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Geophysical observations will provide key information about the inner structure of the planets and satellites and understanding the internal structure is a strong constraint on the bulk composition and thermal evolution of these bodies. Thus, geophysical observations are a key to uncovering the origin and evolution of the Moon. In this article, we propose the development of an autonomous lunar geophysical experiment package, composed of a suite of instruments and a central station with standardized interface, which can be installed on various future lunar missions. By fixing the interface between instruments and the central station, it would be possible to easily configure an appropriate experiment package for different missions. We describe here a series of geophysical instruments that may be included as part of the geophysical package: a seismometer, a magnetometer, a heat flow probe, and a laser reflector. These instruments will provide mechanical, thermal, and geodetic parameters of the Moon that are strongly related to the internal structure. We discuss the functionality required for future geophysical observations of the Moon, including the development of the central station that will be used commonly by different payloads.

This work reviews the long-term evolution of the atmosphere of Venus, and modulation of its composition by interior/exterior cycling. The formation and evolution of Venus’s atmosphere, leading to contemporary surface conditions, remain hotly debated topics, and involve questions that tie into many disciplines. We explore these various inter-related mechanisms which shaped the evolution of the atmosphere, starting with the volatile sources and sinks. Going from the deep interior to the top of the atmosphere, we describe volcanic outgassing, surface-atmosphere interactions, and atmosphere escape. Furthermore, we address more complex aspects of the history of Venus, including the role of Late Accretion impacts, how magnetic field generation is tied into long-term evolution, and the implications of geochemical and geodynamical feedback cycles for atmospheric evolution. We highlight plausible end-member evolutionary pathways that Venus could have followed, from accretion to its present-day state, based on modeling and observations. In a first scenario, the planet was desiccated by atmospheric escape during the magma ocean phase. In a second scenario, Venus could have harbored surface liquid water for long periods of time, until its temperate climate was destabilized and it entered a runaway greenhouse phase. In a third scenario, Venus’s inefficient outgassing could have kept water inside the planet, where hydrogen was trapped in the core and the mantle was oxidized. We discuss existing evidence and future observations/missions required to refine our understanding of the planet’s history and of the complex feedback cycles between the interior, surface, and atmosphere that have been operating in the past, present or future of Venus.

SUMMARY Constraining initial conditions and parameters of mantle convection for a planet often requires running several hundred computationally expensive simulations in order to find those matching certain ‘observables’, such as crustal thickness, duration of volcanism, or radial contraction. A lower fidelity alternative is to use 1-D evolution models based on scaling laws that parametrize convective heat transfer. However, this approach is often limited in the amount of physics that scaling laws can accurately represent (e.g. temperature and pressure-dependent rheologies or mineralogical phase transitions can only be marginally simulated). We leverage neural networks to build a surrogate model that can predict the entire evolution (0–4.5 Gyr) of the 1-D temperature profile of a Mars-like planet for a wide range of values of five different parameters: reference viscosity, activation energy and activation volume of diffusion creep, enrichment factor of heat-producing elements in the crust and initial temperature of the mantle. The neural network we evaluate and present here has been trained from a subset of ∼10 000 evolution simulations of Mars ran on a 2-D quarter-cylindrical grid, from which we extracted laterally averaged 1-D temperature profiles. The temperature profiles predicted by this trained network match those of an unseen batch of 2-D simulations with an average accuracy of $99.7\, {\rm per~cent}$.

The Earth-like planets and moons in our solar system have iron-rich cores, silicate mantles, and a basaltic crust. Differentiated icy moons can have a core and a mantle and an outer water–ice layer. Indirect evidence for several icy moons suggests that this ice is underlain by or includes a water-rich ocean. Similar processes are at work in the interiors of these planets and moons, including heat transport by conduction and convection, melting and volcanism, and magnetic field generation. There are significant differences in detail, though, in both bulk chemical compositions and relative volume of metal, rock and ice reservoirs. For example, the Moon has a small core [~ 0.2 planetary radii (RP)], whereas Mercury’s is large (~ 0.8 RP). Planetary heat engines can operate in somewhat different ways affecting the evolution of the planetary bodies. Mercury and Ganymede have a present-day magnetic field while the core dynamo ceased to operate billions of years ago in the Moon and Mars. Planets and moons differ in tectonic style, from plate-tectonics on Earth to bodies having a stagnant outer lid and possibly solid-state convection underneath, with implications for their magmatic and atmosphere evolution. Knowledge about their deep interiors has improved considerably thanks to a multitude of planetary space missions but, in comparison with Earth, the data base is still limited. We describe methods (including experimental approaches and numerical modeling) and data (e.g., gravity field, rotational state, seismic signals, magnetic field, heat flux, and chemical compositions) used from missions and ground-based observations to explore the deep interiors, their dynamics and evolution and describe as examples Mercury, Venus, Moon, Mars, Ganymede and Enceladus.

The presence of delta deposits on Mars has been thoroughly demonstrated for decades and large scale mapping [1,2] highlighted the presence of several delta fans mainly located on the dichotomy boundary. While a previous delta inventory was compiled by Morgan et al. [3], we aim to update and finalize a complete mapping of delta deposits in order to allow the examination of the evolution and distribution of standing bodies of water on Mars. The objective of our project focuses on the production of a global catalogue of water-related features at the Martian surface, which are commonly studied separately or at smaller scales.Globally, we located around 150 deltas among which many were not previously included in published literature [e.g. 1,2,4]. We then examined the deltas based on two main traits. Firstly, we measured the length of the feeding channels since it may be (i) a proxy for the duration of the aqueous activity in the channel-delta system, and (ii) proportional to the age of the delta [2]. The latter relationship links older deltas near Chryse Planitia (>3 Ga) to longer valleys, while younger deltas are usually fed by shorter valleys [2]. Secondly, we measured the elevation of the delta population and compared the obtained dataset with the hypothesized sea level elevation of -2540 ± 177 m firstly suggested by Di Achille and Hynek [1] for a northern ocean through the analysis of deltas.We observed that, if the relationship between feeding channel length and delta age found for a sub-group of the population [2] is applicable as a rule of thumb to all deltas, many of the deposits have the potential to be Hesperian or Amazonian in age. They would thus be younger than the ocean that might have occupied the northern lowlands during the Noachian-Hesperian boundary period [1] and thus be unrelated to a global sea level range. In fact, less than half of the delta population is related to medium/long feeding channels (>30 km). Abundant pristine morphologies, both related to channels and deltas, also supports the hypothesis that part of the population is younger than Noachian. Additionally, the large variety of elevations where the deltaic deposits can be found and the very small amount of deltas included in the sea level elevation range proposed by Di Achille and Hynek [1] raise questions about the generation and environmental implications of these features, especially when seen at global scale. [1] Di Achille, G. & Hynek, B. M., Nat. Geosci. 3, 459–463 (2010).[2] Hauber, E. et al., J. Geophys. Res. E Planets 118, 1529–1544 (2013).[3] Morgan, A. M., et al., Lunar Planet. Sci. Conf. (2018).[4] Ori, G.G. et al., J. Geophys. Res. E Planets 105, 17629–17641 (2000).

