Nicola Tosi

Rocky super-Earth interiors - Structure and internal dynamics of CoRoT-7b and Kepler-10b

Aims. We present interior structure models of the recently discovered exoplanets CoRoT-7b and Kepler-10b addressing their bulk compositions, present thermal states, and internal dynamics. We investigate how mantle convection patterns are influenced by the depth-dependence of thermodynamic parameters (e.g., thermal expansivity and conductivity) caused by the extended pressure and temperature ranges within rocky super-Earths. Methods. To model the interior of rocky exoplanets, we construct a four-layer structural model solving the mass and energy balance equations in conjunction with a generalized Rydberg equation of state providing the radial density distribution within each layer. The present thermal state is calculated according to a modified mixing-length approach for highly viscous fluids. Furthermore, the obtained internal structure is used to carry out two-dimensional convection simulations to visualize the mantle convection pattern within massive exoplanets such as CoRoT-7b and Kepler-10b. Results. Both CoRoT-7b and Kepler-10b most likely have large iron cores and a bulk composition similar to that of Mercury. For a planetary radius of Rp = (1.58 ± 0.10) R⊕, a revised total mass of Mp = (7.42 ± 1.21) M⊕, and the existence of a third planet in the CoRoT-7 planetary system, calculations suggest that an iron core of 64 wt-% and a silicate mantle of 36 wt-% is produced owing to the relatively high average compressed density of ρavg = (10.4±1.8) g cm −3 . Kepler-10b’s planetary radius and total mass yield an iron core of 59.5 wt-%, which complements the silicate mantle of 40.5 wt-%. An enhanced radiogenic heating rate owing to CoRoT-7b’s young age (1.2−2.3 Gyr) raises the radial distribution of temperature by only a few hundred Kelvin, but reduces the viscosity by an order of magnitude. The planform of mantle convection is found to be strongly modified for depth-dependent material properties, with hot plumes rising across the whole mantle and cold slabs, which stagnate in the mid-mantle because of the loss of buoyancy. Conclusions. We use a new model approach to determine the detailed interior structures and present thermal states of CoRoT-7b and Kepler-10b. Both planets are found to be enriched in iron. The results imply that modest radiogenic heating does not play a significant role in determining the internal structure of rocky exoplanets. The depth-dependence of thermodynamic properties, however, strongly influences the mantle convection patterns within exoplanets such as CoRoT-7b and Kepler-10b. This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

Thickness of the crust of Mercury from geoid-to-topography ratios

To gain insight into the thickness of the crust of Mercury, we use gravity and topography data acquired by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft to calculate geoid-to-topography ratios over the northern hemisphere of the planet. For an Airy model for isostatic compensation of variations in topography, we infer an average crustal thickness of 35 ± 18 km. Combined with the value of the radius of the core of Mercury, this crustal thickness implies that Mercury had the highest efficiency of crustal production among the terrestrial planets. From the measured abundance of heat-producing elements on the surface, we calculate that the heat production in the mantle from long-lived radioactive elements at 4.45 Ga was greater than 5.4 ×10−12W/kg. By analogy with the Moon, the relatively thin crust of Mercury allows for the possibility that major impact events, such as the one that formed the Caloris basin, excavated material from Mercurys mantle.

Is the long‐wavelength geoid sensitive to the presence of postperovskite above the core‐mantle boundary?

[1] The analysis of seismic data represents today the primary tool in the search for the presence of postperovskite in the lowermost mantle (D 00 ). This work aims at testing whether the inversion of gravitational data can also contribute to the detection of postperovskite in D 00 .W e assume that the transition from perovskite to postperovskite is accompanied by a reduction in viscosity and test the effects of such viscosity change on the prediction of the dynamic geoid with a numerical model of subducted lithosphere. Our results show that the long-wavelength component of the geoid is very sensitive to the presence of postperovskite areas in D 00 , especially if their viscosity is significantly lower than the viscosity of the surrounding perovskite and if these areas are located close to density � � � � � � � � � � � � � � � � � � � � � ��

