particles
produced by popping bubbles. They also found that most of the
plume particles did not travel far, returning to the surface of Enceladus relatively near to their plume. This is reinforced by an
observation by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) that has detected the presence of CO2 in the icy surface
adjacent to the plumes (Brown et al., 2006). This is consistent with
CO2 being deposited by plume fallout.
4. Hypothesis
The notional framework that we discuss is illustrated in Fig. 1.
The figure schematically depicts six major components of an ongoing water circulation system below Enceladus’ active south polar
areas.
At the bottom is the subsurface ocean (#1 in Fig. 1) that underlays the South Polar Region. As discussed in more details in Section 6.3, in this study the ocean is below an assumed average
crustal thickness of 10 km. The ocean is a reservoir for the chemical
species detected in the plumes. It underlies the South Polar Region
but its overall extent is unknown.
The seawater contains dissolved gases that exsolve as pressure
falls below the saturation pressure for each gas species according
to Henry’s Law. The pressure reduction and exsolution occur as
water rises toward the surface. Exsolved gases initially form tiny
bubbles that reduce the overall density. With the exsolution of enough gas, the ocean water becomes buoyant with respect to the solid ice crust and rises towards the surface if fractures or fissures in
the ice have provided conduits, shown schematically at #2 in Fig. 1.
(The onset of the ascent of water that triggers initial exsolution is a
matter that is discussed later in Section 6.1.)
Heat loss at the surface: Near the surface the water flows beneath a protective ice cap and spreads out laterally in a pattern
that follows the thermal anomalies. A symbolic surface thermal
anomaly is indicated by #3 where heat from the water is being
conducted through the ice cap to the surface. These areas of anomalously high surface temperatures radiate heat to space, #4.
Depending on the temperature of the surface, the thickness of
the cap can be inferred to vary from a few tens of meters (surface
temperature of 100 K and higher) up to hundreds of meters (surface temperatures 80–100 K).
Plume chambers: The plume chambers are special environments
where ocean water and its contents are converted into vapor and
aerosols. A single symbolic example is shown at #5. We have
adopted the model of Schmidt et al. (2008). We refer the reader
to that paper for the technical details of the properties and processes in the plumes and the plume chambers.
The flow of ocean water through a plume chamber replenishes
the chemicals that have erupted as well as the energy (through
heat transfer) that powers the whole plume process. Bubbles coming into the chamber pop. This process introduces an aerosol spray
of tiny droplets into the ulage of the plume chamber. Some of these
particles are then entrained by the erupting gas. The plumes erupt
(in total) about 150–300 kg s1 (Hansen et al., 2006), most of
which is water. Pressures in the chamber are low and we assume
that all of the CO2 is exsolved from the ocean water and becomes
part of the plume.
Return to the ocean: The water has now lost heat and gas and is
colder and denser. It returns to the ocean, indicated by #6, via fissures or cracks in the icy crust.
5. Quantitative assessment
In this section we delve into the quantitative aspects of the
hypothesis detailed in the previous section in order to assess its
D.L. Matson et al. / Icarus 221 (2012) 53–62
55
Fig. 1. Notional sketch illustrating the hypothesis of ocean water circulation (not to scale). The radiating surface shown could be along a fissure bottom where many of the
thermal anomalies occur in association with plumes. The numbers refer to specific regions and processes described in the text.
viability as a function of the properties of the shell and other input
parameters.
5.1. Ice cap formation and thickness
When water emerges at Enceladus’ surface it boils vigorously.
The latent heat for the vaporization of water is large and is drawn
from the remaining liquid water that rapidly cools and freezes.
Near 273 K the heat of vaporization is 2.26 106 J kg1 and the
latent heat of fusion is 3.35 105 J kg1. Therefore, for each kilogram of water evaporated, about 6.74 kg of water freezes.
Evaporation stops when the weight of the forming ice cap exceeds the vapor pressure of water. The thickness of the ice layer,
hcap, required to shut off the evaporation can be calculated from
hcap ¼ P=qg Enceladus
ð1Þ
where P is the vapor pressure of water at its melting temperature
(610 Pa), q is the density of the ice (920 kg m3), and gEnceladus
(0.11 m s2) is the gravitational acceleration at Enceladus’ surface.
The resulting ice layer is 6 m thick. Approximately
5.5 103 kg m2 of water is frozen. The corresponding amount
evaporated is 8.2 102 kg m2.
By way of comparison, Cassen et al. (1979) carried out these calculations for Europa and found an ice cap thickness of 0.5 m. The
thinner cap is due to the differing gravity between Europa and
Enceladus.
The nascent ice cap is probably porous due to the vigor of the
boiling. Taking this porosity into account adds a factor of 1/(1 p)
to the right-hand side of Eq. (1) (with p the fractional porosity).
As the cap thickens, porosity and permeability decrease and the
escaping water vapor has an evermore tortuous path to the surface.
It is colder near the surface and some vapor solidifies on grains,
fills void space and makes a seal. At this stage the cap thickness is
c = 6/(1 p) (e.g., at 0.5 porosity, the cap would be 12 m thick).
Considering the various uncertainties in the above, the following calculations use 7 m as the equivalent thickness of the ice
cap that sets the lower limit for pressure (710 Pa) in the water circulation that we study below.
5.2. Bringing water to the surface and back to the ocean
The problem in bringing volatile-free ocean water to Enceladus’
surface is that the water column stalls before it reaches the surface.
Seawater has a density of 1020 kg/m3 whereas the density of ice is
920 kg/m3. The height to which water can rise in a vertical opening
in the icy crust is given by:
h ¼ ðqice =qocean water Þhc
ð2Þ
where qice is the density of the crustal ice, qocean water the ocean
water density, and hc the thickness of the crust. Seawater can therefore rise approximately ninety percent of the way up to the surface
in a open conduit. For a 10-km thick crust on Enceladus, proposed
for heavily-fissured terrain such as the South Polar Region, the seawater ‘‘water table’’ will thus stand 1 km below the surface.