Introduction During the early stages of lunar evolution, the large amount of heat available from the lunar forming impact led to extensive melting of the Moon’s silicate mantle giving rise to a magma ocean. The fractional crystallization of the latter resulted in an inhomogeneous mantle with cumulate layers of increasing density towards the surface, due to iron enrichment in the residual magma ocean [1]. Such an unstable density distribution is prone to overturn and sets the stage for the subsequent thermo-chemical history of the mantle. In particular, this initial stage can significantly affect mixing of mantle material and the partial melt production, as well as the melt composition during the later stages of lunar evolution. The melt composition is directly linked to the composition of lunar basalts, whose variability at the lunar surface indicates complex melting processes and the presence of various mantle reservoirs. In this study we model the solid-state convection, mixing and partial melt production in the lunar mantle. We investigate the effects of an initially layered mantle as a consequence of the fractional crystallization of the lunar magma ocean. To this end, we combine geodynamical models using the mantle convection code GAIA with petrological calculations that provide information about the composition and structure at the end of lunar magma ocean (LMO) solidification. While previous mantle convection studies investigated lunar mantle melting in a purely homogeneous mantle [2] or with a localized KREEP layer [3,4], here we combine petrological and geodynamical models to investigate the degree of heterogeneity that can be produced by melting and mixing an initially heterogeneous lunar mantle. Petrological modeling The petrological model computes the crystallization sequence of the LMO. For the calculations in the deeper part of the mantle we use FOXMTR, for the shallower part alphaMELTS, as this approach is in good agreement with experimental data for the whole solidification process. We assume fractional crystallization of a spherical shell with an initial thickness of 1350 km, and a bulk lunar mantle composition from [5]. During crystallization the temperature is lowered stepwise and all minerals (except plagioclase) are assumed to accumulate at the bottom of the LMO and equilibrate with the melt at the respective pressure conditions. Plagioclase is assumed to float to the surface and form anothoritic crust. The resulting mantle structure is characterized by 5 compositional layers, where the predominant minerals are olivine, orthopyroxene, clinopyroxene, clinopyroxene and ilmenite (ilmenite bearing cumulates = IBC) and plagioclase (crust), respectively. For each of those layers an average density is calculated from the density profile after crystallization, as well as the change in density as a function of depletion. The solidus and liquidus temperature profiles are calculated for the average layer compositions using alphaMELTS. The depths and densities of the compositional layers, the initial temperature profile, the solidus and liquidus profiles for each layer and the density-depletion functions of each layer composition are provided in the form of read-out tables. The results from the petrological model are shown in figure 1. The densities of the mantle layers increase with radius due to the enrichment of iron in the melt during crystallization. The crust has a comparative low density (figure 1a). The temperature profile follows the crystallization temperatures of the cumulates. In figure 1b the temperature profile is shown together with the individual layers and their corresponding solidi and liquidi. From olivine to IBC the solidus and liquidus temperatures decrease because of the crystallization sequence (figure 1b). Geodynamical modelling We use the mantle convection code GAIA [6] in a 2D quarter cylinder geometry to model the thermochemical evolution of the compositionally heterogeneous lunar mantle. The nondimensional conservation equations of mass, momentum, thermal energy, and composition are solved under the extended Boussinesq approximation. We use an Arrhenius law to calculate the temperature- and depth-dependent viscosity. To track the composition of the mantle we use a particle-in-cell (PIC) method [7], where tracer particles carry information about material properties such as density, melting temperature, degree of depletion, amount of heat producing elements etc. Our models use between 35 to 50 particles per cell that are advected at each time step according to the velocity field. In our simulations we account for core cooling and radioactive decay, as well as mechanical mixing. In addition, we consider the effects of melting by accounting for the latent heat during mantle melting, as well as solidus and density increase/decrease due to mantle depletion [8]. During melting, low melting point components are extracted from the mantle as the melt rises to the surface to form the basaltic crust. This leads to an increase of the solidus temperature requiring a higher temperature to further melt the residual mantle material. Gradual changes in density and solidus temperatures are extracted from the precomputed read-out tables of the petrological modelling. Summary and Outlook Our coupled petrological-geodynamical model of mantle convection and melt production will be used to investigate the thermochemical evolution of an initially heterogeneous lunar mantle structure (figure 2). Preliminary results show a smaller amount of melt produced in a heterogeneous mantle in comparison to a homogeneous one. We will present the distribution of the compositional layers as a function of time and compare the amount of melting produced from each individual component. With this approach we aim to provide a link between melting processes in the interior of the Moon and the compositional diversity of basalts observed at the lunar surface. This in turn will help us to put constraints on the LMO crystallization and the subsequent thermochemical history of the Moon. Acknowledgements We thank Brian Doherty for his contribution to the numerical implementation. I.B. and S.S. were supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) SFB-TRR170, (subprojects C4 and A5). References [1] Elkins-Tanton et al., Annu. Rev. Earth Planet Sci. 2012; [2] Ziethe et al., PSS, 2009; [3] Laneuville et al., JGR, 2013 [4] Laneuville et al., JGR, 2018; [5] O’Neill et al., 1991; [6] Hüttig et al., PEPI, 2013; [7] Plesa et al., IGI Global, 2013; [8] Doherty et al., AGU, 2018.