A community benchmark for viscoplastic thermal convection in a 2‐D square box

Numerical simulations of thermal convection in the Earth’s mantle often employ a pseudoplastic rheology in order to mimic the plate-like behavior of the lithosphere. Yet the benchmark tests available in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature. Here we present a suite of simple tests based on nonlinear rheologies featuring temperature, pressure, and strain rate-dependent viscosity. Eleven different codes based on the finite volume, finite element, or spectral methods have been used to run five benchmark cases leading to stagnant lid, mobile lid, and periodic convection in a 2-D square box. For two of these cases, we also show resolution tests from all contributing codes. In addition, we present a bifurcation analysis, describing the transition from a mobile lid regime to a periodic regime, and from a periodic regime to a stagnant lid regime, as a function of the yield stress. At a resolution of around 100 cells or elements in both vertical and horizontal directions, all codes reproduce the required diagnostic quantities with a discrepancy of at most

Thermal evolution and Urey ratio of Mars

3% in the presence of both linear and nonlinear rheologies. Furthermore, they consistently predict the critical value of the yield stress at which the transition between different regimes occurs. As the most recent mantle convection codes can handle a number of different geometries within a single solution framework, this benchmark will also prove useful when validating viscoplastic thermal convection simula- tions in such geometries.

Receiver function imaging of the mantle transition zone beneath the South China Block

The upcoming InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission, to be launched in 2016, will carry out the first in situ Martian heat flux measurement, thereby providing an important baseline to constrain the present-day heat budget of the planet and, in turn, the thermal and chemical evolution of its interior. The surface heat flux can be used to constrain the amount of heat-producing elements present in the interior if the Urey ratio (Ur)—the planets heat production rate divided by heat loss—is known. We used numerical simulations of mantle convection to model the thermal evolution of Mars and determine the present-day Urey ratio for a variety of models and parameters. We found that Ur is mainly sensitive to the efficiency of mantle cooling, which is associated with the temperature dependence of the viscosity (thermostat effect), and to the abundance of long-lived radiogenic isotopes. If the thermostat effect is efficient, as expected for the Martian mantle, assuming typical solar system values for the thorium-uranium ratio and a bulk thorium concentration, simulations show that the present-day Urey ratio is approximately constant, independent of model parameters. Together with an estimate of the average surface heat flux as determined by InSight, models of the amount of heat-producing elements present in the primitive mantle can be constrained.

On the habitability of a stagnant lid Earth

Upper mantle discontinuities are influenced by convection-related thermal heterogeneities arising in complex geodynamic settings. Slab rollback of the Pacific plate and mantle upwelling in the Meso-Cenozoic caused the extension and spreading of continental segments in the South China Block leading to profound variations of the local temperature conditions. We processed 201 teleseismic events beneath 87 stations in the Hainan, Guangdong, and Fujian provinces in the South China Block, and extracted 4172 high-quality receiver functions. We imaged the topography of the local mantle discontinuities by using phase-weighted common conversion point stacking of the receiver functions, which effectively improves the P-to-S-converted phases. We found that the average depths of the discontinuities at 410 and 660 km depth are 414 and 657 km, respectively, while no clearly defined discontinuity at 520 km depth was detected. We mapped the thickness of the mantle transition zone (MTZ), which can reflect temperature and/or compositional heterogeneities as well as the presence of water, and discussed possible geodynamic implications. In particular, we found that the MTZ beneath the Leizhou Peninsula in the Hainan province is 42 km thinner than average. This scenario suggests that the Hainan plume is responsible for positive temperature anomalies between ∼270 and 380 K and between ∼200 and 240 K at the 660 and 410 km discontinuities, respectively. We also observed a prominent uplifting of the 660 km boundary beneath the coast regions that may be indicative of lateral flow of the Hainan plume.