The energy required to lift seawater to the surface is given by:
E ¼ mg Enceladus hD ¼ mg Enceladus hc ð1 qice =qocean water Þ
ð3Þ
where m is the mass of water to be lifted, hD = hc(1 qice/qocean
water) is the depth of the water table for a ice crust of thickness hc.
The energy for doing this work comes from expansion of the gas
in the bubbles, which cools the water by a small amount. In fact,
the energy required to raise seawater 1 km from the water table
to the surface is 110 J/kg and results in a 0.03 K reduction of the
temperature of the water.
As ocean water travels from below the crust and rises toward
the surface, the exsolution of bubble-forming gas is governed by
Henry’s Law:
PCO2 ðX CO2 Þ ¼ Hconst X CO2
ð4Þ
where PCO2 is the pressure at which the liquid is saturated with the
dissolved gas, X CO2 is the mole fraction of CO2, and Hconst is Henry’s
Constant which for CO2 is 7.26 107 Pa (mole fraction)1. For the
pressure at the bottom of a 10 km thick crust (1 106 Pa), saturation of CO2 occurs at a molar fraction of 0.014.
Pressure relationships can be used to demonstrate that ocean
water can circulate in Enceladus. Key pressures are the lithostatic
pressure of the ice, and the pressures at the bases of the ascending
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D.L. Matson et al. / Icarus 221 (2012) 53–62
and descending water conduits. An example of the static pressures
for a 10 km thick icy crust and an ascending water column are plotted versus depth in Fig. 2. Line AB is the lithostatic pressure in the
ice. Curve AC is the pressure calculated for ocean water containing
5 104 mole fraction of dissolved CO2. Points B and C are the
pressures at the bottom of the icy crust. The difference in their values is the pressure that is available for moving water to the surface
and will be referred to as the supply pressure.
Pressures for the descending branch of the circulation are plotted in Fig. 3. The ice line, AB, is shown for reference. Curve AD is the
pressure for descending ocean water that has retained some gas, in
this example 3 104 mole fraction CO2. This is about half of the
concentration that enabled water to ascend in Fig. 2. Line AE is
the pressure for water with no dissolved CO2. This might be characteristic of water returning from a plume chamber where it lost
all of its gas. In Fig. 3, points D and E correspond to negative supply
pressures meaning that the descending water can enter the ocean.
Supply pressure is dependent upon the mole-fraction of dissolved CO2. This relationship is shown in Fig. 4 in which supply
pressure is plotted versus mole fraction of dissolved CO2. The vertical axis is drawn at the position of zero supply pressure. To the
left are negative pressures indicating that water can descend and
enter the ocean. To the right are positive values of supply pressure
indicating that ocean water at the bottom of the conduits can flow
up toward the surface. For the 10 km thick crust the supply-pressure zero occurs at 0.00038 mole-fraction of CO2.
As an example we pick 0.0005 mole-fraction of CO2 for the
ocean. This gives a supply pressure of 4.9 104 Pa. If we let the
water lose 0.0002 mole-fraction of CO2 near the surface, the
descending water would be at 0.0003 mole-fraction of CO2 and
have a supply pressure at the bottom of 3.2 104 Pa, allowing
the water to return to the ocean.
The details of the calculation, including considerations of bubble formation, surface tension, and salinity are discussed in Appendix A.
5.3. Heat transfer at the bottom of the ice cap
Fig. 2. Pressure vs. depth relationships for gas-charged ocean water flowing to the
surface. Curve AC is the pressure plot for water containing 0.0005 mole fraction
CO2. Line AB is the lithostatic pressure in the ice.
As the ocean water nears the surface it spreads out laterally beneath an ice cap following the pattern indicated by the thermal
anomalies. Fissures, troughs, and other negative topographic relief
can provide shortcuts for heat and these areas can be hotter, an
example being locations along the ‘‘tiger stripes’’ themselves
(Spencer et al., 2006; Abramov and Spencer, 2009). For example,
Abramov and Spencer used a 2-D model and showed that both total power and the wavelength distribution can be matched quite
well by assuming most heat is radiated from surface areas adjacent
to fractures, which are warmed by conduction through the ice from
the fractures themselves.
The bubble-rich, upwelling water is relatively warm and buoyant. It floats on top of cooler, slightly denser water and contacts the
colder ice cap above. Heat is conducted away from the water and
through the cap to the surface. The loss of heat to the ice cools
the water. The temperature change is about two 2 °C (from an
ocean temperature of 0 °C to 2 °C, the freezing point of seawater). This causes a slight amount of densification of the salty water.
More important to the bulk density is contraction of gas in the bubbles. Reducing the temperature also reduces the value of Henry’s
Constant and this initiates a small amount of reabsorption of the
bubble gas. As a result of the small reduction of the gas volume,
the radii of bubbles decrease. Surface tension then causes the bubble-gas pressure to increase, another small effect that reduces volume. These processes are described in more detail in Appendix B.
A potentially much larger densification effect may occur when
the water spreads out laterally. Although the water is flowing, albeit horizontally, the bubbles in the mixture will continue to rise
vertically. If this continues long enough, some phase separation
may occur leading to the formation of gas pockets below the ice
cap.
After its near-surface passage, the ocean-water-bubble mixture
is now cooler and denser. It has lost heat and an unknown amount
of its gas. It sinks, and begins its return to the ocean via fissures in
the crust. As it goes down, pressure increases and the remaining
gas is absorbed.
5.4. Plume chambers
Fig. 3. Pressure vs. depth relationships for ocean water returning to the ocean from
the surface. Curve AD is the pressure for water with a mole fraction CO2 of 0.0003.
AE is the pressure vs. depth plot for water returning from plume chambers. Line AB
is the lithostatic pressure in the ice.
Some of the upwelling water enters the plume chambers as described by Schmidt et al. (2008) and Postberg et al. (2009). These
chambers differ from the other near-surface reservoirs in that they
are connected to the surface by an open, albeit convoluted, conduit.
