ExoMDN: Rapid characterization of exoplanet interior structures with Mixture Density Networks

Characterizing the interior structure of exoplanets is essential for understanding their diversity, formation, and evolution. As the interior of exoplanets is inaccessible to observations, an inverse problem must be solved, where numerical structure models need to conform to observable parameters such as mass and radius. This is a highly degenerate problem whose solution often relies on computationally-expensive and time-consuming inference methods such as Markov Chain Monte Carlo. We present ExoMDN, a machine-learning model for the interior characterization of exoplanets based on Mixture Density Networks (MDN). The model is trained on a large dataset of more than 5.6 million synthetic planets below 25 Earth masses consisting of an iron core, a silicate mantle, a water and high-pressure ice layer, and a H/He atmosphere. We employ log-ratio transformations to convert the interior structure data into a form that the MDN can easily handle. Given mass, radius, and equilibrium temperature, we show that ExoMDN can deliver a full posterior distribution of mass fractions and thicknesses of each planetary layer in under a second on a standard Intel i5 CPU. Observational uncertainties can be easily accounted for through repeated predictions from within the uncertainties. We use ExoMDN to characterize the interior of 22 confirmed exoplanets with mass and radius uncertainties below 10% and 5% respectively, including the well studied GJ 1214 b, GJ 486 b, and the TRAPPIST-1 planets. We discuss the inclusion of the fluid Love number $k_2$ as an additional (potential) observable, showing how it can significantly reduce the degeneracy of interior structures. Utilizing the fast predictions of ExoMDN, we show that measuring $k_2$ with an accuracy of 10% can constrain the thickness of core and mantle of an Earth analog to $\approx13\%$ of the true values.Comment: 15 pages, 15 figures, accepted for publication in Astronomy & Astrophysics. The ExoMDN model is freely accessible at https://github.com/philippbaumeister/ExoMD

Overturn of ilmenite‐bearing cumulates in a rheologically weak lunar mantle

©2019. American Geophysical UnionThe crystallization of the lunar magma ocean (LMO) determines the initial structure of the solid Moon. Near the end of the LMO crystallization, ilmenite‐bearing cumulates (IBC) form beneath the plagioclase crust. Being denser than the underlying mantle, IBC are prone to overturn, a hypothesis that explains several aspects of the Moon's evolution. Yet the formation of stagnant lid due to the temperature dependence of viscosity can easily prevent IBC from sinking. To infer the rheological conditions allowing IBC to sink, we calculated the LMO crystallization sequence and performed high‐resolution numerical simulations of the overturn dynamics. We assumed a diffusion creep rheology and tested the effects of reference viscosity, activation energy, and compositional viscosity contrast between IBC and mantle. The overturn strongly depends on reference viscosity and activation energy and is facilitated by a low IBC viscosity. For a reference viscosity of 1021 Pa s, characteristic of a dry rheology, IBC overturn cannot take place. For a reference viscosity of 1020 Pa s, the overturn is possible if the activation energy is a factor of 2–3 lower than the values typically assumed for dry olivine. These low activation energies suggest a role for dislocation creep. For lower‐reference viscosities associated with the presence of water or trapped melt, more than 95% IBC can sink regardless of the activation energy. Scaling laws for Rayleigh‐Taylor instability confirmed these results but also showed the need of numerical simulations to accurately quantify the overturn dynamics. Whenever IBC sink, the overturn occurs via small‐scale diapirs

Onset of solid-state mantle convection and mixing during magma ocean solidification

©2017. American Geophysical UnionThe energy sources involved in the early stages of the formation of terrestrial bodies can induce partial or even complete melting of the mantle, leading to the emergence of magma oceans. The fractional crystallization of a magma ocean can cause the formation of a compositional layering that can play a fundamental role for the subsequent long‐term dynamics of the interior and for the evolution of geochemical reservoirs. In order to assess to what extent primordial compositional heterogeneities generated by magma ocean solidification can be preserved, we investigate the solidification of a whole‐mantle Martian magma ocean, and in particular the conditions that allow solid‐state convection to start mixing the mantle before solidification is completed. To this end, we performed 2‐D numerical simulations in a cylindrical geometry. We treat the liquid magma ocean in a parameterized way while we self‐consistently solve the conservation equations of thermochemical convection in the growing solid cumulates accounting for pressure‐, temperature‐, and, where it applies, melt‐dependent viscosity. By testing the effects of different cooling rates and convective vigor, we show that for a lifetime of the liquid magma ocean of 1 Myr or longer, the onset of solid‐state convection prior to complete mantle crystallization is likely and that a significant part of the compositional heterogeneities generated by fractionation can be erased by efficient mantle mixing. We discuss the consequences of our findings in relation to the formation and evolution of compositional reservoirs on Mars and on the other terrestrial bodies of the solar system.DFG, 276817549, Kristallisation des irdischen Magmaozeans: Thermo- und Geodynami

Biology and Treatment of Multiple Myeloma

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Settling of inertial particles in turbulent Rayleigh-Benard convection

The settling behaviour of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary-scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Benard system with Rayleigh number up to 10^12 and Prandtl number from 10 to 50. Under the idealized condition of spherically-shaped particles with small Reynolds number, two limiting behaviours exist for the settling velocity. On the one hand, Stokes' law applies to particles with small but finite response time, leading to a constant settling rate. On the other hand, particles with a vanishing response time are expected to settle at an exponential rate. Based on our simulations, we present a new physical model that bridges the gap between the above limiting behaviours by describing the sedimentation of inertial particles as a random process with two key components: i) the transport of particles from vigorously convecting regions into sluggish, low-velocity "piles" that naturally develop at the horizontal boundaries of the system, and ii) the probability that particles escape such low-velocity regions without settling at their base. In addition, we identify four distinct settling regimes and analyze the horizontal distribution of sedimented particles. For two of these regimes settling is particularly slow and the distribution is strongly non-uniform, with dense particles being deposited preferentially below major clusters of upwellings.Comment: 30 pages, 18 figures, submitted to Phys. Rev. Fluid

How large are present-day heat flux variations across the surface of Mars?