We use a large data set of 3D thermal evolution models to predict the distribution of present-day seismic velocities in the Martian interior. Our models show a difference between maximum and minimum S-wave velocity of up to 10% either below the crust, where thermal variations are largest, or at the depth of the olivine to wadsleyite phase transition, located at around 1000 – 1200 km depth. Models with thick lithospheres on average have weak low-velocity zones that extend deeper than 400 km, and seismic velocity variations in the uppermost 400 – 600 km that closely follow the crustal thickness pattern. For these cases the crust contains more than half of the total amount of heat producing elements. Models with limited crustal heat production have thinner lithospheres and shallower but prominent low-velocity zones that are incompatible with InSight observations. Seismic events suggested to originate in Cerberus Fossae indicate the absence of S-wave shadow zones in 25° - 30° epicentral distance. This result is compatible with previous best-fit models that require a large average lithospheric thickness and a crust containing more than half of the bulk amount of heat producing elements to be compatible with geological and geophysical constraints. Ongoing and future InSight measurements that will determine the existence of a weak low-velocity zone will directly bear on the crustal heat production. ISSN:0148-0227 ISSN:2169-9097 ISSN:2169-9100

The accretion of the debris resulting from the giant collision that formed the Earth‐Moon system caused the formation of a deep lunar magma ocean. The initial composition profile of the Moon results from the solidification of this magma ocean. One of the late solidification products is a thin layer containing ilmenite, which is highly enriched in titanium and forms over a depth of about 40–80 km. This layer is much denser than the underlying mantle, it tends thus to overturn and sink toward the core. The overturn hypothesis explains several features of the evolution of the Moon. However, the strong temperature dependence of the viscosity makes the part of the mantle where this titanium‐rich layer solidifies very stiff and its overturn very difficult. In this work, we used numerical simulations to infer which deformation properties the mantle needs to have for the overturn to be possible. We found that the overturn requires a significantly weaker and less temperature dependent viscosity than usually thought. The required low viscosity and its weak temperature dependence can be explained by the presence of water and residual melt in the Moon and/or by the effects of nonlinear deformation dependent both on temperature and stress.

The thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present‐day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two‐dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log‐likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (1019 − 1022 Pa s), when all the observables are available: core‐mantle‐boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (105 − 5 × 105 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present‐day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10−6 − 10 × 10−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN., Plain Language Summary: The mantle of rocky planets like Mars behaves like a highly viscous fluid over geological time scales. Key parameters and initial conditions for the non‐linear partial differential equations governing mantle flow are poorly known. Machine Learning (ML) can help us avoid running several thousand computationally expensive fluid dynamic simulations each time to determine if an observable can constrain a parameter. Using an ML approach, we invert a set of synthetic observables such as present‐day surface heat flux, duration of volcanism and radial contraction to constrain important parameters controlling the long‐term evolution of the planet's interior, such as the reference mantle viscosity or the partitioning of radiogenic heat sources between mantle and crust. We demonstrate that by training a probabilistic ML algorithm on the data and applying it, we can quantify the constraints on parameters. This provides a high‐dimensional framework for analyzing inverse problems in geodynamics., Key Points: Mixture Density Networks provide a probabilistic framework for inverting observables to infer parameters of Mars' interior evolution Reference viscosity, crustal enrichment in heat‐producing elements and initial mantle temperature can be well constrained Activation energy of diffusion creep can be weakly constrained; constraining activation volume requires new observational signatures, Helmholtz Einstein International Berlin Research School in Data Science (HEIBRiDS), Berlin Institute for the Foundations of Learning and Data (BIFOLD), Deutsche Forschungsgemeinschaft (DFG) Research Unit FOR 2440

Bulletin of the AAS, 53 (4)

We derive synthetic electrical conductivity, seismic velocity, and density distributions from the results of martian mantle convection models affected by basin-forming meteorite impacts. The electrical conductivity features an intermediate minimum in the strongly depleted topmost mantle, sandwiched between higher conductivities in the lower crust and a smooth increase toward almost constant high values at depths greater than 400 km. The bulk sound speed increases mostly smoothly throughout the mantle, with only one marked change at the appearance of $\beta$-olivine near 1100 km depth. An assessment of the detectability of the subsurface traces of an impact suggests that its signature would be visible in both observables at least if efficient melt extraction from the shock-molten target occurs, but it will not always be particularly conspicuous even for large basins; observations with extensive spatial and temporal coverage would improve their detectability. Electromagnetic sounding may offer another possibility to investigate the properties of the mantle, especially in regions of impact structures. In comparison with seismology and gravimetry, its application to the martian interior has received little consideration so far. Of particular interest is its potential for constraining the water content of the mantle. By comparing electromagnetic sounding data of an impact structure with model predictions, it might also be possible to answer the open question of the efficiency of extraction of impact-generated melt., Comment: 5 figures

Charles D. Edwards (Jet Propulsion Laboratory, California Institute of Technology). Co-Authors: 1. Vlada Stamenkovic Jet Propulsion Laboratory, California Institute of Technology; 2. Penelope Boston NASA Ames; 3. Kennda Lynch LPI/USRA … et al.

Primary author: Suzanne Smrekar Jet Propulsion Laboratory/California Institute of Technology, Pasadena CA ; Co-authors: Jeff Andrews-Hanna (U.AZ), Doris Breuer (DLR Berlin), Paul Byrne (NCSU), Debra Buczkowski (JHU/APL), Bruce Campbell (Nat. Air Space Museum), A. Davaille (CNRS/U. Paris-Saclay), Darby Dyar (Mt. Holyoke/PSI), G. Di Achille (INAF/Astro Obs. Teramo), Caleb Fassett (Marshall), Martha Gilmore (Wesleyan), Robert Grimm (SWRI), Jorn Helbert (DLR Berlin), Scott Hensley (JPL), Robert Herrick (U. Alaska), Luciano Iess (U.Roma), Lauren Jozwiak (JHU/APL), Tiffany Katiaria (JPL), Marco Mastrogiuseppe (U. Roma), Erwan Mazarico (Goddard), Nils Mueller (DLR Berlin), Daniel Nunes (JPL), Joseph O'Rourke (ASU); Patrick McGovern (LPI), Maria Raguso (Caltech), Joann Stock (Caltech), Constantine Tsang (SwRI), Thomas Widemann (Obs. Paris), Jennifer Whitten (Tulane), Thomas Widemann (LESIA), Howard Zebker (Stanford)

Basaltic melts are produced when convection adiabatically brings deep and hot mantle to lower pressures. Such primary melts were extracted from the mantle of Mars, crystallized near the surface and...