D.L. Matson et al. / Icarus 221 (2012) 53–62
57
Fig. 4. Supply pressure vs. mole fraction CO2. The vertical axis is drawn at the position of zero supply pressure.
The pressure above the fluid is relatively low. Bubbles burst and
their gases are seen in the plumes. Bursting also lofts small droplets into the ullage. The erupting plume gases entrain some of
these aerosol particles and carry them into the plumes.
We assume that all of the heat and chemicals needed by the
plumes comes from the ocean water. Conserving energy requires
that:
M plume clv ¼ M seawater csp DT
ð5Þ
where Mplume and Mseawater are the eruption rate of the plume and
the rate at which ocean water is flowing through the plume chambers; clv is the specific latent heat of vaporization of water
(2.26 106 J kg1) and csp is the specific heat of water
(3.8 103 J kg1 K1). DT is the difference in the temperature between the water entering and leaving the plume chambers.
Conservation of CO2 requires that the number of moles of CO2
delivered by the ocean water equals the number of moles of CO2
erupted. This leads to:
2X plume CO2 M plume ¼ X ocean CO2 M seawater
ð6Þ
where Xplume CO2 and Xocean CO2 are the mole fraction of CO2 in the
plumes and ocean respectively (the molecular weight of seawater
appears on both sides of the equation and cancels out). The correction factor of two is due to CO2 being used as a surrogate for all gas,
which is 0.1 mole fraction, whereas CO2 itself is only 0.05.
The two equations have three unknowns, X ocean CO2 , Mseawater,
and DT. However, we can use the minimum CO2 concentration
for circulating ocean water as an estimate for X ocean CO2 . Taking
X ocean CO2 ¼ 0:0004 gives the solutions for Mseawater, and DT:
M seawater ¼ M plume X plume CO2 =X ocean CO2
¼ 3:8—7:5 104 kg s1
DT ¼ ðclv =csp ÞðX ocean CO2 =X plume CO2 Þ ¼ 2 K:
ð7Þ
ð8Þ
The amount of heat needed to power the plumes is Mplume clv = 0.3–
0.68 GW, where Mplume is the eruption rate (150–300 kg s1 Hansen et al., 2006). By way of comparison (Spencer et al., 2009) esti-
mated 0.5 GW. The flow rate of water through the plume
chambers is 37–74 m3 s1.
5.5. The required discharge
The rate at which water is required to flow to the surface is set
by the measured heat power of 15 GW (Howett et al., 2009,
2011). For 0 °C ocean water the required discharge rate is
1200 m3 s1. A way of gauging whether this is geologically reasonable is to calculate how much of the surface area must be used
for upwelling of ocean water. Assuming a velocity of a centimeter
per second, the actual area is relatively small, being only several
millionths of the area of the South Polar Region.
6. Discussion
In this section we consider several aspects of the proposed
hypothesis: processes by which the circulation could start and
stop; crustal thickness and composition; the source of Enceladus’
heat; the boundary condition between the ocean and the crust;
and a terrestrial analogue for buoyancy-driven flow. Finally, we
discuss how the ocean water circulation hypothesis might be
definitively tested.
6.1. Starting the circulation
A half-dozen potential starting processes have been noted (Matson et al., 2011). However, here we will only consider the process
that is most consistent with the geological setting of the South Polar Region.
The South Polar Region is replete with fractures and fissures in
the ice crust. Ocean water can rise in these but does not normally
reach the surface because it is too dense. As noted earlier, for a 10km thick crust, seawater will stand as a water table about one kilometer below the surface. It has been proposed that tidal stress is
periodically opening fissures in the South Polar Terrain surface
(Hurford et al., 2007, 2012). Hence we explore the possibility that
fissures can be used to initiate circulation.
58
D.L. Matson et al. / Icarus 221 (2012) 53–62
The depth to which a fluid filled crack can penetrate into the
surface was considered by Weertman. The tension across the crack
can be taken as (cf. Weertman, 1971, Eq. (26)):
6.3. Crustal thickness
where d is depth below the surface and g is gravitational acceleration. The periodic tidal flexing of the South Polar Region due to Enceladus’ orbital eccentricity produces a tensional stress of 105 Pa
(for example see the recent calculation by Hurford et al. (2007)).
For a static crack filled with pure water this level of stress yields
a depth of 18 km. Thus, water-filled fissures in the 10-km thick
crust can remain open. For a fissure without seawater (i.e., qocean
water = 0) the fissure opening can be maintained to a depth of
1.5 km in the ice. Since this is deeper than the water table it is
possible that a suitable fissure can provide a void space that is filled
with water by drawing down the local water table. Upwelling water
from the ocean quickly rises and restores the water table. If the flow
from the ocean is sufficiently fast, bubbles will be formed by exsolution of gas, and a buoyancy-driven circulation can be set in motion and become self-sustaining. If the available fissures
(intersected by the new opening) have sufficient flow capacity to allow seawater chilled near the surface to return to the ocean, then
the circulation will be established and can continue delivering heat
to the surface.
Enceladus is believed to be differentiated (e.g., Schubert et al.,
2007). The subsurface structure in the South Polar Region is
thought to consist of an icy crust underlain by a saline liquid layer
(ocean) and below these a rocky core. The thickness of Enceladus’
crust is not known. Our assumed 10-km-thick shell is consistent
with values suggested or assumed by other researchers. For example Nimmo et al. (2007) adopted 24 km. Ross and Schubert (1989)
observed that geological evidence suggested a thickness of between 5 and 20 km, whereas Hurford et al. (2007) in their study
of periodically opening rifts (the tiger stripes) argued for a thickness of a few tens of kilometers.
If the crust is thinner than 10 km then it becomes difficult to
support surface topography. For crusts thicker than 10 km it becomes more difficult to maintain circulation. As a depth of 15 km
is approached the starting mechanism for circulation (Section 6.1)
becomes less effective and then fails. While the circulation of ocean
water itself can operate with crusts that are many tens of kilometers thick, it is not obvious how a stopped circulation could be restarted with crusts that thick. Given the abundant evidence for
tectonic activity in the South Polar Region one should not expect
any given circulation conduit to remain active for geologically long
timescales.
