Cryovolcanic resurfacing is a popular mechanism to explain relatively young surface units on icy satellites of Jupiter, Saturn, Uranus, and Neptune. Prior to the Galileo data acquired between 1996 and 2001, Europa was thought to have undergone significant cryovolcanic resurfacing, facilitated by a global ocean beneath the icy surface. However, close examination of Galileo data at resolutions much better than those of Voyager images show that many of the features previously thought to be cryovolcanic are commonly best explained by other formative mechanisms, including tectonism and diapirism. In this study, I present an examination of the characteristics of a variety of Europan surface features for which effusive cryovolcanism is a possible origin, including apparently lobate “flows,” certain elliptical to circular lenticulae, and low-lying, smooth, low-albedo surfaces. A review of cryovolcanic eruption theory, together with Galileo data analysis of Europan surface geology and composition, indicates that cryovolcanism is a viable, though not unequivocal, explanation for some of these features. Some constraints on cryomagma properties and lithospheric structure are offered for these cases. The presence of small-volume, low-viscosity effusions is supported by observations and modeling. Some positive relief lenticulae could represent more viscous effusions, although diapirism may be a preferable explanation. However, strong evidence is lacking for cryovolcanic resurfacing on a large scale. On the basis of our experience with Galileo images of Europa (and Ganymede), Voyager-era inferences for widespread cryovolcanism on icy satellites may be overstated and will need to be carefully reexamined in the light of new data from upcoming spacecraft missions.
 Resurfacing by eruptions of fluids derived from a satellite's interior has been postulated to explain various landforms and the apparently smooth and youthful surfaces on some of the icy bodies of the outer solar system. Whether these features do indeed represent resurfacing of this nature remains uncertain. In the case of Europa, bright plains, which appeared smooth at Voyager resolutions of 2 km pixel–1 or lower, were revealed by the superior resolution and optics of the Galileo Solid State Imager (SSI) to be intensely ridged at many different scales [Greeley et al., 1998]. Extensive flooding of Europa's surface might therefore not be a viable process, or if it took place in the past, it has been succeeded by a different resurfacing regime which preserves no record of large-scale effusive events. However, the Galileo data revealed a wide variety of smaller-scale surface landforms that attest to a dynamic interior, endogenous geologic processes, and perhaps, in some cases, extrusion of liquids onto the surface.
 Such resurfacing is termed “cryovolcanism” and is defined as “… the eruption of liquid or vapor phases (with or without entrained solids) of water or other volatiles that would be frozen solid at the normal temperature of the icy satellite's surface” [Geissler, 2000]. This definition reflects the concept of volcanism on the terrestrial planets as eruptions of silicate magmas. Cryovolcanic fluids therefore might include aqueous solutions, vapor-rich sprays, or icy slurries [Stevenson, 1982; Allison and Clifford, 1987; Crawford and Stevenson, 1988; Kargel, 1991, 1992; Kargel et al., 1991; Wilson et al., 1997]. The specific compositions of cryomagmas on a given satellite depend in large part on the location of the planet-satellite system within the solar system. Satellites forming at Jupiter's relatively warm location in the protoplanetary nebula are unlikely to have retained significant quantities of materials more volatile than water (e.g., ammonia, methanol, and methane), whereas icy satellites of Saturn, Uranus, and Neptune would harbor increasingly more volatile compounds with increasing distance from the Sun [Prinn and Fegley, 1981; Kargel, 1991]. For Europa the spectroscopic signature indicates an overwhelming water-ice composition, with minor amounts of sulfur compounds [Carlson et al., 1999, 2002] and hydrated salt minerals such as magnesium sulfates or sodium carbonates [McCord et al., 1998b, 1999] likely acting as contaminants to produce briny (cryomagmatic) fluids.
 However, there remain conflicting arguments concerning the relative thickness of the water and ice layers that compose Europa's crust [Pappalardo et al., 1999], some authors favoring a thin ice shell over a deep water layer [Greenberg et al., 1998, 1999] and other evidence pointing to a thin brittle ice shell overlying a thicker convecting ductile ice layer, which, in turn, overlies a water layer [Head and Pappalardo, 1999; McKinnon, 1999]. The structure of Europa's crust has important implications for the feasibility of delivering liquid to the surface.
 Given that cryovolcanism may be a viable process on Europa (and other icy satellites), this study (1) presents observations and interpretations of Galileo data of possible cryomagmatic features on Europa, (2) summarizes the theory of cryovolcanic eruption mechanisms, (3) investigates the possible origins of endogenic features on Europa, and (4) discusses the implications for cryovolcanic fluid compositions, liquid water, and the nature and structure of Europa's interior. Attention is focused on mechanisms of effusive eruptions, as explosive eruptions have been considered in more detail elsewhere [Fagents et al., 2000]. This study shows that although some features are indicative (but not definitively so) of extrusive origins, cryovolcanic resurfacing on a large scale (e.g., plains volcanism) is evidently not recorded in the current surface of Europa.
2. Observations and Geologic Interpretations at Europa
 Observations from the Voyager era and early Galileo data revealed a variety of features that hinted at cryovolcanic origins [Lucchitta and Soderblom, 1982; Greeley et al., 1998]. Many of these resemble silicate volcanic features, such as dikes, lava domes, or flows. For example, large areas of low-albedo, mottled terrain were interpreted as possible intrusions or extrusions of dirty cryomagmatic slurries [Lucchitta and Soderblom, 1982], and the prominent “triple-band” lineaments were attributed to cryovolcanic flooding of graben [Buratti and Golombek, 1988] or intrusions of hydrated minerals [Finnerty et al., 1981]. With the accumulation of higher-resolution data during the Galileo prime mission and subsequent mission extensions, extrusive cryovolcanic origins for many of these features were ruled out. For example, the mottled terrain was revealed at higher resolutions to be chaotic disruptions of the existing surface rather than superposition of new material [Pappalardo et al., 1998; Spaun et al., 1998; Greenberg et al., 1999]. However, as discussed in sections 2.1–2.3, there remain features for which the morphologic and stratigraphic relations argue strongly for the presence of fluids at the surface. Other features have more equivocal origins, but a cryovolcanic origin cannot be ruled out. Here the diversity of potential effusive cryovolcanic features is examined, and the best candidates for the effusion of liquids at Europa's surface are indicated.
