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-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 \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.
Aims: The long-term carbon cycle for planets with a surface entirely covered by oceans works differently from that of the present-day Earth because inefficient erosion leads to a strong dependence of the weathering rate on the rate of volcanism. In this paper, we investigate the long-term carbon cycle for these planets throughout their evolution. Methods: We built box models of the long-term carbon cycle based on CO$_2$ degassing, seafloor-weathering, metamorphic decarbonation, and ingassing and coupled them with thermal evolution models of stagnant lid and plate tectonics planets. Results: Th…
Coupled models of mantle thermal evolution, volcanism, outgassing, weathering, and climate evolution for Earth-like (in terms of size and composition) stagnant lid planets are used to assess their prospects for habitability. The results indicate that planetary CO$_2$ budgets ranging from $\approx 3$ orders of magnitude lower than Earth's to $\approx 1$ order of magnitude larger, and radiogenic heating budgets as large or larger than Earth's, allow for habitable climates lasting 1-5 Gyrs. The ability of stagnant lid planets to recover from potential snowball states is also explored; recovery is…
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 …
Models of thermal evolution, crustal production, and CO$_2$ cycling are used to constrain the prospects for habitability of rocky planets, with Earth-like size and composition, in the stagnant lid regime. Specifically, we determine the conditions under which such planets can maintain rates of CO$_2$ degassing large enough to prevent global surface glaciation, but small enough so as not to exceed the upper limit on weathering rates provided by the supply of fresh rock, a situation which would lead to runaway atmospheric CO$_2$ accumulation and an inhospitably hot climate. The models show that s…
The ongoing discovery of terrestrial exoplanets accentuates the importance of studying planetary evolution for a wide range of initial conditions. We perform thermal evolution simulations for generic terrestrial planets with masses ranging from that of Mars to 10 Earth-masses in the stagnant-lid regime, the most natural mode of convection with strongly temperature- dependent viscosity. Given considerable uncertainty surrounding the dependency of mantle rheology on pressure, we choose to focus on the end-member case of pressure-independent potential viscosity, where viscosity does not change wi…
Topography on a wet rocky exoplanet could raise land above its sea level. Although land elevation is the product of many complex processes, the large-scale topographic features on any geodynamically-active planet are the expression of the convecting mantle beneath the surface. This so-called "dynamic topography" exists regardless of a planet's tectonic regime or volcanism; its amplitude, with a few assumptions, can be estimated via numerical simulations of convection as a function of the mantle Rayleigh number. We develop new scaling relationships for dynamic topography on stagnant lid planets…
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-dimensio…
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 evolutio…
The evolution of the interior of stagnant-lid bodies is comparatively easier to model and predict with respect to the Earth's due to the absence of the large uncertainties associated with the physics of plate tectonics, its onset time and efficiency over the planet's history. Yet, the observational record for these bodies is both scarcer and sparser with respect to the Earth's. It is restricted to a limited number of samples and a variety of remote-sensing measurements of billions-of-years-old surfaces whose actual age is difficult to determine precisely. Combining these observations into a co…
Little is known about the early evolution of Venus and a potential habitable period during the first one billion years. In particular, it remains unclear whether or not plate tectonics and an active carbonate-silicate cycle were present. In the presence of liquid water but without plate tectonics, weathering would have been limited to freshly produced basaltic crust, with an early carbon cycle restricted to the crust and atmosphere. With the evaporation of surface water, weathering would cease. With ongoing volcanism, carbonate sediments would be buried and sink downwards. Thereby, carbonates …
Numerical experiments of convection with grain-damage are used to develop scaling laws for convective heat flow, mantle velocity, and plate velocity across the stagnant lid and plate-tectonic regimes. Three main cases are presented in order of increasing complexity: a simple case wherein viscosity is only dependent on grainsize, a case where viscosity depends on temperature and grainsize, and finally a case where viscosity is temperature and grainsize sensitive, and the grain-growth (or healing) is also temperature sensitive. In all cases, convection with grain-damage scales differently than N…
Volcanic gases supplied a large part of Earth's early atmosphere, but constraints on their flux are scarce. Here we model how C-O-H outgassing could have evolved through the late Hadean and early Archean, under the conditions that global plate tectonics had not yet initiated, all outgassing was subaerial, and graphite was the stable carbon phase in the melt source regions. The model fully couples numerical mantle convection, partitioning of volatiles into the melt, and chemical speciation in the gas phase. The mantle oxidation state (which may not have reached late Archean values in the Hadean…
The presence of rocky exoplanets with a large refractory carbon inventory is predicted by chemical evolution models of protoplanetary disks of stars with photospheric C/O >0.65, and by models studying the radial transport of refractory carbon. High-pressure high-temperature laboratory experiments show that most of the carbon in these exoplanets differentiates into a graphite outer shell. Our aim is to evaluate the effects of a graphite outer shell on the thermal evolution of rocky exoplanets containing a metallic core and a silicate mantle. We implement a parameterized model of mantle convecti…