6.2. Cessation of circulation
6.4. Crustal composition
There are more than a dozen ways that the circulation of seawater can stop. (1) In the case of the formation of a new fissure (just
discussed Section 6.1), there may be insufficient drainage capacity
to return water to the ocean rapidly enough. In this case the seawater that has filled the fissure will become stagnant and freeze,
forming a slug of ice. (2) Shutting off the conduits, for example,
by severing them by tectonic activity and offsetting the segments,
means that water no longer can pass. Given the fact that the South
Polar Region is geologically young with many fractures and fissures
in the ice, this process might occur quite frequently and might be
the chief determinant of the longevity of a given circulation system. System lifetime is currently unknown, but could be relatively
short compared to the age of the South Polar surface. (3) If the upward flow toward the surface becomes too slow, the bubbles can
ascend faster and outpace the water stream. When such phase separation occurs and the water loses enough buoyancy, then the flow
stops. For example, ocean water, due to its temperature, is expected to erode the walls of the conduits. The melt-water boundary layer that forms adjacent to the ice wall slows, but does not
completely stop, this erosion. If enlargement of the conduit results
in greatly reducing the velocity of the upward flow, then phase
separation will occur and flow stops as the conduit becomes stagnant. (4) Depending upon the composition of the crust there might
be temporary or permanent closure of fissures by clathration; the
severity of the blockage depends on the abundance of guest species
as a function of the pressure and temperature conditions. (5) On
long time scales eruptions will eventually stop if the ocean runs
out of gas, (6) the crust grows too thick, or (7) the entire water
layer freezes.
Processes (5)–(7) permanently shut down the circulation. Since
there is current evidence for some form of hydrothermal activity,
these processes have not occurred.
Processes (2)–(4) do not necessarily lead to permanent cessation of circulation. For example, after they have occurred circulation could be started anew by the opening of a new network of
fissures as suggested in Section 6.1. We do not know how often
these shutoff mechanisms could stop the circulation of water. If
they should occur frequently, then the presence of ongoing activity
suggests that the initiating processes also occur frequently.
The crust is modeled as pure ice. Some clathrates may be present but there is no data on their abundance. We note that the conditions at the interface between Enceladus’ rocky core and crust or
ocean are similar to those found at the bottom of Earth’s oceans
(pressure of about 20 MPa and temperature of about 270 K), where
hydrates of carbon dioxide are stable. A major uncertainty with respect to Enceladus, though, is the concentrations of various solutes
(e.g., NaCl) that can affect the stability field of clathrate hydrates
(e.g., Koh and Sloan, 2007). This and other matters remain to be
studied in detail before their relevance to Enceladus can be
assessed.
T ¼ 2ðqocean water qice Þgd=p
ð9Þ
6.5. Boundary condition at the bottom of the crust
Plume chamber relationships (Section 5.4) indicate that ocean
water arriving there has a temperature of 0 °C. This is about
two degrees above the freezing point of seawater. Consequently,
there will be some melting at the bottom of the crust, and the production of melt water. The melt water is less dense than seawater
and floats on it. As a result, an ice-ocean interface layer is formed.
This layer is stable against Rayleigh-Bénard convection because
in the range of 3.98–0 °C the density of water is an inverse function
of temperature (i.e., colder water is less dense and floats over warmer water). This temperature-density inversion is a function of
salinity. The salinity of seawater is high enough that it does not
have an inversion. Thus, there is no temperature-density inversion
layer just below Enceladus’ cap ice (Section 5.3) because there is no
melt water at that interface.
The ice–water boundary layer has vertical salinity and thermal
gradients. These gradients determine the rate at which heat can be
transferred across the interface and the temperature at which the
ice is melted. Ocean currents are one of the variables that can influence the extent and shape of the interface layer.
A somewhat similar interface layer (but with only a thermal
gradient) has been discussed and modeled for Europa (Melosh
et al., 2002, 2004) and many of these same considerations apply
to Enceladus. In Europa’s case an interface layer thickness of
200 m was suggested by these authors, providing a rough indication of what might be the case for Enceladus.
D.L. Matson et al. / Icarus 221 (2012) 53–62
On Earth, the melting of ice by seawater offers some analogues
(Gade, 1993). In most of the terrestrial analogues the interface conditions are not as placid as the conditions may be for Enceladus.
The terrestrial ocean temperature is often much higher, and laminar flows, as well as advection and eddies set up by the ocean currents, buffet the boundary layer. The boundary layer’s thermal and
salinity gradients are usually modeled as linear. Ice interface temperatures can vary between 1.8 °C and 0.1 °C depending on conditions. Boundary layer thicknesses can vary from as thin as several
millimeters to as thick as several hundred meters.
Other terrestrial analogues are cracks in sea ice that fill with
melt water from below, and the melting at the vertical walls of icebergs (Josberger and Martin, 1981; Gade, 1993).
For Enceladus, some melting of ice at the bottom of the crust
does not necessarily mean that the crust is thinning. The amount
of heat reaching the bottom of the crust is given by:
q ¼ kDT ¼ kðT 1 T 2 Þ=x
ð10Þ
1
1
where k is the thermal conductivity of water (0.57 W m K ), T1
the interface melting temperature (1.5 °C), T2 the ocean temperature (0 °C), and x the thickness of the boundary layer (50 m). Using
these values, q = 0.02 W m2, which could result in a few millimeters per year of ablation. However, the conductivity of ice
(2.22 W m1 K1 at 0 °C) is higher than that of water and
0.05 W m2 can be conducted through a 10-km-thick crust (with
a surface temperature of 65 K) and radiated to space. While the
amount of heat reaching the ice is unconstrained, there must, however, be some melting because melt water is needed to maintain the
interface layer. As a further complication, new ice is being formed
near the surface. A mechanism for replenishing the ice was mentioned earlier (Section 6.2, case 1).