Introduction: Estimates of the bulk silicate Moon (BSM) composition have been proposed based on a number of different geochemical, petrological and geophysical arguments but have yet to arrive at a general consensus.In order to obtain further constraints on the BSM composition, we investigated the effect of the BSM FeO content on the physical properties of lunar mantle reservoirs and tested the consistency of different lunar interior models with the bulk Moon density and moment of inertia. Methods: To cover all lunar interior models that are consistent with a given BSM composition, we modeled the properties of the chemical reservoirs forming from lunar magma ocean (LMO) solidification, considered the re-distribution of these reservoirs in the lunar mantle by solid state convection, and calculated the bulk Moon density and moment of inertia of the resulting interior models, assuming varying core properties and selenotherms.Lunar Magma Ocean Crystallization:We modeled LMO cumulate mineralogies using a combination [1] of crystallization algorithms from the software packages alphaMELTS [2] and SPICES [3], that has been validated against recent experiments on LMO fractional crystallization [4, 5]. Thereby we assumed pure fractional crystallization of a deep LMO, that extends to the core-mantle boundary so that the LMO comprises the whole BSM. The bulk LMO composition was chosen based on the estimate of [6]. FeO/MgO ratios of the bulk LMO composition were varied (8.0-13 wt% FeO) to investigate the effect of the FeO content on the densities and mineralogies of individual cumulate layers. All crystals forming in the LMO were assumed to sink and equilibrate with the liquid at the bottom of the magma ocean prior to fractionation, except for plagioclase which was assumed to float to the surface to form anorthositic crust. The average lunar crust thickness was assumed to be 40 km in accordance with recent GRAIL data [7]. Any excess plagioclase that formed after that final crust thickness was reached was assumed to remain in the mantle due to imperfect plagioclase floatation.Mantle Mixing and Overturn: As a consequence of the higher compatibility of lighter Mg compared to denser Fe in the LMO cumulate minerals, the density of the cumulate increases with progressing LMO solidification. Since the LMO solidifies from bottom to top, this results in a gravitationally unstable cumulate stratification that facilitates convective overturn, during which dense material sinks towards the core mantle boundary while lighter material migrates toward the surface. The respective changes in pressure and temperature experienced by individual cumulate layers, as well as mixing and chemical equilibration of different layers during overturn, can affect the mineralogy and physical properties of the lunar mantle. To investigate these effects, we calculated equilibrium mineral parageneses of different cumulate layers using Perple_X [8]. For simplicity we considered five homogeneous cumulate reservoirs (olivine-dominated, pyroxene-dominated, IBC, KREEP and crust), whose compositions were derived from the results of the LMO crystallization models by averaging the compositions of adjacent cumulate layers with similar mineralogies.The mineralogies and densities of each reservoir were calculated as a function of depth along different selenotherms (e.g. [9]). To evaluate the effect of mixing and chemical equilibration, we also made the same calculations for different compositional mixtures of the layers.The results of these calculations were used as input in a simple density structure model in order to investigate the effect of mantle overturn on the bulk lunar density and moment of inertia. Lunar core sizes and densities were thereby varied within the range of proposed values (e.g. [10]). Results: Changing the FeO/MgO ratio of the BSM composition leads to an earlier appearance and higher abundance of Fe-rich minerals in the LMO cumulate. This results in an increased thickness of the late formed, dense ilmenite bearing cumulate (IBC) reservoir, that we defined based on its high density compared to underlying cumulate layers. As a consequence, IBC thickness correlates linearly with the assumed LMO FeO content, varying by a factor of about 4 over the assumed range of FeO contents.Due to its high density the radial distribution of IBC material in the lunar interior has a significant effect on the BSM moment of inertia, even though its volume is comparatively small. The effect of the distribution of IBC on the BSM moment of inertia increases systematically with increasing IBC volume, which is in turn linked to the FeO content.Depending on the chosen core models and selenotherms, realistic bulk Moon densities and BSM moments of inertia could be reached assuming FeO contents of 8-13.5 wt%. Discussion: The range of possible FeO contents determined here is valid for a large variation of lunar interior properties and can be narrowed considerably by imposing constraints on the selenotherm, core properties or mantle structure. Seismic and selenodetic data indicate a mantle stratigraphy with a pyroxenitic upper mantle and a dunitic lower mantle [11] and suggest the presence of a dense, partially molten zone at the core mantle boundary [12], that might consist of sunken IBC material. These constraints on the interior structure of the lunar mantle indicate that BSM FeO contents of 9 – 11 wt% are most probable. This estimate could be further limited by tighter constraints on the size and density of the lunar core, e.g. by future seismic investigations. References:[1] Schwinger and Breuer (2018), AGU Fall Meeting, Washington, USA.[2] Smith and Asimow (2005), G³, 6.2.[3] Davenport (2013), Planet. Sci Res. Disc. Report 1, 173.[4] Rapp and Draper (2018), Meteoritics & Planet. Sci. 53.7, 1432-1455.[5] Charlier et al. (2018), Geochim. Cosmochim. Acta, 234, 50–69.[6] O’Neill (1991), Geochim. Cosmochim. Acta, 55 (4), 1135-1157.[7] Wieczorek et al. (2013) Science, 339, 671.[8] Connolly (2005), EPSL, 236 (1-2), 524-541.[9] Laneuville et al. (2013), JGR: Planets, 118 (7), 1435-1452.[10] Weber et al. (2011), science, 331 (6015), 309-312.[11] Gagnepain-Beyneix et al. (2006), Physics of the Earth and Planetary Interiors, 159 (3-4), 140-166.[12] Matsumoto et al. (2015), GRL, 42 (18), 7351-7358.

The overturn of mantle cumulates following the crystallization of the lunar magma ocean -- particularly the sinking of ilmenite-bearing cumulates (IBC) -- provides an explanation for several aspect...

