Tidally forced viscous heating in a partially molten Io

We investigate tidal dissipative heating in two different models of Io. The partially molten asthenosphere model consists of a rigid inner core and a thin (less than 40 km thick) partially molten “decoupling” layer (asthenosphere) surrounded by an elastic lithosphere. In the partially molten interior model the interior beneath the lithosphere is partially molten throughout. The partially molten region in each model assumed to possess negligible shear strength and to be characterized by a Newtonian viscosity. Tidal deformation and dissipation in the core of the thin asthenosphere model are assumed negligible. Fluid in the viscous layers is forced to circulate by the tidal distortion of the outer shell, modeled here as a sinusoidal variation with time of the distortion amplitude. As a result, heat is generated in the fluid by viscous dissipation. There are two heating mechanisms in our models: “elastic” dissipation in the lithosphere ∞ 1/Q and viscous dissipation in the partially molten region. Numerical calculatons are carried out for a 90-km-thick lithosphere with Q = 100. This thickness maximizes dissipation in a decoupled lithosphere; other reasonable values of lithosphere thickness do not alter our conclusions. Under the constraint that total dissipation equals the observed radiated heat loss we derived the iscosity of the partially molten region in each model. We a posteriori evaluate the assumption that the lithosphere is decoupled from the interior by calculating the distortion of an elastic shell due to the viscous stresses on the lower surface of the outr shell. If the interior viscosity is such that the total dissipation is equal to the observed heat flux from Io, viscous stresses produce negligible distortion of a 90-km-thick shell. This validates the assumption of a decoupled shell. The derived viscosity for both models is characteristic of a partially molten rock. In the thin asthenosphere model the derived viscosity is so low that a very high degree of partial melt is necessary, about 40% crystal fraction in a 400-km-thick asthenosphere and about 0% in a 1-km-thick asthenosphere. In the partially molten interior model the derived viscosity corresponds to a magma with about 60% crystals. Consideration of convective efficiencies demonstrates the plausibility of a stable thermal steady state for both models. A significant portion (75% for Q = 100) of Io's tidal heating can be the result of viscous dissipation in a partially molten region that decouples the outer shell from the interior. The partially molten layer can be considered a “global magma ocean”.     

Thermal-orbital evolution of Io and Europa

Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io.     

Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

Tidally Induced Volcanism

The dissipation of tidal energy causes the ongoing silicate volcanism on Jupiter's satellite, Io, and cryovolcanism almost certainly has resurfaced parts of Saturn's satellite, Enceladus, at various epochs distributed over the latter's history. The maintenance of tidal dissipation in Io and the occurrence of the same on Enceladus depends crucially on the maintenance of the respective orbital eccentricities by the existence of mean motion resonances with nearby satellites. A formation of the resonances among the Galilean satellites by differential expansion of the satellite orbits from tides raised on Jupiter by the satellites means the onset of the volcanism on Io could be relatively recent. If, on the other hand, the resonances formed by differential migration from resonant interactions of the satellites with the disk of gas and particles from which they formed, Io would have been at least intermittently volcanically active throughout its history. Either means of assembling the Galilean satellite resonances lead to the same constraint on the dissipation function of Jupiter Q _J 10⁶, where the currently high heat flux from Io seems to favor episodic heating as Io's eccentricity periodically increases and decreases. Either of the two models might account for sufficient tidal dissipation in the icy satellite Enceladus to cause at least occasional cryovolcanism over much of its history. However, both models are assumption-dependent and not secure, so uncertainty remains on how tidal dissipation resurfaced Enceladus.     

Io: Thermal models and chemical evolution

A combined thermal and chemical evolution model of Io is presented, outlining limits on the possible starting materials, heating history, chemical history, and present state of Io. Our best scenario starts with Io being accreted from material in a proto-Jovian nebula which condensed between 400–600°K. Radionuclides and tidal heating would lead to large-scale convection within Io and chemical reactions leading to the outgassing of water and methane. Reactions between Fe⁰FeS and water, at least near the surface, go to completion, resulting in all Fe being oxidized with elemental sulfur producing a low-conductivity crust. In the deep interior, these reactions may not completely exhaust Fe metal, and an FeS-rich core may be formed.     

