Thermal evolution of Pluto and implications for surface tectonics and a subsurface ocean

Determining whether or not Pluto possesses, or once possessed, a subsurface ocean is crucial to understanding its astrobiological potential. In this study we use a 3D convection model to investigate Pluto’s thermal and spin evolution, and the present-day observational consequences of different evolutionary pathways. We test the sensitivity of our model results to different initial temperature profiles, initial spin periods, silicate potassium concentrations and ice reference viscosities. The ice reference viscosity is the primary factor controlling whether or not an ocean develops and whether that ocean survives to the present day. In most of our models present-day Pluto consists of a convective ice shell without an ocean. However if the reference viscosity is higher than 5 × 10¹⁵ Pa s, the shell will be conductive and an ocean should be present. For the nominal potassium concentration the present-day ocean and conductive shell thickness are both about 165 km; in conductive cases an ocean will be present unless the potassium content of the silicate mantle is less than 10% of its nominal value. If Pluto never developed an ocean, predominantly extensional surface tectonics should result, and a fossil rotational bulge will be present. For the cases which possess, or once possessed, an ocean, no fossil bulge should exist. A present-day ocean implies that compressional surface stresses should dominate, perhaps with minor recent extension. An ocean that formed and then re-froze should result in a roughly equal balance between (older) compressional and (younger) extensional features. These predictions may be tested by the New Horizons mission.     

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.     

Oceans in the icy Galilean satellites of Jupiter?

Equilibrium models of heat transfer by heat conduction and thermal convection show that the three satellites of Jupiter—Europa, Ganymede, and Callisto—may have internal oceans underneath ice shells tens of kilometers to more than a hundred kilometers thick. A wide range of rheology and heat transfer parameter values and present-day heat production rates have been considered. The rheology was cast in terms of a reference viscosity ν₀ calculated at the melting temperature and the rate of change A of viscosity with inverse homologous temperature. The temperature dependence of the thermal conductivity k of ice I has been taken into account by calculating the average conductivity along the temperature profile. Heating rates are based on a chondritic radiogenic heating rate of 4.5 pW kg⁻¹ but have been varied around this value over a wide range. The phase diagrams of H₂O (ice I) and H₂O + 5 wt% NH₃ ice have been considered. The ice I models are worst-case scenarios for the existence of a subsurface liquid water ocean because ice I has the highest possible melting temperature and the highest thermal conductivity of candidate ices and the assumption of equilibrium ignores the contribution to ice shell heating from deep interior cooling. In the context of ice I models, we find that Europa is the satellite most likely to have a subsurface liquid ocean. Even with radiogenic heating alone the ocean is tens of kilometers thick in the nominal model. If tidal heating is invoked, the ocean will be much thicker and the ice shell will be a few tens of kilometers thick. Ganymede and Callisto have frozen their oceans in the nominal ice I models, but since these models represent the worst-case scenario, it is conceivable that these satellites also have oceans at the present time. The most important factor working against the existence of subsurface oceans is contamination of the outer ice shell by rock. Rock increases the density and the pressure gradient and shifts the triple point of ice I to shallower depths where the temperature is likely to be lower then the triple point temperature. According to present knowledge of ice phase diagrams, ammonia produces one of the largest reductions of the melting temperature. If we assume a bulk concentration of 5 wt% ammonia we find that all the satellites have substantial oceans. For a model of Europa heated only by radiogenic decay, the ice shell will be a few tens of kilometers thinner than in the ice I case. The underlying rock mantle will limit the depth of the ocean to 80-100 km. For Ganymede and Callisto, the ice I shell on top of the H₂O-NH₃ ocean will be around 60- to 80-km thick and the oceans may be 200- to 350-km deep. Previous models have suggested that efficient convection in the ice will freeze any existing ocean. The present conclusions are different mainly because they are based on a parameterization of convective heat transport in fluids with strongly temperature dependent viscosity rather than a parameterization derived from constant-viscosity convection models. The present parameterization introduces a conductive stagnant lid at the expense of the thickness of the convecting sublayer, if the latter exists at all. The stagnant lid causes the temperature in the sublayer to be warmer than in a comparable constant-viscosity convecting layer. We have further modified the parameterization to account for the strong increase in homologous temperature, and therefore decrease in viscosity, with depth along an adiabat. This modification causes even thicker stagnant lids and further elevated temperatures in the well-mixed sublayer. It is the stagnant lid and the comparatively large temperature in the sublayer that frustrates ocean freezing.     