2.1. Cryolava Flows?
 High-resolution imagery was eagerly anticipated for Thrace and Thera Maculae in Europa's southern hemisphere. These low-albedo features (∼160 and ∼80 km in length, respectively) were observed in Voyager data to consist of brownish or gray mottled terrain and were interpreted as either intrusions or extrusions of material from the Europan interior [Finnerty et al., 1981; Lucchitta and Soderblom, 1982]. Later, Wilson et al.  suggested an origin as cryovolcanic flows of dirty water/ice slurries on the basis of the features' lobate morphologies, their apparent stratigraphic relationship to the surrounding terrain, and theoretical modeling of eruption processes.
 However, the images of Thrace acquired by the Galileo spacecraft in orbit E17 suggested a different, more complex origin (Figure 1). These higher-resolution data reveal a quite different stratigraphy, and the margins no longer appear lobate. For example, ridges and lineaments in the background plains can be traced into the interior of Thrace, where they become progressively degraded (e.g., the broad ridged band indicated by white arrows in Figure 1). This suggests that rather than being emplaced as a flow over the surface, the formation of Thrace involved darkening and disruption of the preexisting surface. Only at Thrace's margins are small areas of low-albedo, smooth surfaces observed; these surfaces appear to embay surrounding ridged terrain and may represent confinement of a fluid by topography (Figure 1, inset). The mechanism responsible for upwarping and disrupting the preexisting surface may also have liberated small volumes of low-viscosity, low-albedo fluid, such as a brine.
 Smaller lobate features a few tens of kilometers in length were identified first in ∼630 m pixel−1 images from orbit E4 (Figure 2a) and then in ∼550 m pixel−1 images from orbit G7 (Figure 2b). These features are apparently associated with ridge-fracture systems and have the appearance of emanating from, disrupting, or breaching the ridges (Figures 2a and 2b), although the ubiquity of lineaments on Europa makes this a questionable interpretation. The lobate morphology again suggests the flow of a viscous fluid across the surface. However, this interpretation is called into question by the presence of features in higher-resolution data (∼30 m pixel−1) which clearly are not flows but which, when the image is degraded to lower resolution, mimic the lobate form of fluid flows (Figure 2c, inset). As for Thrace and Thera Maculae this is another instance of apparent disruption of the preexisting terrain (albeit on a much smaller scale) and, as such, casts doubt on volcanic flow origins for all lobate features seen only at resolutions of several hundred meters per pixel. Whether this reinterpretation can be extrapolated to all instances of flow-like morphologies will remain unknown until a future mission maps the surface with greater coverage at a consistently high resolution.
 On the basis of Galileo images, which admittedly cover only a small fraction of Europa at high resolution, I conclude that there is no compelling evidence for the presence on Europa of long, lobate cryovolcanic flows; the acquisition of successively higher resolution data ruled out this origin for the features initially interpreted as flows based on the morphologic similarity to silicate lava flows on the terrestrial planets.
2.2. Cryolava Domes?
 There exists a category of circular to elliptical positive relief features on Europa, typically a few to >10 km in size. Along with similar-sized pits and low-albedo spots these features are collectively termed lenticulae [Pappalardo et al., 1998], and their origins have been explained by two end-member models: (1) They are the surface manifestation of solid-state convection in a relatively thick ice shell and the consequent impingement of warm ice diapirs on the surface [Pappalardo et al., 1998], and (2) they are the result of melt through and breakup of a thin ice shell by a warm subsurface ocean [Greenberg et al., 1999]. Of the positive relief features some are simple upwarpings of the surface ice, with or without the presence of surface fractures [Greeley et al., 2000]. Others have chaotic surfaces, exhibiting jumbles of blocks and fragments of preexisting terrain which can be traced inward from the surrounding plains [Spaun et al., 2002]. However, still others have surface textures bearing no relation to the surrounding terrain, appearing to have obscured and spread over the preexisting surface as a viscous flow, retaining significant relief (Figure 3). Whether this interpretation is again a consequence of inadequate image resolution is unclear. Nevertheless, the morphologies of some positive relief lenticulae are so strikingly reminiscent of silicate lava domes on Earth that it is important to consider an origin by cryovolcanic effusion of a viscous fluid. These features are commonly associated with ridges or fractures that may have provided a pathway for ascent of material from below, but this might simply be coincidence, since Europa's surface is apparently ubiquitously fractured and ridged.
 Morphometric information has been compiled for a number of raised lenticulae exhibiting evidence of effusive emplacement. Figure 4 shows topographic profiles for four of these candidate cryolava domes imaged in ∼200 m pixel−1 data from orbit E6. The profiles were derived from digital elevation models (DEMs) generated by a two-dimensional photoclinometric algorithm [Kirk, 1987]. The errors associated with this DEM generation technique are discussed by Figueredo et al. ; the DEMs are regarded as first-order assessments of the local topography but suffice to place loose constraints on feature heights. For 11 candidate cryolava domes measured in the orbit E6 data, heights are typically on the order of 40 to <100 m. Some domes appear to lie in slight depressions, but in many cases they cast shadows on, and are therefore elevated with respect to, the surrounding terrain (Figure 4). Diameters range from ∼3 to 10 km, and volume estimates derived from the profiles range from 0.3 to 3 km3.
 An extreme example of an emergent dome-like mass can be seen in Figure 5, which shows a ∼100 km diameter feature known as “the Mitten” (Murias Chaos) in ∼230 m pixel−1 data from orbit E17. The size of this feature far exceeds that of the typical candidate extrusive domes shown in Figures 3 and 4 and likely has a more complex history, perhaps involving a combination of diapiric upwelling and viscous, solid-state flow across the surface [Figueredo et al., 2002].
