Maurice et al. (2023) also reported that the redox state of the crystallizing magma ocean evolves systematically towards oxidizing conditions. This owing to the incompatibility of Fe³⁺ in the minerals resulting in its enrichment in the melt and in the increase of the oxygen fugacity throughout magma ocean crystallization. They showed that the outgassed atmosphere at the final stages of crystallization is consistently oxidized and dominated by H₂O and CO₂. Yet, unlike other studies, they found that the cooling and solidification of initially reduced magma oceans is slower than that of initially oxidized magma oceans. Indeed, despite the stronger greenhouse effect of oxidized atmospheric species, they emphasized that initially reduced atmospheres are not able to radiate as efficiently as oxidized atmospheres owing to their steeper lapse rate, so that the molten phase is protracted.

The Gaillard et al. (2022a) magma ocean static outgassing model also supports an enhanced outgassing of C-bearing species compared to H-bearing ones in all oxidation states. They further included N- and S-bearing species and predicted that an oxidized magma ocean would mainly outgas C–N–S. They therefore form atmospheres made of CO₂–SO₂–N₂–H₂O with relative proportions varying according to the degree of oxidation, while a reduced magma ocean would mainly outgas CO–H₂ with some CH₄ for the most reduced cases and N₂ otherwise.

Besides affecting the chemical composition of the outgassed atmosphere, and thus indirectly its thermal evolution through atmospheric opacity, the redox state may affect intrinsic properties of the magma ocean itself. Using high-temperature experiments, Lin et al. (2021) showed that oxygen fugacity has a direct effect on rock melting properties by affecting the liquidus. In particular, they reported that a higher oxygen abundance lowers the liquidus temperature of iron-free basalt at 1 atm, thus facilitating melting. How these findings apply to larger pressures is not yet clear, but they could have significant implications for magma ocean evolution. Indeed, these results suggest that oxidized interiors would melt to a greater extent compared to reduced mantles, and would thus sustain magma ocean and associated outgassing for longer periods of time.

**Summary** Overall, a number of lines of evidence suggest that the magma ocean was initially in a reducing state, because of the coexistence of metal and silicate melt, before the former fully segregated to the core. From then on, whether as a result of self-oxidation, metal segregation to the core, hydrogen escape, or oxidized material endowment (or a combination of all), the crystallizing magma ocean likely became more oxidized with time. Crystallization of the magma ocean is also required to concentrate enough incompatible species in the melt to reach melt-saturation of highly soluble volatile species and their extensive outgassing. By this time, the oxidation state of the magma ocean may have been high enough to reach the present-day QFM buffer. It would have produced an oxidized atmosphere, predominantly composed of H₂O–CO₂–N₂. This is consistent with the earliest terrestrial rock records (see Fig. 1 in Scaillet and Gaillard 2011, for a schematic reconstruction of the mantle redox state evolution). Given their similar size, density, and their vicinity in the Solar System, such a scenario may apply for both early Earth and Venus. Yet, the absence of measurements for the latter makes any statement even more speculative than for Earth. In such an early oxidizing environment after the surface solidified, late impact-induced degassing may have created local and transient reducing conditions. These would be favorable for prebiotic chemistry and life emergence on Earth, while other surface conditions may have compromised its development or sustainability on Venus.

While this scenario might tentatively reconcile the different available pieces of evidence (see Table 2 for a summary of the different early outgassed atmospheres and underlying assumptions/constraints), one should keep in mind that early atmospheric formation was most
<table><caption>**Table 2** Early outgassed atmospheres and underlying constraints or assumptions</caption><thead><tr><th>Associated mechanism</th><th>Reference(s)</th></tr></thead><tbody><tr><td colspan="2">Oxidized atmospheres: dominated by H<sub>2</sub>O-CO<sub>2</sub>-SO<sub>2</sub>-N<sub>2</sub></td></tr><tr><td colspan="2">Geologic constraints</td></tr><tr><td>Crystallization of terrestrial Hadean zircons 4.35<br>Gyr ago under oxidizing conditions</td><td>Trail et al. (2011)</td></tr><tr><td>Oxidation state of terrestrial Archean (up to 3.9<br>Gyr old) igneous rocks at-or-near current<br>oxidizing state</td><td>Canil (1997), Delano (2001), Canil (2002), Lee<br>et al. (2003), Li and Lee (2004), Rollinson et al.<br>(2017), Nicklas et al. (2018)</td></tr><tr><td colspan="2">Prebiotic chemistry</td></tr><tr><td>Production of reduced organics triggered by<br>coronal mass ejection events from the young Sun<br>or impact energy</td><td>Kurosawa et al. (2013), Airapetian et al. (2016)</td></tr><tr><td>Exogenous delivery of reduced organic materials</td><td>Anders (1989), Chyba et al. (1990), Chyba and<br>Sagan (1992), Whittet (1997), Matthews and<br>Minard (2006)</td></tr><tr><td>Production of amino acids and other organic<br>compounds using oxidation inhibitors</td><td>Cleaves et al. (2008)</td></tr><tr><td colspan="2">Accretion</td></tr><tr><td>Accreting bodies of increasing oxidation state<br>(heterogeneous accretion) inferred from trace<br>element abundances</td><td>Wänke et al. (1988), O'Neill (1991), Wood et al.<br>(2009), Rubie et al. (2011, 2015), Fischer et al.<br>(2015), Shi et al. (2022)</td></tr><tr><td>Elemental partitioning and impact erosion during<br>continuous accretion of chondritic bodies</td><td>Sakuraba et al. (2021)</td></tr><tr><td>Impact-generated atmosphere from carbonaceous<br>(CI, CM, CV) chondritic material</td><td>Schaefer and Fegley (2010, 2017)</td></tr><tr><td>Heating and outgassing experiments of<br>carbonaceous chondrites</td><td>Thompson et al. (2021)</td></tr><tr><td colspan="2">Core formation</td></tr><tr><td>Core formation (rapidly) completed with metallic<br>iron fully segregated from the silicate</td><td>Holland (1962), Kleine et al. (2002), Frost and<br>McCammon (2008)</td></tr><tr><td>Deep metal-silicate separation</td><td>Li and Agee (1996), Fischer et al. (2015)</td></tr><tr><td>Chemical equilibrium with molten surface of bulk<br>silicate Earth or molten Earth's continental crust<br>composition</td><td>Lupu et al. (2014)</td></tr><tr><td>Impactor's iron not available to reduce the upper<br>molten layers of the target or the atmosphere</td><td>Itcovitz et al. (2022), Citron and Stewart (2022)</td></tr><tr><td colspan="2">Magma ocean evolution</td></tr><tr><td>Gradient of the magma ocean redox state with<br>oxidized shallow parts</td><td>Hirschmann (2012), Deng et al. (2020)</td></tr><tr><td>Disproportionation of FeO at depth to Fe metal<br>and Fe<sub>2</sub>O<sub>3</sub> components (in post-spinel and<br>perovskite form)</td><td>Mao and Bell (1977), Frost et al. (2004), Galimov<br>(2005), Wade and Wood (2005), Wood and<br>Halliday (2005), Frost et al. (2008), Schaefer and<br>Elkins-Tanton (2018), Armstrong et al. (2019),<br>Hirschmann (2022)</td></tr></tbody></table>

likely a continuous, dynamic, and evolving process. It would have overlapped with stochastic planetary accretion, core formation, and cooling of possibly several episodes of more or less deep magma oceans (e.g., Tucker and Mukhopadhyay 2014). The magma oceans would have been influenced by several mechanisms at play during these early stages, where out-
<table><caption>**Table 2** (Continued)</caption><thead><tr><th>Associated mechanism</th><th>Reference(s)</th></tr></thead><tbody><tr><td>Increasing outgassed CO<sub>2</sub>/CO ratio with magma ocean cooling from ab initio molecular dynamics simulations</td><td>Solomatova and Caracas (2021)</td></tr><tr><td>Self-oxidation of the magma ocean with crystallization owing to Fe<sup>3+</sup> incompatibility</td><td>Maurice et al. (2023)</td></tr><tr><td>Atmospheric evolution</td><td></td></tr><tr><td>Preservation of carbonaceous chondritic D/H signature in the terrestrial oceans</td><td>Pahlevan et al. (2019)</td></tr><tr><td>Photodissociation of H<sub>2</sub>O and/(or) atmospheric escape of H<sub>2</sub></td><td>Hunten (1993), Kasting et al. (1993a), Sharp et al. (2013)</td></tr><tr><td>Reduced atmospheres: dominated by H<sub>2</sub>–CO–CH<sub>4</sub>–NH<sub>3</sub>–H<sub>2</sub>S</td><td></td></tr><tr><td>Prebiotic chemistry</td><td></td></tr><tr><td>Production of amino acids and other organic compounds from electrical discharges</td><td>Miller (1953, 1955), Miller and Urey (1959)</td></tr><tr><td>Accretion</td><td></td></tr><tr><td>Impact-induced degassing</td><td>Kasting (1990), Hashimoto et al. (2007), Sugita and Schultz (2009), Zahnle et al. (2010, 2020)</td></tr><tr><td>Impact-generated atmosphere from ordinary (H, L, LL) and enstatite (EH, EL) chondritic material</td><td>Schaefer and Fegley (2007, 2010, 2017)</td></tr><tr><td>Reduction of the magma ocean during accretion</td><td>Righter and Ghiorso (2012)</td></tr><tr><td>Core formation</td><td></td></tr><tr><td>Incomplete metallic iron–silicate separation in the shallow part of the magma ocean</td><td>Holland (1962), O’Neill (1991), Frost and McCammon (2008)</td></tr><tr><td>Impactor’s iron available to reduce the upper molten layers of the target and the atmosphere</td><td>Itcovitz et al. (2022), Citron and Stewart (2022)</td></tr><tr><td>Magma ocean evolution</td><td></td></tr><tr><td>Graphite precipitation (requires a highly reducing magma ocean) and flotation at the surface of the magma ocean</td><td>Keppler and Golabek (2019)</td></tr><tr><td>Atmospheric evolution</td><td></td></tr><tr><td>Reducing power of the primordial H<sub>2</sub>-dominated atmosphere acting on proto-planets and constituting planetesimals</td><td>Zahnle et al. (2010)</td></tr><tr><td>Outgassing and slow (energy limited) escape of hydrogen</td><td>Tian et al. (2005), Liggins et al. (2020)</td></tr></tbody></table>

gassing of the growing planets' interior, impact degassing of accreting planetesimals, impact erosion, and atmospheric self-escape all affected both its physical and chemical properties over different time scales. A comprehensive theory explaining such a complex process requires further investigation of each of these contributions and would remain elusive without considering further inputs from incoming Venus exploration and ongoing exoplanets characterization.

## 3.3 Magma Ocean–Atmosphere Interactions

In the absence of a thick, long-lasting, viscous boundary layer at the surface of the magma ocean, thermal and volatile exchanges proceed efficiently between the molten interior and
the overlying atmosphere. This is the case for most of the magma ocean evolution sequence. Note that a crust-like, thin, viscous boundary layer might form at the surface, either as observed on lava lakes or by flotation of crystals less dense than the surrounding melt, but would be quickly, i.e., relative to the magma ocean cooling rate, destabilized and broken apart by bursting bubbles and strong convective currents. After having described the partitioning of volatile species between the different reservoirs of the planet in the previous section, we discuss below the interaction between the solidifying magma ocean and the outgassed atmosphere and how they can affect the evolution of the coupled system. In particular, we focus on the heat transfer and exchanges from the magma ocean to space and how they control the cooling of the molten interior.

In its most simple form, the conservation of energy at the top of a planet's atmosphere can be described schematically as the equilibrium between all the incoming, $F_↑$, and outgoing, $F_↓$, fluxes:

$$F_↑ = F_↓, \qquad (16)$$

where the total outgoing flux $F_↑ = F_{IR} + \alpha F_⊕$ comprises the thermal, infrared flux, $F_{IR}$, representing the heat loss at the top of the atmosphere, and the reflected fraction $\alpha$ (i.e., the Bond albedo) of the gross incident solar radiation $F_⊕$ that peaks at shorter wavelengths given the higher temperature of the star (the so-called Wien peak, that is inversely proportional to the temperature), in the visible spectral range, hence referred to as the Outgoing Shortwave Radiation (OSR). The total incoming flux is the sum of the heat sources:

$$F_↓ = F_{\text{abs}} + F_{\text{conv}}, \qquad (17)$$

and includes the contribution of the net (incident minus reflected) solar flux absorbed by the planet, $F_{\text{abs}}$ (Eq. (1)), and the heat flux coming from the planetary interior and generated by the convection of the magma ocean, $F_{\text{conv}}$ (or $F_{\text{MO}}$). Regarding thermal exchanges more specifically, the magma ocean-atmosphere system has then two incoming heat sources: the absorbed solar flux and the convective flux from the magma ocean, that must balance the thermal radiation $F_{\text{IR}}$ emitted to space at the top of the atmosphere (Fig. 5; e.g., Zahnle et al. 1988; Abe 1993a):

$$F_{\text{IR}} = F_{\text{abs}} + F_{\text{conv}}. \qquad (18)$$

During the magma ocean stage, the temperature of the mantle is so hot that the heat flux coming from the boiling convective mantle far exceeds the incoming solar flux ($F_{\text{conv}} \gg F_{\text{abs}}$). This implies that the outgoing thermal flux is dominated by the heat flux from the magma ocean: $F_{\text{IR}} \approx F_{\text{conv}}$. Because the heat flux received from the star is substantially lower than the planetary interior heat flux, i.e., the equilibrium temperature is much lower than the molten surface temperature, the planet has an excess of heat. To evacuate the excess of internal heat and reach thermal and radiative equilibrium with the stellar environment, the magma ocean cools down through convection. The generated heat flux $F_{\text{conv}}$ is initially high and decreases with time. As $F_{\text{IR}} \approx F_{\text{conv}}$, the outgoing thermal flux also decreases with time.

The outgoing heat flux depends on the surface temperature, and the surface temperature itself results from the heat flux balance (Eq. (18)). It can be written $F_{\text{IR}} = \sigma T_{\text{eff}}^4 = \varepsilon \sigma T_{\text{surf}}^4$, where $\sigma$ is the Stefan-Boltzmann constant, $T_{\text{eff}}$ the effective temperature of the planet,<fnref n="7" /> and

<footnote n="7">⁷The effective temperature of the planet, $T_{\text{eff}}$, is the temperature a black body would have to emit the same total amount of radiation ($F_{\text{IR}}$). It should not be confused with the equilibrium temperature, $T_{\text{eq}}$, which is the</footnote>
$\epsilon$ is the emissivity of the atmosphere, which measures its effectiveness in emitting energy as thermal radiation.

In the absence of an atmosphere, as usually initially assumed as a result of giant impact in magma ocean-atmosphere models, Eq. (18) is evaluated at the surface of the planet from which thermal radiation is directly emitted to space. In such a case, the planet efficiently radiates the energy from the magma ocean and emits all incoming absorbed radiation ($\epsilon = 1$). It loses heat to space as a black-body with a temperature of the planet's surface (dashed purple line, Fig. 4): the surface temperature equals the effective temperature, $T_{surf} = T_{eff}$. $F_{IR}$ then only depends on $T_{surf}$, which is directly set by the magma ocean, and $F_{IR}$ and $F_{conv}$ decrease rapidly. In the absence of an atmosphere, complete solidification of a fully molten mantle and global magma ocean would theoretically proceed in less than 5000 years (Lebrun et al. 2013; Nikolaou et al. 2019).

Once the volatile species are exsolved out of the melt and reach the surface of the magma ocean, they progressively build-up the overlying atmosphere alongside magma ocean cooling and solidification. When an atmosphere is present, thermal emission to space is buffered by the blanketing effect of the atmosphere heat-trapping greenhouse gases that absorb part of the incoming (net solar plus interior) radiation ($\epsilon < 1$). The surface temperature is then larger than the effective temperature ($T_{surf} > T_{eff}$). $\epsilon$ is inversely correlated with the atmospheric greenhouse effect: the smaller $\epsilon$, the less radiation is emitted at the top of the atmosphere ($F_{IR}$), i.e., the stronger the blanketing effect. By buffering the amount of heat that can be radiated/dissipated to space through the atmosphere ($F_{IR}$), its blanketing effect buffers the magma ocean cooling rate. The surface temperature is then set by the equilibrium between the heat flux transported by convection in the magma ocean to the surface, and the heat flux that can be radiated through the atmosphere, from the surface of the magma ocean to space (e.g., Solomatov 2015).

The thermal opacity of the atmosphere is due to the absorption of radiation by greenhouse gases and is thus primarily a function of the atmospheric mass and composition, which are direct outcomes of magma ocean outgassing (Sects. 3.2.4 and 3.2.5). For instance, H₂O and CO₂ are two powerful greenhouse gases that can delay the complete magma ocean solidification for a few millions to hundred millions of years, depending on their atmospheric concentration (e.g., Hamano et al. 2013; Lebrun et al. 2013; Salvador et al. 2017; Nikolaou et al. 2019). During this phase where the outgoing emissions at the top of the atmosphere are dominated by the convective flux from the molten mantle (i.e., $F_{IR} \approx F_{conv}$), the evolution of the magma ocean and of the atmosphere are thus inextricably coupled and cannot be addressed separately.

Based on the heat fluxes equilibrium, the thermal evolution can be divided in two main phases: the first one, where thermal emissions going out of the atmosphere are primarily controlled by the convective flux coming from the magma ocean (i.e., $F_{IR} \approx F_{conv}$), as described above, and a second phase starting when $F_{conv}$ decreases below the absorbed solar radiation and becomes negligible in front of it, where $F_{IR}$ is dominated by $F_{abs}$ (i.e., $F_{IR} \approx F_{abs} \gg F_{conv}$). The transition between these two phases may be defined as the time where the convective heat flux from the mantle becomes an order of magnitude lower than the absorbed solar flux ($F_{conv} \le 0.1 \times F_{abs}$) and be referred to as the end of the rapid cooling stage ("ERCS"; Salvador et al. 2017).

From this moment, the planet has lost its excess internal heat and has reached global radiative equilibrium with its stellar environment. The molten interior and associated heat

<footnote>temperature the planet would be at if only heated by the host star, i.e., if the planet was at equilibrium with the absorbed radiation.</footnote>
is no longer dominantly driving the thermal evolution. Both the surface temperature and the thermal emissions at the top of the atmosphere are then set by the radiative equilibrium between the net incoming absorbed solar radiation and the outgoing thermal radiation (e.g., Leconte et al. 2013), and are thus mainly controlled by atmospheric-related parameters: the absorbed solar flux and the atmospheric opacity. Note that the surface temperature reached at global radiative equilibrium may be above (e.g., if the planet absorbs a large amount of sunlight) or below the melting point of the surface. The complete solidification of the molten mantle, i.e., the end of the magma ocean phase, is independent of and should be distinguished from the ERCS/global radiative balance.

For a planet located at a given distance from its host star, because of the relatively slow variation of the total incoming solar flux with time (if stellar properties and orbital distance remain relatively stable), all $F_{\text{abs}}$-governing parameters are relatively constant and unrelated to the thermal evolution, besides the Bond albedo (Eq. (1)). Thus, the formation of a water ocean at the surface critically depends on two main atmospheric properties: its Bond albedo and greenhouse effect, both ultimately relying on the surface temperature and pressure prevailing at the ERCS, that are directly inherited from the magma ocean cooling and outgassing sequences.

In that respect, clouds play a vital role. Indeed, they both regulate the amount of solar energy reaching the surface through their albedo (Pluriel et al. 2019), and affect the amount of heat radiated back into space through their greenhouse effect. Because of their potential cooling or warming effect, their presence, properties, location, and distribution may drastically impact the surface conditions reached at the ERCS. However, they remain the major source of uncertainties in current climate models and in future Earth's climate predictions (e.g., Kasting and Catling 2003; Siebesma et al. 2020). In particular, accounting for their time-dependent, 3D spatial distribution, dynamics and microphysical properties to constrain their optical properties and global contribution is highly challenging. Modelling cloud formation and behavior throughout magma ocean cooling and assessing their significance for the early surface conditions suffers from additional complexities due to the prevailing extreme conditions. Different cloud configurations and their implications regarding the surface conditions of Venus at the ERCS and early water ocean formation are further discussed in the following section.

When discussing the outcomes of the magma ocean phase in the next Section, we focus on the aftermath of the evolutionary phase affected by the mechanisms described throughout Sect. 3. This involves the conditions reached at the ERCS (Fig. 12), regardless of whether the mantle has fully solidified or not at the time global radiative balance is reached. Indeed, the subsequent surface conditions and evolution of both the interior and of the atmosphere rely on other processes. Even if the mantle is still molten at the ERCS, its dynamics may significantly differ from that of the pre-ERCS magma ocean convection, since the excess internal energy would have then been lost and a thermal steady-state reached.

# 4 Outcomes of the Magma Ocean Phase and Implications for the Long-Term Evolution of Venus

## 4.1 Surface Conditions and Potential Early Habitability

At the end of the rapid cooling stage, the conditions may allow for liquid water to condense at the surface and enable ocean formation. Water ocean formation essentially requires both the atmospheric water vapor pressure and the temperature at the surface to lay between
<figure><img src="image_14.png" /></figure>

**Fig. 12** Schematic summary of the various surface conditions reached at the End of the Rapid Cooling Stage (ERCS), i.e., when the heat flux coming from the interior becomes negligible compared to the net absorbed stellar flux. From then on, the latter balances the outgoing thermal radiation and this balance mainly controls the climate. The solid lines represent the transitions between the different types of surface conditions, but note that these are not hard limits. The crosses correspond to the ones shown in Figs. 4 and 13 for H₂O- and CO₂-dominated atmospheres, respectively. Note that alternative atmospheric compositions (e.g., reduced atmospheres or desert worlds) would alter the location and shape of the limits separating the different types of planets (see text). From any surface conditions reached at the ERCS and resulting from the magma ocean evolution, Venus may have transitioned to any other states before reaching its present-day conditions (see Fig. 14).

the triple and critical points of water. We describe below which magma ocean evolution scenarios would favor water ocean formation, both early on at the ERCS and later, and scenarios where water ocean formation is unlikely.