The heat flow of Europa

The heat flow from Europa has profound implications for ice shell thickness and structure, as well as for the existence of an internal ocean, which is strongly suggested by magnetic data. The brittle-ductile transition depth and the effective elastic thickness of the lithosphere are here used to perform heat flow estimations for Europa. Results give preferred heat flow values (for a typical geological strain rate of ¹⁰⁻¹⁵ s⁻¹) of 70-110 mW m⁻² for a brittle-ductile transition 2 km deep (the usually accepted upper limit for the brittle-ductile transition depth in the ice shell of Europa), 24-35 mW m⁻² for an effective elastic thickness of 2.9 km supporting a plateau near the Cilix impact crater, and >130 mW m⁻² for effective elastic thicknesses of ?0.4 km proposed for the lithosphere loaded by ridges and domes. These values are clearly higher than those produced by radiogenic heating, thus implying an important role for tidal heating. The ?19-25 km thick ice shell proposed from the analysis of size and depth of impact structures suggests a heat flow of ?30-45 mW m⁻² reaching the ice shell base, which in turn would imply an important contribution to the heat flow from tidal heating within the ice shell. Tidally heated convection in the ice shell could be capable to supply ∼100 mW m⁻² for superplastic flow, and, at the Cilix crater region, ∼35-50 mW m⁻² for dislocation creep, which suggests local variations in the dominant flow mechanism for convection. The very high heat flows maybe related to ridges and domes could be originated by preferential heating at special settings.     

Constraints on mantle plumes on Venus: Implications for volatile history

The analysis of Venus’ gravity field and topography suggests the presence of a small number of deep mantle plumes (～9). This study predicts the number of plumes formed at the core–mantle boundary, their characteristics, and the production of partial melt from adiabatic decompression. Numerical simulations are performed using a 3D spherical code that includes large viscosity variations and internal heating. This study investigates the effect of several parameters including the core–mantle boundary temperature, the amount of internal heating, and the mantle viscosity. The smallest number of plumes is achieved when no internal heating is present. However, scaling Earth’s radiogenic heating to Venus suggests a value of ～16 TW. Cases with internal heating produce more realistic lid thickness and partial melting, but produce either too many plumes or no plumes if a high mantle temperature precludes the formation of a hot thermal boundary layer. Mantle viscosity must be reduced to at least 10²⁰ Pa s in order to include significant internal heating and still produce hot plumes. In all cases that predict melting, melting occurs throughout the upper mantle. Only cases with high core temperature (>1700 K) produce dry melting. Over time the upper mantle may have lost significant volatiles. Depending on the water content of the lower mantle, deep plumes may contribute to present-day atmospheric water via volcanic outgassing. Assuming 50 ppm water in mantle, 10 plumes with a buoyancy flux of 500 kg/s continuously erupting for 4 myr will outgas an amount of water on the order of that in the lower atmosphere. A higher level of internal heating than achieved to date, as well as relatively low mantle viscosity, may be required to achieve simulations with ～10 plumes and a thinner lid. Alternatively, if the mantle is heating up due to the stagnant lid, the effect is equivalent to having lower rates of internal heating. A temperature increase of 110 K/byr is equivalent to ?13 TW. This value along with the internal heating of 3 TW used in this study may represent the approximate heat budget of Venus’ mantle.     

The impact of a weak south pole on thermal convection in Enceladus’ ice shell

Enceladus exhibits a strong hemispheric dichotomy of tectonism and heat flux, with geologically young, heavily tectonized terrains and a high heat flux in the South Polar Terrain (SPT) and relatively ancient terrains with presumably lower heat fluxes over the rest of the satellite. To understand the convective pattern and its relationship with surface tectonics, we present three-dimensional numerical models of convection in Enceladus’ ice shell including basal heating and tidal heating. Our thermal boundary conditions exhibit no north–south asymmetries, but because the tectonism at the SPT may weaken the ice there, we impose a mechanically weak lithosphere within the SPT. The weakening is parameterized by adopting a reduced viscosity contrast within the SPT. Without such a weak zone, convection (if any) resides in stagnant-lid mode and exhibits no hemispheric dichotomy. In the presence of such an SPT weak zone, however, we find vigorous convection in the ice underneath the SPT, with convective plumes rising close to the surface. In contrast, only stagnant lid convection, or no convection at all, occurs elsewhere over the satellite. Away from the SPT, the heat flux in our models is small (5–10 mW m^?2) and the surface strains are small enough to imply surface ages >10⁹ years. Within the SPT, however, our models yield peak heat fluxes of ～70–200 mW m^?2, implying heat flows integrated across the SPT of up to 5 GW, similar to that inferred from Cassini thermal observations. The surface strains in our models are high enough near the south pole to cause intense tectonism and imply surface ages of ～10⁶–10⁷ years, consistent with age estimates of the SPT.     

