G. Choblet

Coupling mantle convection and tidal dissipation: Applications to Enceladus and Earth‐like planets

[1] Anelastic dissipation of tidal forces likely contributes to the thermal budget of several satellites of giant planets and Earth‐like planets closely orbiting other stars. In order to address how tidal heating influences the thermal evolution of such bodies, we describe here a new numerical tool that solves simultaneously mantle convection and tidal dissipation in a three‐dimensional spherical geometry. Since the two processes occur at different timescales, tidal dissipation averaged over a forcing period is included as a volumetric heat source for mantle dynamics. For the long‐term flow, a purely viscous material is considered, whereas a Maxwell‐like formalism is employed for the tidal viscoelastic problem. Due to the strongly temperature dependent rheological properties of both mechanisms, the coupling is achieved via the temperature field. The model is applied to two examples: Enceladus and an Earth‐like planet. For Enceladus, our new 3‐D method shows that the tidal strain rates are strongly enhanced in hot upwellings when compared with classical methods. Moreover, the heat flux at the base of Enceladus’ ice shell is strongly reduced at the poles, thus favoring the preservation of a liquid reservoir at depth. For Earth‐like planets, tidal dissipation patterns are predicted for different orbital configuration. Thermal runaway is observed for orbital periods smaller than a critical value (e.g., 30 days for an eccentricity of 0.2 and 3:2 resonance). This is likely to promote large‐scale melting of the mantle and Io‐like volcanism.

Constraints on thermal state and composition of the Earth's lower mantle from electromagnetic impedances and seismic data

Despite the tight constraints put by seismology on the elastic properties of the Earths lower mantle, its mineralogical composition and thermal state remain poorly known because the interpretation of seismic measurements suffers from the trade-off between temperature, iron content, and mineralogical composition. In order to overcome this difficulty, we complement seismic data with electromagnetic induction data. The latter data are mostly sensitive to temperature and iron content, while densities and acoustic speeds mostly constrain the mineralogy. A 0.5 log unit increase in electrical conductivity can be caused either by a 400 K increase of the temperature or by an increase of iron content from 10% to 12.5%. Acoustic velocity is only marginally sensitive to temperature but it increases by 0.8 km s−1 on average as the perovskite fraction increases from 50% to 100%. Olsens (1999) apparent resistivities in the period range [15 days, 11 years], and Preliminary reference Earth model (PREM) densities and acoustic speeds are jointly inverted in the depth range [800 km, 2600 km] by using a Monte Carlo Markov Chain method. Given the uncertainties on these data, estimates of perovskite fraction are well constrained over the whole depth range, but information on temperature and iron content is only obtained for depths less than 2000 km, corresponding to the penetration depth of the long-period electromagnetic field. All parameter values are determined with an uncertainty better than 15–20% at the 1σ confidence level. The temperature in the uppermost lower mantle (i.e., down to 1300 km depth) is close to a value of 2200 K and increases along a superadiabatic gradient of 0.4 K km−1 between 1300 and 2000 km depth. Extrapolation of this gradient at greater depth leads to a temperature close to 2800 K at 2600 km depth. The iron content of the lower mantle is found to be almost constant and equal to 10–11% whatever the depth, while a significant linear decrease of the perovskite content is observed throughout the whole depth range, from 80% at 800 km depth down to ∼65% at 2600 km depth.

Tidally induced thermal runaways on extrasolar earths : impact on habitability

We study the susceptibility of extrasolar Earth-like planets to tidal dissipation by varying orbital, rheological, and heat transfer parameters. We employ a three-dimensional numerical method solving the coupled problem of mantle convection and tidal dissipation. A reference model mimicking a plate tectonic regime and reproducing Earths present-day heat output is considered. Four other models representing less efficient heat transfer regimes are also investigated. For these five initial models, we determine the orbital configurations under which a positive feedback between tidal dissipation and temperature evolution leads to a thermal runaway. In order to describe the occurrence of thermal runaways, we develop a scaling that relates the global dissipated power to a characteristic temperature and to the orbital parameters. For all numerical experiments sharing the same initial temperature conditions, we show that the reciprocal value of the runaway timescale depends linearly on the global dissipated power at the beginning of the simulation. In the plate tectonic-like regime, Earth-like planets in the habitable zone (HZ) of 0.1 M ☉ stars experience thermal runaways for 1:1 spin-orbit resonance if the eccentricity is sufficiently high (e>0.02 at a 4 day period, e>0.2 at a 10 day period). For less efficient convective regimes, runaways are obtained for eccentricities as low as ~0.004 at the inner limit of the HZ. In the case of 3:2 spin-orbit resonance, the occurrence of thermal runaways is independent of eccentricity and is predicted for orbital periods lower than 12 days. For less efficient convective regimes, runaways may occur at larger orbital periods potentially affecting the HZ of stars with a mass up to 0.4 M ☉. Whatever the convective regime and spin-orbit resonance, tidal heating within Earth-like planets orbiting in the HZ of stars more massive than 0.5 M ☉ is not significant.