**Insufficient Accreted or Outgassed Water** Prior to magma ocean evolution, the amount of water delivered to the planet during the accretion phase may be the first limiting factor for ocean formation. If the planet accreted dry or did not get enough bulk water, water ocean formation at the end of the rapid cooling stage is compromised (uppermost part of Fig. 12). Unless a substantial amount of water is delivered later in history, through a “late veneer” for instance, and temperate conditions are met, water formation is unlikely over the entire planet lifetime (Fig. 14). Yet, as discussed in Sect. 2.2.1, this dry accretion scenario is currently not favored by planetary formation models for Venus. In addition, as discussed in Sect. 2, based on Venus proximity with Earth, their similar density, and its high atmospheric D/H ratio, a substantial, likely Earth-like, early water endowment is the prevailing scenario for Venus today.

As described in Sect. 3, the amount of atmospheric water vapor is a direct outcome of magma ocean cooling and outgassing. If the water vapor mixing ratio of the outgassed atmosphere is too low (i.e., the relative amount of outgassed water is low), insufficient vapor pressure would prevent water saturation pressure to be reached at the surface. This would happen if magma ocean outgassing is not efficient for water or produces a reduced atmosphere. Early ocean formation at the ERCS would then be impossible (uppermost part of Fig. 12). Later ocean formation could still be possible if enough mantellic remnant water is
volcanically outgassed during the long-term evolution of the planet, if atmospheric water is
delivered by late impacts, and/or if the redox state of the mantle or atmosphere evolves and
becomes more oxidized (Fig. 14). Such late oxidation could be the result of volatile cycling
and geo-/photo-chemical evolution, involving atmospheric hydrogen escape and surface ox-
idation processes.

**H₂O-Dominated Atmospheres** Provided there is sufficient atmospheric water at the ERCS, the surface temperature determines whether water vapor saturation pressure can be reached and a water ocean forms. Recall that surface temperature at the ERCS results from the global radiative balance between the net incoming absorbed solar flux, *F*<sub>abs</sub>, and the thermal outgoing flux the planet is able to radiate to space, *F*<sub>IR</sub>. Both fluxes rely on atmospheric state and composition. These are direct outcomes of the magma ocean outgassing and evolution: atmospheric mass, composition, thermal profile, resulting clouds (and distribution), aerosols types and locations.

For steam, H₂O-dominated atmospheres, the existence of the outgoing radiation limit with respect to surface temperature, at about 280 W.m⁻² (dashed red line in Fig. 4), creates two drastically different types of surface conditions at the ERCS (Fig. 12; Hamano et al. 2013; Salvador et al. 2017). If the planet's outgoing thermal flux is lower than the radiation limit (i.e., F<sub>IR</sub> ≈ F<sub>abs</sub> < F<sub>SNL</sub>), the resulting climate should be temperate. Surface temperatures would be below the water critical temperature and allow water ocean formation (e.g., blue crosses in Figs. 4 and 12). Such planets are expected to have a solidified surface at the ERCS and are referred to as "Type I" planets following Hamano et al. (2013) classification (blue area in Fig. 12). For Venus, an early habitable state could be reconciled with the present-day conditions via water loss resulting from later on atmospheric escape (Fig. 14; see Sect. 4.2). Yet, ocean water would first have to be vaporized, reach the upper atmosphere, and photodissociate. The hydrogen would be lost to space, while most of the oxygen would remain. If temperate conditions and oceans are stable, water loss would be less efficient than if water were found mainly in the vapor phase.

Conversely, at the ERCS if the planet absorbs more solar energy than the Simpson-
Nakajima radiation limit (F<sub>IR</sub> ≈ F<sub>abs</sub> > F<sub>SNL</sub>), climate stability can only be achieved at a
surface temperature above T<sub>surf</sub> ≈ 1500 K (e.g., red crosses in Figs. 4 and 12; Abe and
Matsui 1988; Zahnle et al. 1988; Kasting 1988; Hamano et al. 2013; Goldblatt et al. 2013;
Marcq et al. 2017; Salvador et al. 2017). At this temperature, which is above the solidus
temperature of silicates, the planet surface is expected to be molten and able to radiate in
the visible and near-infrared (NIR). It would have an emission peak around 5 µm (Wien
peak), thus allowing emission through the 4 µm water vapor absorption window to balance
the absorbed solar flux and achieve radiative equilibrium. Such molten surface planets at the
ERCS are referred to as "Type II" planets (red area in Fig. 12; Hamano et al. 2013). Because
the planet is at global radiative balance, the surface of type II planets are expected to remain
molten and the magma ocean phase is sustained until there is a decrease of the net absorbed
solar flux or a decrease of the atmospheric water abundance (Fig. 14). Atmospheric water
could be lost via escape processes. The absorbed flux could then decrease owing to the
weakening greenhouse effect or via the formation of reflective clouds triggered by a change
of rotation rate or water condensation in the upper atmosphere.

The critical distance separating Type I and Type II planets is actually equivalent to the
inner edge of the circumstellar habitable zone (IHZ). The latter is defined in relation to
the radiation limit of the runaway greenhouse state and is classically calculated using atmo-
spheric models (e.g., Kasting et al. 1993b; Selsis et al. 2007; Kopparapu et al. 2013; Leconte
et al. 2013; Ramirez 2018). Such models typically start with temperate Earth-like surface
conditions, with a surface water ocean and an H₂O-dominated atmosphere. From this baseline configuration, they vary the surface temperature (or the insolation; e.g., Leconte et al. 2013) to evaluate the atmospheric/climate response. They then calculate the corresponding solar flux needed to sustain the specified surface temperature. Note that this surface temperature variation could result from a change of insolation, absorbed stellar flux, or greenhouse gases concentration. They proceed until the ocean evaporates and a runaway greenhouse state is reached. The corresponding net absorbed and/or emitted critical flux is translated into a critical insolation threshold and orbital distance – this defines the inner edge of the habitable zone.

Compared to those studies, early evolution magma ocean models start with molten surfaces, where the water is outgassed from the interior and first found in the atmosphere in the vapor phase rather than being condensed into an ocean. As soon as enough water is outgassed, these atmospheres are in a runaway-greenhouse-like state. Coupled models then simulate the cooling and solidification of the magma ocean. As the interior flux decreases, their atmospheres evolve toward thermal equilibrium (reached at the ERCS, when the interior flux becomes negligible compared to the absorbed stellar flux), where their outgoing thermal emission balances the absorbed part of the incoming sunlight. The habitability of the planet is then assessed via the likelihood of water ocean formation given the surface conditions reached at the ERCS. Here, the location of the inner edge of the habitable zone is thus evaluated the other way round. They start from hot, uninhabitable conditions. They next evaluate the insolation threshold and corresponding orbital distance at which a stable climatic state (i.e., *F*<sub>IR</sub> ≈ *F*<sub>abs</sub>) is able to produce a water ocean at the surface of the solidified planet.

It is important to emphasize that while the habitable zone boundaries are generally expressed in terms of insolation thresholds and orbital distances from the star, these two parameters only consider the incoming stellar flux *F*<sub>ł</sub>. Yet, the parameter that determines the climate state and associated surface conditions is the net absorbed stellar flux *F*<sub>abs</sub>, where the albedo is critical. Accordingly, a planet of high Bond albedo (e.g., due to a highly reflective cloud cover) may sustain temperate surface conditions and have an early water ocean (type I planet). This is despite being closer to the star than a type II planet of lower albedo and with an incident flux larger than the predicted insolation threshold. Any parameter affecting the planetary albedo may thus dramatically alter the fate of the planet especially if it is located near the edge of the habitable zone, as is the case for Venus (e.g., Hamano et al. 2013). Provided that Venus' orbital parameters have remained stable and accounting for the lower luminosity of the young Sun (e.g., Gough 1981; Bahcall et al. 2001), the amount of absorbed stellar radiation *F*<sub>abs</sub> and associated surface conditions depend upon the Bond albedo (Fig. 12).

**CO₂-Dominated Atmospheres** Similar to IHZ studies, Hamano et al. (2013) type I and II planet classification is based on steam, water-dominated atmospheres. Indeed, the runaway greenhouse occurs in such atmospheres because their main component is both a condensable and thermal absorber species. For atmospheres that are more diluted with respect to their water vapor concentrations (i.e., those whose composition is not water-dominated but non-condensable<sup>8</sup> species-dominated), the strong runaway greenhouse effect of H₂O-dominated atmospheres is buffered. For instance, as the longwave radiative forcing, or thermal absorption, of CO₂ is lower than that of H₂O (e.g., Kiehl and Trenberth 1997), CO₂-dominated atmospheres are more transparent/less opaque to thermal radiation as a result of atmospheric

<footnote n="8"><sup>8</sup>At least for conditions where water would be able to condense.</footnote>
<figure><img src="image_15.png" /><figcaption>**Fig. 13** Outgoing thermal flux emitted at the top of the atmosphere ($F_{IR}$, black line) as a function of surface temperature for a CO₂-dominated atmosphere. Compared to H₂O-dominated atmospheres (Fig. 4), global radiative equilibrium and stable climatic states can be reached at intermediate surface conditions between temperate Type I (e.g., blue cross, where $\alpha = 0.77$) and molten surface Type II (e.g., red cross, where $\alpha = 0.2$) planets. These Type III planets (e.g., orange crosses, where $\alpha = [0.3, 0.5, 0.7]$ from right to left) have solidified at the ERCS ($T_{surf} < T_{solidus}$) but water does not condense at the surface. This either because the atmosphere is too dry and the saturation vapor pressure of water is not reached or because the temperature is too high and above the critical temperature of water ($T_{surf} > 647$ K). The crosses correspond to the ones shown in the upper part of Fig. 12. The orange dot denotes present-day Venus</figcaption></figure>

water vapor dilution and associated lower specific humidity (Salvador et al. 2017). Owning to their increased thermal transparency, CO₂-dominated atmospheres are able to radiate thermally ($F_{IR}$) even above the Simpson–Nakajima limit in response to an increase of temperature or net absorbed solar flux. These CO₂-dominated atmospheres thus maintain radiative balance at intermediate surface temperatures in contrast to H₂O-dominated atmospheres which are thermally opaque. In order to reach radiative balance, H₂O-dominated atmospheres have to reach higher temperatures to radiate again and stabilize their climate. Here the radiation limit of steam H₂O-dominated atmospheres is no longer relevant. The sharp climatic transition and surface temperature jump between type I and type II planets are soften and additional intermediate stable climate states can be achieved (Fig. 13). These climate states can have intermediate surface temperatures, including temperatures greater than that of the critical point of water, where water ocean formation is not possible (orange crosses in Figs. 13 and 12). In addition to a decrease in atmospheric opacity, the decrease of water vapor partial pressure implied by the atmospheric water vapor dilution effect can prevent water ocean formation even below the critical temperature of water. This is the case if the water vapor saturation pressure is not reached at the surface (e.g., lowermost orange cross in Fig. 13). Thus, for CO₂-dominated atmospheres, water ocean formation becomes highly sensitive to the atmospheric volatile concentration. The water vapor mixing ratio can prevent water ocean formation at any orbital distance if it is too low (Fig. 12). At the ERCS, intermediate and stable surface conditions between that of type I and II planets can be achieved where the surface has completely solidified thanks to surface temperatures below the solidus temperature but where no water ocean is formed (Figs. 12, 13 and 14). Planets reaching this state are referred to as “Type III” planets (orange area in Fig. 12; Salvador et al. 2017).
<figure><img src="image_16.png" /></figure>

**Fig. 14** Possible evolution pathways taken by Venus from the last major magma ocean episode to the present day (not to scale). The End of the Rapid Cooling Stage (ERCS) separates the early and long-term evolution and is reached when the heat flux coming from the interior becomes negligible compared to the net absorbed stellar flux ($F_{abs}$; Eq. (1)). From then on, the latter balances the outgoing thermal radiation ($F_{IR}$) and this balance mainly controls the climate. $F_{SNL}$ is the radiation limit of steam atmospheres. Early evolution: Relatively dry accretion or inefficient magma ocean outgassing of water owing to its retention in the interior or a reduced upper mantle would induce low concentrations of water vapor in the atmosphere. This would prevent the formation of water oceans even if the surface has solidified at the ERCS owing to relatively low absorbed fluxes (MO to Type III; orange area of Fig. 12). Water outgassing from the magma ocean would result in temperate conditions at the ERCS if an efficient cloud–albedo feedback operates (MO to Type I; blue area of Fig. 12). If not, regardless of the water content, high absorbed fluxes would induce a molten surface at the ERCS (MO to Type II; red area of Fig. 12). Long-term evolution: Changes of the amount of water vapor in the atmosphere and of the absorbed stellar flux may trigger transitions from one type to another. Atmospheric water loss could be due to atmospheric escape (Sect. 4.2) or to its incorporation into the interior. It could induce the evaporation of the ocean (Type I to III) or the solidification of the surface by weakening the greenhouse effect (Type II to III). Although less likely, volcanic outgassing of CO₂ would have the same effect. Conversely, an increase of the amount of water vapor in the atmosphere through volcanic outgassing or late accretion of water-rich bodies could trigger a late runaway greenhouse (Type III to II) or the formation of water ocean (Type III to I) depending on the absorbed stellar flux. A temperate climate would thus be favored by synchronous formation of reflective clouds on the dayside of the planet, possibly helped by rotation rate changes, but threatened by the brightening Sun. If the atmosphere is already water-dominated, cloud formation would also initiate a temperate climate era (Type II to I) but their dissipation would end it (Type I to II). Note that these are just examples of the possible mechanisms and that the location of the transitions between the different branches are not indicative of their timing

Type III planets may experience post-ERCS habitable periods if the atmospheric water vapor mixing ratio increases enough, through long-term volcanic outgassing for instance, and provided that the absorbed flux remains/decreases below the runaway greenhouse threshold (Fig. 14). If not, a runaway greenhouse would prevent the formation of water oceans and the planet would be desiccated via atmospheric escape.

**Desert Worlds** Abe et al. (2011) modeled the climate of desert worlds with globally limited but locally abundant surface water, also referred to as “land planets”, to assess their habitability. This is an intermediate case between H₂O- and CO₂-dominated atmospheres. Because the tropics of such land planets have very low relative humidities, the air is unsaturated in those regions where longwave radiation can be efficiently emitted above the traditional runaway greenhouse limit. Compared to planets with globally abundant liquid water, land planets thus have a wider habitable zone. They can sustain moderate climates where liquid water remains stable at the poles despite being closer to their host stars. Abe
et al. (2011) suggested that if Venus were such a land planet with a 1 bar N₂-dominated atmosphere with 345 ppm CO₂, it could have remained habitable until as recently as 1 billion years ago.

Zsom et al. (2013) studied a more extreme case of hot desert/dry worlds representative of greenhouse gas-poor atmospheres. Here the atmospheric composition was dominated by a non-greenhouse gas (e.g., N₂) with low relative humidity (~1%), and low CO₂ mixing ratio (10⁻⁴). They showed that the reduced greenhouse effect may bring the inner edge of the habitable zone as close as 0.38 AU from a Sun-like star, for a surface albedo of 0.8. For a more moderate surface albedo of 0.2, it would be 0.59 AU. Note that for such arid planets where the water budget is limited (e.g., Abe et al. 2011), their definition of habitability is not restricted to the formation of a global water ocean. Despite having a water reservoir limited to cold areas such as the poles or the night side (Abe et al. 2011; Menou 2013; Leconte et al. 2013) they also consider a planet habitable when: (i) water is able to precipitate mostly in the form of rain on a large fraction of the planet's surface, and (ii) where the water reservoir is stable on a multi-billion-year timescale. This way, most of the surface water is in liquid form, a large fraction of the planet remains habitable, and the water cycle is not broken (Zsom et al. 2013). While both early and present-day Venus could be located within this extended habitable zone, this particular atmospheric configuration is hard to relate to any early Venusian evolution scenario. While a low relative humidity could be explained by low water delivery, an inefficient or highly reduced magma ocean outgassing, a low CO₂ mixing ratio is hard to reconcile with the present-day atmospheric CO₂ inventory. Indeed, CO₂ is poorly soluble in the magma ocean and likely outgassed early. Otherwise, if C is not outgassed as CO₂, the outgassing of other carbon-bearing reduced species would challenge the restricted atmospheric composition and the absence of other greenhouse gases required in the Zsom et al. (2013) and Abe et al. (2011) calculations.

**Critical Albedo Value** The key to form early oceans under temperate climates at the ERCS is an optimal magma ocean cooling and outgassing sequence, producing enough water vapor in an atmosphere absorbing the right range of solar flux (e.g., Fig. 12). Abe and Matsui (1988) and Kasting (1988) used 1D radiative-convective, cloud-free atmospheric models to simulate the climates and surface conditions associated with hot H₂O–CO₂ atmospheres. They found that if Venus initially accreted a similar amount of water to Earth, a proto-ocean could form on early Venus. With Pollack (1971), they suggested that clouds could play a crucial role in producing early oceans on Venus by increasing the albedo and deflecting part of the incoming sunlight to space.

Salvador et al. (2017) estimated that less than 0.1 Earth water ocean initially dissolved within the early Venusian magma ocean and efficiently outgassed into the atmosphere would be sufficient to form a water ocean at the ERCS. They used the insolation of the young Sun (~70% of its current value; e.g., Gough 1981; Bahcall et al. 2001) while using Venus' present-day geometric albedo (~0.7) and atmospheric CO₂ content (~90 bar). They also found that using an albedo of 0.45 would reflect enough sunlight to form a water ocean at the ERCS if only 0.3 Earth's ocean of water were initially dissolved within the magma ocean and efficiently outgassed (Fig. 12). This is in good agreement with Abe (1993a), who showed that for an albedo of 0.35, early Venus would lie at the critical flux between a habitable and a runaway greenhouse state, indicating that a water ocean would be stable at Venus' surface for a larger albedo (their Fig. 3). More recent modeling by Krissansen-Totton et al. (2021) showed that all transient habitable solutions for early Venus have a Bond albedo larger than 0.4.
**The Importance of Clouds** As noted above clouds might be the critical factor in producing an albedo suitable for temperate surface conditions, by reducing the amount of absorbed sunlight at Venus' distance. Venus' present-day thick sulfuric acid ($H_2SO_4$) cloud cover is responsible for its high albedo, reflecting more than 75% of incoming stellar flux back to space (Moroz et al. 1985; see Titov et al. 2013, for a review). Despite being 30% closer from the Sun, Venus presently absorbs less solar energy than the Earth does: $F_{abs}^{\circ} \approx 157 \text{ W} \cdot \text{m}^{-2}$ (Moroz et al. 1985) versus $F_{abs}^{\oplus} \approx 240 \text{ W} \cdot \text{m}^{-2}$ on average. The corresponding equilibrium temperatures are ~231 K for Venus and 255 K for the Earth (assuming an albedo of 0.75 and 0.29, respectively). Note that the thick cloud layer also constitutes a second infrared opacity source in the Venusian atmosphere (the first being the 92 bars of $CO_2$), and contributes about 140 K to the greenhouse effect (Titov et al. 2013).

Given the flux received from the young Sun at Venus' orbital distance, if early Venus had enough atmospheric water at the ERCS and a high albedo, water ocean formation would have been likely (Fig. 12; Salvador et al. 2017). Several physical mechanisms and associated cloud effects could produce a high enough albedo to allow water oceans to form on early Venus. While maximizing the cooling effect of clouds by neglecting their warming effect, i.e., by assuming that clouds are transparent to IR outgoing radiation, Selsis et al. (2007) estimated that covering 100% and 50% of a planet's dayside with highly reflecting clouds can produce albedos as high as 0.8 and 0.6. This would shift the runaway greenhouse limit and associated inner edge of the habitable zone to an orbital distance of 0.46 AU and 0.68 AU for the current Sun. Such a highly optimistic habitable zone would encompass both present-day and early Venus.

Using a 3D general circulation model with a modern cloud scheme and Earth-like atmospheric compositions, Yang et al. (2014) showed that Venus' slow planetary rotation rate (of about 243 Earth days; e.g., Carpenter 1970; Campbell et al. 2019; Margot et al. 2021) would induce an albedo high enough to support temperate conditions. Indeed, by weakening the Coriolis force and extending daytime illumination compared to faster rotating planets, slow rotation rates promote strong convergence and convection in the substellar region. This produces a large area of optically thick clouds in the most illuminated part of the atmosphere, which greatly increases the albedo and decreases surface temperatures (as first evidenced for tidally locked planets; see Yang et al. 2013). Even at Venus' present-day orbital distance and insolation, this mechanism would sustain low enough surface temperatures to support surface liquid water.

Way et al. (2016) used early Venus' insolation and an Earth-like atmospheric composition to model the climatic history of Venus via 3D GCM simulations. They included a slow rotation rate like Yang et al. (2014), its present-day orbital parameters, modern topography from the Magellan mission, and an ocean volume consistent with the Pioneer Venus measured D/H ratio (Donahue et al. 1982). By modeling the climate dynamics and resulting surface conditions for several hypothetical scenarios, Way et al. (2016) showed that early Venus could have sustained stable water oceans and a temperate climate until as recently as 0.715 Ga ago. The 0.715 Ga was chosen as the approximate time of Venus' global resurfacing event (e.g., McKinnon et al. 1997). Following Yang et al. (2014) and Abe et al. (2011) they demonstrated that the rotation rate, through the cloud-albedo feedback, and the availability/distribution of surface water play a key role in climate circulation and heat redistribution resulting in the possible habitability of ancient Venus (Fig. 14). Extending their previous analysis to a significantly larger parameter space, Way and Del Genio (2020) showed that a shallow water ocean and habitable conditions could have persisted nearly 3 billion years. They speculated that this clement period ended via large igneous provinces formation (LIPs) before the global resurfacing period (lowermost branch of Fig. 14). However, if liquid water
is not initially present at the surface, subsequent habitability is rather unlikely. Hence the importance of the early history of Venus and its magma ocean evolution cannot be understated.