Titan’s internal structure and the evolutionary consequences

Titan’s moment of inertia (MoI), estimated from the quadrupole gravity field measured by the Cassini spacecraft, is 0.342, which has been interpreted as evidence of a partially differentiated internal mass distribution. It is shown here that the observed MoI is equally consistent with a fully differentiated internal structure comprising a shell of water ice overlying a low-density silicate core; depending on the chemistry of Titan’s subsurface ocean, the core radius is between 1980 and 2120 km, and its uncompressed density is 2570–2460 kg m^?3, suggestive of a hydrated CI carbonaceous chondrite mineralogy. Both the partially differentiated and fully differentiated hydrated core models constrain the deep interior to be several hundred degrees cooler than previously thought. I propose that Titan has a warm wet core below, or buffered at, the high-pressure dehydration temperature of its hydrous constituents, and that many of the gases evolved by thermochemical and radiogenic processes in the core (such as CH₄ and ⁴⁰Ar, respectively) diffuse into the icy mantle to form clathrate hydrates, which in turn may provide a comparatively impermeable barrier to further diffusion. Hence we should not necessarily expect to see a strong isotopic signature of serpentinization in Titan’s atmosphere.     

The role of sputtering and radiolysis in the generation of Europa exosphere

The exosphere of an atmosphereless icy moon is the result of different surface release processes and subsequent modification of the released particles. At Europa icy moon, water molecules are directly released, but photolysis and radiolysis due to solar UV and Jupiter’s magnetospheric plasma, respectively, can result in OH, H, O and (possibly) H₂ production. These molecules can recombine to reform water and/or new chemical species. As a consequence, Europa’s neutral environment becomes a mixture of different molecules, among which, H₂O dominates in the highest altitudes and O₂, formed mainly by radiolysis of ice and subsequent release of the produced molecules, prevails at lower altitudes. In this work, starting from a previously developed Monte Carlo model for the generation of Europa’s exosphere, where the only considered species was water, we make a first attempt to simulate also the H₂ and O₂ components of the neutral environment around Europa, already observed by the Hubble Space Telescope and the Ultraviolet Imaging Spectrograph on board Cassini, during its flyby of Jupiter. Considering a specific configuration where the leading hemisphere coincides with the sunlit hemisphere, we estimate along the Europa–Sun line an O₂ column density of about 1.5 × 10¹⁹ m^?2 at the dayside and 3 × 10¹⁸ m^?2 at the nightside. In this work we also improve our previous estimation of the sputtered H₂O exosphere of this moon, taking into consideration the trailing–leading asymmetry in the magnetospheric ion bombardment and the energy and temperature dependences of the process yields. We find that a density of 1.5 × 10¹² H₂O/m³ is expected at altitudes ～0.1R_E above the surface of the trailing hemisphere. Additionally, we calculate the escape of H₂O, O₂ and H₂. The total number of neutral atoms in Europa’s neutral torus, is estimated to be in the range 7.8 × 10³²–3.3 × 10³³.     

Enceladus: A hypothesis for bringing both heat and chemicals to the surface

The eruptive plumes and large heat flow (～15 GW) observed by Cassini in the South Polar Region of Enceladus may be expressions of hydrothermal activity inside Enceladus. We hypothesize that a subsurface ocean is the heat reservoir for thermal anomalies on the surface and the source of heat and chemicals necessary for the plumes. The ocean is believed to contain dissolved gases, mostly CO₂ and is found to be relatively warm (～0 °C). Regular tidal forces open cracks in the icy crust above the ocean. Ocean water fills these fissures. There, the conditions are met for the upward movement of water and the dissolved gases to exsolve and form bubbles, lowering the bulk density of the water column and making the pressure at its bottom less than that at the top of the ocean. This pressure difference drives ocean water into and up the conduits toward the surface. This transportation mechanism supports the thermal anomalies and delivers heat and chemicals to the chambers from which the plumes erupt. Water enters these chambers and there its bubbles pop and loft an aerosol mist into the ullage. The exiting plume gas entrains some of these small droplets. Thus, nonvolatile chemical species in ocean water can be present in the plume particles. A CO₂ equivalent-gas molar fraction of ～4 × 10^?4 for the ocean is sufficient to support the circulation. A source of heat is needed to keep the ocean warm at ～0 °C (about two degrees above its freezing point). The source of heat is unknown, but our hypothesis is not dependent on any particular mechanism for producing the heat.     

