arXiv subjects

Nicola Tosi

Publications and source records attributed to Nicola Tosi.

At least 19 recordsLinked to original sources

arXiv2026

Core and mantle thermal evolution constraints on the onset of plate tectonics and a long-lived geodynamo

Earth's long-lived geodynamo is difficult to reconcile with recent high estimates of the core thermal conductivity, a problem known as the new core paradox. At the same time, the long-term thermal evolution of the mantle remains uncertain, largely due to the poorly constrained onset of modern-style plate tectonics, which marks the transition to efficient cooling of the interior through mobile-lid convection. Because core cooling -- and thus magnetic field generation -- depends on the efficiency with which the mantle extracts heat from the core, these two problems are closely linked. Here, we investigate the coupled thermal evolution of mantle and core using a 1D model that incorporates a parametrized transition transition from stagnant- to mobile-lid convection, defined by its onset time and with a prescribed duration. This framework allows us to assess how different tectonic histories influence Earth's thermal and magnetic evolution. We perform a Bayesian inversion using constraints from the palaeomagnetic record, mantle cooling history, and present-day thermal state. Our results favour a transition from stagnant- to mobile-lid convection during the Archean, which promotes core cooling and enables a geodynamo throughout Earth's history, even for core thermal conductivities in excess of 100 W/m/K. A delayed onset of mobile-lid convection provides thus a viable solution to the new core paradox.

astro-ph.EP↗

arXiv2025

The influence of interior structure and thermal state on impact melt generation upon large impacts onto terrestrial planets

We investigate the melt production of planetary impacts as a function of planet size ($R/R_\mathrm{Earth}$=0.1-1.5), impactor size ($L$=1-1000 km), and core size ratio ($R_\mathrm{core}/R$=0.2-0.8) using a combination of parameterized convection models and fully dynamical 2D impact simulations. To this end, we introduce a new method to determine impact-induced melt volumes which we normalize by the impactor volume for better comparability. We find that this normalized melt production, or melting efficiency, is enhanced for large planets when struck by smaller impactors, while for small planets, melting efficiency is elevated when impacted by larger impactors. This diverging behavior can be explained by the thickness of the planets' thermal boundary layer and the shapes of their thermal and lithostatic pressure profiles. We also find that melting efficiency maxima are usually highest on Earth-size planets. We show that the melting efficiency is only affected by core size ratio for large cores and older planets, where melt production is decreased significantly compared to smaller core size ratios. Projecting the lunar impactor flux on the generic planets, we find that Moon-sized planets produce the most melt throughout their evolution, relative to planet volume. Contrary to previous scaling laws, our method accounts for melt production by decompression or plastic work in addition to shock melting. We find that traditional scaling laws underestimate melt production on length scales where variations in the target planets' lithology, temperature, and lithostatic pressure become significant. We propose empirical formulas to predict melt generation as a function of radial structure and thermal age.

astro-ph.EP↗

arXiv2025

Physics-based machine learning for mantle convection simulations

Mantle convection simulations are an essential tool for understanding how rocky planets evolve. However, the poorly known input parameters to these simulations, the non-linear dependence of transport properties on pressure and temperature, and the long integration times in excess of several billion years all pose a computational challenge for numerical solvers. We propose a physics-based machine learning approach that predicts creeping flow velocities as a function of temperature while conserving mass, thereby bypassing the numerical solution of the Stokes problem. A finite-volume solver then uses the predicted velocities to advect and diffuse the temperature field to the next time-step, enabling autoregressive rollout at inference. For training, our model requires temperature-velocity snapshots from a handful of simulations (94). We consider mantle convection in a two-dimensional rectangular box with basal and internal heating, pressure- and temperature-dependent viscosity. Overall, our model is up to 89 times faster than the numerical solver. We also show the importance of different components in our convolutional neural network architecture such as mass conservation, learned paddings on the boundaries, and loss scaling for the overall rollout performance. Finally, we test our approach on unseen scenarios to demonstrate some of its strengths and weaknesses.