Impact-induced changes in source depth and volume of magmatism on Mercury and their observational signatures

Context. Plate tectonics is considered a fundamental component for the habitability of the Earth. Yet whether it is a recurrent feature of terrestrial bodies orbiting other stars or unique to the Earth is unknown. The stagnant lid may rather be the most common tectonic expression on such bodies. Aims. To understand whether a stagnant-lid planet can be habitable, i.e. host liquid water at its surface, we model the thermal evolution of the mantle, volcanic outgassing of H 2 O and CO 2 , and resulting climate of an Earth-like planet lacking plate tectonics. Methods. We used a 1D model of parameterized convection to simulate the evolution of melt generation and the build-up of an atmosphere of H 2 O and CO 2 over 4.5 Gyr. We then employed a 1D radiative-convective atmosphere model to calculate the global mean atmospheric temperature and the boundaries of the habitable zone (HZ). Results. The evolution of the interior is characterized by the initial production of a large amount of partial melt accompanied by a rapid outgassing of H 2 O and CO 2 . The maximal partial pressure of H 2 O is limited to a few tens of bars by the high solubility of water in basaltic melts. The low solubility of CO 2 instead causes most of the carbon to be outgassed, with partial pressures that vary from 1 bar or less if reducing conditions are assumed for the mantle to 100–200 bar for oxidizing conditions. At 1 au, the obtained temperatures generally allow for liquid water on the surface nearly over the entire evolution. While the outer edge of the HZ is mostly influenced by the amount of outgassed CO 2 , the inner edge presents a more complex behaviour that is dependent on the partial pressures of both gases. Conclusions. At 1 au, the stagnant-lid planet considered would be regarded as habitable. The width of the HZ at the end of the evolution, albeit influenced by the amount of outgassed CO 2 , can vary in a non-monotonic way depending on the extent of the outgassed H 2 O reservoir. Our results suggest that stagnant-lid planets can be habitable over geological timescales and that joint modelling of interior evolution, volcanic outgassing, and accompanying climate is necessary to robustly characterize planetary habitability.

Present‐Day Mars' Seismicity Predicted From 3‐D Thermal Evolution Models of Interior Dynamics

Mercury’s crust is mostly the result of partial melting in the mantle associated with solid-state convection. Large impacts induce additional melting by generating subsurface thermal anomalies. By numerically investigating the geodynamical effects of impacts, here we show that impact-generated thermal anomalies interact with the underlying convection modifying the source depth of melt and inducing volcanism that can significantly postdate the impact depending on the impact time and location with respect to the underlying convection pattern. We can reproduce the volume and time of emplacement of the melt sheets in the interior of Caloris and Rembrandt if at about 3.7–3.8 Ga convection in the mantle of Mercury was weak, an inference corroborated by the dating of the youngest large volcanic provinces. The source depth of the melt sheets is located in the stagnant lid, a volume of the mantle that never participated in convection and may contain pristine mantle material.Mantle partial melting produced the volcanic crust of Mercury. Here, the authors numerically model the formation of post-impact melt sheets and find that mantle convection was weak at around 3.7–3.8 Ga and that the melt sheets of Caloris and Rembrandt may contain partial melting of pristine mantle material.

Large Scale Numerical Simulations of Planetary Interiors

The Interior Exploration using Seismic Investigations, Geodesy and Heat Transport mission, to be launched in 2018, will perform a comprehensive geophysical investigation of Mars in situ. The Seismic Experiment for Interior Structure package aims to detect global and regional seismic events and in turn offer constraints on core size, crustal thickness, and core, mantle, and crustal composition. In this study, we estimate the present-day amount and distribution of seismicity using 3-D numerical thermal evolution models of Mars, taking into account contributions from convective stresses as well as from stresses associated with cooling and planetary contraction. Defining the seismogenic lithosphere by an isotherm and assuming two end-member cases of 573 K and the 1073 K, we determine the seismogenic lithosphere thickness. Assuming a seismic efficiency between 0.025 and 1, this thickness is used to estimate the total annual seismic moment budget, and our models show values between 5.7 × 1016 and 3.9 × 1019 Nm.