source and the convective cooling would leave the ice layer with a constant thickness. Modifications to the latter model resulted in a reduction in the estimated amount of tidal heating, again opening the question of whether the water layer on Europa would freeze completely over geologic time.36 Various other thermal models have been constructed, including those that took into account the effects of an insulating regolith on the stability of the ice shell.37
The competition between the tendency of tidal heating to maintain a liquid-water ocean and that of subsolidus ice convection to freeze the ocean has now been analyzed for nearly two decades without a definitive conclusion having been reached. The major uncertainty in the modeling is the uncertain rheology of ice and of its control of both convection and dissipation.38 Both dissipative heating and convective cooling involve nonlinear feedback mechanisms associated with the dependence of rheology on temperature and the dependence of temperature on the heating and cooling mechanisms. The amount of tidal heating in the ice depends on the rheology of the ice at tidal periods and on the magnitude of tidal deformation, the latter in turn depending on the internal structure and, in particular, on whether there is a liquid ocean beneath the ice layer and on the ice thickness.
Other properties of the ice are also both important and highly uncertain. The thermal conductivity of the ice is dependent on the temperature and physical state of the ice (its density and the distribution of cracks, for example). A thermally insulating layer at the surface of Europa would promote stabilization of a liquid-water ocean.39 The occurrence of minor constituents in the ice and ocean such as salts and ammonia would affect both the rheology of the ice and the freezing temperature of the ocean.40 Tidal heating along major faults in Europa's ice shell may be important,41 and tidal heating due to forced circulation in a thin liquid-water ocean sandwiched between the rock interior and the overlying ice may prevent complete solidification of the ocean.42 Tidal heating is too dependent on many unknown or poorly known properties of Europa's ice shell, therefore, to settle the debate on the existence of a liquid-water ocean beneath the ice of Europa theoretically, without the benefit of direct observations.
That the moons of Jupiter should have transient atmospheres, undergoing continual production and loss, is one of the many enigmas of the complex jovian system. While volcanism is accepted as the ultimate source of Io's atmosphere, other processes must be responsible for Europa's atmosphere.
To date, remote-sensing techniques have identified two constituents of Europa's atmosphere — molecular oxygen (O2) and atomic sodium (Na). The former is inferred from ultraviolet emissions,43 while the latter comes from detection of light scattered at visible wavelengths. 44 The vertical column abundances (the number of molecules sitting above a unit of area on the surface) are estimated to be ~1015 cm-2 for O2 and ~ 1010 cm-2 for Na, with number densities just above the surface of ~108 cm-3 and ~70 cm-3, respectively. Although sodium is far less abundant than oxygen, it is more easily observed and has been traced out to distances of more than 20 times the radius of Europa. Other gases must also be present with greater or lesser abundances than these and, collectively, may serve as important tracers of the chemical composition of Europa's surface; they have not been detected, however.
While some atmospheric constituents may arise from the impact of micrometer-sized dust grains or from simple evaporation of surface materials, the dominant source for Europa's O2 and Na atmospheres is thought to be sputtering (i.e., the ejection of molecules or atoms from a surface resulting from the impact of ions or electrons) by energetic (100- to 1000-keV) magnetospheric ions (Figure 2.4). The oxygen comes from water ice at the surface. Laboratory experiments have confirmed that ice subjected to ion bombardment yields gaseous H2O, H2, and O245; the water vapor quickly freezes again at Europa's surface temperatures, the hydrogen quickly escapes to space due to the weak surface gravity (with a surface acceleration of about 1.3 m s-2), and the oxygen remains to form a bona fide atmosphere, albeit one subject to loss by subsequent ionization and transport processes. Sodium, on the other hand, comes from impurities (such as salts) intrinsic to the icy surface material, as well as from Io, where sodium escapes and can be implanted subsequently onto Europa's surface. The eventual detection of additional species,