©2016. American Geophysical UnionThe 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

The habitability of stagnant-lid Earths around dwarf stars

The habitability of a planet depends on various factors, such as delivery of water during the formation, the co-evolution of the interior and the atmosphere, as well as the stellar irradiation which changes in time. Since an unknown number of rocky exoplanets may operate in a one-plate convective regime, i.e., without plate tectonics, we aim at understanding under which conditions planets in such a stagnant-lid regime may support habitable surface conditions. Understanding the interaction of the planetary interior and outgassing of volatiles with the atmosphere in combination with the evolution of the host star is crucial to determine the potential habitability. M-dwarf stars in particular possess a high-luminosity pre-main sequence phase which endangers the habitability of planets around them via water loss. We therefore explore the potential of secondary outgassing from the planetary interior to rebuild a water reservoir allowing for habitability at a later stage. We compute the boundaries of the habitable zone around M, K, G, and F-dwarf stars using a 1D cloud-free radiative-convective climate model accounting for the outgassing history of CO2 and H2O from an interior evolution and outgassing model for different interior compositions and stellar luminosity evolutions. The outer edge of the habitable zone strongly depends on the amount of CO2 outgassed from the interior, while the inner edge is mainly determined via the stellar irradiation, as soon as a sufficiently large water reservoir has been outgassed. A build-up of a secondary water reservoir for planets around M-dwarf stars is possible even after severe water loss during the high luminosity pre-main sequence phase as long as some water has been retained within the mantle. Earth-like stagnant-lid planets allow for habitable surface conditions within a continuous habitable zone that is dependent on interior composition.Comment: 15 pages, accepted by A&A, abstract shortene

Evolution and Spectral Response of a Steam Atmosphere for Early Earth with a coupled climate-interior model

The evolution of Earth's early atmosphere and the emergence of habitable conditions on our planet are intricately coupled with the development and duration of the magma ocean phase during the early Hadean period (4 to 4.5 Ga). In this paper, we deal with the evolution of the steam atmosphere during the magma ocean period. We obtain the outgoing longwave radiation using a line-by-line radiative transfer code GARLIC. Our study suggests that an atmosphere consisting of pure H$_{2}$O, built as a result of outgassing extends the magma ocean lifetime to several million years. The thermal emission as a function of solidification timescale of magma ocean is shown. We study the effect of thermal dissociation of H$_{2}$O at higher temperatures by applying atmospheric chemical equilibrium which results in the formation of H$_{2}$ and O$_{2}$ during the early phase of the magma ocean. A 1-6\% reduction in the OLR is seen. We also obtain the effective height of the atmosphere by calculating the transmission spectra for the whole duration of the magma ocean. An atmosphere of depth ~100 km is seen for pure water atmospheres. The effect of thermal dissociation on the effective height of the atmosphere is also shown. Due to the difference in the absorption behavior at different altitudes, the spectral features of H$_{2}$ and O$_{2}$ are seen at different altitudes of the atmosphere. Therefore, these species along with H$_{2}$O have a significant contribution to the transmission spectra and could be useful for placing observational constraints upon magma ocean exoplanets.Comment: 22 pages, 17 Figures, accepted for publication in ApJ on March

Array Antenna Power Pattern Analysis Through Quantum Computing

A method for the analysis of the power pattern of phased array antennas (PAs) based on the quantum Fourier transform (QFT) is proposed. The computation of the power pattern given the set of complex excitations of the PA elements is addressed within the quantum computing (QC) framework by means of a customized procedure that exploits the quantum mechanics principles and theory. A representative set of numerical results, yielded with a quantum computer emulator, is reported and discussed to assess the reliability of the proposed method by pointing out its features in comparison with the classical approach based on the discrete Fourier transform (DFT), as well.Comment: 35 pages, 12 figure

Bifurcation in the growth of continental crust

Is the present-day water-land ratio a necessary outcome of the evolution of plate tectonic planets with a similar age, volume, mass, and total water inventory as the Earth? This would be the case - largely independent of initial conditions - if Earth's present-day continental volume were at a stable unique equilibrium with strong self-regulating mechanisms of continental growth steering the evolution to this state. In this paper, we question this conjecture. Instead we suggest that positive feedbacks in the plate tectonics model of continental production and erosion may dominate and show that such a model can explain the history of continental growth. We investigate the main mechanisms that contribute to the growth of the volume of the continental crust. In particular, we analyze the effect of the oceanic plate speed, depending on the area and thickness of thermally insulating continents, on production and erosion mechanisms. Effects that cause larger continental production rates for larger values of continental volume are positive feedbacks. In contrast, negative feedbacks act to stabilize the continental volume. They are provided by the increase of the rate of surface erosion, subduction erosion, and crustal delamination with the continental volume. We systematically analyze the strengths of positive and negative feedback contributions to the growth of the continental crust. Although the strengths of some feedbacks depend on poorly known parameters, we conclude that a net predominance of positive feedbacks is plausible. We explore the effect of the combined feedback strength on the feasibility of modeling the observed small positive net continental growth rate over the past 2-3 billion years