 While it is difficult to see how the melt through hypothesis might lead to the significant positive relief of these lenticulae, both diapiric upwelling and cryovolcanic mechanisms could produce similar surface expressions (Figure 6). Simple upwarping and cracking of the surface could be produced either by subsurface diapirs or by shallow cyromagmatic intrusions (cryptodomes) [Pappalardo, 2000]. Jumbled, chaotic surfaces might be produced by near-surface diapirs or by disruption of the icy carapace of a viscous extrusion. Masses apparently superposed on the surrounding terrain could be explained by slow creep of a surface-breaching diapir or by effusions of a viscous cryolava. The two hypotheses are not necessarily at odds with one another since there is likely a continuum of behaviors between emplacement of a viscous fluid and solid-state movement of warm ice bodies. In the absence of image data at scales adequate to resolve the details of stratigraphic relationships and surface texture (e.g., flow ridges and radial/concentric fractures), both hypotheses remain viable. In section 5, application of simple analytical models allows constraints to be placed on the material properties required to reproduce the observed morphologies, and I discuss whether it is reasonable to expect cryomagmas possessing such properties to exist on Europa.
2.3. Low-Viscosity Flooding
 There is a range of features which are plausibly explained by the release of a low-viscosity fluid at the surface. Typically, these features consist of smooth, low-albedo surfaces which occupy topographic lows, may embay surrounding ridged terrain, are apparently confined by topographic features such as ridges, and occasionally exhibit lobate morphology [Greeley et al., 2000]. Galileo SSI color images show that low-albedo surfaces tend to be reddish-brown [Clark et al., 1998; Geissler et al., 1998]. These units may be associated with lenticulae (domes, pits, and spots) or larger-scale disruptions of the surface and may range in size from a few to tens of kilometers. For example, Figure 7 shows a smooth, low-albedo pond-like feature lying in a depression in ridged plains near 6°N, 327°W. This feature has been interpreted as a small-volume (0.5 km3) fluid effusion [Head et al., 1998].
 Low-albedo spots a few kilometers in size and low-albedo moats surrounding many raised lenticulae are found extensively superposed on plains regions. Figure 8 shows three examples. In addition to being confined to an apparent depression surrounding the dome, the low-albedo surface is delimited by a high-standing ridge (arrows), as would be the case for a fluid flowing up against and being obstructed by a topographic barrier. Similarly, Figure 1 shows details around the margins of Thrace Macula, where the low-albedo material again appears to be controlled by the background ridges and troughs (black arrows). To the south the low-albedo material appears to embay the finely ridged terrain of a broad band. In addition, apparently lobate morphologies are observed in some locations (Figure 1, inset).
 Another example of a smooth, low-albedo, low-lying surface is shown in Figure 9, this time located at the margins of a doublet ridge. Galileo-era models for ridge formation include upwarping due to linear diapirs [Head et al., 1999], accumulation of icy debris expelled from a tidally worked water-filled fracture [Greenberg et al., 1998], proximal accumulation of explosive cryovolcanic materials [Kadel et al., 1998], incremental injection and refreezing of melt in a near-surface fracture [Turtle et al., 1998], and compressional upwarping of a fractured crust [Sullivan et al., 1997; Patterson and Pappalardo, 2002]. The smooth surface in Figure 9 has been interpreted as a mass-wasting product [Head et al., 1999] or flooding of the marginal trough (formed because of loading by the ridge) when the surface is depressed beneath the local “water line” [Greenberg et al., 1998]. Although the last possibility makes the case for liquid at the surface, it is a passive seeping of H2O to the surface and might not be considered truly cryovolcanic in nature.
 The morphologic characteristics of the various smooth, low-albedo deposits described here are consistent with the emplacement of (relatively small volumes of) fluid at the surface. In some cases (e.g., the “puddle” in Figure 7) these effusions could represent cryovolcanic fluids which ascended from a subsurface liquid body or layer. Alternatively, Head et al.  proposed that mobilization of near-surface pockets of brine or salt-rich ice could result from heating by warm ice convecting or ascending diapirically from depth [Pappalardo et al., 1998; Rathbun et al., 1998]. Furthermore, sulfuric acid (which has been detected by the Near Infrared Mapping Spectrometer (NIMS) [Carlson et al., 1999, 2002]) would also melt readily if heated above ∼220 K by an impinging diapir. Subsequent release of the briny or acidic liquids at the surface might then have produced the observed dark features. This hypothesis is especially plausible for the margins of Thrace Macula and the low-albedo moats associated with some raised lenticulae, which themselves might be the manifestation of warm diapirs impinging on the surface.
 The low albedo and coloration of these features could be the results of compositional or grain-size effects. Although variations in ice grain size can both darken and discolor the surface [Clark, 1981a, 1981b; Clark et al., 1983; Clark and Lucey, 1984], the high degree of correlation between low-albedo areas and NIMS detections of non-ice materials [McCord et al., 1998a, 1998b, 1999; Carlson et al., 1999, 2002] suggests the former. While the presence of hydrated salt minerals adequately explains an origin by brine release, the minerals are colorless and so cannot be the source of reddish-brown coloration. However, polymerized sulfur, a radiolytic product of sulfuric acid [Carlson et al., 1999, 2002], can adequately explain the color of these low-albedo features.
 Another explanation for the confinement of the smooth, low-albedo surfaces to topographically low areas involves changes in the structure of the surface ice due to a subsurface heat source resulting perhaps from a warm ice body [Pappalardo et al., 1998; Rathbun et al., 1998] or a water layer melting upward through the ice [Greenberg et al., 1999]. Elevation of the surface temperature might lead to enhanced sublimation and the production of a low-albedo lag deposit of non-ice material [Fagents et al., 2000]. Alternatively, annealing of ice grains and relaxation of topography could mask preexisting features [Fagents et al., 2000]. The boundaries between the low-albedo (topographically low) surfaces and brighter (apparently higher) preexisting terrain might then represent the limit to which the thermal wave from the subsurface heat source was able to advance and modify the surface (Figure 10). In this way, terrain softening or a lag deposit might mimic the morphologic and stratigraphic characteristics of a low-viscosity fluid effusion.