Ice melting and downward transport of meltwater by two-phase flow in Europa's ice shell

With its young surface, very few impact craters, and the abundance of tectonic and cryovolcanic features, Europa has likely been subjected to relatively recent endogenic activity. Morphological analyses of chaos terrains and double ridges suggest the presence of liquid water within the ice shell a few kilometers below the surface, which may result from enhanced tidal heating. A major issue concerns the thermal/gravitational stability of these water reservoirs. Here we investigate the conditions under which water can be generated and transported through Europas ice shell. We address particularly the downward two-phase flow by solving the equations for a two-phase mixture of water ice and liquid water in one-dimensional geometry. In the case of purely temperate ice, we show that water is transported downward very efficiently in the form of successive porosity waves. The time needed to transport the water from the subsurface region to the underlying ocean varies between ∼1 and 100 kyr, depending mostly on the ice permeability. We further show that water produced in the head of tidally heated hot plumes never accumulates at shallow depths and is rapidly extracted from the ice shell (within less than a few hundred kiloyears). Our calculations indicate that liquid water will be largely absent in the near subsurface, with the possible exception of cold conductive regions subjected to strong tidal friction. Recently active double ridges subjected to large tidally driven strike-slip motions are perhaps the most likely candidates for the detection of transient water lenses at shallow depths on Europa.

Mantle-driven geodynamo features—effects of post-Perovskite phase transition

Exploring the impact of the heterogeneous lower mantle on the geodynamo requires knowledge of the heat flux anomaly across the core-mantle boundary. Most studies so far used a purely thermal interpretation of seismic shear wave anomalies to assign heterogeneous heat flux boundary conditions on numerical dynamo models, ignoring phase transition or compositional origins. A recent study of mantle convection (Nakagawa and Tackley, 2008) provides guidelines to include such non-thermal effects. Here we construct maps of heat flux across the core-mantle boundary based on a lower mantle tomography model (Masters et al, 2000) with a combined thermal and post-Perovskite phase transition interpretation. We impose these patterns as outer boundary conditions on numerical dynamo simulations and study the impact of accounting for post-Perovskite effects on the long-term time-average properties of the dynamo. We then compare our results with geophysical observations. We find in all cases that surface downwellings associated with cyclones concentrate intense non-axisymmetric magnetic flux at high-latitudes, the surface flow contains a large anticlockwise vortex at mid-latitudes of the southern hemisphere, and the inner boundary buoyancy flux is dominated by a Y20 pattern. Boundary-driven time-average surface flow with some equatorial asymmetry is organized in the shell by quasi-axial convective rolls that extract more buoyancy from low-latitudes of the inner-boundary. These positive inner boundary buoyancy flux structures are found at low-latitudes of the northern hemisphere, in some places due to cyclonic flow at mid-latitudes of the southern hemisphere connecting with higher latitude cyclonic flow in the northern hemisphere. Accounting for post-Perovskite effects improves the recovery of several geodynamo observations, including the Atlantic/Pacific hemispherical dichotomy in core flow activity, the single intense paleomagnetic field structure in the southern hemisphere, and possibly the m = 1 dominant mode of inner-core seismic heterogeneity.

Water generation and transport below Europa's strike-slip faults

Jupiters moon Europa has a very young surface with the abundance of unique terrains that indicate recent endogenic activity. Morphological models as well as spectral observations suggest that it might possess shallow lenses of liquid water within its outer ice shell. Here we investigate the generation and possible accumulation of liquid water below the tidally activated strike-slip faults using a numerical model of two-phase ice-water mixture in two-dimensional Cartesian geometry. Our results suggest that generation of shallow partially molten regions underneath Europas active strike-slip faults is possible, but their lifetime is constrained by the formation of Rayleigh-Taylor instabilities due to the negative buoyancy of the melt. Once formed, typically within a few million years, these instabilities efficiently transport the meltwater through the shell. Consequently, the maximum water content in the partially molten regions never exceeds 10% which challenges their possible detection by future exploration mission.