Sea level budget over 2003–2008: A reevaluation from GRACE space gravimetry,satellite altimetry and Argo

From the IPCC 4th Assessment Report published in 2007, ocean thermal expansion contributed by ～ 50% to the 3.1 mm/yr observed global mean sea level rise during the 1993–2003 decade, the remaining rate of rise being essentially explained by shrinking of land ice. Recently published results suggest that since about 2003, ocean thermal expansion change, based on the newly deployed Argo system, is showing a plateau while sea level is still rising, although at a reduced rate (～ 2.5 mm/yr). Using space gravimetry observations from GRACE, we show that recent years sea level rise can be mostly explained by an increase of the mass of the oceans. Estimating GRACE-based ice sheet mass balance and using published estimates for glaciers melting, we further show that ocean mass increase since 2003 results by about half from an enhanced contribution of the polar ice sheets – compared to the previous decade – and half from mountain glaciers melting. Taking also into account the small GRACE-based contribution from continental waters (< 0.2 mm/yr), we find a total ocean mass contribution of ～ 2 mm/yr over 2003–2008. Such a value represents ～ 80% of the altimetry-based rate of sea level rise over that period. We next estimate the steric sea level (i.e., ocean thermal expansion plus salinity effects) contribution from: (1) the difference between altimetry-based sea level and ocean mass change and (2) Argo data. Inferred steric sea level rate from (1) (～ 0.3 mm/yr over 2003–2008) agrees well with the Argo-based value also estimated here (0.37 mm/yr over 2004–2008). Furthermore, the sea level budget approach presented in this study allows us to constrain independent estimates of the Glacial Isostatic Adjustment (GIA) correction applied to GRACE-based ocean and ice sheet mass changes, as well as of glaciers melting. Values for the GIA correction and glacier contribution needed to close the sea level budget and explain GRACE-based mass estimates over the recent years agree well with totally independent determinations.     