astro-ph.EP↗

arXiv2025

Geodynamics of super-Earth GJ 486b

Many super-Earths are on very short orbits around their host star and, therefore, more likely to be tidally locked. Because this locking can lead to a strong contrast between the dayside and nightside surface temperatures, these super-Earths could exhibit mantle convection patterns and tectonics that could differ significantly from those observed in the present-day solar system. The presence of an atmosphere, however, would allow transport of heat from the dayside towards the nightside and thereby reduce the surface temperature contrast between the two hemispheres. On rocky planets, atmospheric and geodynamic regimes are closely linked, which directly connects the question of atmospheric thickness to the potential interior dynamics of the planet. Here, we study the interior dynamics of super-Earth GJ 486b ($R=1.34$ $R_{\oplus}$, $M=3.0$ $M_{\oplus}$, T$_\mathrm{eq}\approx700$ K), which is one of the most suitable M-dwarf super-Earth candidates for retaining an atmosphere produced by degassing from the mantle and magma ocean. We investigate how the geodynamic regime of GJ 486b is influenced by different surface temperature contrasts by varying possible atmospheric circulation regimes. We also investigate how the strength of the lithosphere affects the convection pattern. We find that hemispheric tectonics, the surface expression of degree-1 convection with downwellings forming on one hemisphere and upwelling material rising on the opposite hemisphere, is a consequence of the strong lithosphere rather than surface temperature contrast. Anchored hemispheric tectonics, where downwellings und upwellings have a preferred (day/night) hemisphere, is favoured for strong temperature contrasts between the dayside and nightside and higher surface temperatures.

astro-ph.EP↗

arXiv2024

The effect of a biosphere on the habitable timespan of stagnant-lid planets and implications for the atmospheric spectrum

Temperature-dependent biological productivity controls silicate weathering and thereby extends the potential habitable timespan of Earth. Models and theoretical considerations indicate that the runaway greenhouse on Earth-like exoplanets is generally accompanied by a dramatic increase in atmospheric H$_2$O and CO$_2$, which might be observed with the upcoming generation of space telescopes. If an active biosphere extends the habitable timespan of exoplanets similarly to Earth, observing the atmospheric spectra of exoplanets near the inner edge of the habitable zone could then give insights into whether the planet is inhabited. Here, we explore this idea for Earth-like stagnant-lid planets. We find that while for a reduced mantle, a surface biosphere extends the habitable timespan of the planet by about 1 Gyr, for more oxidising conditions, the biologically enhanced rate of weathering becomes increasingly compensated for by an increased supply rate of CO$_2$ to the atmosphere. Observationally, the resulting difference in atmospheric CO$_2$ near the inner edge of the habitable zone is clearly distinguishable between biotic planets with active weathering and abiotic planets that have experienced a runaway greenhouse. For an efficient hydrological cycle, the increased bioproductivity also leads to a CH$_4$ biosignature observable with JWST. As the planet becomes uninhabitable, the H$_2$O infrared absorption bands dominate, but the 4.3-micron CO$_2$ band remains a clear window into the CO$_2$ abundances. In summary, while the effect of life on the carbonate-silicate cycle leaves a record in the atmospheric spectrum of Earth-like stagnant-lid planets, future work is needed especially to determine the tectonic state and composition of exoplanets and to push forward the development of the next generation of space telescopes.

astro-ph.EP↗

arXiv2024

H$_{2}$-H$_{2}$O demixing in Uranus and Neptune: Adiabatic structure models

Demixing properties of planetary major constituents influence the interior structure and evolution of planets. Comparing experimental and computational data on the miscibility of hydrogen and water to adiabatic profiles suggests phase separation between these components occurs in the ice giants Uranus and Neptune. We aim to predict the atmospheric water abundance and transition pressure between the water-poor outer envelope and the water-rich deep interior in Uranus and Neptune. We construct seven H2-H2O phase diagrams from the available experimental and computational data. We compute interior adiabatic structure models and compare these to the phase diagrams to infer whether demixing is occurring. We obtain a strong water depletion in the top layer due to rain-out of water and find upper limits on the atmospheric water mass fraction Z_atm of 0.21 for Uranus and 0.16 for Neptune. The transition from the water-poor to the water-rich layer is sharp and occurs at pressures P_Z between 4 and 11 GPa. Using these constraints on Z_atm and P_Z, we find that the observed gravitational harmonics J2 and J4 can be reproduced if P_Z > 10 GPa in Uranus and > 5 GPa in Neptune, and if the deep interior has a high primordial water mass fraction of 0.8, unless rocks are also present. The agreement with J4 is improved if rocks are confined deeper than P_Z, for instance below a rock cloud level at 2000 K (20-30 GPa). These findings confirm classical few-layer models and suggest that a layered structure may result from a combination of primordial mass accretion and subsequent phase separation. Reduced observational uncertainty in J4 and its dynamic contribution, atmospheric water abundance measurements from an Orbiter with a Probe mission to Uranus (UOP) or Neptune, and better understanding of the mixing behaviour of constituents are needed to constrain the interiors of ice giants.

