Electromagnetic induction heating as a driver of volcanic activity on massive rocky planets

Aims. We investigate possible driving mechanisms of volcanic activity on rocky super-Earths with masses exceeding 3-4 Mearth. Due to high gravity and pressures in the mantles of these planets, melting in deep mantle layers can be suppressed, even if the energy releae due to tidal heating and radioactive decay is substantial. Here we investigate whether a newly identified heating mechanism, namely induction heating by the star's magnetic field, can drive volcanic activity on these planets due to its unique heating pattern in the very upper part of the mantle. In this region the pressure is not yet high enough to preclude the melt formation. Methods. Using the super-Earth HD 3167b as an example, we calculate induction heating in the planet's interiors assuming an electrical conductivity profile typical of a hot rocky planet and a moderate stellar magnetic field typical of an old inactive star. Then we use a mantle convection code (CHIC) to simulate the evolution of volcanic outgassing with time. Results. We show that although in most cases volcanic outgassing on HD 3167b is not very significant in the absence of induction heating, including this heating mechanism changes the picture and leads to a substantial increase in the outgassing from the planet's mantle. This result shows that induction heating combined with a high surface temperature is capable of driving volcanism on massive super-Earths, which has important observational implications.Comment: Five pages, three figures, accepted for publication in A&A letter

Exoplanet interiors and habitability

More than 1000 exoplanets with a radius smaller than twice that of the Earth are currently known, mainly thanks to space missions dedicated to the search of exoplanets. Mass and radius estimates, which are only available for a fraction (∼ 10%) of the exoplanets, provide an indication of the bulk composition and interior structure and show that the diversity in exoplanets is far greater than in the Solar System. Geophysical studies of the interior of exoplanets are key to understanding their formation and evolution, and are also crucial for assessing their potential habitability since interior processes play an essential role in creating and maintaining conditions for water to exist at the surface or in subsurface layers. For lack of detailed observations, investigations of the interior of exoplanets are guided by the more refined knowledge already acquired about the Solar System planets and moons, and are heavily based on theoretical modelling and on studies of the behaviour of materials under the high pressure and temperature conditions in planets. Here we review the physical principles and methods used in modelling the interior and evolution of exoplanets with a rock or water/ice surface layer and identify possible habitats in or on exoplanets

Intrusive Magmatism Strongly Contributed to the Volatile Release Into the Atmosphere of Early Earth

Magmatic volatile release was crucial for the build-up and composition of the early atmosphere and thus for the origin and evolution of life. Even though the rate of intrusive to extrusive magma production on Earth is high, intrusive volatile release is commonly neglected in studies modeling the composition of the early atmosphere. This can mainly be attributed to the solubility of volatiles like H2O and CO2. The solubility is increasing with depth and thus is thought to prevent the release of these volatiles. However, due to the accumulation of H2O and CO2 within the melt during fractional crystallization, the solubility can be exceeded even at greater depths. In our study, we developed a novel numeric model to quantify the amount of H2O and CO2 that can be released from an intrusive system if we consider the process of fractional crystallization. Additionally, we take the possibility of melt ascent and the formation of hydrous minerals into account. According to our simulations, the release of H2O and CO2 from an intrusive magma body is possible within the whole lithosphere. However, the release strongly depends on the initial volatile budget, the formation of hydrous phases, the depth of the intrusion and the buoyancy of the melt. Considering all these factors, our study suggests that about 0%–85% H2O and 100% CO2 can be released from mafic intrusions. This renders the incorporation of the intrusive volatile release mandatory in order to determine the volatile fluxes and the composition of early Earth's atmosphere

Operator-Splitting Methods Respecting Eigenvalue Problems for Nonlinear Equations and Applications for Burgers Equations

In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator-splitting methods by providing improved results and convergence rates. We apply our results to deposition processes

Iterative operator-splitting methods for nonlinear differential equations and applications of deposition processes

In this article we consider iterative operator-splitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator-splitting methods by providing improved results and convergence rates. We apply our results to deposition processes

Outgassing on stagnant-lid super-Earths

We explore volcanic outgassing on purely rocky, stagnant-lid exoplanets of different interior structures, compositions, thermal states, and age. We focus on planets in the mass range of 1-8 ME (Earth masses). We derive scaling laws to quantify first- and second-order influences of these parameters on volcanic outgassing after 4.5 Gyrs of evolution. Given commonly observed astrophysical data of super-Earths, we identify a range of possible interior structures and compositions by employing Bayesian inference modelling. [..] The identified interiors are subsequently used as input for two-dimensional (2-D) convection models to study partial melting, depletion, and outgassing rates of CO2. In total, we model depletion and outgassing for an extensive set of more than 2300 different super-Earth cases. We find that there is a mass range for which outgassing is most efficient (~2--3 ME, depending on thermal state) and an upper mass where outgassing becomes very inefficient (~5--7 \ME, depending on thermal state). [..] In summary, depletion and outgassing are mainly influenced by planet mass and thermal state. Interior structure and composition only moderately affect outgassing. The majority of outgassing occurs before 4.5 Gyrs, especially for planets below 3 ME. We conclude that for stagnant-lid planets, (1) compositional and structural properties have secondary influence on outgassing compared to planet mass and thermal state, and (2) confirm that there is a mass range for which outgassing is most efficient and an upper mass limit, above which no significant outgassing can occur. Our predicted trend of CO2-atmospheric masses can be observationally tested for exoplanets. These findings and our provided scaling laws are an important step in order to provide interpretative means for upcoming missions such as, e.g., JWST and E-ELT, that aim at characterizing exoplanet atmospheres.Comment: Accepted for publication in A&A, 19 Figures, 20 page