Another important finding regarding the early history and relevant to magma ocean outcomes is that, while early water oceans and temperate climates would be confidently sustained for a few billion years, if liquid water is not initially present at the surface, subsequent habitability and formation of water ocean is likely compromised. It would require to both replenish the atmosphere with water through volcanic outgassing or late accretion and form reflective clouds on the planet's dayside (from type III to type I branch in Fig. 14) while reconciling such scenarios with existing constraints (e.g., Way and Del Genio 2020; Krissansen-Totton et al. 2021). An early enough slow rotation rate and associated highly reflective clouds feedback might then be critical.

At present we have no constraints on early Venus' rotation rate. Its current slow retrograde rotation rate could be a result of a number of processes working together or separately over Venus' lifetime (e.g., Cottereau et al. 2011; Hoolst 2015):

* core–mantle friction (e.g., Goldreich and Peale 1970; Lago and Cazenave 1979; Dobrovolskis 1980);

* solid-body tides (e.g., Correia and Laskar 2003; Hoolst 2015; Way and Del Genio 2020);

* spin–orbit resonance with the Earth (e.g., Goldreich and Peale 1967; Gold and Soter 1969; Bills 2005);

* thermal atmospheric tides (e.g., Gold and Soter 1969; Ingersoll and Dobrovolskis 1978; Dobrovolskis and Ingersoll 1980; Leconte et al. 2015) specific to its dense atmosphere (e.g., Correia and Laskar 2001);

* an impactor (e.g., McCord 1968; Alemi and Stevenson 2006).

In particular, most of these mechanisms depend on the atmospheric thickness, interior structure, or insolation. While insolation was negligible compared to the magma ocean convective flux, the atmosphere was building up and the interior structure was evolving throughout the magma ocean rapid cooling stage. This makes any estimation of the rotation rate at that time and post-ERCS highly challenging.

The cloud–albedo feedback for slowly rotating planets appears to extend the habitable zone to Venus' orbital distance (Yang et al. 2014; Way et al. 2016). Yet such temperate conditions are only possible with a pre-existing water ocean condensed at the surface and an Earth-like, water-poor atmosphere. However, it may not apply to planets with hot and steamy atmospheres. Here water does not condense into water oceans at the surface and is found entirely in the atmosphere, as expected for an efficiently outgassing magma ocean. Under such conditions, 3D GCM simulations by Turbet et al. (2021) demonstrated that water clouds form preferentially on the nightside, while being absent on the dayside. Their result is independent of the planetary rotation speed or day length. Such a day–night cloud asymmetry appears to prevent the efficient cloud–albedo effect at the sub-stellar point found by Yang et al. (2014). The Turbet et al. (2021) result induces strong solar absorption by atmospheric water vapor on the dayside and strong greenhouse effect by clouds (i.e., a net warming effect of clouds) on the nightside. Without the cloud–albedo effect at the substellar point, Turbet et al. (2021) suggested that if water is not first condensed into oceans (as discussed above) Venus would inevitably maintain a runaway greenhouse state from early on (uppermost branch of Fig. 14). High surface temperatures would prevent water oceans from forming at the surface, which would be in agreement with Hamano et al. (2013) cloud-free predictions identifying Venus as a type II planet.
**Limitations and Perspectives** The modeling of Turbet et al. (2021) is more realistic than previous 1D studies in assessing early water ocean formation on Venus under magma ocean-related, hot and steamy conditions. Extensive work yet remains to provide a conclusive statement. Firstly, cloud and atmospheric circulation feedback can vary non-linearly and non-monotonically with the rotation period (Jansen et al. 2019). Turbet et al. (2021) state that the applicability of their results to a wide range of rotation periods and to a slowly rotating Venus should be quantitatively confirmed by a comprehensive sensitivity study. This would also allow for a full characterization of day-night heat transport patterns on hot planets where water is found in the vapor phase in the atmosphere. It would also quantify the atmospheric circulation, climate dynamics, and resulting cloud effects (Noda et al. 2017).

As discussed in Sect. 3, the hot surface temperatures found in the early evolution stages are not ad-hoc conditions: the atmosphere is not an isolated system but instead, its bulk properties result from and are embedded in the coupled magma ocean-atmosphere evolution. Depending on the processes considered, water outgassing efficiency may vary significantly, and the differential outgassing of CO₂ and H₂O may induce additional complexities. To model a realistic early evolution and predict accurate associated surface conditions, such sophisticated 3D GCMs need to be coupled to molten interior models to consider self-consistent outgassing and cooling sequences. Such coupled models could thus account for evolving atmospheric properties, such as composition, surface pressure, and thermal surface boundary conditions, while considering interior-atmosphere feedback and possible non-linearities such as climatic hysteresis and multi-stability (e.g., Abe et al. 2011; Goldblatt 2015; Ishiwatari et al. 2021).

However, if the magma ocean covers the entire surface of the planet its heat flux is likely to be isotropic for most of the rapid cooling stage and would not depend on local time or latitude. The atmosphere would be uniformly and dominantly heated from below, such that atmospheric circulation and associated heat redistribution may not be affected by day-night or latitude-dependent insolation gradients. How the interior flux-controlled climate dynamics would look like in an outgassing atmosphere and how it would transition to a more classic (solar flux-dominated) climate circulation at the ERCS is unknown. In the latter the sunlight becomes the dominant energy source, and the implications for atmospheric circulation patterns and planet surface conditions again remain unknown. These questions will certainly benefit from the ongoing efforts and future improvements of both interior, atmosphere, and coupled numerical models (Sect. 5).

Krissansen-Totton et al. (2021) have developed a sophisticated coupled interior-atmosphere framework accounting for an extensive number of processes. These include geochemical cycling, atmospheric escape, and consistent atmospheric redox evolution, to self-consistently model the thermo-chemical evolution of Venus from the magma ocean stage to present-day. In light of all presently available atmospheric and surface constraints, they show that both habitable and never-habitable histories are possible, and that none can be conclusively ruled out. Indeed, both cases can successfully produce the current dense CO₂-dominated atmosphere with low water and oxygen content. They get consistent ⁴⁰Ar and ⁴He outgassed abundances, and inferred surface heat flow. Importantly, they emphasize that Venus' habitability relies critically on the value of the Bond albedo, which appears to be the main controlling factor. Hence they demonstrate yet again the importance of the cloud-albedo feedback described above.

As it is generally the case for many processes affecting Venus history and evolution, there is a pressing need to update the precision of available constraints to disentangle Venus past. Upcoming missions may provide key in-situ measurements that may significantly help in constraining the likelihood of the different scenarios discussed herein (see Widemann et al. 2023, for an extensive discussion).
## 4.2 Atmospheric Escape and the Fate of Water

A high water vapor content in the early atmosphere of Venus has to be reconciled with its present-day low concentrations of water and oxygen (e.g., Johnson and de Oliveira 2019). It has long been hypothesized that Venus underwent large scale atmospheric escape during its evolution, providing a way to lose its water (e.g., Ingersoll 1969; Rasool and de Bergh 1970; Pollack 1971; Kasting and Pollack 1983). Several mechanisms can be responsible for atmospheric escape and may have operated to various extent throughout Venus evolution (Fig. 14). They include thermal hydrodynamic escape, non-thermal (suprathermal) escape, and mechanical impact erosion that are all discussed below. Note that high energies and temperatures resulting from extreme post-impact conditions may also be responsible for early intense atmospheric escape (Modirrousta-Galian and Korenaga 2023).

### 4.2.1 Hydrodynamic Escape

Part of the water loss could have occurred early during the evolution of the planet (Lammer et al. 2018). At that time, the EUV flux from the Sun was at its highest (Tu et al. 2015), powering hydrodynamic escape of water and possibly heavier species like noble gases and CO₂. Strong EUV heated the upper atmosphere, exciting and photo-dissociating the gas molecules (Lammer 2013). Water being easily dissociated implies that the upper atmosphere was likely dominated by hydrogen (in terms of number of atoms) and oxygen (in terms of mass) (Kasting and Pollack 1983). This upper atmosphere expanded hydrodynamically and “flowed” outward to escape into space. H loss is very efficient (O loss potentially less so; e.g. Chassefière 1996) and can also drag off heavier species (Watson et al. 1981; Erkaev et al. 2014). Hydrodynamic losses are usually estimated by using a simple energy-limited approximation (Watson et al. 1981; Odert et al. 2018).

Mass fractionation can occur as a result of hydrodynamic escape (Hunten 1973; Hunten et al. 1987). Numerous studies have tried to explain the isotopic profile of noble gases through hydrodynamic escape (Sekiya et al. 1980; Hunten et al. 1987; Sasaki and Nakazawa 1988; Zahnle et al. 1990; Pepin 1991; Gillmann et al. 2009; Odert et al. 2018). Simulations have identified scenarios that could reproduce fractionation consistent with current observations. However, the scarcity of data regarding the structure, temperature, and composition of the atmosphere, the energy deposition, the solar wind, and the solar nebula dissipation time implies that the problem is under-constrained, with multiple solutions explaining the available data. In addition, large error bars on the measurements allow for a wide range of acceptable evolutionary scenarios. Finally, the building blocks of the primitive atmosphere themselves may have already been subject to outgassing (Lichtenberg et al. 2019) and escape (Odert et al. 2018) before accretion and thus already fractionated.

The rotation rate of the star is one of the main factors governing EUV emissions (Johnstone et al. 2021). The EUV flux decreases with time as rotation rates decrease (Güdel et al. 1997). During the first 200 Myr, a fast rotating Sun could emit about 500 times higher EUV fluxes than at present-day. A slowly rotating Sun could reach around 30 times present-day EUV fluxes. Most G-stars EUV fluxes converge to a common evolutionary path after 1.5 Gyr. Whether the Sun was a slow, moderate or fast rotator 4+ billion years ago is uncertain. While some clues such as the overall escape intensity or lunar regolith Na and K depletion suggest a slow to moderate rotation rate, the question remains unsolved (Odert et al. 2018; Saxena et al. 2019; Johnstone et al. 2021). Since atmospheric thermal escape depends on the EUV flux heating the upper atmosphere of a planet, uncertainties on EUV fluxes translate into uncertainties in loss rates, with fast stellar rotators leading to more efficient loss.
Loss of water from hydrodynamic escape can be massive but is strongly parameter dependent. The energy available for escape and photodissociation is defined by the EUV flux and therefore, cumulative losses would vary by more than an order of magnitude whether the Sun was a slow or fast rotator. For example, over the first 500 Myr evolution, one Earth ocean equivalent could escape an Earth-like planet orbiting a slow-rotating Sun-like star, compared to 45 Earth oceans for a fast-rotating star (Johnstone 2020). Estimations for Venus are similar, with a total loss ranging from a few (Gillmann et al. 2009) to 15–20 Earth oceans equivalent (Odert et al. 2018). CO₂ can also be lost this way, on the order of 10 bar, for moderate stellar rotators, and up to 100 s of bars for fast rotating stars (Odert et al. 2018), in which case CO₂ is probably photodissociated too. Finally, oxygen escapes together with hydrogen. In the case of fast-rotating stars, the loss of O is efficient and can be so high that most of the initial constituents of water could be lost to space (requiring the loss of tens of Earth oceans; Odert et al. 2018). However, for lower EUV fluxes oxygen loss is less efficient than H escape, which means that oxygen would accumulate in the atmosphere (Gillmann et al. 2009; Wordsworth and Pierrehumbert 2013; Luger and Barnes 2015; Johnstone 2020). The overall escape for planets orbiting slow stellar rotators is weaker but mass fractionation between H and O is more efficient. Considering both aspects, the final remaining oxygen after a hydrodynamic escape phase is of similar order regardless of the rotation rate: around 300–400 bar (Johnstone 2020).

Oxygen accumulation is an interesting problem on Venus, as free oxygen is practically absent from the present-day atmosphere (Johnson and de Oliveira 2019). During the magma ocean phase and the possible extended runaway greenhouse phase, it could have been efficiently trapped and re-injected into the mantle through interaction with the hot surface (Hamano et al. 2013; Wordsworth 2016; Wordsworth et al. 2018), thus oxidizing the interior. If it became the main species in the upper atmosphere, it could also have escaped (Tian 2015). However, those sinks stop with the solidification of the magma ocean and the rise of a volcanically-produced, CO₂-dominated atmosphere (Gillmann et al. 2020).

Later in the evolution, enhanced magmatic production causing extensive resurfacing combined with crustal oxidation could also provide a substantial oxygen sink (Way and Del Genio 2020; Krissansen-Totton et al. 2021), but other later sinks such as non-thermal escape and solid surface oxidation are likely inefficient. It is therefore likely that most of any buildup of oxygen caused by hydrodynamic escape would have been removed by the end of the magma ocean phase, by the time the molten surface completely solidified (Gillmann et al. 2020) or shortly after that (Warren and Kite 2023). While several sink mechanisms can be effective in depleting atmospheric oxygen throughout Venus' early and long-term evolution to match the present-day atmospheric composition, removing water from the atmosphere appears to be more difficult than removing oxygen (Krissansen-Totton et al. 2021). This may confine the end of the habitable period to 1–3 Gyr ago or limit the amount of surface liquid water during that period.

In summary, hydrodynamic escape acts as a potential massive sink of volatiles that could desiccate a planet's atmosphere; but the magnitude of early escape and its consequences for planetary evolution are not governed solely by that sink. Instead they depend on the availability and state of water in the system, which ultimately rely on the interactions with the solidifying magma ocean.

### 4.2.2 Non-thermal Escape

Along with further possible episodes of hydrodynamic escape in a H-rich atmosphere, even after magma ocean solidification, long-term, non-thermal escape will lead to the loss of
water over the last 4 billion years. Over this timescale spanning the entire planet lifetime, it is unlikely that the existence of water oceans limits volatile and water loss, given the relatively fast exchanges between the ocean and the atmosphere. However, the structure of the atmosphere can have large consequences on loss mechanisms. For example, without a functioning cold trap an atmosphere risks a wet stratosphere and is thus prone to efficient water photodissociation and H escape. Kasting et al. (1993b) demonstrated that once an Earth-like planet enters a moist greenhouse state where the stratospheric water vapor mixing ratio is at least $3 \times 10^{-3}$ v/v one may lose an entire Earth's ocean worth of H over ~4.5 Gyr via photodissociation of H$_2$O and hydrogen diffusion-limited escape.

The efficiency of the escape is governed by the atmospheric composition, itself inherited from atmosphere-interior interaction during the magma ocean phase. As an example, a thick CO$_2$ atmosphere outgassed from the magma ocean can reduce the exosphere temperature, and thus lead to slower escape (e.g., Way et al. 2023). This could have buffered the escape of N$_2$ in the CO$_2$-rich atmosphere of Venus and has been suggested to explain the larger amount of N$_2$ in Venus' atmosphere compared to Earth (Lammer et al. 2018).

Interaction between surface minerals and the atmosphere can further affect atmospheric composition both during the magma ocean phase and afterward (see Gillmann et al. 2022, for more details). Fresh surface basalt can trap oxygen by oxidizing iron (e.g., Gillmann et al. 2009, 2020). It has also been suggested that N$_2$ could have been trapped by the magma ocean before being released later on by volcanism (Wordsworth et al. 2018). The specific effects of this process depends on the composition and structure of the atmosphere, as determined by its primordial evolution.

### 4.2.3 Impact Erosion

On growing planets, impact erosion is another possible – yet hard to estimate – atmospheric loss process (e.g., Cameron 1983; Melosh and Vickery 1989; Griffith and Zahnle 1995). In this case, atmospheric escape results from the kinetic energy imparted to the atmosphere by the impact of large objects. When large asteroids or comets collide onto protoplanets with atmospheres, hot vapor plumes and high-speed ejecta resulting from the impact may also provide sufficient energy for part of the atmosphere to escape and be lost to space (e.g., Melosh and Vickery 1989; Zahnle 1990; Ahrens 1993). For giant impacts atmospheric escape can also be caused by subsequent global ground motion (e.g., Genda and Abe 2003, 2005; Schlichting et al. 2015).

Quantitative estimates for impact-induced atmospheric escape have been proposed by Vickery and Melosh (1990), Newman et al. (1999), Shuvalov and Artemieva (2002). Further realistic numerical simulations have been developed by Svetsov (2007) and Shuvalov (2009), who considered the cratering flow induced by impacts on Earth and Mars. Escaping efficiency generally depend on properties such as impactor sizes, impact velocities and angles of impact. These rely on planetary accretion scenarios. The size of impactors typically increases with time as planetesimals grow and would favor impact-induced atmospheric erosion. Yet the frequency of impact decreases with time, which buffers net escaping efficiency.

Atmospheric properties, and in particular density, also affect impact-induced erosion efficiency. For a given impact low density tenuous atmospheres are prone to efficient impact-induced erosion. However, when impactors enter dense atmospheres, such as the ones typically expected for type II planets, aerial burst and projectile fragmentation upon entry may enhance atmospheric erosion (Shuvalov et al. 2014).

Overall, impact-induced atmospheric erosion efficiency and consequences on atmospheric evolution result from a subtle balance between erosion and atmospheric replenishment through impact-induced degassing. It strongly depends on the timing and timescale of
giant impacts relative to that of magma ocean solidification and outgassing. Any conclusive estimation assessing its importance is challenged by the large uncertainties regarding how multiple magma ocean events may be embedded into a bombardment history.

While EUV-driven hydrodynamic escape on early Venus would have (weakly; Kasting and Pollack 1983; Johnstone 2020) contributed to the D/H fractionation, impact erosion does not cause isotopic fractionation because the atmosphere escapes *en masse* in this mechanism. Compared to other flux-triggered escape mechanisms, impact erosion is not sensitive to the presence of a magnetic field. Erosion processes could have been important to set absolute atmospheric abundances (Sakuraba et al. 2019; Gillmann et al. 2020). However, in the presence of condensed reservoirs like liquid water, impact erosion during the late accretion could have affected the atmospheric elemental composition by favoring the escape of inert gases from the atmosphere (Sakuraba et al. 2019). Thus the effect of impact erosion on isotopic composition and elemental abundance is tightly linked to both the accretional history and thermal evolution, and therefore remains hard to assess.

## 4.3 Initial Conditions for the Long-Term Evolution of the Interior

### 4.3.1 Water, Mantle Properties and Evolution

Magma ocean outgassing efficiency and oxidation state are responsible for the water inventory left inside the planet. Atmospheric radiative balance and resulting circulation, escape processes, atmosphere-surface interactions, and volcanic outgassing govern the surface water inventory once the surface has solidified (see Gillmann et al. 2022, for an extensive discussion). The different magma ocean evolution pathways and outcomes discussed above are associated with a broad diversity of scenarios regarding water distribution between the planetary interior, the atmosphere, and the amount lost to space (Fig. 14). Whether Venus' mantle is completely water-depleted at the ERCS and left dry for its long-term evolution, partially depleted, or water-rich remains unclear. Yet, the amount of mantellic water inherited from magma ocean evolution and its distribution would strongly influence the long-term evolution and surface conditions of the planet, by affecting both the atmosphere and the mantle.

For instance, water in the mantle lowers the melting temperature (e.g., Hirschmann 2006; Ni et al. 2016), thus possibly favoring mantle melting and triggering volcanism and volcanic outgassing. If a substantial amount of water is supplied to the atmosphere through post-ERCS volcanic outgassing while the planet is habitable at ERCS, it may trigger a runaway greenhouse. This could lead to complete vaporization of the ocean followed by water photodissociation and hydrogen loss in the upper atmosphere, thus sterilizing the planet and making it uninhabitable. If the magma ocean outgassing efficiency of water were low (e.g., Hier-Majumder and Hirschmann 2017; Miyazaki and Korenaga 2021; Salvador and Samuel 2023), there may not have been enough water to form an ocean at the ERCS. Yet post-ERCS volcanic outgassing may supply enough water for clouds to form in the upper atmosphere, increase the albedo, and possibly create transient temperate conditions suitable for water ocean formation (from type III to type I branch in Fig. 14). If Venus were a faster rotator early on, the decrease of its planetary rotation rate could have helped in the formation of reflective clouds. On the other hand, a decrease in water outgassing rate associated with a steady loss of atmospheric water would slow down atmospheric replenishment and could result in thinner and dissipating clouds (Bullock and Grinspoon 2001). Cloud dissipation would induce a decrease in the Bond albedo and an increase in the absorbed solar flux and surface temperature. This could trigger a runaway greenhouse and vaporize any existing water ocean, making Venus exit a temperate climate (from type I to type II branch in Fig. 14).
Water also decreases mantle viscosity (e.g., Lange 1994) which in turn controls the rhe-
ology and convective dynamics of the interior (e.g., Karato 2015). Seismic wave propaga-
tion and mantle electrical conductivity are also affected by the mantellic water content (see
Karato 2015, for a review). The spatial distribution of mantellic water and potential vertical
and horizontal variations could then induce local changes of mantle properties and possi-
bly lead to very different rheological behaviour and tectonic regimes (e.g., Korenaga 2011).
The low viscosity layer under the stiff lithosphere, i.e., the asthenosphere, is thought to re-
sult from the presence of localized volatiles in Earth's mantle. This could be sustained by
long-term volatile recycling (Richards and Lenardic 2018) and may promote plate tectonics
on Earth (Bunge et al. 1996; Richards et al. 2001). Its absence on modern Venus (inferred
from gravity/topography; e.g., Kiefer et al. 1986) together with the dry conditions at the sur-
face have been historically invoked to explain the lack of modern Earth-style plate tectonics
(Bercovici et al. 2000).