astro-ph.EP↗

arXiv2024

Accelerating the discovery of steady-states of planetary interior dynamics with machine learning

Simulating mantle convection often requires reaching a computationally expensive steady-state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature dependence of the rheology of mantle rocks causes viscosity variations of several orders of magnitude, leading to a slow-evolving stagnant lid where heat conduction dominates, overlying a rapidly-evolving and strongly convecting region. Time-stepping methods, while effective for fluids with constant viscosity, are hindered by the Courant criterion, which restricts the time step based on the system's maximum velocity and grid size. Consequently, achieving steady-state requires a large number of time steps due to the disparate time scales governing the stagnant and convecting regions. We present a concept for accelerating mantle convection simulations using machine learning. We generate a dataset of 128 two-dimensional simulations with mixed basal and internal heating, and pressure- and temperature-dependent viscosity. We train a feedforward neural network on 97 simulations to predict steady-state temperature profiles. These can then be used to initialize numerical time stepping methods for different simulation parameters. Compared to typical initializations, the number of time steps required to reach steady-state is reduced by a median factor of 3.75. The benefit of this method lies in requiring very few simulations to train on, providing a solution with no prediction error as we initialize a numerical method, and posing minimal computational overhead at inference time. We demonstrate the effectiveness of our approach and discuss the potential implications for accelerated simulations for advancing mantle convection research.

physics.flu-dyn↗

arXiv2023

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.

astro-ph.EP↗

arXiv2023

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-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.

astro-ph.EP↗

arXiv2022

Planetary Exploration Horizon 2061 Report, Chapter 3: From science questions to Solar System exploration

This chapter of the Planetary Exploration Horizon 2061 Report reviews the way the six key questions about planetary systems, from their origins to the way they work and their habitability, identified in chapter 1, can be addressed by means of solar system exploration, and how one can find partial answers to these six questions by flying to the different provinces to the solar system: terrestrial planets, giant planets, small bodies, and up to its interface with the local interstellar medium. It derives from this analysis a synthetic description of the most important space observations to be performed at the different solar system objects by future planetary exploration missions. These observation requirements illustrate the diversity of measurement techniques to be used as well as the diversity of destinations where these observations must be made. They constitute the base for the identification of the future planetary missions we need to fly by 2061, which are described in chapter 4. Q1- How well do we understand the diversity of planetary systems objects? Q2- How well do we understand the diversity of planetary system architectures? Q3- What are the origins and formation scenarios for planetary systems? Q4- How do planetary systems work? Q5- Do planetary systems host potential habitats? Q6- Where and how to search for life?

astro-ph.IM↗

arXiv2022

Residence time of inertial particles in 3D thermal convection: implications for magma reservoirs

The dynamic behavior of crystals in convecting fluids determines how magma bodies solidify. In particular, it is often important to estimate how long crystals stay in suspension in the host liquid before being deposited at its bottom (or top, for light particles). We perform a systematic 3D numerical study of particle-laden Rayleigh-Benard convection, and derive a robust model for the particle residence time. For Rayleigh numbers higher than 10^7, inertial particles' trajectories exhibit a monotonic transition from fluid tracer-like to free-fall dynamics, the control parameter being the ratio between particle Stokes velocity and the fluid velocity. The average settling rate is proportional to the particle Stokes velocity in both the end-member regimes, but the distribution of the residence times differs markedly from one to the other. For lower Rayleigh numbers (<10^7), an interaction between large-scale circulation and particle motion emerges, increasing the settling rates on average. Nevertheless, the mean residence time does not exceed the terminal time, i.e. the settling time from a quiescent fluid, by a factor larger than four. An exception are simulations with only a slightly super-critical Rayleigh number (~ 10^4), for which stationary convection develops and some particles become trapped indefinitely. 2D simulations of the same problem overestimate the flow-particle interaction - and hence the residence time - for both high and low Rayleigh numbers, which stresses the importance of using 3D geometries for simulating particle-laden flows. We outline how our model can be used to explain depth changes of crystal size distribution in sedimentary layers of magmatic intrusions that are thought to have formed via settling of a crystal cargo, and discuss how the micro-structural observations of solidified intrusions can be used to infer the past convective velocity of magma.