The parameters and initial conditions governing mantle convection in terrestrial planets like Mars are poorly known meaning that one often needs to randomly vary several parameters to test which ones satisfy observational constraints. However, running forward models in 2D or 3D is computationally intensive to the point that it might prohibit a thorough scan of the entire parameter space. We propose using Machine Learning to find a low-dimensional mapping from input parameters to outputs. We use about 10,000 thermal evolution simulations with Mars-like parameters run on a 2D quarter cylindrical grid to train a fully-connected Neural Network (NN). We use the code GAIA (Hüttig et al., 2013) to solve the conservation equations of mantle convection for a fluid with Newtonian rheology and infinite Prandtl number under the Extended Boussinesq Approximation. The viscosity is calculated according to the Arrhenius law of diffusion creep (Hirth & Kohlstedt, 2003). The model also considers the effects of partial melting on the energy balance, including mantle depletion of heat producing-elements (Padovan et., 2017), as well as major phase transitions in the olivine system. To generate the dataset, we randomly vary 5 different parameters with respect to each other: thermal Rayleigh number, internal heating Rayleigh number, activation energy, activation volume and a depletion factor for heat-producing elements in the mantle. In order to train in time, we take the simplest possible approach, i.e., we treat time as another variable in our input vector. 80% of the dataset is used to train our NN, 10% is used to test different architectures and to avoid over-fitting, and the remaining 10% is used as test set to evaluate the error of the predictions. For given values of the five parameters, our NN can predict the resulting horizontally-averaged temperature profile at any time in the evolution, spanning 4.5 Ga with an average error under 0.3% on the test set. Tests indicate that with as few as 5% of the training samples (= simulations x time steps), one can achieve a test-error below 0.5%, suggesting that for this setup, one can potentially learn the mapping from fewer simulations. Finally, we ran a fourth batch of GAIA simulations and compared them to the output of our NN. In almost all cases, the instantaneous predictions of the 1D temperature profiles from the NN match those of the computationally expensive simulations extremely well, with an error below 0.5%.

SUMMARY Heat transfer in one-plate planets is governed by mantle convection beneath the stagnant lid. Newtonian diffusion creep and non-Newtonian dislocation creep are the main mechanisms controlling large-scale mantle deformation. Diffusion creep strongly depends on the grain size (d), which in turn controls the relative importance of the two mechanisms. However, dislocation creep is usually neglected in numerical models of convection in planetary mantles. These mostly assume linear diffusion creep rheologies, often based on reduced activation parameters (compared to experimental values) that are thought to mimic the effects of dislocation creep and, as a side benefit, also ease the convergence of linear solvers. Assuming Mars-like parameters, we investigated the influence of a non-evolving grain size on Rayleigh–Bénard convection in the stagnant lid regime. In contrast to previous studies based on the Frank–Kamentskii approximation, we used Arrhenius laws for diffusion and dislocation creep—including temperature as well as pressure dependence—based on experimental measurements of olivine deformation. For d ≲ 2.5 mm, convection is dominated by diffusion creep. We observed an approximately equal partitioning between the two mechanisms for d ≈ 5 mm, while dislocation creep dominates for d ≳ 8 mm. Independent estimates of an average grain size of few mm up to 1 cm or more for present-day Mars suggest thus that dislocation creep plays an important role and possibly dominates the deformation. Mimicking dislocation creep convection using an effective linear rheology with reduced activation parameters, as often done in simulations of convection and thermal evolution of Mars, has significant limitations. Although it is possible to mimic mean temperature, mean lid thickness and Nusselt number, there are important differences in the flow pattern, root mean square velocity, and lid shape. The latter in particular affects the amount and distribution of partial melt, suggesting that care should be taken upon predicting the evolution of crust production when using simplified rheologies. The heat transport efficiency expressed in terms of the Nusselt number as a function of the Rayleigh number is thought to depend on the deformation mechanisms at play. We show that the relative volume in which dislocation creep dominates has nearly no influence on the Nusselt–Rayleigh scaling relation when a mixed rheology is used. In contrast, the flow pattern influences the Nusselt number more strongly. We derived a scaling law for the Nusselt number based on the mean lid thickness (〈L〉) and on the effective Rayleigh number (Raeff) obtained by suitably averaging the viscosity beneath the stagnant lid. We found that the Nusselt number follows the scaling $\mathrm{Nu} = 0.37 \langle L \rangle ^{-0.666} \mathrm{Ra}_{\mathrm{eff}}^{0.071}$ regardless of the deformation mechanism.

The InSight mission [1] landed in November 2018 in the Elysium Planitia region [2] bringing the first geophysical observatory to Mars. Since February 2019 the seismometer SEIS [3] has continuously ...