Presently, the matter of whether or not the thickness of the
crust is changing is not resolvable because there are not enough
facts available about conditions at the bottom of the icy crust.
6.6. Source of heat
A source of heat is required not only to supply the 15 GW
being radiated from the observed surface thermal anomalies but
also to keep the ocean liquid with a temperature of 0 °C. A 10km-thick crust above an ocean will conduct about 0.05 W m2 of
heat to the surface. Without a heat source the ocean will freeze
on a time scale of 30 myrs (Roberts and Nimmo, 2008). The
needed heat must either be produced in the ocean, or transferred
to the ocean. Unfortunately, the source of Enceladus’ heat remains
a mystery. Tyler (2008, 2009, 2010, 2011) suggested that the
power may come from dissipation in the ocean. He argues that
the ocean could form a cavity for Rossby–Haurwitz waves excited
by obliquity tides and that these would dissipate enough power to
warm the ocean and keep it liquid. However, these ideas have not
been developed in sufficient detail to evaluate whether or not they
work for Enceladus. In particular, Chen and Nimmo (2011) argue
that the obliquity is not sufficient for Tyler’s suggested mechanism
to produce the needed amount of dissipation. However, Enceladus’
obliquity has not been measured in detail, so this aspect remains
unconstrained for now. Meyer and Wisdom (2008) also noted that
the assumption that the observed heat is tidally dissipated conflicts with Enceladus’ current orbital state (especially its high
eccentricity). On the other hand, these authors suggested that Enceladus’ current state could be the signature of a recent event that
excited Enceladus’ eccentricity. The theoretical tidal dissipation
estimate by Meyer and Wisdom (2008) is a direct function of Saturn’s dissipation factor Q. However the latter property is poorly
constrained. Recent astrometric observations have produced a
new, lower, estimate of Saturn’s Q that is about ten times lower
than previous values that were based upon theoretical arguments
59
(Lainey et al., 2010, 2012), which is opening the door for a reevaluation of the theoretical amount of dissipation expected in
Enceladus.
6.7. Terrestrial analog
There are terrestrial analogs for the hypothesized buoyancy-driven process in Enceladus. Lakes Nyos, Monoun, and Kivu are in
Africa and have waters with an abundance of dissolved gases. Lake
Nyos, in the Northwest Region of Cameroon, is the most notorious
due to its overturn in 1986 that released a large amount of CO2 that
suffocated 1,700 people. The bottom water at Nyos is rich in dissolved CO2 that has seeped up from deeper volcanic sources. Vertical pipes have been installed in the lake. Colder, denser water
coming up the pipes from the bottom of the lake exsolves CO2
gas, forms bubbles, and becomes buoyant. The water rushes up
to the surface and forms fountains many meters high. This process
is self-sustaining and is safely releasing CO2 at a controlled rate
(Woods and Phillips, 1999; Kling et al., 2005).
6.8. Testing the ocean water circulation hypothesis
Definitive testing of the hypothesis presented in this paper requires measurements by future spacecraft. In addition to high resolution imaging and infrared thermal emission maps, high priority
should be given to ground-penetrating radar and gravity measurements to constrain the internal structure of Enceladus to provide a
definitive answer about the existence and properties of an internal
ocean, and to shed light on the mechanism or mechanisms responsible for producing heat in the interior. Very accurate plume composition data (of both dust and gas phases) would enable a better
assessment of the circulation as well as provide information about
Enceladus’ origin and evolution. These data need to include isotopic abundances as well as identification of very large molecules
(i.e., several hundreds of Daltons in mass). Until such data become
available, the best test may be Occam’s Razor, namely, the hypothesis is the simplest process suggested that brings to the surface
both heat and the chemicals observed in the plumes.
7. Conclusions
The pressure-driven circulation of water from a subsurface
ocean can supply heat to Enceladus’ South Polar Region’s thermal
anomalies and the heat and chemicals required by the erupting
plumes. Gas, that is assumed to be mostly CO2, is dissolved in
the ocean water. Regular tidal fracturing and fissuring of the South
Polar crust provides conduits for the water to reach the surface.
The gas exsolves as the water moves toward the surface. Bubbles
formed by exsolution can decrease the bulk density of the vertical
column of water enough that the pressure at its bottom is less than
that at the top of the ocean. This pressure difference drives ocean
water into and up the conduit toward the surface. The amount of
gas needed to support circulation is relatively small. A CO2 equivalent gas concentration of 4 104 mole fraction is sufficient.
In the plume chambers, water vapor is produced which makes
up some ninety percent of the gas in the plumes. The heat required
to evaporate the water comes from the ocean water passing
through the plume chambers. By giving up this heat the ocean
water is cooled by 2 °C. Since the near-surface ice–seawater
interface is at 2 °C, this suggests that the ocean water arriving
at the plume chambers has a temperature of 0 °C.
The popping of bubbles in the plume chambers lofts an aerosol
spray of tiny seawater droplets. This allows dissolved, non-volatile
species (such as NaCl) to become entrained in the exiting plume
gas. The popping of essentially all of the bubbles as well as the
60
D.L. Matson et al. / Icarus 221 (2012) 53–62
chilling of the water are processes that increase the density of the
seawater. This water sinks and returns to the ocean.
Due to fissuring of the icy crust, water may be exposed to space
where it immediately boils. The heat used for boiling results in liquid water freezing. On Enceladus this continues until an icy cap
has formed that is thick enough to suppress boiling. For this, the
necessary cap thickness is equivalent to 6 m of ice. Based upon
reported thermal anomaly temperatures the ice-equivalent cap
thicknesses vary from a few tens of meters to several hundreds
of meters. At the bottom of these caps the ocean water loses heat
and is cooled to 2 °C. Also, an unknown amount of its gas is lost
as water lingers below the cap ice. These volatile losses increase
the density of the water, which sinks and returns to the ocean.