physics.geo-ph↗

arXiv2021

Deep learning for surrogate modelling of 2D mantle convection

Traditionally, 1D models based on scaling laws have been used to parameterized convective heat transfer rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus to tackle the computational bottleneck of high-fidelity forward runs in 2D or 3D. However, these are limited in the amount of physics they can model (e.g. depth dependent material properties) and predict only mean quantities such as the mean mantle temperature. We recently showed that feedforward neural networks (FNN) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally-averaged temperature profile in time for complex models. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a dataset of 10,525 two-dimensional simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e. surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the temperature fields by a factor of 142 and then use FNN and long-short term memory networks (LSTM) to predict the compressed fields. On average, the FNN predictions are 99.30% and the LSTM predictions are 99.22% accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean absolute relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to 96.51% and 97.66% relative to the coefficients of the original simulations, respectively.

astro-ph.EP↗

arXiv2021

Early habitability and crustal decarbonation of a stagnant-lid Venus

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 would heat up until they become unstable and the crust would become depleted in carbonates. With CO$_2$ supply to the atmosphere the surface temperature rises further, the depth below which decarbonation occurs decreases, causing the release of even more CO$_2$. We assess the habitable period of an early stagnant-lid Venus by employing a coupled interior-atmosphere evolution model accounting for CO$_2$ degassing, weathering, carbonate burial, and crustal decarbonation. We find that if initial surface conditions allow for liquid water, weathering can keep the planet habitable for up to 900 Myr, followed by evaporation of water and rapid crustal carbonate depletion. For the atmospheric CO$_2$ of stagnant-lid exoplanets, we predict a bimodal distribution, depending on whether or not these planets experienced a runaway greenhouse in their history. Planets with high atmospheric CO$_2$ could be associated with crustal carbonate depletion as a consequence of a runaway greenhouse, whereas planets with low atmospheric CO$_2$ would indicate active silicate weathering and thereby a habitable climate.

astro-ph.EP↗

arXiv2020

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.

physics.flu-dyn↗

arXiv2019

Mercury, Moon, Mars: Surface expressions of mantle convection and interior evolution of stagnant-lid bodies

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 coherent picture of the thermal and convective evolution of the planetary interior represents thus a major challenge. In this chapter, we review key processes and (mostly geophysical) observational constraints that can be used to infer the global characteristics of mantle convection and thermal evolution of the interior of Mercury, the Moon and Mars, the three major terrestrial bodies where a stagnant lid has likely been present throughout most of their history.

astro-ph.EP↗

arXiv2019

Machine learning inference of the interior structure of low-mass exoplanets

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures.

astro-ph.EP↗

arXiv2019

Carbon cycling and interior evolution of water-covered plate tectonics and stagnant lid planets

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: The assumed relationship between the seafloor-weathering rate and the atmospheric CO$_2$ or the surface temperature strongly influences the climate evolution for both tectonic regimes. For a plate tectonics planet, the atmospheric CO$_2$ partial pressure is characterised by an equilibrium between ingassing and degassing and depends on the temperature gradient in subduction zones affecting the stability of carbonates. For a stagnant lid planet, partial melting and degassing are always accompanied by decarbonation, such that the combined carbon content of the crust and atmosphere increases with time. Whereas the initial mantle temperature for plate tectonics planets only affects the early evolution, it influences the evolution of the surface temperature of stagnant lid planets for much longer. Conclusions: For both tectonic regimes, mantle cooling results in a decreasing atmospheric CO$_2$ partial pressure. For a plate tectonics planet this is caused by an increasing fraction of subduction zones that avoid crustal decarbonation, and for stagnant lid planets this is caused by an increasing decarbonation depth. This mechanism may partly compensate for the increase of the surface temperature due to increasing solar luminosity with time and hereby contribute to keep planets habitable in the long-term.

astro-ph.EP↗

arXiv2019

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.

astro-ph.EP↗