 While none of the explanations discussed above satisfactorily accounts for all the observed characteristics of the low-albedo deposits, all remain viable hypotheses based on the data in hand. Having made these rather equivocal interpretations based on geomorphology, it is necessary to turn to theoretical fluid dynamic and thermal considerations to help determine if fluid volcanism is a feasible mechanism on Europa.
3. Overcoming Negative Buoyancy
 The greater density of pure water ρw with respect to that of pure ice ρi is commonly cited as an impediment to watery cryovolcanism. The buoyancy force, defined as Fb = g(ρi − ρw) per unit volume, is negative. Therefore water present in a global layer beneath an ice shell should remain in this stable configuration. Squyres and Croft  proposed that fractures penetrating to a liquid layer could, if they opened sufficiently rapidly, facilitate delivery of liquid to the surface because the momentum of the liquid rising in the fracture would cause it to overshoot its level of neutral buoyancy. This is likely to produce only limited volumes of water at the surface, and it is unclear whether the ice shell thickness is sufficiently small and the magnitude of crustal stresses sufficiently great to allow penetration of fractures to the water [Crawford and Stevenson, 1988; Gaidos and Nimmo, 2000]. However, there are a number of other mechanisms by which fluid may ascend through an icy crust to produce surface activity, as summarized in Figure 11.
3.1. Volatile-Bearing Liquid
 Water at depth may contain dissolved volatiles. Candidate species proposed for Europa include CO2, CO, and SO2 [Lane et al., 1981; Prinn and Fegley, 1989; Noll et al., 1995; McCord et al., 1998a; Carlson et al., 1999, 2002], which may have originated as volcanogenic inputs to the putative water layer from silicate volcanism on Europa's rocky interior. Depressurization of the volatile-charged water would permit the volatiles to exsolve, greatly increasing the buoyancy of the fluid. Crawford and Stevenson  proposed a mechanism whereby water-filled cracks propagate upward from the interface between the water and ice. The low pressure at the crack tip permits volatile exsolution. As the crack reaches its maximum stable height and pinches off from the ice-water interface, the buoyancy provided by the vapor permits continued ascent. The low viscosity of the water allows effective segregation of the vapor so that upon reaching the surface the material erupts as a spray of condensing vapor with minor amounts of entrained water droplets. This explosive venting mechanism was proposed to explain an enigmatic elliptical feature identified in Voyager images as a potential cryoclastic deposit [Cook et al., 1982], but this feature has since been discounted as an artifact produced by vidicon distortion [Phillips et al., 2000]. Cryoclastic eruptions have also been proposed as one possibility for the origin of low-albedo, diffuse halos associated with some lenticulae and triple bands, with the low albedo resulting from impurities in the erupting mixture or annealing of ice grains [Fagents et al., 2000]. However, the vapor-rich nature of such eruptions, and the likelihood that small water droplets would rapidly freeze in Europa's frigid environment, imply that it is unlikely that such a mechanism would produce significant surface flows.
3.2. Presence of Non-Ice Substances in Water or Ice
 The addition of non-ice materials either to the water or to the ice could potentially modify the density contrast sufficiently for positive buoyancy to be achieved. Kargel [1991, 1992] and Kargel et al. [1991, 2000] considered brines and mixtures of water, ammonia, methanol, methane, and nitrogen as possible compositions of cryomagmatic fluids on icy satellites.
 Galileo NIMS evidence for the presence of sulfur compounds [Carlson et al., 1999, 2002] and hydrated salt minerals (particularly magnesium and sodium sulfates/carbonates) associated with low-albedo surfaces of possible endogenic origin [McCord et al., 1998a, 1998b] supports the possibility of non-ice contaminants. Addition of MgSO4 or Na2SO4, for example, acts to increase the density of both the solid and liquid phase, but although negative buoyancy is somewhat diminished, the liquid does not become positively buoyant [Kargel, 1991, 1995]. Addition of ammonia, on the other hand, would produce a positive buoyancy [Croft et al., 1988; Kargel, 1992, 1995]. However, as discussed in section 1, significant quantities of ammonia, methane, nitrogen, and methanol might not be available on Europa, leaving magnesium and sodium-based brines as the most likely possibility. Hence the addition of contaminants to water may not be a plausible mechanism for overcoming negative buoyancy on Europa.
 Alternatively, the density of the ice might be increased by addition of denser materials. Figure 12 shows the effects of the presence of different amounts of non-ice material distributed in an intimate mixture with the ice. It can be seen that <4% by volume of a dense (3000 kg m−3) silicate contaminant is required for the liquid phase to become buoyant with respect to the solid. Somewhat lower amounts are required if the contaminant has a greater density. Although it is plausible that dense contaminants derived from Europa's silicate interior or implanted by micrometeorite falls could be present on the surface, the composition (hence density) and amount of such material is currently unknown. The spectral evidence for non-ice compositions on Europa is limited to hydrated sulfates and carbonates [McCord et al., 1998b] and sulfur compounds [Carlson et al., 1999, 2002]; however, the dominant H2O signature might mask the presence of minor amounts of other minerals.
 The presence of gas clathrate hydrates also has potential to alter buoyancy properties. These compounds form at elevated pressures, where crystalline water ice is stabilized by volatiles (e.g., CO2, SO2, N2) in a somewhat open structure into which other species are incorporated. In the case of Europa, pure water would be buoyant with respect to the relatively dense clathrate compounds which could potentially form at the pressures imposed by tens of kilometers of water-ice overburden [Davidson, 1983; Kargel et al., 2000]. Furthermore, decompression or thermal decomposition of clathrates could liberate gases for volatile-driven eruptions [Stevenson, 1982].
3.3. Fluid Pressurization
 If liquid is present as discrete reservoirs within the ice crust rather than as a continuous layer, then pressurization of the liquid could provide the driving force to overcome the negative buoyancy. A fluid body experiencing an excess pressure with respect to the surrounding lithospheric ice could deliver material to the surface through fissures opening to the surface if that excess pressure is sufficiently great and the fluid body is sufficiently shallow. One possibility for generating an excess pressure involves the partial freezing of a liquid reservoir contained within the ice lithosphere. In contrast to silicate volcanism this is plausible for icy volcanism because of the unusual properties of the liquid and solid phases of water: The density decreases on freezing.