Redox state and interior structure control on the long-term habitability of stagnant-lid planets

A major goal in the search for extraterrestrial life is the detection of liquid water on the surface of exoplanets. On terrestrial planets, volcanic outgassing is a significant source of atmospheric and surface water and a major contributor to the long-term evolution of the atmosphere. The rate of volcanism depends on the interior evolution and on numerous feedback processes between atmosphere and interior, which continuously shape atmospheric composition, pressure, and temperature. We present the results of a comprehensive 1D model of the coupled evolution of the interior and atmosphere of rocky exoplanets that combines central feedback processes between these two reservoirs. We carried out more than \num{280000} simulations over a wide range of mantle redox states and volatile content, planetary masses, interior structures and orbital distances in order to robustly assess the emergence, accumulation and preservation of surface water on rocky planets. To establish a conservative baseline of which types of planets can outgas and sustain water on their surface, we focus here on stagnant-lid planets. We find that only a narrow range of the mantle redox state around the iron-w\"ustite buffer allows the formation of atmospheres that lead to long-term habitable conditions. At oxidizing conditions similar to those of the Earth's mantle, most stagnant-lid planets end up in a hothouse regime akin to Venus due to strong \ce{CO2} outgassing. At more reducing conditions, the amount of outgassed greenhouse gases is often too low to keep surface water from freezing. In addition, Mercury-like planets with large metallic cores are able to sustain habitable conditions at an extended range of orbital distances as a result of lower volcanic activity.Comment: 23 pages, 18 figures, accepted for publication in Astronomy & Astrophysic

Redox state and interior structure control on the long-term habitability of stagnant-lid planets

Context. A major goal in the search for extraterrestrial life is the detection of liquid water on the surface of exoplanets. On terrestrial planets, volcanic outgassing is a significant source of atmospheric and surface water and a major contributor to the long-term evolution of the atmosphere. The rate of volcanism depends on the interior evolution and on numerous feedback processes between the atmosphere and interior, which continuously shape atmospheric composition, pressure, and temperature. Aims. We explore how key planetary parameters, such as planet mass, interior structure, mantle water content, and redox state, shape the formation of atmospheres that permit liquid water on the surface of planets. Methods. We present the results of a comprehensive 1D model of the coupled evolution of the interior and atmosphere of rocky exoplanets that combines central feedback processes between these two reservoirs. We carried out more than 280 000 simulations over a wide range of mantle redox states and volatile content, planetary masses, interior structures, and orbital distances in order to robustly assess the emergence, accumulation, and preservation of surface water on rocky planets. To establish a conservative baseline of which types of planets can outgas and sustain water on their surface, we focus here on stagnant-lid planets. Results. We find that only a narrow range of the mantle redox state around the iron-wüstite buffer allows the formation of atmospheres that lead to long-term habitable conditions. At oxidizing conditions similar to those of the Earth's mantle, most stagnant-lid planets end up in a hothouse regime akin to Venus due to strong CO2 outgassing. At more reducing conditions, the amount of outgassed greenhouse gases is often too low to keep surface water from freezing. In addition, Mercury-like planets with large metallic cores are able to sustain habitable conditions at an extended range of orbital distances as a result of lower volcanic activity

Magma ocean evolution of the TRAPPIST-1 planets

Funding: P.B. acknowledges a St Leonard’s Interdisciplinary Doctoral Scholarship from the University of St Andrews. L.C. acknowledges support from the DFG Priority Programme SP1833 Grant CA 1795/3. R.B.’s contribution was supported by NASA grant number 80NSSC20K0229 and the NASA Virtual Planetary Laboratory Team through grant number 80NSSC18K0829. Th.H. acknowledges support from the European Research Council under the Horizon 2020 Framework Program via the ERC Advanced Grant Origins 83 24 28.Recent observations of the potentially habitable planets TRAPPIST-1 e, f, and g suggest that they possess large water mass fractions of possibly several tens of weight percent of water, even though the host star's activity should drive rapid atmospheric escape. These processes can photolyze water, generating free oxygen and possibly desiccating the planet. After the planets formed, their mantles were likely completely molten with volatiles dissolving and exsolving from the melt. To understand these planets and prepare for future observations, the magma ocean phase of these worlds must be understood. To simulate these planets, we have combined existing models of stellar evolution, atmospheric escape, tidal heating, radiogenic heating, magma-ocean cooling, planetary radiation, and water-oxygen-iron geochemistry. We present MagmOc, a versatile magma-ocean evolution model, validated against the rocky super-Earth GJ 1132b and early Earth. We simulate the coupled magma-ocean atmospheric evolution of TRAPPIST-1 e, f, and g for a range of tidal and radiogenic heating rates, as well as initial water contents between 1 and 100 Earth oceans. We also reanalyze the structures of these planets and find they have water mass fractions of 0–0.23, 0.01–0.21, and 0.11–0.24 for planets e, f, and g, respectively. Our model does not make a strong prediction about the water and oxygen content of the atmosphere of TRAPPIST-1 e at the time of mantle solidification. In contrast, the model predicts that TRAPPIST-1 f and g would have a thick steam atmosphere with a small amount of oxygen at that stage. For all planets that we investigated, we find that only 3–5% of the initial water will be locked in the mantle after the magma ocean solidified.Publisher PDFPeer reviewe