The arrival of 0 °C water at the plume chambers suggests that
the ocean must be at least this warm. The maintenance of this temperature requires a source of heat in Enceladus. The nature of this
source is unknown. Fortunately, the circulation hypothesis proposed in this paper is not dependent on any particular mechanism
for producing the heat.
The periodic fissuring of the South Polar Region together with a
relatively thin (10 km thick) crust allows the possibility of starting
oceanic circulation by filling new, open fissures with water
brought up from the ocean. Consequently, the ongoing hydrothermal activity is not required to be long-lasting. A circulating system
can wear out, for example, by erosion of its conduits, or be shut off
by tectonic activity, and later be replaced by a new system. Also,
under the right conditions, water freezes in fissures, adding material to the crust near to the surface. The formation of such ice may
compensate for the melting of ice at the bottom of the crust. Unfortunately, not enough is known about Enceladus to assess if the
crustal thickness of the South Polar Region is increasing, is steady-state, or is thinning.
culate the new volume for a parcel, the volume of the exsolved
gas, V CO2 , must be added to the volume of the water.
The relevant relationships are as follows:
The excolved CO2 weight fraction, wCO2 , is
wCO2 ¼ ðX o X 1 Þð44=20:6Þ:
ðA1Þ
where 44 is the molecular weight of CO2 and 20.6 is the molecular
weight estimated for the ocean water. The mass of CO2 exsolved per
cubic meter of water is
mCO2 ¼ wCO2 qocean ¼ wCO2 ð1020 kg m3 Þ
ðA2Þ
The number of moles of CO2 exsolved from a cubic meter of water is
Kmoles CO2 ¼ mCO2 =44
ðA3Þ
The volume of a kmole of gas is
V kmole ðT; PÞ ¼ RT=P
ðA4Þ
where R is the universal gas constant, T temperature, and P pressure. The volume of liberated gas is
V CO2 ¼ ðkmoles CO2 Þ V kmole
ðA5Þ
The first parcel lies immediately below the base of the 7 m thick
ice cap where the pressure, Pice-cap, is 710 Pa. The parcel number increases with depth and is the parcel’s relative position in the vertical column. The pressure on the bottom of the nth parcel is
Pn ¼ Pice-cap þ ng Enceladus qocean-water hparcel
ðA6Þ
2
where gEnceladus (0.11 m s ) is the surface gravity, qocean-water is the
density of ocean water (1020 kg m3) and hparcel is the parcel height
dimension (i.e., 10 m).
The depth of the bottom of the nth parcel, dn, is
dn ¼ dice-cap þ
X
ðhparcel þ ðV CO2 Þi Þ
ðA7Þ
i¼1;n
Acknowledgments
This paper has benefited very much from two reviews, especially from Dave Stevenson. Jonathan Lunine was a participant in
early phases of this work and we are grateful for his insights and
ongoing interest. This work has been conducted at the Jet Propulsion Laboratory, California Institute of Technology under a contract
with the National Aeronautics and Space Administration. Copyright 2012 California Institute of Technology. All rights reserved.
Government sponsorship acknowledged.
Appendix A. Buoyant flow of ocean water
In considering the rise of water toward the surface it is convenient to formulate the problem in terms of parcels of water. For
example, a liquid parcel could be thought of as an imaginary container of dimensions one square meter by ten meters. As gas exsolves, the parcel height will be increased as necessary to
accommodate the volume of the gas. A column consists of a vertical stack of parcels. The mass of the parcel is fixed (1.020 104 kg
in the example for a parcel starting out as seawater without bubbles, i.e., all gas is dissolved) but volume increases as gas exsolves.
The pressure on a parcel is the weight of the parcels in the column
above it. The top parcel is directly under the cap ice and the pressure on it is 710 Pa, which is equivalent to 7 m of ice.
Let the ocean contain Xo mole fraction of CO2. Given the pressure, P, Henry’s Law is used to determine the saturation concentration, X1, or the amount of gas that can remain in solution when
P < HconstXo. The amount of gas that has been exsolved is the difference between the initial value of Xo and the value X1. From this
information the volume of exsolved gas can be calculated. To cal-
where dice-cap is the thickness of the ice cap (7 m) and hparcel is the
height of a parcel of water with no bubbles (10 m).
The results of these pressure vs. depth calculations are shown in
Figs. 2 and 3.
Surface tension: An additional complication of the exsolving gas
forming bubbles is that the surface tension on the bubble wall acts
to compress the gas. Near the surface this can become significant
and can be added to the fluid pressure to obtain the pressure given
by Henry’s Law. Thus,
PHenry ¼ Phydrostatic þ P bubble
ðA8Þ
where Phydrostatic is the fluid pressure due to the weight of the fluid
above and Pbubble is the pressure due to surface tension given by:
Pbubble ¼ Pi Po ¼ 2T=r
ðA9Þ
where Pi is the pressure inside the bubble, Po is the pressure outside
the bubble, T is surface tension and r is the radius of the bubble. The
surface tension of seawater at 0 °C is 0.07565 N m1 (Sharqawy
et al., 2010). For a bubble of 1 mm diameter the bubble pressure
is 300 Pa. We use these as nominal values in our test calculations.
However, accurate values of surface tension require knowledge of
the effect of the ocean chemistry, especially the nature of any surfactants that may be present. Related to that is the bubble size, r,
that is also unknown. The surface tension increases slightly with
salinity. The composition of average terrestrial ocean water has
been assumed. Organic surfactants in the ocean may reduce the surface tension. To assess this possibility we have recalculated the concentration bounds assuming that the surface tension is zero. The
resulting concentrations for CO2 equivalent gas were only
7 105 mole fraction less in each case.
Bubble size and rise rate: Bubble size in the bubbly ocean water
is unknown. The possibilities range from bubbles that grow large
D.L. Matson et al. / Icarus 221 (2012) 53–62
(e.g., cm) to bubbles that remain small as a resultant of surfactants
that increase surface tension. The very small bubbles in fine champagne come to mind as an example of the latter (Liger-Belair et al.,
2000; Liger-Belair and Jeandet, 2003).