 Consider a rigid reservoir having a fixed volume VT filled with water of density ρw, located at a depth H in an ice crust. All notation is given in Table 1. A fraction n of the water freezes to form ice of density ρi and volume Vi given by
leaving a volume Vw0 in the reservoir, given by
 The ice occupies a greater volume than the water from which it formed because ρi < ρw. If the reservoir size is assumed to be fixed (i.e., the walls do not deform to accommodate freezing), the volume increase on freezing is accommodated by a decrease in the volume of the remaining water as a result of its finite compressibility β. Thus the new water volume must be equal to
 Assuming the water obeys a linear equation of state, Vw1 is given by
where Pw0 and Pw1 are the initial and final pressure of the water, respectively. Rearranging equation (4) yields the pressure increase in the reservoir
 The initial water pressure Pw0 is taken as being equal to the local hydrostatic pressure Ph(z) due to the weight of the ice overlying the reservoir, i.e.,
where g is acceleration due to gravity. From equations (5) and (6) the pressure increase ΔP due to freezing of some volume of reservoir fluid, i.e., the excess driving pressure in the reservoir, can be derived. This is discussed further in section 4.1.
 Another method of generating an excess pressure would be cyclic tidal stresses acting on a liquid body. Although it is difficult to envision a mechanism of pressurizing a global water layer, this might be possible for a discrete reservoir. Furthermore, Greenberg et al.  offer an explanation for the formation of ridge systems by tidal pumping of shallow, water-filled fractures connecting the surface to a global ocean. In this scenario, tidal working of the fracture over ∼80 hour intervals allows for water to freeze partially during the opening cycle and then be compressed and driven upward during the closing cycle. Although this model is contested [e.g., Head et al., 1999] and might not be considered true cryovolcanism, it does provide a possible mechanism for delivering limited volumes of subsurface ice (and water?) to the surface.
4. Low-Viscosity Effusions
 Given that some mechanism can be invoked for cryomagmas to rise from depth to the surface (section 3), it is informative to explore the conditions under which this may take place, as well as the eruptive consequences.
4.1. Pressure-Driven Ascent
 Consider the ascent of water from the pressurized reservoir described in section 3.3 through a vertical fracture of constant half-width rc and length L. A mechanism for fracture propagation is assumed to have been provided (e.g., by tidal forces or stresses due to reservoir overpressure), and the forces required to maintain an open pathway are assumed to be insignificant [Turcotte, 1990]. For now, the problem is treated as purely a dynamical one, neglecting heat transfer.
 Assuming steady flow in the vertical direction, the momentum equation can be expressed as
where w is the vertical (z direction) velocity, x is measured across the width of the fracture, p is pressure, and ρw and μ are the fluid density and viscosity, respectively.
 If the vertical pressure gradient in the fluid arises both from the hydrostatic overburden and from an excess pressure in the reservoir, i.e.,
which is a parabolic velocity distribution across the width of the fissure, with the maximum velocity wmax occurring at x = 0.
 The volumetric discharge Q for length L along the strike of the fissure is obtained by integration of w(x):
 The velocity averaged across the width of the fissure is obtained by dividing the discharge by the cross-sectional area 2rcL of the fissure:
 Note that for a pure water cryomagma in an ice crust, ρi − ρw is negative, so the force due to the excess pressure in the reservoir must overcome the negative buoyancy force for to be positive. Therefore, for ascent to occur the condition to be satisfied is
 Having thus obtained values for the minimum excess pressures required for negatively buoyant water cryomagmas to ascend from various plausible depths in Europa's ice lithosphere, equation (6) can be rearranged to find the fraction of the reservoir volume that must freeze in order for this pressure to be achieved:
Figure 13 shows the excess reservoir pressure as a function of the volume fraction of reservoir fluid that freezes (n), with vertical dashed lines indicating the minimum requirements to drive fluid from depths of 1, 10, and 100 km to the surface. Note that this very simplistic treatment does not account for the volume change that would be accommodated by reservoir wall deformation, which would be facilitated by the ductile flow of warm ice “country rock.” However, Figure 13 shows that even if high excess pressures could not be developed, eruptions could still be driven from depths up to 10 km by relatively low reservoir pressures (105–106 Pa, roughly 9% of the ambient lithostatic pressure) developed by minimal freezing.
4.2. Buoyancy-Driven Ascent
 The motion induced in a liquid of density ρl through a lithosphere of density ρs (either or both of which may consist of impure H2O) by a positive buoyancy (i.e., ρl < ρs) is obtained through a similar, though somewhat simpler, derivation:
 An interesting point to note is that because of the low viscous resistance to flow of watery cryomagmas, only marginal values of pressure or buoyancy driving force terms are required to produce rapid ascent rates (equations (14) and (19)). Driving force terms greater than these critical values easily produce ascent velocities of tens to hundreds of meters per second or more, which are obviously outside of the laminar regime treated here and therefore are not realistic to address with these equations. However, these equations illustrate that once even a marginal driving force has been developed, ascent would readily be facilitated.
4.3. Exposure of Water to the External Environment
Allison and Clifford  describe in detail the consequences of eruptions of water onto the surface of Ganymede. Given the similar conditions at Europa, the same processes might be expected (Figure 14), whether the effusion is the result of localized brine release [Head and Pappalardo, 1999] or ascent from a deeper cryomagma reservoir. Upon exposure to the cold, vacuum environment a water flow will experience intense “boiling” due to the H2O vapor pressure (61 Pa at 273 K) exceeding the ambient (essentially zero) pressure. This would produce a spray of vapor and water droplets. The extraction of heat of vaporization, together with the large temperature gradients between the water and its environment, would induce ice formation at the flow surface and base. Consequently, an icy crust might begin to develop but would undergo repeated disruption due to the explosive vaporization and motion of the flowing fluid. Once a thickness of surface ice is attained such that the hydrostatic pressure will prevent further vaporization (∼0.5 m), explosive disruption of the upper surface will cease, leading to insulation of the liquid and continued flow. Meanwhile, the flow front would remain a chaotic mixture of ice blocks, ice crystals, vaporizing water, and water “breakouts.” Flow would cease when the supply diminishes such that the hydraulic gradient drops below the critical level required to prevent the flow front freezing to the substrate.