Characterizing Io’s Pele,Tvashtar and Pillan plumes: Lessons learned from Hubble

Hubble Space Telescope/Wide Field and Planetary Camera 2 (HST/WFPC2) images of Io obtained between 1995 and 2007 between 0.24 and 0.42 μm led to the detection of the Pele plume in reflected sunlight in 1995 and 1999; imaging of the Pele plume via absorption of jovian light in 1996 and 1999; detection of the Prometheus-type Pillan plume in reflected sunlight in 1997; and detection of the 2007 Pele-type Tvashtar plume eruption in reflected sunlight and via absorption of jovian light. Based on a detailed analysis of these observations we characterize and compare the gas and dust properties of each of the detected plumes. In each case, the brightness of the plumes in reflected sunlight is less at 0.26 μm than at 0.33 μm. Mie scattering analysis of the wavelength dependence of each plume’s reflectance signature suggests that range of particle sizes within the plumes is quite narrow. Assuming a normal distribution of particle sizes, the range of mean particle sizes is ～0.035–0.12 μm for the 1997 Pillan eruption, ～0.05–0.08 μm for the 1999 Pele and 2007 Tvasthar plumes, and ～0.05–0.11 μm for the 1995 Pele plume, and in each case the standard deviation in the particle size distribution is <15%. The Mie analysis also suggests that the 2007 Tvashtar eruption released ～10⁹ g of sulfur dust, the 1999 Pele eruption released ～10⁹ g of SO₂ dust, the 1997 Pillan eruption released ～10¹⁰ g of SO₂ dust, and the 1995 Pele plume may have released ～10¹⁰ g of SO₂ dust. Analysis of the plume absorption signatures recorded in the F255W filter bandpass (0.24–0.28 μm) indicates that the opacity of the 2007 Tvashtar plume was 2× that of the 1996 and 1999 Pele plume eruptions. While the sulfur dust density estimated for the Tvashtar from the reflected sunlight data could have produced 61% of the observed plume opacity, <10% of the 1999 Pele F255W plume opacity could have resulted from the SO₂ dust detected in the eruption. Accounting for the remaining F255W opacity level of the Pele and Tvasthar plumes based on SO₂ and S₂ gas absorption, the SO₂ and S₂ gas density inferred for each plume is almost equivalent corresponding to ～2–6 × 10¹⁶ cm^?2 and 3–5 × 10¹⁵ cm^?2, respectively, producing SO₂ and S₂ gas resurfacing rates ～0.04–0.2 cm yr^?1 and 0.007–0.01 cm yr^?1; and SO₂ and S₂ gas masses ～1–4 × 10¹⁰ g and ～2–3 × 10⁹ g; for a total dust to gas ratio in the plumes ～10^?1–10^?2. The 2007 Tvashtar plume was detected by HST at ～380 ± 40 km in both reflected sunlight and absorbed jovian light; in 1999, the detected Pele plume altitude was 500 km in absorbed jovian light, but in reflected sunlight the detected height was ～2× lower. Thus, for the 1999 Pele plume, similar to the 1979 Voyager Pele plume observations, the most efficient dust reflections occurred in the region closest to the plume vent. The 0.33–0.42 μm brightness of the 1997 Pillan plume was 10–20× greater than the Pele or Tvashtar plumes, exceeding by a factor of 3 the average brightness levels observed within 200 km of 1979 Loki eruption vent. But, the 0.26 μm brightness of the 1997 Pillan plume in reflected sunlight was significantly lower than would be predicted by the dust scattering model. Presuming that the 0.26 μm brightness of the 1997 Pillan plume was attenuated by the eruption plume’s gas component, then an SO₂ gas density ～3–6 × 10¹⁸ cm^?2 is inferred from the data (for S₂/SO₂ ratios ?4%), comparable to the 0.3–2 × 10¹⁸ cm^?2 SO₂ density detected at Loki in 1979 (Pearl, J.C. et al. [1979]. Nature 280, 755; Lellouch et al., 1992), and producing an SO₂ gas mass ～3–8 × 10¹¹ g and an SO₂ resurfacing rate ～8–23 cm yr^?1. These results confirm the connection between high (?10¹⁷ cm^?2) SO₂ gas content and plumes that scatter strongly at nearly blue wavelengths, and it validates the occurrence of high density SO₂ gas eruptions on Io. Noting that the SO₂ gas content inferred from a spectrum of the 2003 Pillan plume was significantly lower ～2 × 10¹⁶ cm^?2 (Jessup, K.L., Spencer, J., Yelle, R. [2007]. Icarus 192, 24–40); and that the Pillan caldera was flooded with fresh SO₂ frost/slush just prior to the 1997 Pillan plume eruption (Geissler, P., McEwen, A., Phillips, C., Keszthelyi, L., Spencer, J. [2004a]. Icarus 169, 29–64; Phillips, C.B. [2000]. Voyager and Galileo SSI Views of Volcanic Resurfacing on Io and the Search for Geologic Activity at Europa. Ph.D. Thesis, Univ. of Ariz., Tucson); we propose that the density of SO₂ gas released by this volcano is directly linked to the local SO₂ frost abundance at the time of eruption.     

Non-thermal water loss of the early Mars: 3D multi-ion hybrid simulations

In this study we analyze the non-thermal loss rates of O⁺, O₂⁺ and CO₂⁺ ions over the last 4.5 billion years (Gyr) in the Martian history by using a 3D hybrid model. For this reason we derived the past solar wind conditions in detail. We take into account the intensified particle flux of the early Sun as well as an Martian atmosphere, which was exposed to a sun's extreme ultraviolet (EUV) radiation flux 4.5 Gyr ago that was 100 times stronger than today. Furthermore, we model the evolution of the interplanetary magnetic field by a Weber & Davis solar wind model. The ‘external’ influences of the Sun's radiation flux and solar wind flux lead to the formation of an ionospheric obstacle by photoionization, charge exchange and electron impact. For the early Martian conditions we could show that charge exchange was the dominant ionization mechanism. Several hybrid simulations for different stages in the evolution of the Martian atmosphere, at 1, 2, 5, 10, 30 and 100 EUV, were performed to analyze the non-thermal escape processes by ion pick-up, momentum transfer from the solar wind to the ionosphere and detached ionospheric plasma clouds. Our results show a non-linear evolution of the loss rates. Using mean solar wind parameters the simulations result in an oxygen loss equivalent to the depth of a global Martian ocean of about 2.6 m over the last 4.5 Gyr. The induced magnetic field strength could be increased up to about 2000 nT. A simulation run with high solar wind density results in an oxygen loss of a Martian ocean up to 205 m depth during 150 million years after the sun reached the zero age mean sequence (ZAMS).     