Indeed, the state of water at the planetary surface has crucial implications for the mantle convective regime. The presence or absence of liquid water at the planetary surface affects the rheological behavior of the lithosphere, lithosphere–mantle lubrication, upper mantle hydration, and plate bending (Grevemeyer et al. 2018). These may all influence subduction initiation, sustainability, and the prevailing tectonic regime (Regenauer-Lieb et al. 2001; Gerya et al. 2008; Bercovici and Ricard 2014; Korenaga et al. 2017; Stern 2018; Westall et al. 2023). In turn, those differences that are inextricably inherited from the magma ocean evolution affect magmatic and tectonic processes throughout the entire thermochemical evolution of the planet (e.g., Smrekar et al. 2007; Stamenković and Breuer 2014). This has implications for the mantle convection regime (e.g., Weller and Kiefer 2020), thermal history, volatile redistribution (e.g., Korenaga 2017) and outgassing (e.g., Driscoll and Bercovici 2013), that must all ultimately match present-day conditions (see Rolf et al. 2022; Gillmann et al. 2022, for reviews).

4.3.2 Late Impacts

After the end of the hypothetical last global magma ocean phase caused by the final giant im-
pact (or Moon-forming impact in the case of Earth), a number of subsequent and additional
large impacts may have occurred (Rubie et al. 2015), during the so-called “late accretion”.
The highly siderophile elements in Earth’s mantle could be explained by such collisions
(Chyba 1991). If they occurred, they also certainly affected water distribution (Sakuraba
et al. 2019, 2021). As discussed previously, large impacts could have opposite effects on the
planet’s atmosphere depending on the balance between atmospheric erosion and replenish-
ment (e.g., Pham et al. 2011). Large collisions could also cause widespread melting of the
mantle of the target body and deplete its shallow layers through subsequent degassing of the
molten parts (see Gillmann et al. 2022).

In cases where the impactor is not fully vaporized upon impact, the collision could also
inject water-bearing material from the impactor into the impacted mantle. The nature of the
material, as well as the portion of the total water inventory delivered to Venus during this
late accretion era are still debated. It has been suggested that significant amounts of water
could be delivered to a planet's surface and/or mantle through these late impacts (Albarede
2009). On the other hand, recent studies and Earth-based isotopic data imply that most of
a terrestrial planet's water inventory is already accreted by the end of its main accretion
phase (e.g., Gillmann et al. 2020), and that late accretion is mostly composed of volatile-
poor material (e.g., Fischer-Gödde and Kleine 2017; Dauphas 2017). Depending on the
composition of the impactors and on how they merge with the target (e.g., Itcovitz et al.
2022; Citron and Stewart 2022), the oxidation state of both the atmosphere and mantle could be significantly affected, with implications for prebiotic chemistry (Sect. 3.2.5 and Table 2). Late collisions could also have affected the mantellic convection style of the planet, since impacts could favor lithospheric damage and mobility, and thus trigger subduction (Gillmann et al. 2016; O'Neill et al. 2017; Borgeat and Tackley 2022).

### 4.3.3 Interior-Atmosphere Volatile Exchanges: The Carbonate-Silicate Cycle

After the magma ocean has fully solidified, solid-state convection takes over in mixing the entire mantle. It is most likely already in place in the solid-state part of the mantle while the upper molten mantle continues to cool down (e.g., Maurice et al. 2017; Ballmer et al. 2017). It produces partial melting, and ultimately volcanism and outgassing, thereby bringing water and other volatiles to the surface while locally depleting the mantle. The convection regime of the mantle thus determines the specifics of the volatile exchanges (see Rolf et al. 2022; Gillmann et al. 2022) and is therefore thought to play a major role in how young planets could branch in or out of a habitable state (Fig. 14). Long-term climate stability is required to maintain habitability throughout eons and is believed to rely on specific interior-atmosphere volatile cycling such as the critical carbon cycle and associated CO₂-climate feedback (e.g., Walker et al. 1981; Kasting et al. 1993b; Kasting and Catling 2003; Ramirez 2018).

On Earth, to compensate for the increase in surface temperature due to the brightening Sun, long-term habitability may have required quick removal of most of the early atmospheric CO₂ outgassed during the magma ocean phase (or delivered to the atmosphere by other means), thus reducing the greenhouse effect. Interaction with the surface and interior of the planet (and convection regime) would be involved in the process. The mechanism is not yet understood, given the significant differences between the conditions at that time and at present-day. Notably, the higher temperatures of a thicker atmosphere or the lack of modern-day plate tectonics. The latter plays a major role in the present-day carbon cycle and volatile return flux from the atmosphere into the Earth's interior.

The carbon cycle regulates the atmospheric concentration of CO₂ and has several different parts. The most important one in terms of long-term climate ($t > 10^6$ years) is the inorganic carbonate-silicate cycle. It results from slow interactions of atmospheric CO₂ with the crustal rock reservoir (e.g., Holland 1978; Walker et al. 1981; Kasting et al. 1993b; Kasting and Catling 2003). Dissolution of atmospheric CO₂ into liquid water drives the cycle. CO₂ is first dissolved into rainwater to form carbonic acid that dissolves continental silicate rocks over time. The products of such silicate weathering, including calcium ($Ca^{2+}$), magnesium ($Mg^{2+}$), and bicarbonate ($HCO_3^-$) ions, flow within streams and rivers into the ocean. There they react with more ocean-dissolved atmospheric CO₂ to precipitate as carbonate minerals. Those carbonates deposit and accumulate on the seafloor where they are buried in sediments. Their subduction, with that of continental carbonates and carbonatized oceanic basalt, injects carbon into the mantle (e.g., Sleep and Zahnle 2001). At depth, high temperatures and pressures force carbonate minerals to recombine with SiO₂ to reform silicate minerals while releasing CO₂. Following this so-called carbonate metamorphism, the released CO₂ is eventually volcanically outgassed and thus re-enters the atmosphere, therefore closing the cycle.

Because evaporation (and hence, precipitation) and chemical reaction rates rise with surface temperature, silicate weathering rates increase with increasing surface temperatures. This consumes more atmospheric CO₂, and buffers the rise of surface temperature. Conversely, atmospheric CO₂ consumption by silicate weathering decreases when surface temperatures fall, while volcanically-outgassed atmospheric CO₂ concentrations increase and
counteract falling temperatures. This carbonate–silicate cycle thus contains a negative feedback regulating surface temperatures and atmospheric CO₂ concentrations. It is responsible for long-term climate stability (e.g., Walker et al. 1981; Sleep and Zahnle 2001; Kasting 2019).

If ancient Venus had liquid water, emerged lands (to allow silicate weathering), and an initially CO₂-dominated atmosphere, the carbonate–silicate cycle may have been in place, therefore stabilizing a long-term temperate climate (Way and Del Genio 2020). Via this cycle, Venus' atmosphere could have evolved toward a more Earth-like atmospheric composition (i.e., CO₂-poor) and maintained a stable temperate climate against the brightening Sun. In addition, temporarily sequestering CO₂ in carbonates through an effective carbonate–silicate cycle permits elevated H₂O loss before CO₂ is volcanically outgassed and returned to the atmosphere, which is key to recover the modern Venusian atmospheric composition from habitable scenarios (Krissansen-Totton et al. 2021).

Yet, the existence and efficiency of an early carbonate–silicate cycle on Venus strongly relies on its mantle dynamic regime and associated convection/tectonic style. Subduction from an active/mobile-lid regime (possibly plate tectonics) would allow for the complete cycle to operate. Other non-classical tectonic signatures of convective regimes, such as a post-magma ocean, non-plate tectonic, sluggish subduction may be alternative ways of injecting CO₂ into the mantle and removing it from the atmosphere (Foley et al. 2014). On the other hand, a stagnant lid regime, possibly operating today on Venus (e.g., Smrekar et al. 2007), limits the magnitude of any recycling of atmosphere/surface species into the mantle. However, even in this regime, progressive burial of material by successive lava flows could ultimately allow temporary storage of volatiles, or even a limited return flux of material into the mantle, provided the water-bearing minerals are not destabilized by the increasing pressure and temperature conditions before delamination (Höning et al. 2021).

Thus, the present-day stagnant lid regime likely prevents significant incorporation of CO₂ into the mantle and could even be responsible for its accumulation into the atmosphere through long-term volcanism (e.g., Way and Del Genio 2020; Krissansen-Totton et al. 2021; Gillmann et al. 2022). However, it is clear that terrestrial planets, including Earth itself, experience different tectonic styles through the eons (e.g., Stern 2018; Spencer et al. 2021), indicating that other mantle convective regimes certainly prevailed in Venus' past. This could allow for a transient effective carbonate–silicate cycle under a habitable climate. Yet, for both planets, the various convective regimes that have been in place, their relative timing and transition time scales and the magnitude of associated volatile exchanges remain unclear (e.g., Stern 2018).

# 5 Perspectives and Future Research Directions

Many parameters and processes with direct or indirect implications for the magma ocean phase and evolution remain highly unconstrained. The influence of some of them has not even been assessed yet. They concern both the molten interior and the outgassed atmosphere themselves, but also include external and indirect factors such as the planet's early environment and history.

**Accretion Sequence and Stellar Environment** The magma ocean phase is not an isolated process: it is inextricably embedded into the accretion sequence and related to the evolution of the stellar environment. To provide a more accurate understanding of the early evolution
of rocky planets and implications for their habitability and long-term evolution, magma ocean models should be coupled to stellar evolution and planetary formation models.

In particular, planetary formation models would provide self-consistent constraints regarding volatile delivery timing, type, and budget (e.g., Morbidelli et al. 2012; Li et al. 2016; Burger et al. 2020; Venturini et al. 2020). They would also provide the frequency and energetics of impacts, and avoid making implicit assumptions regarding number occurrence of magma oceans, timing, initial depth, thermal state (e.g., Nakajima et al. 2021), and evolving chemical constituents abundance and distribution (e.g., Maas et al. 2021; It-covitz et al. 2022; Citron and Stewart 2022). In particular, the effect of late giant impacts, that may affect volatile species and melt redistribution, atmospheric and mantle oxidation states, atmospheric erosion or replenishment (e.g., Pham et al. 2011; Modirrousta-Galian and Korenaga 2023), would be worth systematically assessing.

Stellar evolution models would allow for a more realistic treatment of upper atmospheric properties, including photochemistry and escape (e.g., Airapetian et al. 2020). This may in turn affect the heat flux balance and resulting climate stability, dynamics, and circulation, as well as atmospheric volatile abundance and oxidation state.

**Molten Interior** Regarding the mechanisms at play within the molten interior, many fluid dynamics aspects of terrestrial magma oceans emphasized in Solomatov (2000) remain poorly understood. They include the mode of crystallization (fractional vs equilibrium) resulting from the competition between crystals settling and re-entrainment, the convective regime or the effect of rotation (Maas and Hansen 2015, 2019). Additional complexities may arise from the convection in a multi-phase system (Boukaré and Ricard 2017), or spatial and time variations of melt and crystal properties such as density, viscosity, crystals size and shape, or chemical affinity. In that respect, magma ocean numerical models could significantly benefit from advances in characterization of material properties and behaviors at magma ocean extreme conditions performed by laboratory experiments.

The oxidation state of the molten mantle is also highly unconstrained. It is influenced by the timing, location, extent, and fashion of metal-silicate separation and how it may evolves in space and time. Yet it is highly influential regarding the partitioning behavior of chemical elements and the identity of outgassed volatile species.

Some possibly critical physical aspects of magma ocean outgassing have been poorly studied. For example, the processes of bubble formation, nucleation, and ascent; and the crystal-melt-gas partitioning and chemical affinity of many volatile species at magma ocean relevant conditions remain uncertain. Ingassing processes are generally not considered in magma ocean studies. Yet, how, when, which, and how much volatile species could be re-incorporated into the melt and then into the mantle may alter many aspects of the early and long-term evolution.

The thermo-chemical conditions at the base of the molten mantle, the interaction with the underlying metallic core (Foley and Driscoll 2016), and the potential existence of a basal magma ocean (Labrosse et al. 2007; O'Rourke 2020) have also received little attention in the framework of magma ocean-atmosphere evolution modeling. Yet, all of these processes may significantly affect the convective dynamics, outgassing, heat transfer, dynamo generation, and chemical differentiation of the solidifying mantle, and their relative influence remains to be quantified.

**Long-Term Evolution of the Interior** Addressing the subsequent long-term evolution of the planet requires considering the outcomes of the early molten evolution as potential initial states. Indeed, considering the surface conditions, the heat budget, and the distribution of
volatiles resulting from the magma ocean evolution would help constrain the solid-state mantle convective regime, and the sustainability of possible habitable climates. Furthermore, the transition from the magma ocean to the solidified mantle may significantly affect the post-magma ocean mantellic convective regime and the long-term evolution of the planet (Maurice et al. 2017; Ballmer et al. 2017; Agrusta et al. 2019; Bolrão et al. 2021). In particular the transition to a global solid-state convecting mantle can be affected by the coexistence of convective layers of different rheological behavior, i.e., one melt-dominated and another crystal-dominated, and how they interact. Coupling the highly influential magma ocean evolution with subsequent solid-state mantle convection models would thus help reconcile the modelled evolution paths with the present-day observed constraints, allowing one to assess the likelihood of different evolutionary pathways (e.g., Gillmann et al. 2022).

**Atmospheric State and Properties** Planets are complex systems and their evolution results from the strong interaction between the different planetary reservoirs. Understanding their evolving surface conditions and determining their potential past habitability demand to account for both atmospheric and interior processes.

As discussed earlier, the evolving Bond albedo of Venus and resulting absorbed sunlight is one of the most important parameters to solve its potential habitability. Yet, the contribution of clouds remains poorly constrained and assessing the effect of realistic clouds remains a key challenge for atmospheric modeling. In particular, microphysical and optical properties of aerosols, including photochemical hazes and others cloud condensation nuclei, as well as their time-dependent 3D spatial distribution are poorly constrained, and even more uncertain under extreme magma ocean conditions.

The occurrence of silicate vapor atmospheres after giant impacts is expected but their behavior and how they affect the thermo-chemical state of the planet is unknown. The resulting cloud behaviour, heat redistribution, climate circulation and escape post-impacts, changes in atmospheric composition, oxidation state throughout the magma ocean cooling, as well as the climatic transition from an interior- to a sunlit-heated atmosphere are all poorly understood. Further coupling between sophisticated interior outgassing and thermal evolution models with 3D climate models are required to provide a self-consistent scenario. Yet the development of such coupled models is hobbled by our understanding of these processes and by current computational capabilities. For now, a feasible and promising avenue would be to use available parameterized models to conduct sensitivity studies and assess the relative influence of each of these processes.

**Observational Constraints and Future Missions** In addition to these modeling shortcomings, our understanding of Venus history and present state is challenged by the lack of in-situ measurements as well as by important uncertainties in existing observations. Along with the aforementioned future research directions, forthcoming planned Venus missions are expected to significantly improve our comprehension of Venus' past evolution and present state. How these missions are expected to address key science questions regarding Venus evolution is discussed in Widemann et al. (2023, this issue).

Crucial measurements include elemental abundances and isotopic composition of noble gases (He, Ne, Ar, Kr, Xe), and stable isotopes (C, H, O, N, S) in the atmosphere. These are well suited to track outgassing throughout the coupled interior-atmosphere evolution (see Table 1 in Baines et al. 2013). For a thorough discussion see Avice et al. (2022, this collection). As an example, hydrogen isotopic measurements may provide valuable insight into the primordial atmospheric composition and associated early mantle oxidation state (Pahlevan et al. 2019).
Regarding planetary formation, tungsten isotopic composition can be used to constrain the timing of core formation and planetary growth rate (e.g., Zahnle et al. 2007). In particular, because W is moderately siderophile and Hf is lithophile, Hf/W ratios are strongly fractionated by core formation. The $^{182}$Hf-$^{182}$W chronometer can then be used to assess planetary formation time-scales that ultimately relate to the energetic of accretion and thus have direct implications regarding the timing of the magma ocean phase, its initial depth and spatial extent. Constraints on core formation timing can be used to infer the depth and timing of metal-silicate separation. They would also infer the resulting molten mantle oxidation state and hence, that of the outgassed volatile species.

As discussed throughout the chapter, water (and its distribution) is a key element for early planetary evolution, but it is also highly influential over the entire planet's lifetime. A present-day signature of the evolution path taken could be the amount of remaining water in the mantle. The water content of the mantle affects its properties, the resulting mantle dynamics, rheology, tectonic style, melting behavior, and outgassing. It also affects the surface composition and mineralogy. Any constraint on these parameters could be in-turn used to inform the amount of mantellic water associated with the interior state, thus providing indirect hints of the past and of the evolutionary pathway. Surface mineralogy measurements could similarly indicate what conditions prevailed by the time ancient rocks or mineral inclusions have been put in place.

Finally, together with future missions dedicated to Venus (e.g., Widemann et al. 2023, this collection), the expanding field of rocky exoplanets detection and characterization is key to improve our general understanding of planetary formation, evolution, and habitability, that will in turn inform Venus' evolutionary history and help us unveil the potential habitable past of our closest planetary neighbor (see Way et al. 2023, this collection).

## 6 Conclusion

Given the strong coupling between all planetary reservoirs, the magma ocean stage has critical implications for terrestrial planet evolution and habitability. Importantly, it determines the initial chemical and thermal state that will dictate the pathways taken by the planet during its entire history. In addition to being a required ingredient for the emergence and development of life, water abundance and distribution between the planetary layers influences many of the processes at play. Its partitioning is the result of magma ocean crystallization and is of primary importance. The present-day dichotomy between Earth and Venus surface conditions and habitable state might be directly inherited from the cooling and solidification of the coupled magma ocean-atmosphere system. If not, the latter remains the determining factor by setting the initial conditions for the long-term evolution of the planet.

Many uncertainties, unconstrained processes and associated parameters still exist and need further investigation in the coming years to build a consistent picture of the earliest stages of planetary evolution. Combined with interdisciplinary modeling efforts, future measurements of Earth's twin planet may provide significant clues to the early mechanisms at play. They could also shed light not only on Venus' and Earth's distant pasts, but also improve our understanding of what makes a planet habitable and how to search for life elsewhere in the Universe.

**Acknowledgements** The authors thank the anonymous reviewer for their comments who helped us to greatly improve the manuscript. The authors also thank Tilman Spohn and team members of the International Space Science Institute in Bern for hosting the "Venus: Evolution through Time" workshop. AS also warmly thanks them for inviting him as a visiting scientist. AS gratefully acknowledges support from NASA's Habitable
Worlds Program (No. 80NSSC20K0226). MJW acknowledges support from the GSFC Sellers Exoplanet Environments Collaboration (SEEC) and ROCKE-3D: The evolution of solar system worlds through time, funded by the NASA Planetary and Earth Science Divisions Internal Scientist Funding Model. Work by C.G. was carried out within the framework of the NCCR PlanetS.

**Funding** Open Access funding enabled and organized by Projekt DEAL.

**Declarations**

**Competing Interests** The authors have no conflict of interest to declare that are relevant to the content of this article.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

**References**

Abe Y (1993a) Physical state of the very early Earth. Lithos 30(3-4):223-235. https://doi.org/10.1016/0024-4937(93)90037-D

Abe Y (1993b) Thermal evolution and chemical differentiation of the terrestrial magma ocean. In: Takahashi E, Jeanloz R, Rubie D (eds) Evolution of the Earth and planets. AGU, Washington DC, pp 41–54. https://doi.org/10.1029/GM074p0041

Abe Y (1997) Thermal and chemical evolution of the terrestrial magma ocean. Phys Earth Planet Inter 100(1-4):27–39. https://doi.org/10.1016/S0031-9201(96)03229-3.