 Both the development of an ice crust and the mixing of ice crystals through the flow will modify the bulk rheology of the flow, inducing a higher viscosity. However, without significant non-ice contaminants it seems likely that the resulting flow deposits would be thin, and once ponded in topographic lows, such watery effusions are likely to take on a smooth appearance at Galileo resolutions. This sequence of events is plausibly responsible for the low-lying features seen in Figures 1, 7, and 8.
5. Viscous Effusions
 On the other hand, the processes described in section 4.3 probably would not lead to the relief of the features in Figures 3–5. These appear to be the result of more viscous effusions (if they are not, in fact, the manifestation of ice diapirism), possibly involving non-ice contaminants or water-ice slurries. It is therefore appropriate to explore models for more viscous cryomagma ascent and emplacement. By analogy with terrestrial lava domes the candidate Europan extrusive domes are assumed to have erupted from a central vent and to have spread radially.
5.1. Conduit Ascent
 First, consider the rheological requirements for conduit ascent. Wilson and Head  derived expressions for minimum rise rates of buoyant magmas given an assumed set of magma properties. Modification of their treatment to encompass both pressure-driven and buoyancy-driven ascent leads to the following expressions for the critical rheological properties required for magma ascent through an assumed conduit geometry:
Here μ is the fluid viscosity, τy is the yield strength, rc is the conduit radius, H is the depth from which ascent begins, κ is the thermal diffusivity of the cryomagmatic fluid, χ is a dimensionless function of the amount of cooling [Jaeger, 1964; Fedotov, 1978], which for the cryovolcanic system under consideration here takes a value of 0.7, a and b are dimensionless factors related to conduit geometry (see Table 1), and Φ is the combined buoyancy and excess pressure term [g(ρs − ρl) + (ΔP/H)], i.e., the driving force per unit volume.
Source is Wilson and Head ; b for a fissure is given as (1 + 2rc/L), where L is the fissure length. For fissures that are long with respect to their width (as appropriate for Europan fractures), b ∼ 1.
 The concept underlying equation (20) is that the lava must reach the surface before excessive cooling restricts motion, whereas for equation (21) the driving force must overcome the yield strength for vertical motion to occur. These expressions allow limits to be placed on the rheology required for cryomagma ascent.
Figure 15 shows viscosity and yield strength plotted as a function of the upward driving force acting on the cryomagmatic fluid for source depths of 1, 10, and 100 km and conduit widths of 1, 10, and 100 m according to equations (20) and (21). The expressions were evaluated for a cylindrical conduit geometry appropriate to effusions fed from central vents. The viscosity and yield strength values would be 2.67 and 2 times greater, respectively, for eruptions fed by elongate fissures.
 The curves in Figure 15 represent the maximum possible viscosities and yield strengths for any given combination of source depth and conduit width; it is entirely possible that fluids of lower viscosity and yield strength could ascend through a given conduit geometry at greater rates.
 In order to place tighter constraints on the material properties, measurements on fractures (which may have provided a pathway for ascent of a cryomagma) just resolved in high-resolution images yield widths of ∼50–80 m. These may be somewhat overestimated because of processes such as mass wasting. For modest driving forces appropriate either to marginally buoyant cryomagmas or to low reservoir excess pressures, the upper limits on viscosity and yield strength are ∼107–1011 Pa s and 102–104 Pa, respectively. Although these are loose limits, which allow for a wide range of possible cryomagma compositions, these values indicate that solid-state ascent of warm ice (μ ≥ 1014 Pa s) would not be possible through the inferred conduit geometries.
5.2. Viscous Dome Emplacement
 Once the cryomagma reaches the surface, the material will spread radially if emplaced on an essentially flat surface. Huppert  developed a treatment of radially spreading Newtonian viscous gravity currents to explain lava dome emplacement on Earth, shown schematically in Figure 16. The governing equation,
can be solved numerically to derive the lava dome morphology as a function of time. Here, hr is the height of the dome surface as a function of radial distance, ν is the lava kinematic viscosity, and ∇r2 is the radial gradient. Using a time-dependent viscosity to simulate cooling [Sakimoto and Zuber, 1995], the height at the center of the lava dome h0 as a function of time t is found from
where V is the dome volume and ξ is a dimensionless constant related to the cooling behavior of basalt. Thus, using measured values for h and V as constraints on the model, ranges of viscosity and eruption duration can be derived for the candidate Europan extrusive domes. Figure 17 shows an example of the results for the feature shown in Figure 3b; combinations of emplacement duration and initial dynamic viscosity (= ρν) that reproduce the observed dimensions are shown.
 One flaw of this model, as can be seen in Figure 17, is that the theoretical extrusive dome will continue to spread indefinitely, given sufficient time. Therefore, without an independent constraint on the emplacement time, it is impossible to determine the initial viscosity uniquely. One remedy to this solution is to use a characteristic timescale based on dome cooling, which would determine when emplacement ceases because of freezing. In analyzing the growth of pillow lavas on Titan, Lorenz  discusses the use of characteristic timescales based on conductive cooling [Jankowski and Squyres, 1988; McKenzie et al., 1992] and radiative cooling [Schenk, 1991] of the spreading fluid. The conductive timescale, given by τ = h0/π2κ, represents a lower limit on emplacement time and initial dynamic viscosity. Conversely, the radiative timescale provides an upper limit and is given by Γ = ρcph0/εσT03, in which cp is the specific heat of the fluid, ε is the emissivity, σ is the Stefan-Boltzmann constant, and T0 is the eruption temperature. The much tighter constraints on emplacement duration (merely months to years) and hence initial viscosity provided by use of these expressions are indicated by dashed lines in Figure 17; for the feature in Figure 3b the initial dynamic viscosity μ lies between 2.5 and 23 × 106 Pa s, indicating a cryolava rheology roughly comparable to that of dome-forming silicate lavas. Further examples of cryolava dome emplacement parameters are given in Table 2, which shows somewhat lower viscosities for the smaller features.