A model for the temperature-dependence of tidal dissipation in convective plumes on icy satellites: Implications for Europa and Enceladus

To explain the formation of surface features on Europa, Enceladus, and other satellites, many authors have postulated the spatial localization of tidal heating within convective plumes. However, the concept that enhanced tidal heating can occur within a convective plume has not been rigorously tested. Most models of this phenomenon adopt a tidal heating with a temperature-dependence derived for an incompressible, homogeneous (zero-dimensional) Maxwell material, but it is unclear whether this formulation is relevant to the heterogeneous situation of a warm plume surrounded by cold ice. To determine whether concentrated dissipation can occur in convective plumes, we develop a two-dimensional model to compute the volumetric dissipation rate for an idealized, vertically oriented, isolated convective plume obeying a Maxwellian viscoelastic compressible rheology. We apply the model to the Europa and Enceladus ice shells, and we investigate the consequences for partial melting and resurfacing processes on these bodies. We find that the tidal heating is strongly temperature dependent in a convective ice plume and could produce elevated temperatures and local partial melting in the ice shells of Europa and Enceladus. Our calculation provides the first quantitative verification of the hypothesis by Sotin et al. [Sotin, C., Head, J.W., Tobie, G., 2002. Geophys. Res. Lett. 29. 74-1] and others that the tidal dissipation rate is a strong function of temperature inside a convective plume. On Europa, such localized heating could help allow the formation of domes and chaos terrains by convection. On Enceladus, localized tidal heating in a thermal plume could explain the concentrated activity at the south pole and its associated heat transport of 2-7 GW.     

The effect of orbital evolution on the Haumea (2003 EL61) collisional family

The Haumea family is currently the only identified collisional family in the Kuiper belt. We numerically simulate the long-term dynamical evolution of the family to estimate a lower limit of the family’s age and to assess how the population of the family and its dynamical clustering are preserved over Gyr timescales. We find that the family is not younger than 100 Myr, and its age is at least 1 Gyr with 95% confidence. We find that for initial velocity dispersions of 50–400 m s^?1, approximately 20–45% of the family members are lost to close encounters with Neptune after 3.5 Gyr of orbital evolution. We apply these loss rates to two proposed models for the formation of the Haumea family, a graze-and-merge type collision between two similarly sized, differentiated KBOs or the collisional disruption of a satellite orbiting Haumea. For the graze-and-merge collision model, we calculate that >85% of the expected mass in surviving family members within 150 m s^?1 of the collision has been identified, but that one to two times the mass of the known family members remains to be identified at larger velocities. For the satellite-break-up model, we estimate that the currently identified family members account for ～50% of the expected mass of the family. Taking observational incompleteness into account, the observed number of Haumea family members is consistent with either formation scenario at the 1σ level, however both models predict more objects at larger relative velocities (>150 m s^?1) than have been identified.     

Empirical constraints on the salinity of the europan ocean and implications for a thin ice shell

Induced electrical currents within Europa inferred from Galileo spacecraft magnetometer instrument data have been interpreted as due to a salty europan ocean. Published compositional models for Europa's ocean, based on aqueous leaching of carbonaceous chondrites, range over five orders of magnitude in predicted magnesium sulfate concentrations. We combine the Galileo spacecraft magnetometer-derived oceanic conductivities and radio Doppler data-derived interior models with laboratory conductivity vs concentration data for both magnesium sulfate solutions and terrestrial seawater to determine empirically the range of salt concentrations permitted for Europa's ocean. Solutions for both a three-layer spherical model, and a five-layer half-space model, that satisfy current preferred best fits to magnetometer data imply high, near-saturation salt concentrations and require a europan ice shell of less than 15 km thick, with a best fit at 4 km ice thickness. Adding a conductive core and mantle has a negligible effect on the amplitude when ocean conductivities are greater than a few Siemens per meter. Similarly, we find that including a realistic ionosphere has a negligible effect. We examine the implications of these results for the subsurface habitability of Europa.     