Thermal structure of the Jovian plasmasphere

An equation of heat transport in the Jovian magnetosphere is formulated and solved in the L range between 2 and 7. Sources of thermal energy include the heating associated with inward radial diffusion and a hypothetical heat supply originating from Io's dynamo action. The principal sink of the thermal energy is charge exchange in Io's hydrogen torus. In order to explain the density and temperature profile reported by Frank et al. (1976), the presence of the heat source at Io is essential and the density of the torus hydrogen has to be considerably lower than the value inferred from L_α observations by Carlson and Judge (1975). Radial diffusion represents the principal heating mechanism for plasma at very low L values.     

Tidal dissipation,orbital evolution,and the nature of Saturn's inner satellites

Estimates of tidal damping times of the orbital eccentricities of Saturn's inner satellites place constraints on some satellite rigidities and dissipation functions Q. These constraints favor rock-like rather than ice-like properties for Mimas and probably Dione. Photometric and other observational data are consistent with relatively higher densities for these two satellites, but require lower densities for Tethys, Enceladus, and Rhea. This leads to a nonmonotonic density distribution for Saturn's inner satellites, apparently determined by different mass fractions of rocky materials. In spite of the consequences of tidal dissipation for the orbital eccentricity decay and implications for satellite compositions, tidal heating is not an important contributor to the thermal history of any Saturnian satellite.     

Convective-conductive transitions and sensitivity of a convecting ice shell to perturbations in heat flux and tidal-heating rate: Implications for Europa

We investigate the response of conductive and convective ice shells on Europa to variations of heat flux and interior tidal-heating rate. We present numerical simulations of convection in Europa's ice shell with Newtonian, temperature-dependent viscosity and tidal heating. Modest variations in the heat flux supplied to the base of a convective ice shell, ΔF, can cause large variations of the ice-shell thickness Δδ. In contrast, for a conductive ice shell, large ΔF involves relatively small Δδ. We demonstrate that, for a fluid with temperature-dependent viscosity, the heat flux undergoes a finite-amplitude jump at the critical Rayleigh number Racr. This jump implies that, for a range of heat fluxes relevant to Europa, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. We show that, as a result, modest variations in heat flux near the critical Rayleigh number can force the ice shell to switch between the thin, conductive and thick, convective configurations over a ∼10⁷-year interval, with thickness changes of up to ∼10-30 km. Depending on the orbital and thermal history, such switches might occur repeatedly. However, existing evolution models based on parameterized-convection schemes have to date not allowed these transitions to occur. Rapid thickening of the ice shell would cause radial expansion of Europa, which could produce extensional tectonic features such as fractures or bands. Furthermore, based on interpretations for how features such as chaos and ridges are formed, several authors have suggested that Europa's ice shell has recently undergone changes in thickness. Our model provides a mechanism for such changes to occur.     

Microscale simulations of Venus’ convective adjustment and mixing near the surface: Thermal and material transport processes

Heat and material transport processes caused by convective adjustment and mixing are important in modeling of Venus’ atmosphere. In the present study, microscale atmospheric simulations near the venusian surface were conducted using a Weather Research and Forecasting model to elucidate the thermal and material transport processes of convective adjustment and mixing. When convective adjustment occurs, the heat and passive tracer are rapidly mixed into the upper stable layer with convective penetration. The convective adjustment produces large eddy diffusions of heat and passive tracer, which may explain the large eddy diffusions estimated in the radiative-convective equilibrium model.For values of surface heat flux Q greater than a threshold (=0.064 K m s⁻¹ in the present study), the convectively mixed layer with high eddy diffusion coefficients grows with time. In contrast, the mixed layer decays with time for Q values smaller than the threshold. The thermal structure near the surface is controlled not only by extremely long-term radiative processes, but also by microscale dynamics with time scales of several hours. A mixed layer with high eddy diffusion coefficients may be maintained or grow with time if the surface heat flux is high in the volcanic hotspot and adjacent areas.     