Abe Y, Matsui T (1985) The formation of an impact-generated H₂O atmosphere and its implications for the early thermal history of the Earth. J Geophys Res, Solid Earth 90(S02):545–559. https://doi.org/10.1029/JB090iS02p0C545

Abe Y, Matsui T (1988) Evolution of an impact-generated H₂O-CO₂ atmosphere and formation of a hot proto-ocean on Earth. J Atmos Sci 45(21):3081–3101. https://doi.org/10.1175/1520-0469(1988)045<3081:EOAIGH>2.0.CO;2

Abe Y, Ohtani E, Okuchi T, Righter K, Drake M (2000) Water in the early Earth. In: Canup R, Righter K et al (eds) Origin of the Earth and Moon. University of Arizona Press, Tucson, pp 413–433

Abe Y, Abe-Ouchi A, Sleep NH, Zahnle KJ (2011) Habitable zone limits for dry planets. Astrobiology 11(5):443–460. https://doi.org/10.1089/ast.2010.0545

Abelson PH (1966) Chemical events on the primitive Earth. Proc Natl Acad Sci 55(6):1365–1372. https://doi.org/10.1073/pnas.55.6.1365

Agrusta R, Morison A, Labrosse S, Deguen R, Alboussiére T, Tackley PJ, Dubuffet F (2019) Mantle convection interacting with magma oceans. Geophys J Int 220(3):1878–1892. https://doi.org/10.1093/gji/ggz549

Ahrens TJ (1993) Impact erosion of terrestrial planetary atmospheres. Annu Rev Earth Planet Sci 21(1):525–555

Airapetian VS, Glocer A, Gronoff G, Hébrard E, Danchi W (2016) Prebiotic chemistry and atmospheric warming of early Earth by an active young Sun. Nat Geosci 9(6):452–455. https://doi.org/10.1038/ngeo2719

Airapetian VS, Barnes R, Cohen O, Collinson GA, Danchi WC, Dong CF, Del Genio AD, France K, Garcia-Sage K, Glocer A, Gopalswamy N, Grenfell JL, Gronoff G, Güdel M, Herbst K, Henning WG, Jackman CH, Jin M, Johnstone CP, Kaltenegger L, Kay CD, Kobayashi K, Kuang W, Li G, Lynch BJ, Lüftinger T, Luhmann JG, Maehara H, Mlyczak MG, Notsu Y, Osten RA, Ramirez RM, Rugheimer S, Scheucher M, Schlieder JE, Shibata K, Sousa-Silva C, Stamenković V, Strangeway RJ, Usmanov AV, Vergados P, Verkhoglyadova OP, Vidotto AA, Voytek M, Way MJ, Zank GP, Yamashiki Y (2020) Impact of space weather on climate and habitability of terrestrial-type exoplanets. Int J Astrobiol 19(2):136–194. https://doi.org/10.1017/S1473550419000132
Albarede F (2009) Volatile accretion history of the terrestrial planets and dynamic implications. Nature 461(7268):1227-1233

Alemi A, Stevenson D (2006) Why Venus has no Moon. In: AAS/division for planetary sciences meeting abstracts #38, AAS/division for planetary sciences meeting abstracts. p 07.03

Altwegg K, Balsiger H, Bar-Nun A, Berthelier JJ, Bieler A, Bochsler P, Briois C, Calmonte U, Combi M, De Keyser J, Eberhardt P, Fiethe B, Fuselier S, Gasc S, Gombosi TI, Hansen KC, Hässig M, Jackel A, Kopp E, Korth A, LeRoy L, Mall U, Marty B, Mousis O, Neefs E, Owen T, Reme H, Rubin M, Semon T, Tzou CY, Waite H, Wurz P (2015) 67P/Churyumov-Gerasimenko, a Jupiter family comet with a high D/H ratio. Science 347(6220):3. https://doi.org/10.1126/science.1261952

Amelin Y, Lee DC, Halliday AN, Pidgeon RT (1999) Nature of the Earth's earliest crust from hafnium isotopes in single detrital zircons. Nature 399:252 EP. https://doi.org/10.1038/20426

Anders E (1989) Pre-biotic organic matter from comets and asteroids. Nature 342(6247):255-257. https://doi.org/10.1038/342255a0

Andrault D (2019) Thermodynamical constraints on the crystallization of a deep magma-ocean on Earth. C R Géosci. https://doi.org/10.1016/j.crte.2018.06.003

Andrault D, Bolfan-Casanova N, Nigro GL, Bouhifd MA, Garbarino G, Mezouar M (2011) Solidus and liquidus profiles of chondritic mantle: implication for melting of the Earth across its history. Earth Planet Sci Lett 304(1-2):251-259. https://doi.org/10.1016/j.epsl.2011.02.006

Andrault D, Petitgirard S, Lo Nigro G, Devidal JL, Veronesi G, Garbarino G, Mezouar M (2012) Solid-liquid iron partitioning in Earth's deep mantle. Nature 487(7407):354-357. https://doi.org/10.1038/nature11294

Andrault D, Monteux J, Bars ML, Samuel H (2016) The deep Earth may not be cooling down. Earth Planet Sci Lett 443:195-203. https://doi.org/10.1016/j.epsl.2016.03.020

Andrault D, Bolfan-Casanova N, Bouhifd MA, Boujibar A, Garbarino G, Manthilake G, Mezouar M, Monteux J, Parisiades P, Pesce G (2017) Toward a coherent model for the melting behavior of the deep Earth's mantle. Phys Earth Planet Inter 265:67-81. https://doi.org/10.1016/j.pepi.2017.02.009

Andrews SM, Huang J, Pérez LM, Isella A, Dullemond CP, Kurtovic NT, Guzmán VV, Carpenter JM, Wilner DJ, Zhang S, Zhu Z, Birnstiel T, Bai XN, Benisty M, Hughes AM, Öberg KI, Ricci L (2018) The disk substructures at high angular resolution project (DSHARP). I. Motivation, sample, calibration, and overview. Astrophys J Lett 869(2):L41. https://doi.org/10.3847/2041-8213/aaf741

Armitage PJ, Eisner JA, Simon JB (2016) Prompt planetesimal formation beyond the snow line. Astrophys J Lett 828(1):L2. https://doi.org/10.3847/2041-8205/828/1/L2

Armstrong LS, Hirschmann MM, Stanley BD, Falksen EG, Jacobsen SD (2015) Speciation and solubility of reduced C-O-H-N volatiles in mafic melt: Implications for volcanism, atmospheric evolution, and deep volatile cycles in the terrestrial planets. Geochim Cosmochim Acta 171:283-302. https://doi.org/10.1016/j.gca.2015.07.007

Armstrong K, Frost DJ, McCammon CA, Rubie DC, Ballaran TB (2019) Deep magma ocean formation set the oxidation state of Earth's mantle. Science 365(6456):903-906. https://doi.org/10.1126/science.aax8376

Asimow PD (2018) Chap. 15 - Melts under extreme conditions from shock experiments. In: Kono Y, Sanloup C (eds) Magmas under pressure, vol 15. Elsevier, Amsterdam, pp 387-418. https://doi.org/10.1016/B978-0-12-811301-1.00015-0

Asimow PD, Langmuir CH (2003) The importance of water to oceanic mantle melting regimes. Nature 421(6925):815-820. https://doi.org/10.1038/nature01429

Asphaug E (2014) Impact origin of the moon? Annu Rev Earth Planet Sci 42(1):551-578. https://doi.org/10.1146/annurev-earth-050212-124057

Asphaug E, Agnor CB, Williams Q (2006) Hit-and-run planetary collisions. Nature 439(7073):155-160. https://doi.org/10.1038/nature04311

Avice G, Marty B (2020) Perspectives on atmospheric evolution from noble gas and nitrogen isotopes on Earth, Mars & Venus. Space Sci Rev 216(3):36. https://doi.org/10.1007/s11214-020-00655-0

Avice G, Marty B, Burgess R (2017) The origin and degassing history of the Earth's atmosphere revealed by Archean xenon. Nat Commun 8:15455. https://doi.org/10.1038/ncomms15455

Avice G, Parai R, Jacobson S, Labidi J, Trainer MG, Petkov MP (2022) Noble gases and stable isotopes track the origin and early evolution of the Venus atmosphere. Space Sci Rev 218(8):60. https://doi.org/10.1007/s11214-022-00929-9

Badro J, Brodholt JP, Piet H, Siebert J, Ryerson FJ (2015) Core formation and core composition from coupled geochemical and geophysical constraints. Proc Natl Acad Sci 112(40):12310-12314. https://doi.org/10.1073/pnas.1505672112

Bahcall JN, Pinsonneault MH, Basu S (2001) Solar models: current epoch and time dependences, neutrinos, and helioseismological properties. Astrophys J 555(2):990. https://doi.org/10.1086/321493
Baines KH, Atreya SK, Bullock MA, Grinspoon DH, Mahaffy P, Russell CT, Schubert G, Zahnle K (2013) The atmospheres of the terrestrial planets: clues to the origins and early evolution of Venus, Earth, and Mars. In: Mackwell SJ, Simon-Miller AA, Harder JW, Bullock MA (eds) Comparative climatology of terrestrial planets. University of Arizona Press, Tucson, pp 137–160. https://doi.org/10.2458/azu_uapress_9780816530595-ch006

Baker DR, Alletti M (2012) Fluid saturation and volatile partitioning between melts and hydrous fluids in crustal magmatic systems: the contribution of experimental measurements and solubility models. Earth-Sci Rev 114:298–324. https://doi.org/10.1016/j.earscirev.2012.06.005

Ballmer MD, Lourenço DL, Hirose K, Caracas R, Nomura R (2017) Reconciling magma-ocean crystallization models with the present-day structure of the Earth's mantle. Geochem Geophys Geosyst 18(7):2785–2806. https://doi.org/10.1002/2017GC006917

Banzhaf W (2003) Self-organizing systems. In: Meyers RA (ed) Encyclopedia of physical science and technology, 3rd edn. Academic Press, New York, pp 589–598. https://doi.org/10.1016/B0-12-227410-5/00681-5

Barth P, Carone L, Barnes R, Noack L, Mollière P, Henning T (2021) Magma ocean evolution of the TRAPPIST-1 planets. Astrobiology 21(11):1325–1349. https://doi.org/10.1089/ast.2020.2277

Bekaert DV, Broadley MW, Marty B (2020) The origin and fate of volatile elements on Earth revisited in light of noble gas data obtained from comet 67P/Churyumov-Gerasimenko. Sci Rep 10(1):5796. https://doi.org/10.1038/s41598-020-62650-3

Benlow A, Meadows AJ (1977) The formation of the atmospheres of the terrestrial planets by impact. Astrophys Space Sci 46(2):293–300. https://doi.org/10.1007/BF00644376

Benner SA, Bell EA, Biondi E, Brasser R, Carell T, Kim HJ, Mojzsis SJ, Omran A, Pasek MA, Trail D (2020) When did life likely emerge on Earth in an RNA-first process? ChemSystemsChem 2(2):e1900035. https://doi.org/10.1002/syst.201900035

Bennett VC, Nutman AP, McCulloch MT (1993) Nd isotopic evidence for transient, highly depleted mantle reservoirs in the early history of the Earth. Earth Planet Sci Lett 119(3):299–317. https://doi.org/10.1016/0012-821X(93)090140-5

Benz W, Slattery WL, Cameron AGW (1986) The origin of the moon and the single-impact hypothesis. I. Icarus 66(3):515–535. https://doi.org/10.1016/0019-1035(86)90088-6

Bercovici D, Ricard Y (2014) Plate tectonics, damage and inheritance. Nature 508:513 EP. https://doi.org/10.1038/nature13072

Bercovici D, Ricard Y, Richards MA (2000) The relation between mantle dynamics and plate tectonics: a primer. In: Richards MA, Gordon RG, Van Der Hilst RD (eds) The history and dynamics of global plate motions. AGU, Washington DC, pp 5–46. https://doi.org/10.1029/GM121p0005

Berg MTL, Bromiley GD, Le Godef Y, Philippe J, Mezouar M, Perrillat JP, Potts NJ (2018) Rapid Core Formation in Terrestrial Planets by Percolative Flow: in-Situ Imaging of Metallic Melt Migration Under High Pressure/Temperature Conditions. Front Earth Sci 6(77). https://doi.org/10.3389/feart.2018.00077

Berlo K, Gardner JE, Blundy JD (2011) Timescales of magma degassing. In: Timescales of magmatic processes: from core to atmosphere, vol 11. Wiley, New York. https://doi.org/10.1002/9781444328509.ch11

Bhatia GK (2021) Early thermal evolution of the embryos of Earth: role of $^{26}$Al and impact-generated steam atmosphere. Planet Space Sci 207:105335. https://doi.org/10.1016/j.pss.2021.105335

Bills BG (2005) Variations in the rotation rate of Venus due to orbital eccentricity modulation of solar tidal torques. J Geophys Res, Planets 110(E11). https://doi.org/10.1029/2003JE002190

Binder AB (1986) The initial thermal state of the Moon. In: Hartmann W, Phillips R, Taylor G (eds) Origin of the Moon. Lunar and Planetary Institute, p 425. https://ui.adsabs.harvard.edu/abs/1986ormo.conf..425B/abstract

Birch F (1952) Elasticity and constitution of the Earth's interior. J Geophys Res 57(2):227–286

Birstiel T, Klahr H, Ercolano B (2012) A simple model for the evolution of the dust population in protoplanetary disks. Astron Astrophys 539:A148. https://doi.org/10.1051/0004-6361/201118136

Bitsch B, Johansen A, Lambrechts M, Morbidelli A (2015) The structure of protoplanetary discs around evolving young stars. Astron Astrophys 575:A28. https://doi.org/10.1051/0004-6361/201424964

Bizzarro M, Baker JA, Haack H, Ulfbeck D, Rosing M (2003) Early history of Earth's crust-mantle system inferred from hafnium isotopes in chondrites. Nature 421(6926):931–933. https://doi.org/10.1038/nature01421

Blum J, Wurm G (2008) The growth mechanisms of macroscopic bodies in protoplanetary disks. Annu Rev Astron Astrophys 46(1):21–56. https://doi.org/10.1146/annurev.astro.46.060407.145152

Bodenheimer P, Lin DNC (2002) Implications of extrasolar planets for understanding planet formation. Annu Rev Earth Planet Sci 30(1):113–148. https://doi.org/10.1146/annurev.earth.30.091201.140357

Bolfan-Casanova N, Keppler H, Rubie DC (2003) Water partitioning at 660 km depth and evidence for very low water solubility in magnesium silicate perovskite. Geophys Res Lett 30(17). https://doi.org/10.1029/2003GL017182
Bollard J, Connelly JN, Whitehouse MJ, Pringle EA, Bonal L, Jørgensen JK, Nordlund Å, Moynier F, Biz-zarro M (2017) Early formation of planetary building blocks inferred from Pb isotopic ages of chon-drules. Sci Adv 3(8):e1700407. https://doi.org/10.1126/sciadv.1700407

Bolráo DP, Ballmer MD, Morison A, Rozel AB, Sanan P, Labrosse S, Tackley PJ (2021) Timescales of chemical equilibrium between the convecting solid mantle and over- and underlying magma oceans. Solid Earth 12(2):421–437. https://doi.org/10.5194/se-12-421-2021

Borgeat X, Tackley PJ (2022) Hadean/Eoarchean tectonics and mantle mixing induced by impacts: a three-dimensional study. Prog Earth Planet Sci 9(1):38. https://doi.org/10.1186/s40645-022-00497-0

Boslough M, Weldon R, Ahrens T (1980) Impact-induced water loss from serpentine, nontronite and kernite. In: Lunar and planetary science conference proceedings, vol 3, pp 2145–2158. https://ui.adsabs.harvard.edu/abs/1980LPSC...11.2145B/abstract

Boss AP (1986) The origin of the moon. Science 231(4736):341–345. https://doi.org/10.1126/science.231.4736.341

Boukaré CE, Ricard Y (2017) Modeling phase separation and phase change for magma ocean solidification dynamics. Geochem Geophys Geosyst. https://doi.org/10.1002/2017GC006902

Boukaré CE, Ricard Y, Fiquet G (2015) Thermodynamics of the MgO-FeO-SiO₂ system up to 140 GPa: application to the crystallization of Earth's magma ocean. J Geophys Res, Solid Earth 120(9):6085–6101. https://doi.org/10.1002/2015JB011929

Boulliung J, Füri E, Dalou C, Tissandier L, Zimmermann L, Marrocchi Y (2020) Oxygen fugacity and melt composition controls on nitrogen solubility in silicate melts. Geochim Cosmochim Acta 284:120–133. https://doi.org/10.1016/j.gca.2020.06.020

Bouvier A, Blichtert-Toft J, Moynier F, Vervoort JD, Albarède F (2007) Pb–Pb dating constraints on the accretion and cooling history of chondrites. Geochim Cosmochim Acta 71(6):1583–1604. https://doi.org/10.1016/j.gca.2006.12.005

Bower DJ, Kitzmann D, Wolf AS, Sanan P, Dorn C, Oza AV (2019) Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations. Astron Astrophys 631:A103. https://doi.org/10.1051/0004-6361/201935710

Bower DJ, Hakim K, Sossi PA, Sanan P (2022) Retention of water in terrestrial magma oceans and carbon-rich early atmospheres. Planet Sci. J. 3(4):93. https://doi.org/10.3847/psj/ac5fb1

Boyet M, Carlson RW (2005) $^{142}$Nd evidence for early (>$4.53$ Ga) global differentiation of the silicate Earth. Science 309(5734):576–581. https://doi.org/10.1126/science.1113634

Boyet M, Blichtert-Toft J, Rosing M, Storey M, Télouk P, Albarède F (2003) $^{142}$Nd evidence for early Earth differentiation. Earth Planet Sci Lett 214(3):427–442. https://doi.org/10.1016/S0012-821X(03)00423-0

Brasser R, Mojzsis SJ (2020) The partitioning of the inner and outer Solar System by a structured protoplanetary disk. Nat Astron 4(5):492–499. https://doi.org/10.1038/s41550-019-0978-6

Brasser R, Matsumura S, Ida S, Mojzsis SJ, Werner SC (2016) Analysis of terrestrial planet formation by the grand tack model: system architecture and tack location. Astrophys J 821(2):75. https://doi.org/10.3847/0004-637X/821/2/75

Briceño C, Vivas AK, Calvet N, Hartmann L, Pacheco R, Herrera D, Romero L, Berlind P, Sánchez G, Snyder JA, Andrews P (2001) The CIDA-QUEST large-scale survey of orion OB1: evidence for rapid disk dissipation in a dispersed stellar population. Science 291(5501):93–96. https://doi.org/10.1126/science.291.5501.93

ALMA Partnership, Brogan CL, Pérez LM, Hunter TR, Dent WRF, Hales AS, Hills RE, Corder S, Fomalont EB, Vlahakis C, Asaki Y, Barkats D, Hirota A, Hodge JA, Impellizzeri CMV, Kneissl R, Liuzzo E, Lucas R, Marcelino N, Matsushita S, Nakanishi K, Phillips N, Richards AMS, Toledo I, Aladro R, Broguiere D, Cortes JR, Cortes PC, Espada D, Galarza F, Appadoo DG, Ramirez LG, Humphreys EM, Jung T, Kameno S, Laing RA, Leon S, Marconi G, Mignano A, Nikolic B, Nyman LA, Radiszcz M, Remijan A, Rodón JA, Sawada T, Takahashi S, Tilanus RPJ, Vilaro BV, Watson LC, Wiklind T, Akiyama E, Chapillon E, de Gregorio-Monsalvo I, Francesco JD, Gueth F, Kawamura A, Lee CF, Luong QN, Mangum J, Pietu V, Sanhueza P, Saigo K, Takakuwa S, Ubach C, van Kempen T, Wootten A, Carrizo AC, Francke H, Gallardo J, Garcia J, Gonzalez S, Hill T, Kaminski T, Kurono Y, Liu HY, Lopez C, Morales F, Plarre K, Schieven G, Testi L, Videla L, Villard E, Andreani P, Hibbard JE, Tatematsu K (2015) The 2014 ALMA long baseline campaign: first results from high angular resolution observations toward the HL tau region. Astrophys J Lett 808(1):L3. https://doi.org/10.1088/2041-8205/808/1/L3

Brož M, Chrenko O, Nesvorný D, Dauphas N (2021) Early terrestrial planet formation by torque-driven convergent migration of planetary embryos. Nat Astron 5(9):898–902. https://doi.org/10.1038/s41550-021-01383-3

Budde G, Burkhardt C, Brennecka GA, Fischer-Gödde M, Kruijer TS, Kleine T (2016) Molybdenum isotopic evidence for the origin of chondrules and a distinct genetic heritage of carbonaceous and noncarbonaceous meteorites. Earth Planet Sci Lett 454:293–303. https://doi.org/10.1016/j.epsl.2016.09.020
Bullock MA, Grinspoon DH (2001) The recent evolution of climate on Venus. Icarus 150(1):19-37. https://doi.org/10.1006/icar.2000.6570

Bunge HP, Richards MA, Baumgardner JR (1996) Effect of depth-dependent viscosity on the planform of mantle convection. Nature 379(6564):436-438. https://doi.org/10.1038/379436a0

Burger C, Bazsó Á, Schäfer CM (2020) Realistic collisional water transport during terrestrial planet formation - self-consistent modeling by an N-body-SPH hybrid code. Astron Astrophys 634:A76. https://doi.org/10.1051/0004-6361/201936366

Burgisser A, Scaillet B (2007) Redox evolution of a degassing magma rising to the surface. Nature 445(7124):194-197. https://doi.org/10.1038/nature05509

Burkhardt C, Kleine T, Bourdon B, Palme H, Zipfel J, Friedrich JM, Ebel DS (2008) Hf-W mineral isochron for Ca, Al-rich inclusions: age of the solar system and the timing of core formation in planetesimals. Geochim Cosmochim Acta 72(24):6177-6197. https://doi.org/10.1016/j.gca.2008.10.023

Burkhardt C, Spitzer F, Morbidelli A, Budde G, Render JH, Kruijer TS, Kleine T (2021) Terrestrial planet formation from lost inner solar system material. Sci Adv 7(52):eabj7601. https://doi.org/10.1126/sciadv.abj7601

Cameron AG (1983) Origin of the atmospheres of the terrestrial planets. Icarus 56(2):195-201

Cameron A (1986) The impact theory for origin of the moon. In: Hartmann W, Phillips R, Taylor G (eds) Origin of the Moon, Lunar and Planetary Institute, p 609. https://ui.adsabs.harvard.edu/abs/1986ormo.conf.609C/abstract

Cameron AGW, Ward WR (1976) The origin of the moon. In: Lunar and planetary science conference, vol 7, pp 120-122. https://ui.adsabs.harvard.edu/abs/1976LPI.....7..120C/abstract

Campbell BA, Campbell DB, Carter LM, Chandler JF, Giorgini JD, Margot JL, Morgan GA, Nolan MC, Perillat PJ, Whitten JL (2019) The mean rotation rate of Venus from 29 years of Earth-based radar observations. Icarus 332:19-23. https://doi.org/10.1016/j.icarus.2019.06.019

Canil D (1997) Vanadium partitioning and the oxidation state of Archaean komatiite magmas. Nature 389(6653):842-845. https://doi.org/10.1038/39860

Canil D (2002) Vanadium in peridotites, mantle redox and tectonic environments: Archean to present. Earth Planet Sci Lett 195(1):75-90. https://doi.org/10.1016/S0012-821X(01)00582-9

Canup RM (2004) Simulations of a late lunar-forming impact. Icarus 168(2):433-456. https://doi.org/10.1016/j.icarus.2003.09.028