If the vertical flow rate slows too much the upwelling column
will lose buoyancy (Section 6.2, case 3). When the bubbles can rise
faster than the fluid is ascending they may escape out the top of
the column. If this happens then the positive buoyancy of the seawater column will be lost. Using Stokes’ Law and assuming that the
bubbles have negligible mass one can obtain a rough estimate for
possible bubble velocities. A 1 mm diameter bubble can ascend
at 3.4 mm s1, covering a 10 km distance in 2.9 106 s (33 days).
Thus, in this case, if the transit time for the upwelling water is less
than a few days, phase separation between the gas and the liquid
will not significantly reduce the buoyancy of the seawater column.
Gas composition: Several caveats need to be attached to these
concentration estimates for the dissolved oceanic gas. The words
‘‘CO2 equivalent gas concentrations’’ has been used because, given
the uncertainties in the Cassini measurements and their variations
as reported between different flybys, we do not accurately know
the composition of the dissolved gas and have used the most abundant component as a surrogate for all of the gas species. These
other species have different values for the Henry’s Law constant
and their resulting exsolution profiles will differ from that for CO2.
Appendix B. Re-circulation of ocean water
Seawater reaching the 2 °C bottom of the ice cap loses heat
and may also lose part of its gas content. The resulting increase
in the seawater density initiates its downward motion and return
to the ocean. These quantities can be estimated.
Using the ideal gas law,
pV ¼ nRT
ðB1Þ
and then
p1 V 1 =T 1 ¼ p2 V 2 =T 2
ðB2Þ
Since the pressure at the bottom of the cap does not change as the
water loses heat, we have p1 = p2, and get V1/V2 = T2/T1. For the two
degree temperature range from 2 to 0 °C (for the upwelling water)
there is 0.7% change in gas volume.
To estimate the depth at which the gas is reabsorbed we first
calculate the value of Henry’s constant, kH(T) for a temperature
of 271.15 K (2 °C). Thus,
kH ðTÞ ¼ kH ðT standard Þ expðCð1=T 1=T standard ÞÞ
ðB3Þ
where Tstandard = 273.15 K, kH(Tstandard) = 726, and C = 2400. This
gives kH(271 K) = 677. Using this value together with Eqs. (3) and
(4) we find the saturation depth for complete absorption to be
about half a kilometer less than the depth at which CO2 exsolved
in the upwelling seawater.
References
Abramov, O., Spencer, J.R., 2009. Endogenic heat from Enceladus’ south polar
fractures: New observations, and models of conductive surface heating. Icarus
199, 189–196.
Albers, N., Spahn, F., 2006. The influence of particle adhesion on the stability of
agglomerates in Saturn’s rings. Icarus 181, 292–301.
Brown, R.H. et al., 2006. Composition and physical properties of Enceladus’ surface.
Science 311, 1425–1428.
Cassen, P., Reynolds, R.T., Peale, S.J., 1979. Is there liquid water on Europa. Geophys.
Res. Lett. 6, 731–734.
Chen, E., Nimmo, F., 2011. Obliquity tides do not significantly heat Enceladus. Icarus
214, 779–781.
Crow-Willard, E., Pappalardo, R., 2010. Global geological mapping of Enceladus.
Bull. Am. Astron. Soc. 42, 995.
Dougherty, M.K. et al., 2006. Identification of a dynamic atmosphere at Enceladus
with the Cassini magnetometer. Science 311, 1406–1409.
61
Gade, H.G., 1993. When ice melts in sea water: A review. Atmos. Ocean 31, 139–
165.
Hansen, C.J. et al., 2006. Enceladus’ water vapor plume. Science 311,
1422–1425.
Hansen, C. et al., 2008. Water vapour jets inside the plume of gas leaving Enceladus.
Nature 456, 477–479.
Hansen, C.J. et al., 2011. The composition and structure of the Enceladus plume.
Geophys. Res. Lett. 38, L11202.
Helfenstein, P. et al., 2006. Patterns of fracture and tectonic convergence near the
south pole of Enceladus. Lunar Planet. Sci. 37, 2182.
Howett, C., Spencer, J.R., Pearl, J., Segura, M., 2009. Spatial variations in Enceladus’
endogenic emission. Bull. Am. Astron. Soc. 41, 1122.
Howett, C., Spencer, J., Pearl, J., Segura, M., 2011. High heat flow from Enceladus’
south polar region measured using 10–600 cm-1 Cassini/CIRS data. J. Geophys.
Res. 116, E03003.
Hsu, H., Postberg, F., Kempf, S., Trieloff, M., 2010. Saturnian stream particles as a
probe of Enceladus’ interior. EOS Trans. AGU ID# P23C–07.
Hurford, T.A., Helfenstein, P., Hoppa, G.V., Greenberg, R., Bills, B.G., 2007. Eruptions
arising from tidally controlled periodic openings of rifts on Enceladus. Nature
447, 292–294.
Hurford, T., Helfenstein, P., Spitale, J., 2012. Tidal control of jet eruptions observed
by Cassini ISS. Lunar Planet. Sci. 43. Abstract 2154.
Josberger, E.G., Martin, S., 1981. A laboratory and theoretical study of the boundary
layer adjacent to a vertical melting ice wall in salt water. J. Fluid Mech. 111,
439–473.
Kling, G.W. et al., 2005. Degassing Lakes Nyos and Monoun: Defusing certain
disaster. Proc. Natl. Acad. Sci. USA 102, 14185–14190.
Koh, C., Sloan, E., 2007. Natural gas hydrates: Recent advances and challenges in
energy and environmental applications. AIChE J. 53, 1636–1643.
Lainey, V., Karatekin, Ö., Desmars, J., Charnoz, S., 2010. Saturnian tidal dissipation
from astrometric observations. EPSC Abstracts 5, 123.