Impact-induced mantle dynamics on Mars

At least 20 impact basins with diameters ranging from 1000 to 3380 km have been identified on Mars, with five exceeding 2500 km. The coincidental timing of the end of the sequence of impacts and the disappearance of the global magnetic field has led to investigations of impact heating crippling an early core dynamo. The rate of core cooling (and thus dynamo activity) is limited by that of the overlying mantle. Thus, the pre-existing thermal state of the mantle controls the extent to which a sequence of impacts may affect dynamo activity. Here, we examine the effects of the initial thermal structure of the core and mantle, and the location of an impact with respect to the pre-existing convective structure on the mantle dynamics and surface heat flux.We find that the impacts that formed the five largest basins dominate the impact-driven effects on mantle dynamics. A single impact of this size can alter the entire flow field of the mantle. Such an impact promotes the formation of an upwelling beneath the impact site, resulting in long-lived single-plume convection. The interval between the largest impacts is shorter than the initial recovery time for a single impact. Hence, the change in convective pattern due to each impact sets up a long term change in the global heat flow. These long-term changes are cumulative, and multiple impacts have a synergistic effect.     

Thermal and transport properties of mantle rock at high pressure: Applications to super-Earths

In the present study, the temperature- and pressure-dependent transport and thermal properties, i.e., viscosity, phonon thermal conductivity, thermal expansivity and heat capacities, as well as electronic and radiative thermal conductivities, have been derived for the mantles of super-Earths. These properties are necessary to understand the interior dynamics and the thermal evolution of those planets. We assume that the mantles consist of MgSiO₃ perovskite (pv), but we discuss the effects of the post-perovskite transition, and we elaborate on an addition of periclase MgO and incorporated Fe. However, MgO is found to only significantly influence the phonon thermal conductivity – the viscosities, heat capacities and thermal expansivities of pv and MgO remain comparable. We use the Keane theory of solids, which takes into account the behavior of solid matter at the infinite pressure limit, adopt the Keane equations of state, and adjust for pv and MgO by comparison with experimental high-pressure and high-temperature data. We find the theory of the infinite pressure limit of Keane to be in excellent agreement with recent ab initio studies and experiments. To calculate the melting curve, we further use the Lindemann–Stacey scaling law and fit it to available experimental data. The best data fitting melting temperature for pv reaches 5700 K at 135 GPa and increases to 20,000 K at 1.1 TPa, corresponding to the core-mantle boundary of a 10 Earth mass super-Earth (10M_Earth). We find the pv adiabatic temperature (with a potential temperature of 1700 K) to reach 2570 K at 135 GPa and 5000 K at 1.1 TPa. To calculate the pressure-and temperature-dependent viscosity, we use the semi-empirical homologous temperature scaling to relate enthalpy change, and hence viscosity, to the melting temperature. We find that the resulting activation volume of pv decreases from 2.8 cm³/mol at 25 GPa to 1.4 cm³/mol at 1.1 TPa-resulting in a viscosity increase by ～15 orders of magnitude through the adiabatic mantle of a 10M_Earth planet. Furthermore, the thermal expansivity (of pv and MgO) decreases by a factor of eight, and the total thermal conductivity (phonon, radiative and electronic) of an Earth-like pv/MgO composite increases by a factor of seven through an adiabatic mantle of a 10M_Earth super-Earth. At higher temperatures, i.e., for super-adiabatic temperature profiles, the electronic and radiative thermal conductivities strongly increase and dominate the conductive heat transport. All findings indicate an increase of heat transfer solely by conduction in the lower mantles of super-Earths. Thus our results disagree with Earth-biased full-mantle convection assumptions made by previous models for super-Earths, and additionally raise questions about the differentiation of massive rocky exoplanets and their ability to generate magnetic fields or sustain plate tectonics.     