Canup RM (2008) Accretion of the Earth. Philos Trans R Soc, Math Phys Eng Sci 366(1883):4061-4075. https://doi.org/10.1098/rsta.2008.0101

Canup RM (2012) Forming a moon with an Earth-like composition via a giant impact. Science 338(6110):1052-1055. https://doi.org/10.1126/science.1226073

Canup RM, Asphaug E (2001) Origin of the moon in a giant impact near the end of the Earth's formation. Nature 412:708 EP. https://doi.org/10.1038/35089010

Caracas R, Hirose K, Nomura R, Ballmer MD (2019) Melt-crystal density crossover in a deep magma ocean. Earth Planet Sci Lett 516:202-211. https://doi.org/10.1016/j.EPSL.2019.03.031

Caro G (2011) Early silicate Earth differentiation. Annu Rev Earth Planet Sci 39(1):31-58. https://doi.org/10.1146/annurev-earth-040610-133400

Caro G, Bourdon B, Birck JL, Moorbath S (2003) <sup>146</sup>Sm-<sup>142</sup>Nd evidence from Isua metamorphosed sed- iments for early differentiation of the Earth's mantle. Nature 423(6938):428-432. https://doi.org/10.1038/nature01668

Carpenter R (1970) A radar determination of the rotation of Venus. Astron J 75:61. https://doi.org/10.1086/110941

Carroll MR, Holloway JR (eds) (1994) Volatiles in magmas, vol 30. Mineralogical Society of America, Wash-ington

Castaing B, Gunaratne G, Heslot F, Kadanoff L, Libchaber A, Thomae S, Wu XZ, Zaleski S, Zanetti G (1989) Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J Fluid Mech 204:1-30. https://doi.org/10.1017/S0022112089001643

Cataldi G, Brandeker A, Olofsson G, Larsson B, Liseau R, Blommaert J, Fridlund M, Ivison R, Pantin E, Sibthorpe B, Vandenbussche B, Wu Y (2014) Herschel/HIFI observations of ionised carbon in the Pic-toris debris disk. Astron Astrophys 563:A66. https://doi.org/10.1051/0004-6361/201323126

Catling DC (2006) Comment on “A hydrogen-rich early Earth atmosphere”. Science 311(5757):38. https://doi.org/10.1126/science.1117827

Catling DC (2014) 6.7 - The great oxidation event transition. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, 2nd edn. Elsevier, Oxford, pp 177-195. https://doi.org/10.1016/B978-0-08-095975-7.01307-3

Catling DC (2015) 10.13 - Planetary atmospheres. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 429-472. https://doi.org/10.1016/B978-0-444-53802-4.00185-8
Catling DC, Claire MW (2005) How Earth's atmosphere evolved to an oxic state: a status report. Earth Planet Sci Lett 237(1):1-20. https://doi.org/10.1016/j.epsl.2005.06.013

Catling DC, Zahnle KJ (2020) The Archean atmosphere. Sci Adv 6(9). https://doi.org/10.1126/sciadv.aax1420

Chambers JE (2001) Making more terrestrial planets. Icarus 152(2):205-224. https://doi.org/10.1006/icar.2001.6639

Chambers JE (2010) Terrestrial planet formation. In: Seager S (ed) Exoplanets. University of Arizona Press, Tucson, pp 297-317

Chambers JE (2016) Pebble accretion and the diversity of planetary systems. Astrophys J 825(1):63. https://doi.org/10.3847/0004-637X/825/1/63

Chassefière E (1996) Hydrodynamic escape of oxygen from primitive atmospheres: applications to the cases of Venus and Mars. Icarus 124(2):537-552. https://doi.org/10.1006/icar.1996.0229

Chaussidon M, Gounelle M (2007) Short-lived radioactive nuclides in meteorites and early solar system processes. C R Géosci 339(14):872-884. https://doi.org/10.1016/j.crte.2007.09.005

Chillà F, Schumacher J (2012) New perspectives in turbulent Rayleigh-Bénard convection. Eur Phys J E 35(7):58. https://doi.org/10.1140/epje/i2012-12058-1

Chyba CF (1991) Terrestrial mantle siderophiles and the lunar impact record. Icarus 92(2):217-233

Chyba C, Sagan C (1992) Endogenous production, exogenous delivery and impact-shock synthesis of organic molecules: an inventory for the origins of life. Nature 355(6356):125-132. https://doi.org/10.1038/355125a0

Chyba CF, Thomas PJ, Brookshaw L, Sagan C (1990) Cometary delivery of organic molecules to the early Earth. Science 249(4967):366-373. https://doi.org/10.1126/science.11538074

Citron RI, Stewart ST (2022) Large impacts onto the early Earth: planetary sterilization and iron delivery. Planet Sci. J. 3(5):116. https://doi.org/10.3847/psj/ac66e8

Cleaves HJ, Chalmers JH, Lazcano A, Miller SL, Bada JL (2008) A reassessment of prebiotic organic synthesis in neutral planetary atmospheres. Orig Life Evol Biosph 38(2):105-115. https://doi.org/10.1007/s11084-007-9120-3

Clement MS, Kaib NA, Raymond SN, Walsh KJ (2018) Mars' growth stunted by an early giant planet instability. Icarus 311:340-356. https://doi.org/10.1016/j.icarus.2018.04.008

Clement MS, Kaib NA, Raymond SN, Chambers JE, Walsh KJ (2019) The early instability scenario: terrestrial planet formation during the giant planet instability, and the effect of collisional fragmentation. Icarus 321(7):78-790. https://doi.org/10.1016/j.icarus.2018.12.033

Clement MS, Raymond SN, Kaib NA (2019b) Excitation and depletion of the asteroid belt in the early instability scenario. Astron J 157(1):38. https://doi.org/10.3847/1538-3881/aaf21e

Clement MS, Kaib NA, Raymond SN, Chambers JE (2021) The early instability scenario: Mars' mass explained by Jupiter's orbit. Icarus 367:114585. https://doi.org/10.1016/j.icarus.2021.114585

Clesi V, Bouhifd MA, Bolfan-Casanova N, Manthilake G, Schiavi F, Raepsaet C, Bureau H, Khodja H, Andrault D (2018) Low hydrogen contents in the cores of terrestrial planets. Sci Adv 4(3). https://doi.org/10.1126/sciadv.1701876

Clesi V, Monteux J, Qaddah B, Le Bars M, Wacheul JB, Bouhifd MA (2020) Dynamics of core-mantle separation: influence of viscosity contrast and metal/silicate partition coefficients on the chemical equilibrium. Phys Earth Planet Inter 306:106547. https://doi.org/10.1016/j.pepi.2020.106547

Correia ACM, Laskar J (2001) The four final rotation states of Venus. Nature 411:767 EP. https://doi.org/10.1038/35081000

Correia ACM, Laskar J (2003) Different tidal torques on a planet with a dense atmosphere and consequences to the spin dynamics. J Geophys Res, Planets 108(E11). https://doi.org/10.1029/2003JE002059

Cottereau L, Rambaux N, Lebonnois S, Souchay J (2011) The various contributions in Venus rotation rate and LOD. Astron Astrophys 531:A45. https://doi.org/10.1051/0004-6361/201116606

Ćuk M, Stewart ST (2012) Making the moon from a fast-spinning Earth: a giant impact followed by resonant despinning. Science 338(6110):1047-1052. https://doi.org/10.1126/science.1225542

Dasgupta R, Grewal DS (2019) Origin and early differentiation of carbon and associated life-essential volatile elements on Earth. In: Deep carbon. Cambridge University Press, Cambridge, pp 4-39

Dauphas N (2017) The isotopic nature of the Earth's accreting material through time. Nature 541(7638):521-524

Dauphas N, Morbidelli A (2014) 6.1 - Geochemical and planetary dynamical views on the origin of Earth's atmosphere and oceans. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, 2nd edn. Elsevier, Oxford, pp 1-35. https://doi.org/10.1016/B978-0-08-095975-7.01301-2

Deguen R, Landeau M, Olson P (2014) Turbulent metal-silicate mixing, fragmentation, and equilibration in magma oceans. Earth Planet Sci Lett 391:274-287. https://doi.org/10.1016/j.epsl.2014.02.007

Dehant V, Debaille V, Dobos V, Gaillard F, Gillmann C, Goderis S, Grenfell JL, Höning D, Javaux EJ, Karatekin Ö, Morbidelli A, Noack L, Rauer H, Scherf M, Spohn T, Tackley P, Van Hoolst T, Wünnemann
K (2019) Geoscience for understanding habitability in the solar system and beyond. Space Sci Rev. https://doi.org/10.1007/s11214-019-0608-8

Delano JW (2001) Redox history of the Earth's interior since ~3900 Ma: implications for prebiotic molecules. Orig Life Evol Biosph 31(4):311-341. https://doi.org/10.1023/A:1011895600380

DeMeo FE Carry B (2014) Solar system evolution from compositional mapping of the asteroid belt. Nature 505(7485):629-634. https://doi.org/10.1038/nature12908

Demouchy S, Bolfan-Casanova N (2016) Distribution and transport of hydrogen in the lithospheric mantle: a review. Lithos 240-243:402-425. https://doi.org/10.1016/j.lithos.2015.11.012

Deng J, Du Z, Karki BB, Ghosh DB, Lee KKM (2020) A magma ocean origin to divergent redox evolutions of rocky planetary bodies and early atmospheres. Nat Commun 11(1):2007. https://doi.org/10.1038/s41467-020-15757-0

Dent WRF, Wyatt MC, Roberge A, Augereau JC, Casassus S, Corder S, Greaves JS, de Gregorio-Monsalvo I, Hales A, Jackson AP, Hughes AM, Lagrange AM, Matthews B, Wilner D (2014) Molecular gas clumps from the destruction of icy bodies in the *β* pictoris debris disk. Science 343(6178):1490-1492. https://doi.org/10.1126/science.1248726

Dobrovolskis AR (1980) Atmospheric tides and the rotation of Venus II. Spin evolution. Icarus 41(1):18-35. https://doi.org/10.1016/0019-1035(80)90157-8

Dobrovolskis AR, Ingersoll AP (1980) Atmospheric tides and the rotation of Venus I. Tidal theory and the balance of torques. Icarus 41(1):1-17. https://doi.org/10.1016/0019-1035(80)90156-6

Donahue TM (1999) New analysis of hydrogen and deuterium escape from Venus. Icarus 141(2):226-235. https://doi.org/10.1006/icar.1999.6186

Donahue TM, Hoffman JH, Hodges RR, Watson AJ (1982) Venus was wet: a measurement of the ratio of deuterium to hydrogen. Science 216(4546):630-633. https://doi.org/10.1126/science.216.4546.630

Drake MJ (2000) Accretion and primary differentiation of the Earth: a personal journey. Geochim Cosmochim Acta 64(14):2363-2369. https://doi.org/10.1016/S0016-7037(00)00372-0

Drake MJ, Newsom HE, Capobianco CJ (1989) V, Cr, and Mn in the Earth, Moon, EPB, and SPB and the origin of the Moon: experimental studies. Geochim Cosmochim Acta 53(8):2101-2111. https://doi.org/10.1016/0016-7037(89)90328-1

Drażkowska J, Alibert Y (2017) Planetesimal formation starts at the snow line. Astron Astrophys 608:A92. https://doi.org/10.1051/0004-6361/201731491

Drażkowska J, Dullemond CP (2018) Planetesimal formation during protoplanetary disk buildup. Astron Astrophys 614:A62. https://doi.org/10.1051/0004-6361/201732221

Drażkowska J, Alibert Y, Moore B (2016) Close-in planetesimal formation by pile-up of drifting pebbles. Astron Astrophys 594:A105. https://doi.org/10.1051/0004-6361/201628983

Dreibus G, Wänke H (1987) Volatiles on Earth and Mars: a comparison. Icarus 71(2):225-240. https://doi.org/10.1016/0019-1035(87)90148-5

Driscoll P, Bercovici D (2013) Divergent evolution of Earth and Venus: influence of degassing, tectonics, and magnetic fields. Icarus 226(2):1447-1464. https://doi.org/10.1016/j.icarus.2013.07.025

Edmonds M, Woods AW (2018) Exsolved volatiles in magma reservoirs. J Volcanol Geotherm Res 368:13-30. https://doi.org/10.1016/j.jvolgeores.2018.10.018

Elkins-Tanton LT (2008) Linked magma ocean solidification and atmospheric growth for Earth and Mars. Earth Planet Sci Lett 271(1-4):181-191. https://doi.org/10.1016/j.epsl.2008.03.062

Elkins-Tanton LT (2011) Formation of early water oceans on rocky planets. Astrophys Space Sci 332(2):359-364. https://doi.org/10.1007/s10509-010-0535-3

Elkins-Tanton LT (2012) Magma oceans in the inner solar system. Annu Rev Earth Planet Sci 40:113-139. https://doi.org/10.1146/annurev-earth-042711-105503

Elkins-Tanton LT, Grove TL (2011) Water (hydrogen) in the lunar mantle: results from petrology and magma ocean modeling. Earth Planet Sci Lett 307(1-2):173-179. https://doi.org/10.1016/j.epsl.2011.04.027

Elkins-Tanton LT, Parmentier EM, Hess PC (2003) Magma ocean fractional crystallization and cumulate overturn in terrestrial planets: implications for Mars. Meteorit Planet Sci 38(12):1753-1771. https://doi.org/10.1111/j.1945-5100.2003.tb00013.x

Elkins-Tanton LT, Weiss BP, Zuber MT (2011) Chondrites as samples of differentiated planetesimals. Earth Planet Sci Lett 305(1):1-10. https://doi.org/10.1016/j.epsl.2011.03.010

Emsenhuber A, Asphaug E, Cambioni S, Gabriel TSJ, Schwartz SR (2021) Collision chains among the terrestrial planets. II. An asymmetry between Earth and Venus. Planet Sci. J. 2(5):199. https://doi.org/10.3847/psj/ac19b1

Erkaev NV, Lammer H, Elkins-Tanton LT, Stökl A, Odert P, Marcq E, Dorfi EA, Kislyakova KG, Kulikov Y, Güdel M (2014) Escape of the Martian protoatmosphere and initial water inventory. Planet Space Sci 98:106-119. https://doi.org/10.1016/j.pss.2013.09.008

Faul UH, Jackson I (2007) Diffusion creep of dry, melt-free olivine. J Geophys Res, Solid Earth 112(B4). https://doi.org/10.1029/2006JB004586
Fegley B, Zolotov MY, Lodders K (1997) The oxidation state of the lower atmosphere and surface of Venus. Icarus 125(2):416-439. https://doi.org/10.1006/icar.1996.5628

Feig ST, Koepke J, Snow JE (2010) Effect of oxygen fugacity and water on phase equilibria of a hydrous tholeiitic basalt. Contrib Mineral Petrol 160(4):551-568. https://doi.org/10.1007/s00410-010-0493-3

Fiquet G (2018) Chap. 4 - Melting in the Earth's deep interior. In: Kono Y, Sanloup C (eds) Magmas under pressure. Elsevier, Amsterdam, pp 115-134. https://doi.org/10.1016/B978-0-12-811301-1.00004-6

Fiquet G, Auzende AL, Siebert J, Corgne A, Bureau H, Ozawa H, Garbarino G (2010) Melting of peridotite to 140 gigapascals. Science 329(5998):1516-1518. https://doi.org/10.1126/science.1192448

Fischer RA, Nakajima Y, Campbell AJ, Frost DJ, Harries D, Langenhorst F, Miyajima N, Pollok K, Rubie DC (2015) High pressure metal-silicate partitioning of Ni, Co, V, Cr, Si, and O. Geochem Cosmochim Acta 167:177-194. https://doi.org/10.1016/j.gca.2015.06.026

Fischer-Gödde M, Kleine T (2017) Ruthenium isotopic evidence for an inner solar system origin of the late veneer. Nature 541(7638):525-527

Fish RA, Goles GG, Anders E (1960) The record in the meteorites. III. On the development of meteorites in asteroidal bodies. Astrophys J 132:243. https://doi.org/10.1086/146918

Flasar FM, Birch F (1973) Energetics of core formation: a correction. J Geophys Res 78(26):6101-6103. https://doi.org/10.1029/JB078i026p06101

Foley BJ, Driscoll PE (2016) Whole planet coupling between climate, mantle, and core: implications for rocky planet evolution. Geochem Geophys Geosyst 17(5):1885-1914. https://doi.org/10.1002/2015GC006210

Foley BJ, Bercovici D, Elkins-Tanton LT (2014) Initiation of plate tectonics from post-magma ocean thermochemical convection. J Geophys Res, Solid Earth 119(11):8538-8561. https://doi.org/10.1002/2014JB011121

French BM (1966) Some geological implications of equilibrium between graphite and a C-H-O gas phase at high temperatures and pressures. Rev Geophys 4(2):223-253. https://doi.org/10.1029/RG004i002p00223

Frost BR (1979) Mineral equilibria involving mixed-volatiles in a C-O-H fluid phase; the stabilities of graphite and siderite. Am J Sci 279(9):1033-1059. https://doi.org/10.2475/ajs.279.9.1033

Frost BR (1991) Chap. 1. Introduction to oxygen fugacity and its petrologic importance. Rev Mineral Geochem 25(1):1-9. https://doi.org/10.1515/9781501508684-004

Frost DJ, McCammon CA (2008) The redox state of Earth's mantle. Annu Rev Earth Planet Sci 36(1):389-420. https://doi.org/10.1146/annurev.earth.36.031207.124322

Frost DJ, Liebske C, Langenhorst F, McCammon CA, Trønnes RG, Rubie DC (2004) Experimental evidence for the existence of iron-rich metal in the Earth's lower mantle. Nature 428(6981):409-412. https://doi.org/10.1038/nature02413

Frost DJ, Mann U, Asahara Y, Rubie DC (2008) The redox state of the mantle during and just after core formation. Philos Trans R Soc, Math Phys Eng Sci 366(1883):4315-4337. http://www.jstor.org/stable/25197401

Fu RR, Young ED, Greenwood RC, Elkins-Tanton LT (2017) Silicate melting and volatile loss during differentiation in planetesimals. In: Planetesimals: early differentiation and consequences for planets. Cambridge University Press, Cambridge. https://doi.org/10.1017/9781316339794.006

Gabriel TSJ, Cambioni S (2023) The role of giant impacts in planet formation. Annu Rev Earth Planet Sci 51(1):671-695. https://doi.org/10.1146/annurev-earth-031621-055545

Gaillard F, Bouhifd MA, Füri E, Malavergne V, Marrocchi Y, Noack L, Ortenzi G, Roskosz M, Vulpius S (2021) The diverse planetary ingassing/outgassing paths produced over billions of years of magmatic activity. Space Sci Rev 217(1):22. https://doi.org/10.1007/s11214-021-00802-1

Gaillard F, Bernadou F, Roskosz M, Bouhifd MA, Marrocchi Y, Iacono-Marziano G, Moreira M, Scaillet B, Rogerie G (2022a) Redox controls during magma ocean degassing. Earth Planet Sci Lett 577:117255. https://doi.org/10.1016/j.epsl.2021.117255

Gaillard F, Malavergne V, Bouhifd MA, Rogerie G (2022b) A speciation model linking the fate of carbon and hydrogen during core - magma ocean equilibration. Earth Planet Sci Lett 577:117266. https://doi.org/10.1016/j.epsl.2021.117266

Galimov EM (2005) Redox evolution of the Earth caused by a multi-stage formation of its core. Earth Planet Sci Lett 233(3):263-276. https://doi.org/10.1016/j.epsl.2005.01.026

Gallet F, Charbonnel C, Amard L, Brun S, Palacios A, Mathis S (2017) Impacts of stellar evolution and dynamics on the habitable zone: the role of rotation and magnetic activity. Astron Astrophys 597:A14. https://doi.org/10.1051/0004-6361/201629034

Garvin J, Getty S, Arney G, Johnson N, Malespin C, Webster C, Ravine M, Lorenz R, Kiefer W, Atreya S et al (2020) Deep atmosphere of Venus investigation of noble gases, chemistry, and imaging plus (DAVINCI+): discovering a new Venus via a flyby, probe, orbiter mission. In: AGU fall meeting abstracts, vol 2020, p P026-0001
Garvin JB, Getty SA, Arney GN, Johnson NM, Kohler E, Schwer KO, Sekerak M, Bartels A, Saylor RS, Elliott VE, Goodloe CS, Garrison MB, Cottini V, Izenberg N, Lorenz R, Malespin CA, Ravine M, Webster CR, Atkinson DH, Aslam S, Atreya S, Bos BJ, Brinckerhoff WB, Campbell B, Crisp D, Filiberto JR, Forget F, Gilmore M, Gorius N, Grinspoon D, Hofmann AE, Kane SR, Kiefer W, Lebonnois S, Mahaffy PR, Pavlov A, Trainer M, Zahnle KJ, Zolotov M (2022) Revealing the mysteries of Venus: the DAVINCI mission. Planet Sci. J. 3(5):117. https://doi.org/10.3847/PSJ/ac63c2

Geiss J, Gloeckler G (1998) Abundances of deuterium and helium-3 in the protosolar cloud. Space Sci Rev 84(1):239-250. https://doi.org/10.1023/A:1005039822524

Genda H (2016) Origin of Earth's oceans: an assessment of the total amount, history and supply of water. Geochem J 50(1):27-42. https://doi.org/10.2343/geochemj.2.0398

Genda H, Abe Y (2003) Survival of a proto-atmosphere through the stage of giant impacts: the mechanical aspects. Icarus 164(1):149-162. https://doi.org/10.1016/S0019-1035(03)00010-5

Genda H, Abe Y (2005) Enhanced atmospheric loss on protoplanets at the giant impact phase in the presence of oceans. Nature 433(7028):842-844