The ideal exoplanets to search for life are those within a star's habitable zone. However, even within the habitable zone planets can still develop uninhabitable climate states. Sustaining a temperate climate over geologic ($\sim$Gyr) timescales requires a planet contain sufficient internal energy to power a planetary-scale carbon cycle. A major component of a rocky planet's energy budget is the heat produced by the decay of radioactive elements, especially $^{40}$K, $^{232}$Th, $^{235}$U and $^{238}$U. As the planet ages and these elements decay, this radiogenic energy source dwindles. Here w…
Venus's past climate evolution is uncertain. General circulation model simulations permit a habitable climate as late as ~0.7 Ga, and there is suggestive-albeit inconclusive-evidence for previous liquid water from surface geomorphology and mineralogy. However, it is unclear whether a habitable past can be reconciled with Venus's inferred atmospheric evolution. In particular, the lack of leftover atmospheric oxygen argues against recent water loss. Here, we apply a fully coupled model of Venus's atmospheric-interior-climate evolution from post-accretion magma ocean to present. The model self-co…
We used a thermal model of an iron core to calculate magnetodynamo evolution in Earth-mass rocky planets to determine the sensitivity of dynamo lifetime and intensity to planets with different mantle tectonic regimes, surface temperatures, and core properties. The heat flow at the core-mantle boundary (CMB) is derived from numerical models of mantle convection with a viscous/pseudo-plastic rheology that captures the phenomenology of plate-like tectonics. Our thermal evolution models predict a long-lived (~8 Gyr) field for Earth and similar dynamo evolution for Earth-mass exoplanets with plate …
The impact heat accumulated during the late stage of planetary accretion can melt a significant part or even the entire mantle of a terrestrial body, giving rise to a global magma ocean. [...] Assuming fractional crystallization of the magma ocean, dense cumulates are produced close to the surface, largely due to iron enrichment in the evolving magma ocean liquid (Elkins-Tanton et al., 2003). A gravitationally unstable mantle thus forms, which is prone to overturn. We investigate the cumulate overturn and its influence on the thermal evolution of Mars using mantle convection simulations in 2D …
Ridge-and-trough terrain is a common landform on outer Solar System icy satellites. Examples include Ganymede's grooved terrain, Europa's gray bands, Miranda's coronae, and several terrains on Enceladus. The conditions associated with the formation of each of these terrains are similar: heat flows of order tens to a hundred milliwatts per meter squared, and deformation rates of order $10^{-16}$ to $10^{-12}$ s$^{-1}$. Our prior work shows that the conditions associated with the formation of these terrains on Ganymede and the south pole of Enceladus are consistent with vigorous solid-state ice …
The coupled interior-atmosphere system of terrestrial exoplanets remains poorly understood. Exoplanets show a wide variety of sizes, densities, surface temperatures, and interior structures, with important knock-on effects for this coupled system. Many exoplanets are predicted to have a "stagnant lid" at the surface, with a rigid stationary crust, sluggish mantle convection, and only minor volcanism. However, if exoplanets have Earth-like plate tectonics, which involves several discrete, slowly moving plates and vigorous tectono-magmatic activity, then this may be critical for planetary habita…
Massive steam and CO$_2$ atmospheres have been proposed for magma ocean outgassing of Earth and terrestrial planets. Yet formation of such atmospheres depends on volatile exchange with the molten interior, governed by volatile solubilities and redox reactions. We determine the evolution of magma ocean--atmosphere systems for a range of oxygen fugacities, C/H ratios and hydrogen budgets that include redox reactions for hydrogen (H$_2$--H$_2$O), carbon (CO--CO$_2$), methane (CH$_4$), and solubility laws for H$_2$O and CO$_2$. We find that small initial budgets of hydrogen, high C/H ratios, and o…
Thermal history calculations provide important insights into the interior evolution of planets, but incorporate simplified dynamics from the systems they represent. Planetary interiors typical incorporate complex rheologies, viscous layering, lateral heterogeneities, and time delays in processes, which have not been traditionally represented by parameterised approaches. Here we develop numerical models for planetary evolution, incorporating the physical complexity of Earth's interior, and use them to generate statistically-based Nu-Ra scalings. These encapsulate the main effects of tectonic tr…
A sufficient amount of water is required at the surface to develop water oceans. A significant fraction of water, however, remains in the mantle during magma ocean solidification, and thus the existence of water oceans is not guaranteed even for exoplanets located in the habitable zone. To discuss the likelihood of ocean formation, we built two models to predict the rate of mantle degassing during the magma ocean stage and the subsequent solid-state convection stage. We find that planets with low H$_2$O/CO$_2$ ratios would not have a sufficient amount of surface water to develop water oceans i…
Since the Archean, N2 has been a major atmospheric constituent in Earth's atmosphere. Nitrogen is an essential element in the building blocks of life, therefore the geobiological nitrogen cycle is a fundamental factor in the long term evolution of both Earth and Earth-like exoplanets. We discuss the development of the Earth's N2 atmosphere since the planet's formation and its relation with the geobiological cycle. Then we suggest atmospheric evolution scenarios and their possible interaction with life forms: firstly, for a stagnant-lid anoxic world, secondly for a tectonically active anoxic wo…
Aims: The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk composition on the interior--atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres. Methods: We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO2) following the crystallization of a magma ocean after planet formation, predicting a compositional profile …