Librations of the Galilean satellites: The influence of global internal liquid layers

The four Galilean satellites are thought to harbor one or even two global internal liquid layers beneath their surface layer. The iron core of Io and Ganymede is most likely (partially) liquid and also the core of Europa may be liquid. Furthermore, there are strong indications for the existence of a subsurface ocean in Europa, Ganymede, and Callisto. Here, we investigate whether libration observations can be used to prove the existence of these liquid layers and to constrain the thickness of the overlying solid layers. For Io, the presence of a small liquid core increases the libration of the mantle by a few percent with respect to an entirely solid Io and mantle libration observations could be used to determine the mantle thickness with a precision of several tens of kilometers given that the libration amplitude can be measured with a precision of 1 m. For Europa, Ganymede, and Callisto, the presence of a water ocean close to the surface increases by at least an order of magnitude the ice shell libration amplitude with respect to an entirely solid satellite. The shell libration depends essentially on the shell thickness and to a minor extent on the density difference between the ocean and the ice shell. The possible presence of a liquid core inside Europa and Ganymede has no noticeable influence on their shell libration. For a precision of several meters on the libration measurements, in agreement with the expected accuracy with the NASA/ESA EJSM orbiter mission to Europa and Ganymede, an error on the shell thickness of a few tens kilometers is expected. Therefore, libration measurements can be used to detect liquid layers such as Io’s core or water subsurface oceans in Europa, Ganymede, and Callisto and to constrain the thickness of the overlying solid surface layers.     

Hydrothermal dynamics in a CM‐based model of Ceres

A 2‐D numerical study of the evolution of Ceres from a “frozen mudball” to the present era emphasizes the importance of hydrothermal processes. Particulates released as the “frozen mudball” thaws settle to form a roughly 290 km radius core. Hydrothermal flow is driven by radiogenic heating and serpentinization. Both salt‐free and brine fluids are considered. Our modeling suggests that Ceres’s core has been warm over most of its history and is still above freezing, and convective processes are active in core and mantle to the present. The addition of low eutectic solutes greatly expands the region of active convection. A global muddy ocean persists for the first 3 Gyr, and at present, there may be several regional mud seas buried under a frozen crust. Transport of interior material to the near surface occurs throughout our model's history. Eutectic brines drive convective flow to near the surface, even breaching the surface in isolated regions, on the order of 30 km in width, similar in size to some mounds detected using the Dawn visible imaging camera (Sizemore et al. 2015). Surface features such as the bright spot in Occator crater and Ahuna Mons could be the result of eutectic plumes. The CM‐based model density profile is within 10% of Ermakov et al.'s ( 2017 ) results. The model mud mantle has a roughly 42:58 volumetric partitioning of H₂O to rock. Our mud model is consistent with the absence of large craters (Marchi et al. 2016 ) and an internal viscosity decreasing with depth (Fu et al. 2017 ).     

Coupled convection and tidal dissipation in Europa’s ice shell

We performed 2D numerical simulations of oscillatory tidal flexing to study the interrelationship between tidal dissipation (calculated using the Maxwell model) and a heterogeneous temperature structure in Europa’s ice shell. Our 2D simulations show that, if the temperature is spatially uniform, the tidal dissipation rate peaks when the Maxwell time is close to the tidal period, consistent with previous studies. The tidal dissipation rate in a convective plume encased in a different background temperature depends on both the plume and background temperature. At a fixed background temperature, the dissipation increases strongly with plume temperature at low temperatures, peaks, and then decreases with temperature near the melting point when a melting-temperature viscosity of 10¹³ Pa s is used; however, the peak occurs at significantly higher temperature in this heterogeneous case than in a homogeneous medium for equivalent rheology. For constant plume temperature, the dissipation rate in a plume decreases as the surrounding temperature increases; plumes that are warmer than their surroundings can exhibit enhanced heating not only relative to their surroundings but relative to the Maxwell-model prediction for a homogeneous medium at the plume temperature. These results have important implications for thermal feedbacks in Europa’s ice shell.To self-consistently determine how convection interacts with tidal heating that is correctly calculated from the time-evolving heterogeneous temperature field, we coupled viscoelastic simulations of oscillatory tidal flexing (using Tekton) to long-term simulations of the convective evolution (using ConMan). Our simulations show that the tidal dissipation rate resulting from heterogeneous temperature can have a strong impact on thermal convection in Europa’s ice shell. Temperatures within upwelling plumes are greatly enhanced and can reach the melting temperature under plausible tidal-flexing amplitude for Europa. A pre-existing fracture zone (at least 6 km deep) promotes the concentration of tidal dissipation (up to ∼20 times more than that in the surroundings), leading to lithospheric thinning. This supports the idea that spatially variable tidal dissipation could lead locally to high temperatures, partial melting, and play an important role in the formation of ridges, chaos, or other features.