While liquid water is not thermodynamically stable at the surface due to the low temperature and pressure conditions, liquid groundwater may still exist in the Martian subsurface [1, 2]. In this study, we use fully dynamical 3D thermal evolution models [3] and 3D parametrized models [4] to calculate the depth at which favorable conditions for liquid water are present, assuming that a global subsurface cryosphere exists on Mars today. While fully dynamical 3D models take into account the effect of mantle plumes self-consistently, they are computationally expensive compared to 3D parametrized models that can cover a large range of mantle conditions, although requiring additional parametrizations for thermal anomalies in the interior. In all calculations, we use a 3D crustal model that is compatible with today’s gravity and topography data [5, 6]. Some of the most important parameters that affect the depth of liquid water are the spatial variations of crustal thickness and crustal thermal conductivity, since the crust has a lower thermal conductivity compared to that of the mantle and thickness variations can shift the groundwater table locally closer to the surface (Fig. 1). The amount and distribution of heat sources, and the presence of mantle plumes, can introduce additional perturbations to the depth of groundwater. The surface temperature distribution and the presence of salts and clathrate hydrates considerably affect the depth and locations where subsurface liquid water may be stable. Hydrated magnesium (Mg) and calcium (Ca) perchlorate salts, whose presence has been suggested at various locations on Mars [7], may significantly reduce the melting point of water ice. In addition to thick regolith layers, clathrate hydrates, if present in the subsurface, would provide an insulating effect reducing the crustal thermal conductivity at least locally [e.g., 8]. The effects of the crustal thermal conductivity and salt abundance on the depth of subsurface liquid water are shown in Fig. 1, where we use the same crustal thickness variations and crustal enrichment in radioactive heat sources in all simulations. The model in Fig. 1a assumes an average crustal conductivity of 3 W/mK, while the model in Fig. 1b has a lower conductivity of only 2 W/mK (see panel 1e for the spatially averaged conductivity profiles that, due to crustal thickness variations, show average values between mantle and crust in the topmost 110 km). Fig. 1d shows the effect of the crustal thermal conductivity on the subsurface temperature profile. For the lower conductivity case the subsurface temperature is warmer, and the groundwater table shifts, on average, 2.5 km closer to the surface. The model shown in Fig. 1c is similar to the one in Fig. 1a but assumes the presence of salts. Instead of using the melting temperature of pure water ice, as was done for the models in Fig. 1a and b, we lower the melting temperature to 199 K [9] over the entire depth, by assuming that Ca(ClO4)2 is present in eutectic concentration (Fig. 1f). This extreme, and unrealistic, assumption places constraints on the minimum depth at which liquid water may be present in the Martian subsurface today, since kinetic factors such as the flow of groundwater due to gravity may increase the depth of the water table, depending on the total amount of liquid water, porosity and permeability. In Fig. 1a and b, the depth of the groundwater shows the combined effect of crustal thickness distribution and surface temperature variations. Mantle plumes have only a small effect and may introduce perturbations only if the groundwater is located, on average, at about 5 km depth or deeper. The effect of the crustal thickness is evident in basins, along the dichotomy, and in volcanic provinces, whereas surface temperatures give general water table depth trends with latitude. In Fig. 1c, the depth variations of the groundwater table are mainly caused by the surface temperature distribution, as the groundwater table is located very close to the surface (between 0 – 1 km for latitudes between -57° and 57°). Nevertheless, in all cases (Fig. 1a – c), the water table is significantly shallower in equatorial regions compared to polar regions, mainly governed by lower surface temperatures at the poles. Our results suggest that the Martian subsurface has had, and still has, the potential to enable deep environments with stable liquid groundwater. Combined with the analysis of geomorphological features at the Martian surface that testify the involvement of water/ice activity and maps of subsurface water ice [10], such models could provide valuable estimates of the depth of liquid groundwater on past and present-day Mars providing key knowledge on the planet dynamics, evolution and astrobiological potential. The technology to probe the Martian subsurface at depths of many kilometers is maturing [2]: TH2OR (Transmissive H2O Reconnaissance), a low-mass and average low-power transient electromagnetic sounder capable of detecting the presence of liquid water to depths of many kilometers is currently being developed at JPL [11]. Moreover, mission concepts such as VALKYRIE (Volatiles And Life: KeY Reconnaissance & In-situ Exploration) [12], which would add to the liquid water sounder a drill capable of accessing depths of 10s-100s of meters or more and employ a (bio)geochemical analysis package on the surface, would provide the measurements necessary to characterize the modern-day subsurface habitability of Mars. References: [1] Clifford et al., 2010, JGR, 115(E7); [2] Stamenković V. et al., 2019, Nat. Astron., 3(2); [3] Plesa A.-C. et al., 2018, GRL, 45(22); [4] Breuer D. & Spohn T., 2006, PSS, 54(2); [5] Plesa A.-C. et al., 2016, JGR, 121(12); [6] Wieczorek M. & Zuber M., 2004, JGR, 109(E8); [7] Leshin L. et al., 2013, Science, 341; [8] Kargel J. et al. 2007, Geology, 35(11); [9] Marion G. et al., 2010, Icarus, 207(2); [10] Piqueux S. et al., 2019, GRL, 46.; [11] Burgin M. et al., 2019, AGU Fall Meeting, P44B-02; [12] Mischna M. et al., 2019, AGU Fall Meeting, P41C-3466. Acknowledgments: This work was performed in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. © 2020, California Institute of Technology.

Understanding the processes that led Venus to its current state and will drive its future evolution is a major objective of the next generation of orbiters. In this work we analyze the retrieval of the spin vector, the tidal response, and the moment of inertia of Venus with VERITAS, a NASA Discovery-class mission. By simulating a systematic joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar, we show that VERITAS will provide accuracies (3σ) in the estimates of the tidal Love number k2 to 4.6 × 10−4, its tidal phase lag to 0°.05, and the moment of inertia factor to 9.8 × 10−4 (0.3% of the expected value). Applying these results to recent models of the Venus interior, we show that VERITAS will provide much-improved constraints on the interior structure of the planet.

We ran several series of two-dimensional numerical mantle convection simulations representing in idealized form the thermochemical evolution of a Mars-like planet. In order to study the importance of compositional buoyancy of melting mantle, the models were set up in pairs of one including all thermal and compositional contributions to buoyancy and one accounting only for the thermal contributions. In several of the model pairs, single large impacts were introduced as causes of additional strong local anomalies, and their evolution in the framework of the convecting mantle was tracked. The models confirm that the additional buoyancy provided by the depletion of the mantle by regular melting can establish a global stable stratification of the convecting mantle and throttle crust production. Furthermore, the compositional buoyancy is essential in the stabilization and preservation of local compositional anomalies directly beneath the lithosphere and offers a possible explanation for the existence of distinct, long-lived reservoirs in the martian mantle. The detection of such anomalies by geophysical means is probably difficult, however; they are expected to be detected by gravimetry rather than by seismic or heat flow measurements. The results further suggest that the crustal thickness can be locally overestimated by up to ∼20 km if impact-induced density anomalies in the mantle are neglected.

Energy sources involved in the early stages of planetary formation can cause partial or even complete melting of the mantle of terrestrial bodies leading to the formation of magma oceans. Upon planetary cooling, solidification is expected to take place from the bottom upwards because of the steeper slope of the liquid adiabat with respect to the liquidus (Elkins-Tanton, 2012; Solomatov, 2015). Fractional solidification, in particular, can lead to the formation of a compositional layering that can play a fundamental role for the subsequent long-term dynamics and evolution of the interior (Tosi et al., 2013; Plesa et al., 2014). In order to assess to what extent primordial compositional heterogeneities generated upon magma ocean solidification can be preserved, we investigate the cooling and solidification of a whole-mantle magma ocean along with the conditions that allow solid-state convection to start mixing the mantle before solidification has completed. To this end, we run 2-D numerical simulations in cylindrical geometry using the finite-volume code GAIA (Huttig et al., 2013). We treat the liquid magma ocean in a parametrized fashion while we self-consistently solve the conservation equations of thermochemical convection in the growing solid mantle accounting for pressure-, temperature- and melt-dependent rheology. We consider two end-member cases: fractional crystallization, where melt is instantaneously extracted into the overlying liquid leaving beneath a differentiated mantle, and batch crystallization where melt remains in contact with the silicate matrix throughout solidification causing no differentiation. By testing the effects of different cooling rates and Rayleigh numbers, we show that for a lifetime of the liquid magma ocean between 1 and 10 Myr (Lebrun et al., 2013), the onset of solid state convection prior to complete mantle crystallization is possible and that part or even all of the compositional heterogeneities generated upon fractionation can be erased by efficient mantle stirring (Figure 1). We discuss the consequences of our findings in relation to the early and long-term evolution of compositional heterogeneities generated via fractional crystallization of magma oceans in terrestrial bodies with emphasis on Mars' thermochemical history.