Lainey, V. et al., 2012. Strong tidal dissipation in Saturn and constraints on
Enceladus’ thermal state from astrometry. Astrophys. J., 752, 14,http://
dx.doi.org/10.1088/0004-637X/752/1/14.
Liger-Belair, G., Jeandet, P., 2003. More on the surface state of expanding
champagne bubbles rising at intermediate Reynolds and high Peclet numbers.
Langmuir 19, 801–808.
Liger-Belair, G. et al., 2000. On the velocity of expanding spherical gas bubbles rising
in line in supersaturated hydroalcoholic solutions: Application to bubble trains
in carbonated beverages. Langmuir 16, 1889–1895.
Matson, D., Castillo-Rogez, J., Johnson, T., Lunine, J., Davies, A., 2011. Enceladus and
Europa: How does hydrothermal activity begin at the surface? Lunar Planet. Sci.
42, 1565 (abstract).
Melosh, H., Ekholm, A., Showman, A., Lorenz, R., Is Europa’s Subsurface Water Ocean
Warm? Lunar and Planetary Science 33, Abstract No. 1824.
Melosh, H., Ekholm, A., Showman, A., Lorenz, R., 2004. The temperature of Europa’s
subsurface water ocean. Icarus 168, 498–502.
Meyer, J., Wisdom, J., 2008. Episodic volcanism on Enceladus: Application of the
Ojakangas-Stevenson model. Icarus 198, 178–180.
Nimmo, F., Spencer, J., Pappalardo, R., Mullen, M., 2007. Shear heating as the origin
of the plumes and heat flux on Enceladus. Nature 447, 289–291.
Porco, C.C. et al., 2005. Cassini Imaging Science: Initial results on Saturn’s rings and
small satellites. Science 307, 1226–1236.
Porco, C.C. et al., 2006. Cassini observes the active south pole of Enceladus. Science
311, 1393–1401.
Postberg, F., Kemp, S., Hillier, J.K., Srama, R., Green, S.F., McBride, N., Grun, E., 2008.
The E-ring in the vicinity of Enceladus: II. Probing the moon’s interior – The
composition of E-ring particles. Icarus 193, 438–454.
Postberg, F. et al., 2009. Sodium salts in E-ring ice grains from an ocean below the
surface of Enceladus. Nature 459, 1098–1101.
Postberg, F., Schmidt, J., Hillier, J., Kempf, S., Srama, R., 2010. The compositional
profile of the Enceladus’ ice plume. Bull. Am. Astron. Soc. 42, 977.
Postberg, F., Schmidt, J., Hillier, J., Kempf, S., Srama, R., 2011. A salt-water reservoir
as the source of a compositionally stratified plume on Enceladus. Nature 474,
620–622.
Roberts, J.H., Nimmo, F., 2008. Tidal heating and the long-term stability of a
subsurface ocean on Enceladus. Icarus 194, 675–689.
Ross, M., Schubert, G., 1989. Viscoelastic models of tidal heating in Enceladus. Icarus
78, 90–101.
Schmidt, J., Brilliantov, N., Spahn, F., Kempf, S., 2008. Slow dust in Enceladus’ plume
from condensation and wall collisions in tiger stripe fractures. Nature 451, 685–
688.
Schmidt, J., Postberg, F., Kempf, S., 2010. Modeling the composition of the Enceladus
dust plume. Bull. Am. Astron. Soc. 42, 977.
Schubert, G., Anderson, J.D., Travis, B.J., Palguta, J., 2007. Enceladus: Present internal
structure and differentiation by early and long-term radiogenic heating. Icarus
188, 345–355.
Sharqawy, M.H., Lienhard, V., Zubair, S.M., 2010. Thermophysical properties of
seawater: A review of existing correlations and data. Desalinat. Water Treat. 16,
354–380.
Smith, B.A. et al., 1982. A new look at the Saturn system – The Voyager-2 images.
Science 215, 504–537.
Spahn, F. et al., 2006. Cassini dust measurements at Enceladus and implications for
the origin of the E ring. Science 311, 1416–1418.
Spencer, J.R. et al., 2006. Cassini encounters Enceladus: Background and the
discovery of a south polar hot spot. Science 311, 1401–1405.
62
D.L. Matson et al. / Icarus 221 (2012) 53–62
Spencer, J. et al., 2009. Enceladus: An active cryovolcanic satellite. In: Dougherty,
M.K. et al. (Eds.), Saturn from Cassini–Huygens. Springer, pp. 683–724.
Tyler, R., 2008. Strong ocean tidal flow and heating on moons of the outer planets.
Nature 456, 770–772.
Tyler, R., 2009. Ocean tides heat Enceladus. Geophys. Res. Lett. 36, L15205.
Tyler, R., 2010. Water worlds and oceans may be common in the universe. J. Cosmol.
5, 959–970.
Tyler, R., 2011. Tidal dynamical considerations constrain the state of an ocean on
Enceladus. Icarus 211, 770–779.
Waite Jr., J.H. et al., 2006. Cassini ion and neutral mass spectrometer: Enceladus
plume composition and structure. Science 311, 1419–1422.
Waite, J.H. et al., 2009. Liquid water on Enceladus from observations of ammonia
and 40ar in the plume. Nature 460, 487–490.
Waite, J.H. et al., 2010. Plume Composition as Observed by the Cassini Ion-Neutral
Mass Spectrometer COSPAR 2010 Committee on Space Research (COSPAR),
Bremen, Germany, 18–25 July 2010, 2010.
Weertman, J., 1971. Theory of water-filled crevasses in glacier as applied to vertical
magma transport beneath oceanic ridges. J. Geophys. Res. 76, 1171–1183.
Woods, A.W., Phillips, J.C., 1999. Turbulent bubble plumes and CO2-driven lake
eruptions. J. Volcanol. Geoth. Res. 92, 259–270.
Zolotov, M.Y., 2007. An oceanic composition on early and today’s Enceladus.
Geophys. Res. Lett. 34, L23203.