1. Introduction

Scientific speculation on the physical habitats for life elsewhere than Earth is primarily an effort to carefully assemble a plausible and self‐consistent set of initial guesses about a habitat system…and then derive important inferences for the system that do not overly depend on these particular choices! This seemingly paradoxical approach makes sense when one acknowledges that one of the assumptions chosen, often implicitly, is that the system is constantly subject to perturbations. The system may allow states that, like a coin standing on its edge, can come about only in a rare choice of starting assumptions, and then show little persistence. But in other cases opposing forces on the system state can be identified and some persistence expected for the system state describing a balance of these forces. Such persistence does not immediately demand that these states are likely, but it does strongly suggests this if the balanced state appears to be an attractor for a wide range of initial states. The goal of this paper is to show that there are such balances that can maintain an ocean in a liquid state using heat that ultimately comes from orbital energy and intimately involves the ocean’s dynamic response to tidal forces. Liquid states might then be expected to harbor life.

Little more than a decade ago, Earth could still be considered the only “water planet” in the solar system; Earth provided the only known example of a liquid‐water ocean. Given this belief as to the rarity of water, it could seem that oceans might typically freeze or boil off, and that the conditions for maintaining an ocean in a liquid state might be relatively uncommon on other planets. But observations from the Galileo spacecraft in the 1990s provided the first strong evidence for other oceans in the solar system. The evidence came from several types of observations, but one of the most compelling was the magnetic anomalies observed around Jupiter’s moon Europa, and then Ganymede and Callisto as well (Khurana, et al., 1998, Kivelson, et al., 1999, 2000). These anomalies could not be attributed to an intrinsic magnetic field generated deep within the interior of these moons. Rather, these observations indicated an inductive response to the apparent time‐varying component of Jupiter’s field, especially in regard to Europa. In this case electric eddy currents within Europa are excited in response to these fluctuations in the ambient magnetic field. Associated with these electric currents are magnetic fields that tend to cancel or deflect the ambient field. Because the level of this cancellation inferred from the magnetic measurements was very high, it has been inferred that there must be a layer near this moon’s surface of global extent and high electrical conductivity (Hand and Chyba, 2007, Schilling, et al., 2004, 2007, Zimmer, et al., 2000). From other observations, it appears that this layer must also have the density of water (Anderson, et al., 1998, Hand and Chyba, 2007). A salt‐bearing global ocean provides an explanation for these observations.

More recently, the Cassini spacecraft (currently operating in the Saturnian System) has discovered high heat fluxes and a geyser of water particles emanating from the small moon Enceladus (see Porco, et al., 2006, and citations in Tyler, 2009). A subsurface ocean is a primary contender in also explaining these observations.

Fig. 6. credits: NASA/JPL/Space Science Institute

Then there is the water world, GJ 1214b, which was discovered just 13 parsecs away from Earth (Charbonneau et al., 2009). GJ 1214b is a "Super Earth" (6.5 times that of the Earth), and is believed to have liquid ocean and a thin hydrogen atmosphere. Does this discovery coupled with the findings from Europa and Enceladus indicate that oceans are common throughout the universe? And what does this say about the possibilities of extra-terrestrial life?

To decide whether oceans should be relatively abundant and common among moons and planets requires a broad range of considerations and here we shall focus only on discussing elements of the ocean dynamics that may explain how an ice‐covered, global ocean can avoid complete freezing. A liquid, warm water ocean, in turn, would not only be conducive to maintaining life, but could provide a varied environment which would promote the evolution of life. The goal then is to identify an internal heat source capable of matching the rate of heat lost to space, and to decide if such a balance would be typically met along the path to freezing. One is then attempting to distinguish between situations that allow a liquid ocean state, and ones in which the maintenance of a liquid ocean appears unavoidable.