Probabilistic surface reconstruction of coastal sea level rise during the twentieth century

We present a new surface reconstruction procedure based on the Bayesian inference method for coastal relative sea level variation during the twentieth century. Average rates are computed from tide gauge records. Models based on a Voronoi tessellation adapt to the level of information which proves well suited to the strong heterogeneity of data. Each point of the reconstructed surface is defined through a probability density function, a format particularly well adapted to this climate-related datum. The resolution of reconstructed surfaces strongly varies among the six large regions considered and within a given region. Anomalous sea level variations recorded locally are shown to reflect either anthropogenic effects or well-identified fast tectonics. For a poor data coverage, these can cause a problematic distortion of the reconstructed surface. Europe, North America, Australia, and Africa present a single trend with a decreasing precision of the reconstructed surface as a function of resolution of the tide gauge record. The most prominent feature in Europe is the pronounced uplift of Fennoscandia. Coasts of United States have the best resolution in North America and present stronger rates of sea level rise on the Atlantic than their European counterparts. Australia (especially in the North) and Africa are poorly resolved. Asia and South America depart clearly from this trend: a relatively uniform rise is obtained for Asia in spite of a good tide gauge record. Conversely, the reconstructed surface for South America presents an exceptional degree of roughness, at odds with a relatively poor record. Overall, this method not only offers a new assessment of sea level change (validating earlier results) but also quantifies the reliability of estimates.

Towards more realistic core-mantle boundary heat flux patterns: a source of diversity in planetary dynamos

Mantle control on planetary dynamos is often studied by imposing heterogeneous core-mantle boundary (CMB) heat flux patterns on the outer boundary of numerical dynamo simulations. These patterns typically enter two main categories: Either they are proportional to seismic tomography models of Earth’s lowermost mantle to simulate realistic conditions, or they are represented by single spherical harmonics for fundamental physical understanding. However, in reality the dynamics in the lower mantle is much more complicated and these CMB heat flux models are most likely oversimplified. Here we term alternative any CMB heat flux pattern imposed on numerical dynamos that does not fall into these two categories, and instead attempts to account for additional complexity in the lower mantle. We review papers that attempted to explain various dynamo-related observations by imposing alternative CMB heat flux patterns on their dynamo models. For present-day Earth, the alternative patterns reflect non-thermal contributions to seismic anomalies or sharp features not resolved by global tomography models. Time-dependent mantle convection is invoked for capturing past conditions on Earth’s CMB. For Mars, alternative patterns account for localized heating by a giant impact or a mantle plume. Recovered geodynamo-related observations include persistent morphological features of present-day core convection and the geomagnetic field as well as the variability in the geomagnetic reversal frequency over the past several hundred Myr. On Mars the models aim at explaining the demise of the paleodynamo or the hemispheric crustal magnetic dichotomy. We report the main results of these studies, discuss their geophysical implications, and speculate on some future prospects.

Macromolecular organic compounds from the depths of Enceladus

Saturn’s moon Enceladus harbours a global water ocean1, which lies under an ice crust and above a rocky core2. Through warm cracks in the crust3 a cryo-volcanic plume ejects ice grains and vapour into space4–7 that contain materials originating from the ocean8,9. Hydrothermal activity is suspected to occur deep inside the porous core10–12, powered by tidal dissipation13. So far, only simple organic compounds with molecular masses mostly below 50 atomic mass units have been observed in plume material6,14,15. Here we report observations of emitted ice grains containing concentrated and complex macromolecular organic material with molecular masses above 200 atomic mass units. The data constrain the macromolecular structure of organics detected in the ice grains and suggest the presence of a thin organic-rich film on top of the oceanic water table, where organic nucleation cores generated by the bursting of bubbles allow the probing of Enceladus’ organic inventory in enhanced concentrations.The detection of complex organic molecules with masses higher than 200 atomic mass units in ice grains emitted from Enceladus indicates the presence of a thin organic-rich layer on top of the moon’s subsurface ocean.

A particle-in-cell method for studying double-diffusive convection in the liquid layers of planetary interiors

Abstract Many planetary bodies contain internal liquid layers in their metallic cores or as buried water oceans. Convection in these layers is usually driven by buoyancy sources of thermal or compositional origin, with very different molecular diffusivities. Such conditions can potentially trigger double-diffusive instabilities and fundamentally affect the convective features. In numerical models, the weak diffusivity of the compositional field requires the use of a semi-Lagrangian description to produce minimal numerical diffusion. We implemented a “particle-in-cell” (PIC) method into a pre-existing geodynamo code in 3D spherical geometry to describe the compositional field properly. We developed several numerical strategies to solve various problems inherent to the implementation of a PIC method for convection in spherical geometry and coded a hybrid scheme suitable for massively parallel platforms. We tested our new code on two benchmark cases which validate its applicability to the study of double-diffusive convection in the internal liquid layers of planets. As a first application, we study a case of non-magnetic double-diffusive convection at infinite Lewis number. Major differences emerge both in the compositional field and the convective pattern when the compositional diffusivity is neglected.