The production of Ganymede's magnetic field

One of the great discoveries of NASA's Galileo mission was the presence of an intrinsically produced magnetic field at Ganymede. Generation of the relatively strong (750 nT) field likely requires dynamo action in Ganymede's metallic core, but how such a dynamo has been maintained into the present epoch remains uncertain. Using a one-dimensional, three layer thermal model of Ganymede, we find that magnetic field generation can only occur if the sulfur mass fraction in Ganymede's core is very low (?3%) or very high (?21%), and the silicate mantle can cool rapidly (i.e. it has a viscosity like wet olivine). However, these requirements are not necessarily compatible with cosmochemical and physical models of the satellite. We therefore investigate an alternative scenario for producing Ganymede's magnetic field in which passage through an eccentricity pumping Laplace-like resonance in Ganymede's past enables present day dynamo action in the metallic core. If sufficient tidal dissipation occurs in Ganymede's silicate mantle during resonance passage, silicate temperatures can undergo a runaway which prevents the core from cooling until the resonance passage ends. The rapid silicate and core cooling that follows resonance escape triggers dynamo action via thermal and/or compositional convection. To test the feasibility of this mechanism we couple our thermal model with an orbital evolution model to examine the effects of resonance passage on Ganymede's silicate mantle and metallic core. We find that, contrary to expectations, there are no physically plausible scenarios in which tidal heating in the silicates is sufficient to cause the thermal runaway necessary to prevent core cooling. These findings are robust to variations in the silicate rheology, tidal dissipation factor of Jupiter (QJ), structure of the ice shell, and the inclusion of partial melting in the silicate mantle. Resonance passage therefore appears unlikely to explain Ganymede's magnetic field and we must appeal to the special conditions described above to explain the presence of the field.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

Early martian dynamo generation due to giant impacts

During late-stage planet formation, giant impacts produce localized mantle melt regions within which impactor iron droplets settle to the bottom near a permeability horizon. After accumulation, iron heated by the impact migrates downward to the core through colder, mostly solid mantle. The degree of thermal equilibration and partitioning of viscous heating between impactor iron and silicates depends on the mechanism of iron transport to the core. Simple estimates suggest that, following a giant impact, the temperature difference between iron delivered to the core and the mantle outside the impact heated region can be ∼10³ K. Hot impactor iron mergers with the core where it may be efficiently mixed or remain stratified due to thermal buoyancy. In either case, collisional energy carried to the core by impactor iron helps establish conditions favorable for early core cooling and dynamo generation. In this study, we consider the end-member scenario in which impactor iron forms a layer at the top of the core. Energy transfer from the impactor iron layer to the mantle is sufficient to power a dynamo for up to ∼30 Myr even in the limit of a very viscous mantle and heat flux limited by conduction. Using two-dimensional finite element calculations of mantle convection, we show that large-scale mantle flow driven by the buoyancy of the impact thermal anomaly focuses plumes in the impact region and increases both dynamo strength and duration. Melting within the mantle thermal boundary layer likely leads to formation of a single superplume in the location of the impact anomaly driven upwelling. We suggest that formation of magnetized southern highland crust may be related to spreading and differentiation of an impact melt region during the impact-induced dynamo episode.     