2. Ocean freezing as a selflimiting process

It is well appreciated that ice cover acts as a thermal insulator that slows the escape of ocean heat to space. A model of this process where heat transfer through the ice is assumed to occur through thermal conduction shows heat loss simply proportional to the conductivity gradient. The temperature of the water (near freezing) and the temperature of the moon surface can be estimated, and the temperature gradient and rate of heat loss then become inversely proportional to the ice thickness. In this case, the rate of ocean heat loss decreases as the ice layer thickens and, provided there is both a maintained internal heat source and enough liquid water initially present, freezing of the ocean is a self‐limiting process. Very thick ice layers may also allow thermal transfer through convection within the ice, and while the model for heat transfer becomes more complex we expect that increased ice thickness will typically be accompanied by a reduction in the rate of ocean heat loss.

Less appreciated is that the strength of sources of ocean heat may also vary as freezing leads to an increase in the ice thickness and a reduction in the thickness of the remaining liquid layer. It has been easy to overlook this possibility because up until recently none of the suggested heat sources occurred within the ocean itself. The two sources most widely discussed have been radiogenesis and tidal flexing, both associated with only the solid part of the planetary body. Estimates on both are uncertain because of incomplete knowledge of the composition of the body, but important to note here is that both of these sources can be expected to scale with the volume of the body (increasing with the radius cubed), while heat loss increases with surface area (radius squared). Such a situation might be expected to favor liquid oceans on large bodies and make liquid oceans less likely on very small satellites.

While radiogenesis and tidal flexing may provide a sufficient heat source for oceans on the large Jovian satellites, these sources appear inadequate in explaining the case of tiny Enceladus with a radius of only 250 km. While the subsurface ocean on Enceladus is still a speculation and the geyser of water particles might be explained without the need for an ocean, Cassini also observed high heat fluxes from Enceladus that cannot be explained by these traditional sources (Meyer and Wisdom, 2007). New heat sources have been proposed, such as tidally forced shearing within the ice cover (Nimmo, et al., 2007), and exotic ocean compositions including antifreeze agents have also been considered but these have not provided a clear explanation of the heat source.

Only recently has dissipation of ocean tidal flow been considered as a significant heat source for the oceans on these icy satellites (Tyler, 2008, 2009). To admit tidal heat generated within the solid body but not the ocean may seem at first strange as it has long been known that tidal dissipation on Earth occurs primarily in the ocean. The likely reasons for this assumption have been reviewed (Tyler, 2008) and shown to be based on an incomplete or incorrect description of the ocean’s tidal response and an antiquated understanding of the ocean tidal dissipation process. It may be that the tidal dissipation process is quite different for these satellites with oceans, but the reasons for once assuming that the case would be quite different than for Earth can now be seen to be faulty.

Earlier treatments assumed an equilibrium response while the new treatment more realistically allows the ocean inertia and therefore a dynamic response. The difference in the ocean tidal response can be remarkable when a constituent of the tidal forces has a frequency and configuration that can excite natural modes of oscillation of the ocean. Earth’s ocean is a clear case in point. While the Bay of Fundy has no special priority in the scheme of tidal forces, its tidal response shows 10 m surface displacements and exceptionally strong tidal flow. The large response is due to a coincidental match between the configuration of forces and the natural modes of oscillation in the Bay. Indeed when characterizing the Earth’s ocean tides by surface displacements and flow speeds (though not necessarily depth integrated flow transports), one sees these tides as prevalently products of resonant excitations.

The focus of this paper is on ice‐covered oceans and in this case one need not rely on coincidence for such resonances. Rather, an ocean attempting to freeze may be driven into such states, and the path toward freezing may become blocked. There are a number of dynamical considerations we can use to suggest that such a situation may be quite common. Let us address several of these in succession:

First consider even the simple equilibrium tide solution, which is often a reasonable approximation for the response to some but not all tidal force constituents. In this case it is assumed that the sea surface conforms to the so‐called “equilibrium tidal height” which is just a rescaled version the time‐dependent gravitational potential. The time‐dependent variation in the sea‐surface displacement is then prescribed, but the lateral flow velocities required by mass conservation to fill this displaced height increase inversely with ocean thickness. As the ocean freezes the flow speeds increase, and because flow dissipation schemes typically scale with the square or cube of the flow speed, the amount of heat generated increases remarkably. Eventually the increasing dissipation must make the starting assumption of the equilibrium tidal response untenable, but this expected tendency provides another indication that ocean freezing can be self limiting.