The first in situ Martian heat flux measurement to be carried out by the InSight Discovery-class mission will provide an important baseline to constrain the present-day heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3-D spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the present-day surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peak-to peak variations lie between 17.2 and 49.9 mW m−2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW m−2, while at the InSight location it lies between 18.8 and 24.2 mW m−2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km.

International audience; Abstract The Interior exploration using Seismic Investigations, Geodesy, and Heat Trans-port (InSight) Mission will focus on Mars’ interior structure and evolution. The basic structure of crust, mantle, and core form soon after accretion. Understanding the early differentiation process on Mars and how it relates to bulk composition is key to improving our understanding of this process on rocky bodies in our solar system, as well as in other solar systems. Current knowledge of differentiation derives largely from the layers observed via seismology on the Moon. However, the Moon’s much smaller diameter make it a poor analog with respect to interior pressure and phase changes. In this paper we review the current knowledge of the thickness of the crust, the diameter and state of the core, seismic attenuation, heat flow, and interior composition. InSight will conduct the first seismic and heat flow measurements of Mars, as well as more precise geodesy. These data reduce uncertainty in crustal thickness, core size and state, heat flow, seismic activity and meteorite impact rates by a factor of 3–10× relative to previous estimates. Based on modeling of seismic wave propagation, we can further constrain interior temperature, composition, and the location of phase changes. By combining heat flow and a well constrained value of crustal thickness, we can estimate the distribution of heat producing elements between the crust and mantle. All of these quantities are key inputs to models of interior convection and thermal evolution that predict the processes that control subsurface temperature, rates of volcanism, plume distribution and stability, and convective state. Collectively these factors offer strong controls on the overall evolution of the geology and habitability of Mars.

The earliest stage of the evolution of a fully assembled planet is profoundly affected by a number of basin-forming impacts large enough to change the dynamics of its deeper interior. These impacts are in some cases quite closely spaced and follow one another in short time intervals, so that their effects interact and result in behavior that may differ from a simple sum of the effects of two individual and isolated impacts. We use two-dimensional models of mantle convection in a Mars-like planet and a simple parameterized representation of the principal effects of impacts to study some of the dynamical effects and interactions of multiple large impacts. In models of only two impacts, we confirm that the dynamical effects of the impacts reinforce each other the closer they are in space and time but that the effects do not always correspond to straightforward superpositions of those of single, isolated impacts. In models with multiple (4-8) impacts with variable sizes, distances, and frequencies, the global response of the mantle is as variable as the impact sequences in the short term, but in the long term the different evolutionary paths converge for several indicator variables such as the mean flow velocity, temperature, or heat flow. Nonetheless, beyond a certain impact frequency and energy, lithospheric instabilities triggered by large impacts occur on a global scale, reinvigorate mantle dynamics for long time spans, and entail a late stage of melt production in addition to the initial melting stage that is not observed in one- or two-impact models. After one or several very large impacts, some lithospheric material may founder and sink to the core-mantle boundary, and if enough of it accumulates there, it enhances the heat flux out of the core for several hundred millions of years, with possible effects on dynamo activity., Comment: 24 pages, 10 figures

Impactors of different types and sizes can produce a final crater of the same diameter on a planet under certain conditions. We derive the condition for such "isocrater impacts" from scaling laws, as well as relations that describe how the different impactors affect the interior of the target planet; these relations are also valid for impacts that are too small to affect the mantle. The analysis reveals that in a given isocrater impact, asteroidal impactors produce anomalies in the interior of smaller spatial extent than cometary or similar impactors. The differences in the interior could be useful for characterizing the projectile that formed a given crater on the basis of geophysical observations and potentially offer a possibility to help constrain the demographics of the ancient impactor population. A series of numerical models of basin-forming impacts on Mercury, Venus, the Moon, and Mars illustrates the dynamical effects of the different impactor types on different planets. It shows that the signature of large impacts may be preserved to the present in Mars, the Moon, and Mercury, where convection is less vigorous and much of the anomaly merges with the growing lid. On the other hand, their signature will long have been destroyed in Venus, whose vigorous convection and recurring lithospheric instabilities obliterate larger coherent anomalies., Comment: 32 pages, 12 figures

©2018. American Geophysical Union, 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.

Context. The mass and radius of a planet directly provide its bulk density, which can be interpreted in terms of its overall composition. Any measure of the radial mass distribution provides a first step in constraining the interior structure. The fluid Love number $k_2$ provides such a measure, and estimates of $k_2$ for extrasolar planets are expected to be available in the coming years thanks to improved observational facilities and the ever-extending temporal baseline of extrasolar planet observations. Aims. We derive a method for calculating the Love numbers $k_n$ of any object given its density profile, which is routinely calculated from interior structure codes. Methods. We used the matrix-propagator technique, a method frequently used in the geophysical community. Results. We detail the calculation and apply it to the case of GJ 436b, a classical example of the degeneracy of mass-radius relationships, to illustrate how measurements of $k_2$ can improve our understanding of the interior structure of extrasolar planets. We implemented the method in a code that is fast, freely available, and easy to combine with preexisting interior structure codes. While the linear approach presented here for the calculation of the Love numbers cannot treat the presence of nonlinear effects that may arise under certain dynamical conditions, it is applicable to close-in gaseous extrasolar planets like hot Jupiters, likely the first targets for which $k_2$ will be measured., Comment: 10 pages, 9 figures

Ganymede shows signs of a present-day magnetic field, whose origin is thought to be in its core. The Fe snow regime has been suggested to be vital in Ganymede's history. In this regime, Fe crystals first form at the core-mantle boundary and later settle to the deeper core due to their higher density (Fe snow). A stable chemical gradient arises within the liquid of the snow zone. Below the snow zone the Fe particles remelt. We propose that the remelting of Fe in the deeper, entirely liquid core initiates compositional convection, which could be the origin of the dynamo. Such a dynamo is restricted by the period of time the snow zone needs to grow across the core. We investigate this time period with a 1-D core evolution model by varying the initial sulfur concentration, the core heat flux, and the thermal conductivity of the core. For the proposed dynamo in the deeper liquid core, we obtain necessary time periods of between 320 and 800 Myr and magnetic field strengths at the surface that match the observed value of 719 nT. To explain the present magnetic field, we favor cores with high sulfur concentrations because those lead to a late start and a long duration of the dynamo. Furthermore, a present dynamo below the snow zone suggests the absence of an inner core.