 Finally, for comparison, the dotted line in Figure 17 indicates the implications for a viscosity representative of warm ice; the emplacement duration is on the order of billions of years (comparable to the age of the solar system!). Clearly, this is unrealistic, and the extrusive dome-like features observed on Europa thus cannot be explained by effusions of warm ice from a point source.
 Another deficiency of this viscous spreading model for lava dome emplacement is that the material is assumed to be emplaced at the surface instantaneously: There is no provision for continued effusion, so the model does not adequately describe endogenous dome growth. However, given the limitations in image data and our understanding of cryomagma compositions, the application of this model serves well to give an approximate grasp of the rheological properties of the materials involved.
5.3. Viscoelastic Fluid Model
 As an alternative approach to understanding silicate lava dome emplacement on Earth, Blake  considered the final dome morphology to be controlled by the yield strength of the lava. Such a viscoelastic (Bingham) fluid would spread radially as long as the shear stresses at the base exceed the yield strength. Blake  derived the following expression from measurements on terrestrial lava domes, relating the yield strength to the dome morphology,
where h0 is the maximum (central) lava dome height and R is the radius.
 If the emplacement of candidate extrusive domes on Europa is considered to be analogous to the effusion of a viscoelastic lava dome, then the yield strengths required to explain the observed dimensions can be calculated from equation (24). Table 2 shows yield strengths in the range 160–2200 Pa.
6. Implications for Rheology and Composition
 In section 5, constraints on cryomagma rheological properties were provided by two sets of models. The first models considered the rheological requirements for a cryomagma to ascend a conduit to the surface, and the others determined cryolava rheology on the basis of the morphology of the candidate extrusive domes. These two sets of models are complementary and, taken together, provide mutually consistent estimates of viscosity and yield strength for candidate cryolava domes erupted from central vents. These constraints on rheological properties have implications for the nature and composition of the cryomagmatic materials.
 The upper limits on viscosity calculated from the conduit ascent model (equation (20)) lie in the range 107–1011 Pa s. The lower end of this range is consistent with the viscosities calculated from the dome morphologies (equation (23)): ∼103–107 Pa s, for which the emplacement duration ranges from months to years. The two methods for determining yield strength also produce similarly consistent results. The ascent criterion gives maximum yield strengths of 102–104 Pa, and the dome morphology implies yield strengths in the range 160–2200 Pa.
 Clearly, the rheologies suggested by these models imply that, assuming these features do indeed represent effusive eruptions, they are not simple effusions of pure water. Figure 18 illustrates a number of alternate possibilities. For example, if the material erupted contained a large proportion of ice crystals, the rheology could be significantly altered (Figure 18a). This would also be the case if the H2O were mixed with certain non-ice contaminants [Kargel et al., 1991], although as discussed in section 1, it is unlikely that significant quantities would be available on Europa. (For comparison, viscosity and yield strength estimates derived from Voyager data for inferred cryovolcanic effusions on Ganymede, Enceladus, Ariel, and Miranda range from 106 to 1010 Pa s and 3 × 102 to 105 Pa [Schenk, 1991; Schenk and Moore, 1995], respectively, indicating a wider range of possible cryovolcanic fluid types elsewhere in the solar system.)
 Alternatively, more complex (and more realistic) effusion models might be needed. For example, exogenous lava dome growth on Earth involves superposition of successive small-volume effusions which freeze and gradually build the dome (Figure 18b). On the other hand, endogenous lava dome growth (Figure 18c) involves injection of molten material beneath a frozen outer carapace, the strength of which controls the dome morphology. Both of these processes could mimic the viscosities and yield strengths suggested by the simple Newtonian and Bingham effusion models.
 Note that the candidate lava dome morphologies cannot be explained by central vent effusions of “warm ice” having a viscosity of ∼1014 Pa s [Pappalardo et al., 1998]. First, such a viscous material could not rise through a conduit on the order of 100 m width, and, second, it would take billions of years for warm ice to relax to form the observed morphologies at the surface. However, the possibility that the volcanic dome-like features represent diapirs that breached the surface and subsequently relaxed to give the illusion of having been produced by a flow cannot be ruled out (Figure 6) [Pappalardo et al., 1998], as has been suggested for the “Mitten” feature (Figure 5) [Figueredo et al., 2002].
 Finally, note that the upper limits on viscosity and yield strength calculated by equations (20) and (21) certainly do not preclude delivery of low-viscosity, Newtonian fluids to the surface. Pure water and brines would be readily mobilized with minimal driving forces to produce surface effusions.
 All models applied in this study are relatively simple and, as with most models, undoubtedly do not adequately describe the details of the natural processes. However, given that we currently have limited understanding of what those natural processes are (e.g., cryovolcanism versus diapirism, lithospheric convection versus melt through), the inaccuracies of these simple models are masked by the uncertainties of our conceptual models and the associated assumptions. Development of more complex theoretical models is therefore not justified, and these first-order assessments of eruptive processes and cryomagma properties are offered on the basis that we are investigating but one of a variety of plausible formative mechanisms. As such, this approach serves as a useful comparison for similar studies on other icy satellites [e.g., Schenk, 1991; Schenk and Moore, 1995; Lorenz, 1996].
7. Implications for Europa's Subsurface
 Given that some of the surface features discussed in this study plausibly represent cryovolcanic eruptions (low-albedo fluid effusions and viscous cryolava domes), it is pertinent to ask, What are the implications for the nature and structure of Europa's subsurface, and how do these observations relate to the various models for the interior? Recall that two end-member models have been proposed: (1) a thin ice shell overlying a deep ocean above the silicate interior [Greenberg et al., 1998, 1999] and (2) a brittle ice layer overlying a thicker ductile ice layer with a liquid water layer lying between the ice shell and silicate mantle [Head and Pappalardo, 1999; McKinnon, 1999].