The tendency of reduced heat loss with thickening ice and increased heat generation with the thinning remaining liquid layer may not even be the primary obstacle for a freezing ocean. When we allow the ocean a dynamic response, even bigger obstacles to freezing can arise and may be quite common. This is because the frequency of many of the ocean’s natural modes of oscillation depend on the ocean’s depth (i.e. thickness); an ocean initially far from resonant tidal excitation can be pushed toward this as freezing alters the frequency of the ocean’s natural modes of oscillation and brings it closer to that of the tidal forcing. Brief discussion of this point is difficult because the oceans possess a wide variety of natural oscillation modes which express a variety of different behaviors. But some important aspects can be discussed:

Coriolis forces should typically be important in the tidal response (they most certainly are in the case of synchronously rotating satellites where the tidal forces share the same frequency as rotation). Hence, beyond simply the gravity‐wave modes (which have the essence of a bathtub oscillation, though in spherical geometry), we also expect a suite of inertial and Rossby‐wave modes as well as hybrid oscillations where Coriolis and gravity are simultaneously important restoring forces. We can also expect that the oceans will be stratified (a perfectly unstratified ocean is only a theoretical idealization) and so a suite of internal wave modes are also expected. The full suite of possible oscillations is the product of these two sets. Luckily, understanding of the unstratified suite extends to the stratified case if one replaces the physical depth with the so‐called “equivalent depth”. The equivalent depth is always less than the physical depth and is calculated through weighting by stratification parameters. There is in principle an infinite set of equivalent depths, one for each of the internal‐wave modes. The external‐mode oscillations (the ones that can occur without stratification), and the internal‐mode oscillations are referred to as the barotropic and baroclinic modes, respectively.

The theoretical basis for calculating the barotropic and baroclinic natural modes of oscillation for a global ocean of uniform depth has been available since at least a century, though more explicit description of these eigenmodes have appeared more recently (Longuet‐Higgins, 1968). The strongest complaint that might be raised about the general applicability of these results appears in the case where the ocean depth has decreased so much that the assumption of its uniformity becomes untenable. Indeed these natural modes would provide a poor description of tides on Earth because of the most extreme breach of the uniform depth assumption (continents).

A second item might be the non‐included effects of the ice layer on the tidal flow response. While ice cover can affect the propagation and dispersion properties of ocean waves, the expected effect for long tidal wavelengths is likely to be small typically (Tyler, 2008). An exception is the case where the ice layer is much thicker than the remaining liquid layer. This, taken together with the caveat on the uniform depth assumption, are regarded here as an indication that some results providing a frozen ocean as a theoretical impossibility can not be entirely trusted, at least when a balance between heating and heat loss is expected only when so much freezing has occurred that only a tiny fraction of the liquid ocean remains. This point must be regarded in the case of barotropic gravity‐wave modes on Europa, for example.

The conditions for barotropic resonances can be calculated and seen to require quite small depths (< 1 km) which can be compared with depths of ~105‐ 180 km that can be expected from combinations of observations and analyses (Hand and Chyba, 2007). Obviously theoretical discussion of a Europan ocean of ~1 km depth and a ~100‐km ice layer would inflate caveats presented above and is anyway in conflict with observations. But considering the baroclinic modes, with the physical ocean depth replaced by the equivalent depths, such resonant states for Europa’s ocean are quite plausible. To show this explicitly one would need stratification and other parameters that are not currently available. For the objective of this paper, it is sufficient to simply point out that these resonances lie in the path to freezing.