Gerya TV, Connolly JAD, Yuen DA (2008) Why is terrestrial subduction one-sided? Geology 36(1):43-46. https://doi.org/10.1130/G24060A.1

Ghanbarzadeh S, Hesse MA, Prodanović M (2017) Percolative core formation in planetesimals enabled by hysteresis in metal connectivity. Proc Natl Acad Sci 114(51):13406-13411. https://doi.org/10.1073/pnas.1707580114

Gillmann C, Chassefière E, Lognonné P (2009) A consistent picture of early hydrodynamic escape of Venus atmosphere explaining present Ne and Ar isotopic ratios and low oxygen atmospheric content. Earth Planet Sci Lett 286(3-4):503-513. https://doi.org/10.1016/j.epsl.2009.07.016

Gillmann C, Golabek GJ, Tackley PJ (2016) Effect of a single large impact on the coupled atmosphere-interior evolution of Venus. Icarus 268:295-312. https://doi.org/10.1016/j.icarus.2015.12.024

Gillmann C, Golabek G, Raymond S, Schönbäckler M, Tackley P, Dehant V, Vinciane D (2020) Dry late accretion inferred from Venus's coupled atmosphere and internal evolution. Nat Geosci 13:1-5. https://doi.org/10.1038/s41561-020-0561-x

Gillmann C, Way MJ, Avice G, Breuer D, Golabek GJ, Höning D, Krissansen-Totton J, Lammer H, O'Rourke JG, Persson M, Plesa AC, Salvador A, Scherf M, Zolotov MY (2022) The long-term evolution of the atmosphere of Venus: processes and feedback mechanisms. Space Sci Rev 218(7):56. https://doi.org/10.1007/s11214-022-00924-0

Godin PJ, Ramirez RM, Campbell CL, Wizenberg T, Nguyen TG, Strong K, Moores JE (2020) Collision-induced absorption of CH₄-CO₂ and H₂-CO₂ complexes and their effect on the ancient Martian atmosphere. J Geophys Res, Planets 125(12):e2019JE006357. https://doi.org/10.1016/10.1029/2019JE006357

Gold T, Soter S (1969) Atmospheric tides and the resonant rotation of Venus. Icarus 11(3):356-366. https://doi.org/10.1016/0019-1035(69)90068-2

Goldblatt C (2015) Habitability of waterworlds: runaway greenhouses, atmospheric expansion, and multiple climate states of pure water atmospheres. Astrobiology 15. https://doi.org/10.1089/ast.2014.1268

Goldblatt C, Watson AJ (2012) The runaway greenhouse: implications for future climate change, geoengineering and planetary atmospheres. Philos Trans R Soc Lond Ser A 370(1974):4197-4216. https://doi.org/10.1098/rsta.2012.0004. arXiv:1201.1593

Goldblatt C, Robinson TD, Zahnle KJ, Crisp D (2013) Low simulated radiation limit for runaway greenhouse climates. Nat Geosci 6(8):661-667. https://doi.org/10.1038/ngeo1892

Goldreich P, Peale S (1967) Spin-orbit coupling in the solar system. II. The resonant rotation of Venus. Astron J 72:662-666. https://doi.org/10.1086/110289

Goldreich P, Peale S (1970) The obliquity of Venus. Astron J 75:273. https://doi.org/10.1086/110975

Gomes R, Levison HF, Tsiganis K, Morbidelli A (2005) Origin of the cataclysmic late heavy bombardment period of the terrestrial planets. Nature 435:466-469. https://doi.org/10.1038/nature03676

Gonnermann HM (2015) Magma fragmentation. Annu Rev Earth Planet Sci 43(1):431-458. https://doi.org/10.1146/annurev-earth-060614-105206

Gough DO (1981) Solar interior structure and luminosity variations. Sol Phys 74(1):21-34. https://doi.org/10.1007/BF00151270

Gounelle M (2011) The asteroid–comet continuum: in search of lost primitivity. Elements 7(1):29-34. https://doi.org/10.2113/gselements.7.1.29

Greenberg R, Wacker JF, Hartmann WK, Chapman CR (1978) Planetesimals to planets: numerical simulation of collisional evolution. Icarus 35(1):1-26. https://doi.org/10.1016/0019-1035(78)90057-X

Grevesmeyer I, Ranero CR, Ivandic M (2018) Structure of oceanic crust and serpentinization at subduction trenches. Geosphere 14(2):395-418. https://doi.org/10.1130/GES01537.1

Grewal DS, Dasgupta R, Farnell A (2020) The speciation of carbon, nitrogen, and water in magma oceans and its effect on volatile partitioning between major reservoirs of the Solar System rocky bodies. Geochim Cosmochim Acta 280:281-301. https://doi.org/10.1016/j.gca.2020.04.023
Griffith CA, Zahnle K (1995) Influx of cometary volatiles to planetary moons: the atmospheres of 1000 possible titans. J Geophys Res, Planets 100(E8):16907-16922

Grossmann S, Lohse D (2000) Scaling in thermal convection: a unifying theory. J Fluid Mech 407:27-56.
https://doi.org/10.1017/S0022112099007545

Güdel M, Guinan EF, Skinner SL (1997) The X-ray sun in time: a study of the long-term evolution of coronae of solar-type stars. Astrophys J 483(2):947-960. https://doi.org/10.1086/304264

Haghighipour N, Boss AP (2003) On pressure gradients and rapid migration of solids in a nonuniform solar nebula. Astrophys J 583(2):996. https://doi.org/10.1086/345472

Halliday AN (2004) Mixing, volatile loss and compositional change during impact-driven accretion of the Earth. Nature 427(6974):505-509. https://doi.org/10.1038/nature02275

Halliday AN (2013) The origins of volatiles in the terrestrial planets. Geochim Cosmochim Acta 105:146-171. https://doi.org/10.1016/j.gca.2012.11.015

Hallis LJ, Huss GR, Nagashima K, Taylor GJ, Halldórsson SA, Hilton DR, Mottl MJ, Meech KJ (2015) Evidence for primordial water in Earth's deep mantle. Science 350(6262):795-797. https://doi.org/10.1126/science.aac4834

Hamano K, Abe Y, Genda H (2013) Emergence of two types of terrestrial planet on solidification of magma ocean. Nature 497(7451):607-610. https://doi.org/10.1038/nature12163

Hamano K, Kawahara H, Abe Y, Onishi M, Hashimoto GL (2015) Lifetime and spectral evolution of a magma ocean with a steam atmosphere: its detectability by future direct imaging. Astrophys J 806(2):216. https://doi.org/10.1088/0004-637X/806/2/216

Hanel RA, Conrath BJ, Jennings DE, Samuelson RE (2003) Retrieval of physical parameters from measurements. In: Exploration of the solar system by infrared remote sensing, 2nd edn. Cambridge University Press, Cambridge, pp 352-404. https://doi.org/10.1017/CBO9780511536106.010

Hansen BMS (2009) Formation of the terrestrial planets from a narrow annulus. Astrophys J 703(1):1131-1140. https://doi.org/10.1088/0004-637X/703/1/1131

Harper CL, Jacobsen SB (1996) Evidence for 182Hf in the early Solar System and constraints on the timescale of terrestrial accretion and core formation. Geochim Cosmochim Acta 60(7):1131-1153. https://doi.org/10.1016/0016-7037(96)00027-0

Harrison TM (2009) The hadean crust: evidence from >4 Ga zircons. Annu Rev Earth Planet Sci 37(1):479-505. https://doi.org/10.1146/annurev-earth.031208.100151

Harrison TM, Blichtert-Toft J, Müller W, Albarede F, Holden P, Mojzsis SJ (2005) Heterogeneous hadean hafnium: evidence of continental crust at 4.4 to 4.5 Ga. Science 310(5756):1947-1950. https://doi.org/10.1126/science.1117926

Hartmann WK (1986) Moon origin: the impact-trigger hypothesis. In: Hartmann W, Phillips R, Taylor G (eds) Origin of the Moon, Lunar and Planetary Institute, pp 579-608. https://ui.adsabs.harvard.edu/abs/1986ormo.conf..579H/abstract

Hartmann WK, Davis DR (1975) Satellite-sized planetesimals and lunar origin. Icarus 24(4):504-515. https://doi.org/10.1016/0019-1035(75)90070-6

Hashimoto GL, Abe Y, Sugita S (2007) The chemical composition of the early terrestrial atmosphere: Formation of a reducing atmosphere from CI-like material. J Geophys Res, Planets 112(E5). https://doi.org/10.1029/2006JE002844

Hayashi C, Nakazawa K, Mizuno H (1979) Earth's melting due to the blanketing effect of the primordial dense atmosphere. Earth Planet Sci Lett 43(1):22-28. https://doi.org/10.1016/0012-821X(79)90152-3

Helffrich G, Kaneshima S (2004) Seismological constraints on core composition from Fe-O-S liquid immiscibility. Science 306(5705):2239-2242. https://doi.org/10.1126/science.1101109

Herbert F, Sonett CP, Wiskerchen MJ (1977) Model 'zero-age' lunar thermal profiles resulting from electrical induction. J Geophys Res 82(14):2054-2060. https://doi.org/10.1029/JB082i014p02054

Herd CDK, Borg LE, Jones JH, Papike JJ (2002) Oxygen fugacity and geochemical variations in the Martian basalts: implications for Martian basalt petrogenesis and the oxidation state of the upper mantle of Mars. Geochim Cosmochim Acta 66(11):2025-2036. https://doi.org/10.1016/S0016-7037(02)00828-1

Hier-Majumder S, Hirschmann MM (2017) The origin of volatiles in the Earth's mantle. Geochem Geophys Geosyst 18(8). https://doi.org/10.1002/2017GC006937. arXiv:1011.1669v3

Hillgren VJ (1991) Partitioning behavior of NI, CO, MO, and W between basaltic liquid and Ni-rich metal: implications for the origin of the moon and lunar core formation. Geophys Res Lett 18(11):2077-2080. https://doi.org/10.1029/91GL02534

Hirose K, Labrosse S, Hernlund J (2013) Composition and state of the core. Annu Rev Earth Planet Sci 41(1):657-691. https://doi.org/10.1146/annurev-earth-050212-124007

Hirose K, Wood B, Vočadlo L (2021) Light elements in the Earth's core. Nat. Rev. Earth Environ. 2(9):645-658. https://doi.org/10.1038/s43017-021-00203-6

Hirschmann MM (2006) Water, melting, and the deep Earth H₂O cycle. Annu Rev Earth Planet Sci 34(1):629-653. https://doi.org/10.1146/annurev.earth.34.031405.125211
Hirschmann MM (2012) Magma ocean influence on early atmosphere mass and composition. Earth Planet Sci Lett 341–344:48–57. https://doi.org/10.1016/j.epsl.2012.06.015

Hirschmann MM (2016) Constraints on the early delivery and fractionation of Earth's major volatiles from C/H, C/N, and C/S ratios. Am Mineral 101(3):540–553. https://doi.org/10.2138/am-2016-5452

Hirschmann MM (2021) Iron-wüstite revisited: a revised calibration accounting for variable stoichiometry and the effects of pressure. Geochim Cosmochim Acta 313:74–84. https://doi.org/10.1016/j.gca.2021.08.039

Hirschmann MM (2022) Magma oceans, iron and chromium redox, and the origin of comparatively oxidized planetary mantles. Geochim Cosmochim Acta 328:221–241. https://doi.org/10.1016/j.gca.2022.04.005

Hirschmann MM, Aubaud C, Withers AC (2005) Storage capacity of H₂O in nominally anhydrous minerals in the upper mantle. Earth Planet Sci Lett 236(1):167–181. https://doi.org/10.1016/j.epsl.2005.04.022

Hirschmann MM, Withers AC, Ardia P, Foley NT (2012) Solubility of molecular hydrogen in silicate melts and consequences for volatile evolution of terrestrial planets. Earth Planet Sci Lett 345–348:38–48. https://doi.org/10.1016/j.epsl.2012.06.031

Hirth G, Kohlstedt DL (1995) Experimental constraints on the dynamics of the partially Molten upper mantle: 2. Deformation in the dislocation creep regime. J Geophys Res, Solid Earth 100(B8):15441–15449. https://doi.org/10.1029/95JB01292

Hirth G, Kohlstedt DL (1996) Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere. Earth Planet Sci Lett 144(1):93–108. https://doi.org/10.1016/0012-821X(96)00154-9

Hirth G, Kohlstedt DL (2004) Rheology of the upper mantle and the mantle wedge: a view from the experimentalists. In: Eiler J (ed) Inside the subduction factory. AGU, Washington DC, pp 83–105. https://doi.org/10.1029/138GM06

Hoehler TM, Som SM, Kiang NY (2018) Life's requirements. In: Deeg HJ, Belmonte JA (eds) Handbook of exoplanets. Springer, Berlin, pp 2795–2816. https://doi.org/10.1007/978-3-319-55333-7_74

Holland HD (1962) Model for the evolution of the Earth's atmosphere. In: Engel AEJ, James HL, Leonard BF (eds) Petrologic studies: a volume in honor of A. F. Buddington. The Geological Society of America, New York, pp 447–477. https://doi.org/10.1130/Petrologic.1962.447

Holland HD (1978) The chemistry of the atmosphere and oceans. Wiley, New York

Holland HD (2006) The oxygenation of the atmosphere and oceans. Philos Trans R Soc B, Biol Sci 361(1470):903–915. https://doi.org/10.1098/rstb.2006.1838

Holloway JR (1981) Volatile interactions in magmas. In: Thermodynamics of minerals and melts. Springer, New York, pp 273–293. https://doi.org/10.1007/978-1-4612-5871-1_13

Holloway JR, Blank JG (1994) Application of experimental results to C-O-H species in natural melts. In: Carroll MR, Holloway JR (eds) Volatiles in magmas, vol 6. Mineralogical Society of America, Washington. https://doi.org/10.1515/9781501509674-012

Holzheid A, Borisov A, Palme H (1994) The effect of oxygen fugacity and temperature on solubilities of nickel, cobalt, and molybdenum in silicate melts. Geochim Cosmochim Acta 58(8):1975–1981. https://doi.org/10.1016/0016-7037(94)90429-4

Höning D, Baumeister P, Grenfell JL, Tosi N, Way MJ (2021) Early habitability and crustal decarbonation of a stagnant-lid Venus. J Geophys Res, Planets 126(10):e2021JE006895

Hoolst TV (2015) 10.04 - Rotation of the terrestrial planets. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 121–151. https://doi.org/10.1016/B978-0-444-53802-4.00168-8

Hopp T, Dauphas N, Abe Y, Aléon J, Alexander CMO, Amari S, Amelin Y, Bajo K, Bizzarro M, Bouvier A, Carlson RW, Chaussidon M, Choi BG, Davis AM, Rocco TD, Fujiya W, Fukai R, Gautam I, Haba MK, Hibiya Y, Hidaka H, Homma H, Hoppe P, Huss GR, Ichida K, Iizuka T, Ireland TR, Ishikawa A, Ito M, Itoh S, Kawasaki N, Kita NT, Kitajima K, Kleine T, Komatani S, Krot AN, Liu MC, Masuda Y, McKeeegan KD, Morita M, Motomura K, Moynier F, Nakai I, Nagashima K, Nesvorný D, Nguyen A, Nittler L, Onose M, Pack A, Park C, Piani L, Qin L, Russell SS, Sakamoto N, Schönbächler M, Tafla L, Tang H, Terada K, Terada Y, Usui T, Wada S, Wadhwa M, Walker RJ, Yamashita K, Yin QZ, Yokoyama T, Yoneda S, Young ED, Yui H, Zhang AC, Nakamura T, Naraoka H, Noguchi T, Okazaki R, Sakamoto K, Yabuta H, Abe M, Miyazaki A, Nakato A, Nishimura M, Okada T, Yada T, Yogata K, Nakazawa S, Saiki T, Tanaka S, Terui F, Tsuda Y, Watanabe S, Yoshikawa M, Tachibana S, Yurimoto H (2022) Ryugu's nucleosynthetic heritage from the outskirts of the Solar System. Sci Adv 8(46):eadd8141. https://doi.org/10.1126/sciadv.add8141

Horan MF, Smoliar MI, Walker RJ (1998) 182W and 187Re-187Os systematics of iron meteorites: chronology for melting, differentiation, and crystallization in asteroids. Geochim Cosmochim Acta 62(3):545–554. https://doi.org/10.1016/S0016-7037(97)00368-2

Hostetler C, Drake M (1980) On the early global melting of the terrestrial planets. In: Lunar and planetary science conference proceedings, vol 11, pp 1915–1929
Hughes AM, Duchêne G, Matthews BC (2018) Debris disks: structure, composition, and variability. Annu Rev Astron Astrophys 56(1):541–591. https://doi.org/10.1146/annurev-astro-081817-052035

Humphreys MCS, Brooker RA, Fraser DG, Burgisser A, Mangan MT, McCammon C (2015) Coupled interactions between volatile activity and Fe oxidation state during Arc crustal processes. J Petrol 56(4):795–814. https://doi.org/10.1093/petrology/egv017

Hunten DM (1973) The escape of light gases from planetary atmospheres. J Atmos Sci 30(8):1481–1494. https://doi.org/10.1175/1520-0469(1973)030<1481:TEOLGF>2.0.CO;2

Hunten DM (1993) Atmospheric evolution of the terrestrial planets. Science 259(5097):915–920. https://doi.org/10.1126/science.259.5097.915

Hunten DM, Pepin RO, Walker JCG (1987) Mass fractionation in hydrodynamic escape. Icarus 69(3):532–549. https://doi.org/10.1016/0019-1035(87)90022-4

Ida S, Yamamura T, Okuzumi S (2019) Water delivery by pebble accretion to rocky planets in habitable zones in evolving disks. Astron Astrophys 624:A28. https://doi.org/10.1051/0004-6361/201834556

Iizuka-Oku R, Yagi T, Gotou H, Okuchi T, Hattori T, Sano-Furukawa A (2017) Hydrogenation of iron in the early stage of Earth’s evolution. Nat Commun 8(1):14096. https://doi.org/10.1038/ncomms14096

Ikoma M, Genda H (2006) Constraints on the mass of a habitable planet with water of nebular origin. Astrophys J 648(1):696–706. https://doi.org/10.1086/505780

Ikoma M, Elkins-Tanton L, Hamano K, Suckale J (2018) Water partitioning in planetary embryos and protoplanets with magma oceans. Space Sci Rev 214(4):76. https://doi.org/10.1007/s11214-018-0508-3. arXiv:1804.09294

Ingersoll AP (1969) The runaway greenhouse: a history of water on Venus. J Atmos Sci 26(6):1191–1198. https://doi.org/10.1175/1520-0469(1969)026<1191:TRGAHO>2.0.CO;2

Ingersoll AP, Dobrovolskis AR (1978) Venus’ rotation and atmospheric tides. Nature 275(5675):37–38. https://doi.org/10.1038/275037a0

Ishiwatari M, Takehiro S, Nakajima K, Hayashi YY (2002) A numerical study on appearance of the runaway greenhouse state of a three-dimensional gray atmosphere. J Atmos Sci 59(22):3223–3238. https://doi.org/10.1175/1520-0469(2002)059<3223:ANSOAO>2.0.CO;2

Ishiwatari M, Nakajima K, Takehiro S, Hayashi YY, Kawai Y, Takahashi YO (2021) Revision of “Dependence of climate states of gray atmosphere on solar constant: from the runaway greenhouse to the snowball states” by Ishiwatari et al. (2007). J Geophys Res, Atmos 126(11):e2019JD031761. https://doi.org/10.1029/2019JD031761

Itcovitz JP, Rae ASP, Citron RI, Stewart ST, Sinclair CA, Rimmer PB, Shorttle O (2022) Reduced atmospheres of post-impact worlds: the early Earth. Planet Sci. J. 3(5):115. https://doi.org/10.3847/psj/ac67a9

Izidoro A, Bitsch B, Dasgupta R (2021a) The effect of a strong pressure bump in the Sun’s natal disk: terrestrial planet formation via planetesimal accretion rather than pebble accretion. Astrophys J 915(1):62. https://doi.org/10.3847/1538-4357/abfe0b

Izidoro A, Bitsch B, Raymond SN, Johansen A, Morbidelli A, Lambrechts M, Jacobson SA (2021b) Formation of planetary systems by pebble accretion and migration - Hot super-Earth systems from breaking compact resonant chains. Astron Astrophys 650:A152. https://doi.org/10.1051/0004-6361/201935336

Izidoro A, Dasgupta R, Raymond SN, Deienno R, Bitsch B, Isella A (2022) Planetesimal rings as the cause of the Solar System’s planetary architecture. Nat Astron 6(3):357–366. https://doi.org/10.1038/s41550-021-01557-z

Jacobsen SB (2005) The Hf-W isotopic system and the origin of the Earth and Moon. Annu Rev Earth Planet Sci 33(1):531–570. https://doi.org/10.1146/annurev.earth.33.092203.122614

Jacobson SA, Morbidelli A (2014) Lunar and terrestrial planet formation in the Grand Tack scenario. Philos Trans R Soc A, Math Phys Eng Sci 372(2024):20130174. https://doi.org/10.1098/rsta.2013.0174

Jacobson SA, Walsh KJ (2015) Earth and terrestrial planet formation. In: The early Earth. Am. Geophys. Union, Washington, pp 49–70. https://doi.org/10.1002/9781118860359.ch3

Jatosky BM, Ahrens T (1979) The history of an atmosphere of impact origin. In: Lunar and planetary science conference proceedings, vol 3, pp 2727–2739. https://ui.adsabs.harvard.edu/abs/1979LPSC...10.2727J

Jatosky BM, Phillips RJ (2001) Mars’ volatile and climate history. Nature 412(6843):237–244. https://doi.org/10.1038/35084184

Jansen T, Scharf C, Way M, Genio AD (2019) Climates of warm Earth-like planets. II. Rotational “Goldilocks” zones for fractional habitability and silicate weathering. Astrophys J 875(2):79. https://doi.org/10.3847/1538-4357/ab113d

Jaupart C, Labrosse S, Lucazeau F, Mareschal JC (2015) 7.06 - Temperatures, heat, and energy in the mantle of the Earth. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 223–270. https://doi.org/10.1016/B978-0-444-53802-4.00126-3

Ji J, Guo D, Liu J, Chen S, Ling Z, Ding X, Han K, Chen J, Cheng W, Zhu K, Liu J, Wang J, Chen J, Ouyang Z (2022) The 1:2,500,000-scale geologic map of the global Moon. Sci Bull. https://doi.org/10.1016/j.scib.2022.05.021
Johansen A, Lambrechts M (2017) Forming planets via pebble accretion. Annu Rev Earth Planet Sci 45(1):359-387. https://doi.org/10.1146/annurev-earth-063016-020226

Johansen A, Youdin A, Low MMM (2009) Particle clumping and planetesimal formation depend strongly on metallicity. Astrophys J 704(2):L75-L79. https://doi.org/10.1088/0004-637X/704/2/L75

Johansen A, Blum J, Tanaka H, Ormel C, Bizzarro M, Rickman H (2014) The multifaceted planetesimal formation process. In: Beuther H et al (eds) Protostars and planets VI. University of Arizona Press, Tucson, p 547. https://doi.org/10.2458/azu_uapress_9780816531240-ch024

Johansen A, Ronnet T, Bizzarro M, Schiller M, Lambrechts M, Nordlund Å, Lammer H (2021) A pebble accretion model for the formation of the terrestrial planets in the Solar System. Sci Adv 7(8):eabc0444. https://doi.org/10.1126/sciadv.abc0444.