The orbital-thermal evolution and global expansion of Ganymede

The tectonically and cryovolcanically resurfaced terrains of Ganymede attest to the satellite's turbulent geologic history. Yet, the ultimate cause of its geologic violence remains unknown. One plausible scenario suggests that the Galilean satellites passed through one or more Laplace-like resonances before evolving into the current Laplace resonance. Passage through such a resonance can excite Ganymede's eccentricity, leading to tidal dissipation within the ice shell. To evaluate the effects of resonance passage on Ganymede's thermal history we model the coupled orbital-thermal evolution of Ganymede both with and without passage through a Laplace-like resonance. In the absence of tidal dissipation, radiogenic heating alone is capable of creating large internal oceans within Ganymede if the ice grain size is 1 mm or greater. For larger grain sizes, oceans will exist into the present epoch. The inclusion of tidal dissipation significantly alters Ganymede's thermal history, and for some parameters (e.g. ice grain size, tidal Q of Jupiter) a thin ice shell (5 to 20 km) can be maintained throughout the period of resonance passage. The pulse of tidal heating that accompanies Laplace-like resonance capture can cause up to 2.5% volumetric expansion of the satellite and contemporaneous formation of near surface partial melt. The presence of a thin ice shell and high satellite orbital eccentricity would generate moderate diurnal tidal stresses in Ganymede's ice shell. Larger stresses result if the ice shell rotates non-synchronously. The combined effects of satellite expansion, its associated tensile stress, rapid formation of near surface partial melt, and tidal stress due to an eccentric orbit may be responsible for creating Ganymede's unique surface features.     

Tidal evolution of Mimas, Enceladus, and Dione

The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus-Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k₂/Q. Past evolution of the system is marked by temporary capture into the Enceladus-Dione 4:2 ee^′-mixed resonance. We find that the free libration of the Enceladus-Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus-Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1(18,000/QS) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas-Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k₂/Q for the satellites.     

Editorial

The Galilean satellites Io, Europa, and Ganymede interact through several stable orbital resonances where $\text{λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_1\text{= 0, λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_2\text{= 180°, λ}{}_2\text{? 2λ}{}_3\text{+}\text{ω}{}_2\text{= 0}$ and λ₁ ? 3λ₂ + 2λ₃ = 180°, with λ_i being the mean longitude of the ith satellite and $\text{ω}{}_{\mathrm{i}}$ the longitude of the pericenter. The last relation involving all three bodies is known as the Laplace relation. A theory of origin and subsequent evolution of these resonances outlined earlier (C. F. Yoder, 1979b, Nature279, 747–770) is described in detail. From an initially quasi-random distribution of the orbits the resonances are assembled through differential tidal expansion of the orbits. Io is driven out most rapidly and the first two resonance variables above are captured into libration about 0 and 180° respectively with unit probability. The orbits of Io and Europa expand together maintaining the 2:1 orbital commensurability and Europa's mean angular velocity approaches a value which is twice that of Ganymede. The third resonance variable and simultaneously the Laplace angle are captured into libration with probability ～0.9. The tidal dissipation in Io is vital for the rapid damping of the libration amplitudes and for the establishment of a quasi-stationary orbital configuration. Here the eccentricity of Io's orbit is determined by a balance between the effects of tidal dissipation in Io and that in Jupiter, and its measured value leads to the relation $\text{k}{}_1\text{?}{}_1\text{/Q}{}_1\text{≈ 900k}{}_{\mathrm{<mtext>J</mtext>}}\text{/Q}{}_{\mathrm{<mtext>J</mtext>}}$ with the k's being Love numbers, the Q's dissipation factors, and f a factor to account for a molten core in Io. This relation and an upper bound on Q₁ deduced from Io's observed thermal activity establishes the bounds 6 × 10⁴ < Q_J < 2 × 10⁶, where the lower bound follows from the limited expansion of the satellite orbits. The damping time for the Laplace libration and therefore a minimum lifetime of the resonance is 1600 Q_J years. Passage of the system through nearby three-body resonances excites free eccentricities. The remnant free eccentricity of Europa leads to the relation $\text{Q}{}_2\text{/?}{}_2\text{? 2 × 10}{}^{\mathrm{?4}}\text{Q}{}_{\mathrm{<mtext>J</mtext>}}$ for rigidity μ₂ = 5 × 10¹¹ dynes/cm². Probable capture into any of several stable 3:1 two-body resonances implies that the ratio of the orbital mean motions of any adjacent pair of satellites was never this large.A generalized Hamiltonian theory of the resonances in which third-order terms in eccentricity are retained is developed to evaluate the hypothesis that the resonances were of primordial origin. The Laplace relation is unstable for values of Io's eccentricity e₁ > 0.012 showing that the theory which retains only the linear terms in e₁ is not valid for values of e₁ larger than about twice the current value. Processes by which the resonances can be established at the time of satellite formation are undefined, but even if primordial formation is conjectured, the bounds established above for Q_J cannot be relaxed. Electromagnetic torques on Io are also not sufficient to relax the bounds on Q_J. Some ideas on processes for the dissipation of ideal energy in Jupiter yield values of Q_J within the dynamical bounds, but no theory has produced a Q_J small enough to be compatible with the measurements of heat flow from Io given the above relation between Q₁ and Q_J. Tentative observational bounds on the secular acceleration of Io's mean motion are also shown not to be consistent with such low values of Q_J. Io's heat flow may therefore be episodic. Q_J may actually be determined from improved analysis of 300 years of eclipse data.     