 For the thin ice model it is possible that limited-volume liquid effusions could result from material rising through fractures between the water layer and surface (Figures 11a and 11d), especially if volatiles were present to help generate a buoyant fluid or dense materials were mixed in the ice layer. However, generation of an excess pressure or delivery of a viscous fluid to the surface is problematic for the thin ice model. It seems likely that if an excess pressure is to be generated to overcome negative buoyancy, then a discrete fluid reservoir is required (Figures 11b and 11c), as local pressures generated in a continuous fluid layer would be instantaneously transmitted throughout the whole layer. The Galileo magnetometer evidence suggests a global water layer is required to carry the induced currents [Khurana et al., 1998; Kivelson et al., 1999, 2000]. Is it possible that in addition to a global ocean, discrete liquid reservoirs exist within the overlying ice? Perhaps localized zones of salt enrichment exist, leading to reservoirs of briny fluid, or residual liquid bodies remained trapped within the ice as it froze. The calculations of section 4.1 suggest such reservoirs could reside at depths up to 100 km and still permit pressure-driven ascent, but those depths less than ∼10 km would be most favorable for delivering fluid to the surface. This scenario might be favored by the thick ice shell model; a thin ice shell is unlikely to be able to accommodate discrete reservoirs of significant size [Pappalardo, 2000] unless ice thickness was very heterogeneous.
 An interesting point arises from inspection of equations (14) and (19), which show that even for very modest driving forces (due to excess pressure or buoyancy), very rapid ascent velocities are produced for the low viscosities of pure water or brine. If large excess pressures were generated (which, according to section 4.1, could be accomplished relatively easily), this would produce unrealistically high eruption velocities and discharge rates. The question is, If it should be relatively easy to deliver large volumes of material to the surface at high rates, why do we not see evidence for extensive cryovolcanic flooding at the surface? Perhaps the excess pressures or buoyancy are simply not generated; this would imply either that there were no discrete reservoirs present, that the overpressure was accommodated by deformation of the reservoir walls, or that fracture propagation takes place before high pressures are reached. It is also possible that there is no mechanism for propagating and maintaining an open pathway to the surface [Crawford and Stevenson, 1988; Wilson et al., 1997; Gaidos and Nimmo, 2000]. Finally, one might consider that the fluid is too viscous to ascend through narrow conduits, but given the restricted range of non-ice compositions likely on Europa, this last option seems unlikely.
 While not ruling out pressure-driven ascent from a subsurface water body, the simplest explanation for the low-albedo, smooth surfaces (Figures 1, 7, and 8) might be mobilization and release of near-surface brines [Head and Pappalardo, 1999] to produce small-volume effusions. Since all that is required is local brine pockets in the near surface during a heating episode, the implications for deeper structure are unclear.
 Three broad categories of landform on Europa have been considered as possible candidate cryovolcanic features: elongate lobate features reminiscent of lava flows (Figures 1 and 2); generally positive relief features resembling lava domes (Figures 3 and 4); and low-albedo, smooth surfaces controlled by topography, analogous to low-viscosity effusions (Figures 1, 7, 8, and 9). Whereas a cryovolcanic flow origin is not borne out by high-resolution images of the lobate features of Figures 1 and 2, the origin of lava dome-like masses remains equivocal, and the third class of feature offers the best evidence for effusions of liquids at the surface. However, even for this last case, other origins cannot be ruled out (mass wasting, terrain softening, lag deposits, ice grain annealing, etc.). What can be stated with some confidence is that cryovolcanism is not a widespread resurfacing process on Europa; rather, tectonic and chaotic disruption is the dominant manifestation of endogenic activity [Greenberg et al., 1998, 1999; Spaun et al., 1998; Head and Pappalardo, 1999; Head et al., 1999], with evidence of possible diapiric activity within the ice lithosphere [Pappalardo et al., 1998].
 Low-viscosity flooding appears to take place on a small scale, with fluids having briny compositions. Certain lava dome-like lenticulae might result from eruptions of viscous icy slurries; successive stacking of thin, fluid flows; or inflation of ice-covered water flows (Figure 18). However, the morphology and stratigraphic relationships of these features are also adequately explained by breaching of the surface by warm ice diapirs and subsequent “flow” or relaxation of the ice for short distances over the surface (Figure 6). The current data sets offer little to distinguish between these possibilities, but future Europa missions, such as the Jupiter Icy Moons Orbiter, provide hope for unraveling the remaining problems. For morphologic studies, orbital design and instrumentation that could provide high-resolution (<100 m pixel−1) surface coverage, with very high resolution targeting of specific features, would be highly beneficial. An imaging spectrometer covering visible to infrared wavelengths could fulfill these resolution requirements, yield information on the composition of specific features, and provide detections of thermal anomalies indicative of recent activity. The topographic precision afforded by laser altimetry, together with supplemental stereo and photoclinometric analyses, would be extremely valuable in elucidating the topographic and stratigraphic relationships of candidate cryovolcanic features, which would be particularly helpful in addressing the origins of lenticulae.
 The Galileo mission has amply demonstrated how geologic relationships can be misinterpreted based on limited image coverage and resolution. Where relatively low resolution Voyager images were previously deemed to show strong evidence for cryovolcanic features (smooth surfaces, embayment relationships, lobate morphologies, etc.), this has largely been refuted by higher-resolution Galileo data. Therefore, on the basis of our experience with Europa (and Ganymede) one has to question whether the other icy satellites for which extensive cryovolcanic resurfacing has been proposed did in fact experience significant cryovolcanism or whether other processes may be dominant (such as the “tectonic resurfacing” proposed for Ganymede [Head et al., 2002]). A careful reexamination of all the outer planet satellites with future mission data at superior resolutions is warranted.
 The author gratefully acknowledges the members and affiliates of the Galileo Solid State Imaging team for many stimulating discussions regarding Europan geology during the Jupiter tour. In particular, the author expresses gratitude to R. Greeley for providing the initial impetus for this study. L. Wilson and N. Spaun provided helpful reviews to improve the quality of the initial manuscript. This work was supported in part by NASA Jovian System Data Analysis grant NAG5-8898. This is HIGP contribution 1303 and SOEST contribution 6234.