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 planet's 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.

We compare estimates of atmospheric precipitation during the Martian Noachian-Hesperian boundary 3.8 Gyr ago as calculated in a radiative-convective column model of the atmosphere with runoff values estimated from a geomorphological analysis of dendritic valley network discharge rates. In the atmospheric model, we assume CO2-H2O-N2 atmospheres with surface pressures varying from 20 mb to 3 bar with input solar luminosity reduced to 75% the modern value. Results from the valley network analysis are of the order of a few mm d-1 liquid water precipitation (1.5-10.6 mm d-1, with a median of 3.1 mm d-1). Atmospheric model results are much lower, from about 0.001-1 mm d-1 of snowfall (depending on CO2 partial pressure). Hence, the atmospheric model predicts a significantly lower amount of precipitated water than estimated from the geomorphological analysis. Furthermore, global mean surface temperatures are below freezing, i.e. runoff is most likely not directly linked to precipitation. Therefore, our results strongly favor a cold early Mars with episodic snowmelt as a source for runoff. Our approach is challenged by mostly unconstrained parameters, e.g. greenhouse gas abundance, global meteorology (for example, clouds) and planetary parameters such as obliquity- which affect the atmospheric result - as as well as by inherent problems in estimating discharge and runoff on ancient Mars, such as a lack of knowledge on infiltration and evaporation rates and on flooding timescales, which affect the geomorphological data. Nevertheless, our work represents a first step in combining and interpreting quantitative tools applied in early Mars atmospheric and geomorphological studies., Comment: accepted in Planetary and Space Science, 37 pages, 14 figures, 2 tables

Plate tectonics is 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. 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. 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). 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$_2$. 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. 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.

International audience; The present-day thermal state, interior structure, composition, and rheology of Mars can be constrained by comparing the results of thermal history calculations with geophysical, petrological, and geological observations. Using the largest-to-date set of 3-D thermal evolution models, we find that a limited set of models can satisfy all available constraints simultaneously. These models require a core radius strictly larger than 1,800 km, a crust with an average thickness between 48.8 and 87.1 km containing more than half of the planet's bulk abundance of heat producing elements, and a dry mantle rheology. A strong pressure dependence of the viscosity leads to the formation of prominent mantle plumes producing melt underneath Tharsis up to the present time. Heat flow and core size estimates derived from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will increase the set of constraining data and help to confine the range of admissible models. Plain Language Summary We constrain the thermal state and interior structure of Mars by combining a large number of observations with thermal evolution models. Models that match the available observations require a core radius larger that half the planetary radius and a crust thicker than 48.8 km but thinner than 87.1 km on average. All best-fit models suggest that more than half of the planet's bulk abundance of heat producing elements is located in the crust. Mantle plumes may still be active today in the interior of Mars and produce partial melt underneath the Tharsis volcanic province. Our results have important implications for the thermal evolution of Mars. Future data from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission can be used to validate our models and further improve our understanding of the thermal evolution of Mars.

We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to $k_2$ using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius, that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured $k_2$ to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision $\leq$ 65 ppm/$\sqrt{2\,min}$ is required to reliably retrieve $k_2$ with present understanding of stellar limb darkening, therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar limb darkening would increase such performance., Comment: Accepted for publication in The Astrophysical Journal

Journal of Fluid Mechanics, 735, ISSN:0022-1120, ISSN:1469-7645

[1] The Moon possesses a clear dichotomy in geological processes between the nearside and farside hemispheres. The most pronounced expressions of this dichotomy are the strong concentration of radioactive heat sources on the nearside in a region known as the Procellarum KREEP Terrane (PKT) and the mare basaltic lava flows that erupted in or adjacent to this terrane. We model the thermochemical evolution of the Moon using a 3-D spherical thermochemical convection code in order to assess the consequences of a layer enriched in heat sources below the PKT on the Moon's global evolution. We find that in addition to localizing most of the melt production on the nearside, such an enriched concentration of heat sources in the PKT crust has an influence down to the core-mantle boundary and leaves a present-day temperature anomaly within the nearside mantle. Moderate gravitational and topographic anomalies that are predicted in the PKT, but not observed, may be masked either by crustal thinning or gravitational anomalies from dense material in the underlying mantle. Our models also predict crystallization of an inner core for sulfur concentrations less than 6 wt %.

[1] Early in the history of terrestrial planets, the fractional crystallization of a magma ocean can lead to a mantle stratification characterized by a progressive enrichment in heavy elements from the core-mantle boundary to the surface. Such configuration is gravitationally unstable; it causes mantle overturn and the formation of a stable chemical layering. Using simulations of thermo-chemical convection, we analyzed the consequences of overturn and subsequent layering on mantle dynamics assuming Mars' scaling parameters. We found that the time needed to achieve chemical homogenization via convective mixing scales exponentially with the buoyancy-ratio inline image, which measures the relative importance of chemical to thermal buoyancy. In addition, when using a strongly temperature-dependent viscosity, the formation of a stagnant-lid prevents the uppermost crystallized layers from sinking into the mantle. In order to obtain their subduction an yielding mechanism must be invoked. [2] In the context of Mars' evolution, our results suggest that complete chemical mixing is unlikely to take place within time-scales comparable with the planet's age. Magma ocean freezing could be thus responsible for the long-term preservation of compositional heterogeneities as required by meteoritic evidence. The lack of a surface highly enriched in incompatible elements and of a high-density lid is difficult to reconcile with a stagnant-lid regime operating throughout Mars' history. An episode of surface mobilization induced by compositional overturn can resolve this difficulty provided that inline image is large enough. Too large buoyancy ratios, however, tend to suppress convective heat transport, rendering it problematic to explain the late volcanic history of Mars.