A whole-moon thermal history model of Europa: Impact of hydrothermal circulation and salt transport

A whole-moon numerical model of Europa is developed to simulate its thermal history. The thermal evolution covers three phases: (i) an initial, roughly 0.5 Gyr-long period of radiogenic heating and differentiation, (ii) a long period from 0.5 Gyr to 4 Gyr with continuing radiogenic heating but no tidal dissipative heating (TDH), and (iii) a final period covering the last 0.5 Gyr until the present, during which TDH is active. Hydrothermal plumes develop after the initial period of heating and differentiation and transport heat and salt from Europa’s silicate mantle to its ice shell. We find that, even without TDH, vigorous hydrothermal convection in the rocky mantle can sustain flow in an ocean layer throughout Europa’s history. When TDH becomes active, the ice shell melts quickly to a thickness of about 20 km, leaving an ocean 80 km or more deep. Parameterized convection in the ice shell is non-uniform spatially, changes over time, and is tied to the deeper ocean–mantle dynamics. We also find that the dynamics are affected by salt concentrations. An initially non-uniform salt distribution retards plume penetration, but is homogenized over time by turbulent diffusion and time-dependent flow driven by initial thermal gradients. After homogenization, the uniformly distributed salt concentrations are no longer a major factor in controlling plume transport. Salt transport leads to the formation of a heterogeneous brine layer and salt inclusions at the bottom of the ice shell; the presence of salt in the ice shell could strongly influence convection in that layer.     

Equilibrium Convection on a Tidally Heated and Stressed Icy Shell of Europa for a Composite Water Ice Rheology

Water ice I rheology is a key factor for understanding the thermal and mechanical state of the outer shell of the icy satellites. Ice flow involves several deformation mechanisms (both Newtonian and non-Newtonian), which contribute to different extents depending on the temperature, grain size, and applied stress. In this work I analyze tidally heated and stressed equilibrium convection in the ice shell of Europa by considering a composite viscosity law which includes diffusion creep, basal slip, grain boundary sliding and dislocation creep, and. The calculations take into account the effect of tidal stresses on ice flow and use grain sizes between 0.1 and 100 mm. An Arrhenius-type relation (useful for parameterized convective models) is found then by fitting the calculated viscosity between 170 and 273 K to an exponential regression, which can be expressed in terms of pre-exponential constant and effective activation energy. I obtain convective heat flows between ~40 and ~60 mW m^?2, values lower than those usually deduced (~100 mW m^?2) from geological indicators of lithospheric thermal state, probably indicating heterogeneous tidal heating. On the other hand, for grain sizes larger than ~0.3 mm the thicknesses of the ice shell and convective sublayer are ~20–30 km and ~5–20 km respectively, values in good agreement with the available information for Europa. So, some fundamental geophysical characteristics of the ice shell of Europa could be arising from the properties of the composite water ice rheology.     

Turbulent viscosity and Jupiter's tidal Q

A recent estimate of tidal dissipation by turbulent viscosity in Jupiter's convective interior predicts that the current value of the planet's tidal Q ～ 5 × 10⁶. We point out a fundamental error in this calculation, and show that turbulent dissipation alone implies that at present Q ～ 5 × 10¹³. Our reduced estimat for the rate of tidal dissipation shows conclusively that tidal torques have produced only negligible modifications of the orbits of the Galilean satellites over the age of the solar system.