Whether the increased heat approaching these resonant states is enough to halt further freezing requires further considerations that include not only the amplitude of the tidal forces and flow‐response parameters, but also prescription of the dissipation process. The best analogy for the dissipation process in Europa’s ocean is probably that of dissipation in Earth’s deep ocean. It was formerly expected that almost all of the ocean tidal dissipation on Earth occurred on the continental shelves and shallow seas. It is now known that a substantial part takes place in the deep ocean and is predicted not by barotropic boundary‐layer theory but rather it involves transference of tidal energy to baroclinic components (internal waves) which ultimately dissipate. Hence, stratification is important in both the flow response and the dissipation process.

We have previously discussed a resonant excitation of Rossby modes by a tidal force constituent arriving from a non‐zero axial tilt (obliquity) of the moon. This is expected to be a very important part of the ocean tidal response but at least in the non‐dissipative solutions is seen to be independent of the ocean depth because the flow involves only tangentially non‐divergent components. This flow surely generates heat, and the realistic amplitude is expected to vary as depth changes, but the functional relationship sensitively depends on the dissipation process and parameters assumed. It should be noted that this heat source draws its energy from the moon’s obliquity rather than its eccentricity, and that tidal dissipation need not quickly remove the obliquity because a forced component can be provided in systems with more than one satellite (Bills, 2005).

3. Implications for Life

There are two competing but not mutually exclusive explanations for life on Earth and the possibility of life on other planets, i.e. abiogenesis (Russell and Kanik, 2010) and panspermia (Joseph 2009, Joseph and Schild, 2010). There are also a number of explanations for the sources of water on Earth, our Moon, and the oceans of Europa and Enceladus, e.g. oceans of water delivered by comets.

We can only speculate about the source of these oceans, and the possibilities the overlying ice-crust may or may not have been liquid, or liquified, during the early stages of planet and moon formation, or during their subsequent histories. However, regardless of how we choose to believe this water was delivered or how life began, we know that water is associated with life, and is necessary for the development and evolution of complex life. The possible presence of warm liquid oceans on Europa and Enceladus therefore, invites speculation about the nature of life within these two Jovian moons. The basis of these speculations are the life forms which proliferate within the oceans of Earth, beginning with the life forms which proliferate near thermal and volcanic vents.

On Earth these vents dissolve a variety of life-sustaining chemicals which serve the nutritional needs of chemosynthetic archaea. These archaea form the basis of a food chain, and thus hydrothermal vents are typically biologically productive and host complex and diverse communities, including giant tube worms, clams, crabs, and shrimp. These deep ocean communities are self-sustaining and do not require sunlight. There is good reason to suspect the oceans of Europa may have numerous active thermal and volcanic vents. Likewise, it does not become unreasonable to suspect complex eukayotic life may have also evolved within the oceans beneath the surface of Europa. It is also possible that microbial life proliferates within the oceans of Enceladus, but less likely that complex life may have evolved.

4. Conclusion

Combining several elements we have discussed, it appears that the fluid‐ and thermo‐dynamics of these oceans present important obstacles to complete freezing of the ocean. Orbital energy of the moon (and neighboring moons as well) is converted to ocean heat, and a common scenario may be that oceans can freeze only after all or much of this energy has been converted. Because the time scales for this can be quite long, the persistence of liquid oceans from even primordial times might be a common feature in the Universe.

We have presented theoretical arguments based in thermo‐ and fluid‐dynamics that indicate the persistence of liquid oceans, and suggest with this that liquid oceans may be a common feature in the universe. Does this change what we should expect for the chances of extra‐terrestrial life? All life known requires water, and the special properties of the water molecule provide essential functions that are not easily replaced in speculations of living systems that do not require water. While such alternative forms of life have also not been ruled out, an explicitly stated strategy in NASA’s search for extra‐terrestrial life is to “follow the water” (Ball, 2004). Programmatically, at the very least, the expected pervasiveness of liquid oceans has direct bearing on the search for extra‐terrestrial life. However, at this juncture we can only speculate about the nature of any possible life forms which dwell within the oceans of Enceladus and Europa.

Acknowledgments: This work was conducted with support through the NASA Outer Planets Research Program, Grant Number: NNX09AU30G, and has also benefitted from helpful discussions with B. Bills, S. Vance, K. Hand, F. Nimmo, and J. Goodman.