Johnson NM de Oliveira MRR (2019) Venus atmospheric composition in situ data: a compilation. Earth Space Sci 6(7):1299-1318. https://doi.org/10.1029/2018EA000536

Johnson KTM, Dick HJB (1992) Open system melting and temporal and spatial variation of peridotite and basalt at the Atlantis II Fracture Zone. J Geophys Res, Solid Earth 97(B6):9219-9241. https://doi.org/10.1029/92JB00701

Johnstone CP (2020) Hydrodynamic escape of water vapor atmospheres near very active stars. Astrophys J 890(1):79. https://doi.org/10.3847/1538-4357/ab6224

Johnstone CP, Bartel M, Güdel M (2021) The active lives of stars: a complete description of the rotation and XUV evolution of F, G, K, and M dwarfs. Astron Astrophys 649:A96. https://doi.org/10.1051/0004-6361/202038407. arXiv:2009.07695

Karato S (2015) 9.05 - Water in the evolution of the Earth and other terrestrial planets. In: Schubert G (ed) Treatise on geophysics, 2nd edn. Elsevier, Oxford, pp 105-144. https://doi.org/10.1016/B978-0-444-53802-4-00156-1

Kasting JF (1988) Runaway and moist greenhouse atmospheres and the evolution of Earth and Venus. Icarus 74(3):472-494. https://doi.org/10.1016/0019-1035(88)90116-9

Kasting JF (1990) Bolide impacts and the oxidation state of carbon in the Earth's early atmosphere. Orig Life Evol Biosph 20(3):199-231. https://doi.org/10.1007/BF01808105

Kasting JF (1993) Earth's early atmosphere. Science 259(5097):920-926. https://doi.org/10.1126/science.11536547

Kasting JF (2013) What caused the rise of atmospheric O₂? Chem Geol 362:13-25. https://doi.org/10.1016/j.chemgeo.2013.05.039

Kasting JF (2014) 6.6 - Modeling the archean atmosphere and climate. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, 2nd edn. Elsevier, Oxford, pp 157-175. https://doi.org/10.1016/B978-0-08-095975-7.01306-1

Kasting JF (2019) The Goldilocks planet? How silicate weathering maintains Earth "just right". Elements 15(4):235-240. https://doi.org/10.2138/gselements.15.4.235

Kasting JF, Catling D (2003) Evolution of a habitable planet. Annu Rev Astron Astrophys 41(1):429-463. https://doi.org/10.1146/annurev.astr.41.071601.170049

Kasting JF, Pollack JB (1983) Loss of water from Venus. I. Hydrodynamic escape of hydrogen. Icarus 53(3):479-508. https://doi.org/10.1016/0019-1035(83)90212-9

Kasting JF, Zahnle KJ, Walker JCG (1983) Photochemistry of methane in the Earth's early atmosphere. Precambrian Res 20(2):121-148. https://doi.org/10.1016/0301-9268(83)90069-4

Kasting JF, Eggler DH, Raeburn SP (1993a) Mantle redox evolution and the oxidation state of the archean atmosphere. J Geol 101(2):245-257. https://doi.org/10.1086/648219

Kasting JF, Whitmire DP, Reynolds RT (1993b) Habitable zones around main sequence stars. Icarus 101(1):108-128. https://doi.org/10.1006/icar.1993.1010

Katyal N, Ortenzi G, Lee Grenfell J, Noack L, Sohl F, Godolt M, García Muñoz A, Schreier F, Wunderlich F, Rauer H (2020) Effect of mantle oxidation state and escape upon the evolution of Earth's magma ocean atmosphere. Astron Astrophys 643:A81. https://doi.org/10.1051/0004-6361/202038779

Kaula WM (1979) Thermal evolution of Earth and Moon growing by planetesimal impacts. J Geophys Res, Solid Earth 84:999-1008. https://doi.org/10.1029/JB084iB03p00999

Ke Y, Solomatov VS (2006) Early transient superplumes and the origin of the Martian crustal dichotomy. J Geophys Res, Planets 111(E10). https://doi.org/10.1029/2005JE002631

Ke Y, Solomatov VS (2009) Coupled core-mantle thermal evolution of early Mars. J Geophys Res, Planets 114(E7). https://doi.org/10.1029/2008JE003291

Kennedy GM, Kenyon SJ (2008) Planet formation around stars of various masses: the snow line and the frequency of giant planets. Astrophys J 673(1):502. https://doi.org/10.1086/524130

Keppler H, Bolfan-Casanova N (2006) Thermodynamics of water solubility and partitioning. Rev Mineral Geochem 62(1):193-230. https://doi.org/10.2138/rmg.2006.62.9

Keppler H, Golabek G (2019) Graphite floatation on a magma ocean and the fate of carbon during core formation. Geochem Perspect Lett 11:12-17. https://doi.org/10.7185/geochemlet.1918
Khan A, Sossi PA, Liebske C, Rivoldini A, Giardini D (2022) Geophysical and cosmochemical evidence for a volatile-rich Mars. Earth Planet Sci Lett 578:117330. https://doi.org/10.1016/j.epsl.2021.117330

Kiefer WS, Richards MA, Hager BH, Bills BG (1986) A dynamic model of Venus's gravity field. Geophys Res Lett 13(1):14-17. https://doi.org/10.1029/GL013i001p00014

Kiehl JT, Trenberth KE (1997) Earth's annual global mean energy budget. Bull Am Meteorol Soc 78(2):197-208. https://doi.org/10.1175/1520-0477(1997)078<0197:EAGMEB>2.0.CO;2

Kislyakova K, Noack L (2020) Electromagnetic induction heating as a driver of volcanic activity on massive rocky planets. Astron Astrophys 636:L10. https://doi.org/10.1051/0004-6361/202037924

Kislyakova KG, Noack L, Johnstone CP, Zaitsev VV, Fossati L, Lammer H, Khodachenko ML, Odert P, Güdel M (2017) Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating. Nat Astron 1(12):878-885. https://doi.org/10.1038/s41550-017-0284-0

Kleine T, Walker RJ (2017) Tungsten isotopes in planets. Annu Rev Earth Planet Sci 45(1):389-417. https://doi.org/10.1146/annurev-earth-063016-020037

Kleine T, Münker C, Mezger K, Palme H (2002) Rapid accretion and early core formation on asteroids and the terrestrial planets from Hf-W chronometry. Nature 418(6901):952-955. https://doi.org/10.1038/nature00982

Kleine T, Touboul M, Bourdon B, Nimmo F, Mezger K, Palme H, Jacobsen SB, Yin QZ, Halliday AN (2009) Hf-W chronology of the accretion and early evolution of asteroids and terrestrial planets. Geochim Cosmochim Acta 73(17):5150-5188. https://doi.org/10.1016/j.gca.2008.11.047

Kokubo E, Ida S (1996) On runaway growth of planetesimals. Icarus 123(1):180-191. https://doi.org/10.1006/icar.1996.0148

Kokubo E, Ida S (1998) Oligarchic growth of protoplanets. Icarus 131(1):171-178. https://doi.org/10.1006/icar.1997.5840

Kokubo E, Ida S (2000) Formation of protoplanets from planetesimals in the solar nebula. Icarus 143(1):15-27. https://doi.org/10.1006/icar.1999.6237

Kono Y (2018) Chap. 10 - Viscosity measurement. In: Kono Y, Sanloup C (eds) Magmas under pressure. Elsevier, Amsterdam, pp 261-280. https://doi.org/10.1016/B978-0-12-811301-1.00010-1

Kopp G, Lean JL (2011) A new, lower value of total solar irradiance: Evidence and climate significance. Geophys Res Lett 38(1). https://doi.org/10.1029/2010GL045777

Kopparapu RK, Ramirez R, Kasting JF, Eymet V, Robinson TD, Mahadevan S, Terrien RC, Domagal-Goldman S, Meadows V, Deshpande R (2013) Habitable zones around main-sequence stars: new estimates. Astrophys J 770(1). https://doi.org/10.1088/0004-637X/770/1/82

Korenaga J (2011) Thermal evolution with a hydrating mantle and the initiation of plate tectonics in the early Earth. J Geophys Res, Solid Earth 116(12):1-20. https://doi.org/10.1029/2011JB008410

Korenaga J (2017) On the extent of mantle hydration caused by plate bending. Earth Planet Sci Lett 457:1-9. https://doi.org/10.1016/j.epsl.2016.10.011

Korenaga J, Planavsky NJ, Evans DA (2017) Global water cycle and the coevolution of the Earth's interior and surface environment. Philos Trans R Soc A, Math Phys Eng Sci 375(2094). https://doi.org/10.1098/rsta.2015.0393

Kortenkamp SJ, Wetherill GW, Inaba S (2001) Runaway growth of planetary embryos facilitated by massive bodies in a protoplanetary disk. Science 293(5532):1127-1129. https://doi.org/10.1126/science.1062391

Kral Q, Matrà L, Wyatt MC, Kennedy GM (2017) Predictions for the secondary CO, C and O gas content of debris discs from the destruction of volatile-rich planetesimals. Mon Not R Astron Soc 469(1):521-550. https://doi.org/10.1093/mnras/stx730

Kral Q, Davoult J, Charnay B (2020) Formation of secondary atmospheres on terrestrial planets by late disk accretion. Nat Astron 4(8):769-775. https://doi.org/10.1038/s41550-020-1050-2

Krishnamurti R, Howard LN (1981) Large-scale flow generation in turbulent convection. Proc Natl Acad Sci. https://doi.org/10.1073/pnas.78.4.1981

Krissansen-Totton J, Fortney JJ, Nimmo F (2021) Was Venus ever habitable? Constraints from a coupled interior-atmosphere-redox evolution model. Planet Sci. J. 2(5):216. https://doi.org/10.3847/psj/ac2580

Krot AN, Keil K, Scott ERD, Goodrich CA, Weisberg MK (2014) 1.1 - Classification of meteorites and their genetic relationships. In: Holland HD, Turekian KK (eds) Treatise on geochemistry, 2nd edn. Elsevier, Oxford, pp 1-63. https://doi.org/10.1016/B978-0-08-095975-7.00102-9

Kruijer TS, Burkhardt C, Budde G, Kleine T (2017) Age of Jupiter inferred from the distinct genetics and formation times of meteorites. Proc Natl Acad Sci 114(26):6712-6716. https://doi.org/10.1073/pnas.1704461114

Kruijer TS, Kleine T, Borg LE (2020) The great isotopic dichotomy of the early Solar System. Nat Astron 4(1):32-40. https://doi.org/10.1038/s41550-019-0959-9

Kuhn WR, Atreya SK (1979) Ammonia photolysis and the greenhouse effect in the primordial atmosphere of the Earth. Icarus 37(1):207-213. https://doi.org/10.1016/0019-1035(79)90126-X
Kuramoto K, Matsui T (1996) Partitioning of H and C between the mantle and core during the core formation in the Earth: its implications for the atmospheric evolution and redox state of early mantle. J Geophys Res, Planets 101(E6):14909-14932. https://doi.org/10.1029/96JE00940

Kuramoto K, Umemoto T, Ishiwatari M (2013) Effective hydrodynamic hydrogen escape from an early Earth atmosphere inferred from high-accuracy numerical simulation. Earth Planet Sci Lett 375:312-318. https://doi.org/10.1016/j.epsl.2013.05.050

Kurosawa K, Sugita S, Ishibashi K, Hasegawa S, Sekine Y, Ogawa NO, Kadono T, Ohno S, Ohkouchi N, Nagaoka Y Matsui T (2013) Hydrogen cyanide production due to mid-size impacts in a redox-neutral N2-rich atmosphere. Orig Life Evol Biosph 43(3):221-245. https://doi.org/10.1007/s11084-013-9339-0

Labrosse S, Hernlund JW, Coltice N (2007) A crystallizing dense magma ocean at the base of the Earth's mantle. Nature 450(7171):866-869. https://doi.org/10.1038/nature06355

Lago B, Cazenave A (1979) Possible dynamical evolution of the rotation of Venus since formation. Moon Planets 21(2):127-154. https://doi.org/10.1007/BF00897084

Lambrechts M, Johansen A (2014) Forming the cores of giant planets from the radial pebble flux in protoplanetary discs. Astron Astrophys 572:A107. https://doi.org/10.1051/0004-6361/201424343

Lammer H (2013) Origin and evolution of planetary atmospheres. Springer, Berlin. https://doi.org/10.1007/978-3-642-32087-3

Lammer H, Zerkle AL, Gebauer S, Tosi N, Noack L, Scherf M, Pilat-Lohinger E, Güdel M, Grenfell JL, Godolt M, Nikolaou A (2018) Origin and evolution of the atmospheres of early Venus, Earth and Mars. Astron. Astrophys. Rev. 26:2. https://doi.org/10.1007/s00159-018-0108-y

Lammer H, Brasser R, Johansen A, Scherf M, Leitzinger M (2020a) Formation of Venus, Earth and Mars: constrained by isotopes. Space Sci Rev 217(1):7. https://doi.org/10.1007/s11214-020-00778-4

Lammer H, Leitzinger M, Scherf M, Odert P, Burger C, Kubyshkina D, Johnstone C, Maindl T, Schäfer CM, Güdel M, Tosi N, Nikolaou A, Marcq E, Erkaev NV, Noack L, Kislyakova KG, Fossati L, Pilat-Lohinger E, Ragossnig F, Dorfi EA (2020b) Constraining the early evolution of Venus and Earth through atmospheric Ar, Ne isotope and bulk K/U ratios. Icarus 339:113551. https://doi.org/10.1016/j.icarus.2019.113551

Landeau M, Olson P, Deguen R, Hirsh BH (2016) Core merging and stratification following giant impact. Nat Geosci 9(1). https://doi.org/10.1038/ngeo2808

Landeau M, Deguen R, Phillips D, Neufeld JA, Lherm V, Dalziel SB (2021) Metal-silicate mixing by large Earth-forming impacts. Earth Planet Sci Lett 564:116888. https://doi.org/10.1016/j.epsl.2021.116888

Lange RA (1994) Chap. 9. The effect of H₂O, CO₂ and F on the density and viscosity of silicate melts. In: Carroll MR, Holloway JR (eds) Volatiles in magmas, vol 9. Mineralogical Society of America, Washington, pp 331-370. https://doi.org/10.1515/9781501509674-015

Lange MA, Ahrens TJ (1982) The evolution of an impact-generated atmosphere. Icarus 51(1):96-120. https://doi.org/10.1016/0019-1035(82)90031-8

Lasaga AC, Holland HD, Dwyer MJ (1971) Primordial oil slick. Science 174(4004):53-55. https://doi.org/10.1126/science.174.4004.53

Lebrun T, Massol H, Chassefière E, Davaille A, Marcq E, Sarda P, Leblanc F, Brandeis G (2013) Thermal evolution of an early magma ocean in interaction with the atmosphere. J Geophys Res, Planets 118(6):1155-1176. https://doi.org/10.1002/jgre.20068

Lecar M, Podolak M, Sasselov D, Chiang E (2006) On the location of the snow line in a protoplanetary disk. Astrophys J 640(2):1115-1118. https://doi.org/10.1086/500287

Leconte J, Forget F, Charnay B, Wordsworth R, Pottier A (2013) Increased insolation threshold for runaway greenhouse processes on Earth-like planets. Nature 504(7479):268. https://doi.org/10.1038/nature12827

Leconte J, Forget F, Charnay B, Wordsworth R, Selsis F, Millour E, Spiga A (2013) 3D climate modeling of close-in land planets: circulation patterns, climate moist bistability, and habitability. Astron Astrophys 554:A69. https://doi.org/10.1051/0004-6361/201321042

Leconte J, Wu H, Menou K, Murray N (2015) Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars. Science 347(6222):632-635. https://doi.org/10.1126/science.1258686

Lécuyer C, Ricard Y (1999) Long-term fluxes and budget of ferric iron: implication for the redox states of the Earth's mantle and atmosphere. Earth Planet Sci Lett 165(2):197-211. https://doi.org/10.1016/S0012-821X(98)00267-2

Lee DC, Halliday AN (1995) Hafnium-tungsten chronometry and the timing of terrestrial core formation. Nature 378(6559):771-774. https://doi.org/10.1038/378771a0

Lee DC, Halliday AN (1997) Core formation on Mars and differentiated asteroids. Nature 388(6645):854-857. https://doi.org/10.1038/42206

Lee T, Papanastassiou DA, Wasserburg GJ (1976) Demonstration of $^{26}$Mg excess in Allende and evidence for $^{26}$Al. Geophys Res Lett 3(1):41-44. https://doi.org/10.1029/GL003i001p00041
Lee CTA, Brandon AD, Norman M (2003) Vanadium in peridotites as a proxy for paleo-$fO_2$ during partial melting: prospects, limitations, and implications. *Geochim Cosmochim Acta* 67(16):3045–3064. https://doi.org/10.1016/S0016-7037(03)00268-0

Leighton PA, Steiner AB (1936) The photochemical decomposition of methane. J Am Chem Soc 58(9):1823. https://doi.org/10.1021/ja01300a512

Lejeune AM, Richet P (1995) Rheology of crystal-bearing silicate melts: an experimental study at high viscosities. J Geophys Res, Solid Earth 100(B3):4215–4229. https://doi.org/10.1029/94JB02985

Lesher CE, Spera FJ (2015) Chap. 5 - Thermodynamic and transport properties of silicate melts and magma. In: Sigurdsson H (ed) The encyclopedia of volcanoes, 2nd edn. Academic Press, Amsterdam, pp 113–141. https://doi.org/10.1016/B978-0-12-385938-9-00005-5

Levison HF, Kretke KA, Duncan MJ (2015) Growing the gas-giant planets by the gradual accumulation of pebbles. Nature 524(7565):322–324. https://doi.org/10.1038/nature14675

Li J, Agee CB (1996) Geochemistry of mantle-core differentiation at high pressure. Nature 381(6584):686–689. https://doi.org/10.1038/381686a0

Li ZXA, Lee CTA (2004) The constancy of upper mantle $fO_2$ through time inferred from V/Sc ratios in basalts. Earth Planet Sci Lett 228(3):483–493. https://doi.org/10.1016/j.epsl.2004.10.006

Li Y, Dasgupta R, Tsuno K, Monteleone B, Shimizu N (2016) Carbon and sulfur budget of the silicate Earth explained by accretion of differentiated planetary embryos. Nat Geosci. https://doi.org/10.1038/ngeo2801

Li Y, Vočadlo L, Sun T, Brodholt JP (2020) The Earth's core as a reservoir of water. Nat Geosci 13(6):453–458. https://doi.org/10.1038/s41561-020-0578-1

Libourel G, Marty B, Humbert F (2003) Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity. Geochim Cosmochim Acta 67(21):4123–4135. https://doi.org/10.1016/S0016-7037(03)00259-X

Lichtenberg T, Golabek G, Burn R, Meyer M, Alibert Y, Gerya T, Mordasini C (2019) A water budget dichotomy of rocky protoplanets from 26al-heating. Nat Astron 307. https://doi.org/10.1038/s41550-018-0688-5

Lichtenberg T, Bower DJ, Hammond M, Boukrouche R, Sanan P, Tsai SM, Pierrehumbert RT (2021) Vertically resolved magma ocean–protoatmosphere evolution: $H_2$, $H_2O$, $CO_2$, $CH_4$, $CO$, $O_2$, and $N_2$ as primary absorbers. J Geophys Res, Planets 126(2):e2020JE006711. https://doi.org/10.1029/2020JE006711

Lichtenberg T, Drażkowska J, Schönbächler M, Golabek GJ, Hands TO (2021b) Bifurcation of planetary building blocks during Solar System formation. Science 371(6527):365–370. https://doi.org/10.1126/science.abb3091

Liggins P, Shorttle O, Rimmer PB (2020) Can volcanism build hydrogen-rich early atmospheres? Earth Planet Sci Lett 550:116546. https://doi.org/10.1016/j.epsl.2020.116546

Lin Y, van Westrenen W, Mao HK (2021) Oxygen controls on magmatism in rocky exoplanets. Proc Natl Acad Sci 118(45). https://doi.org/10.1073/pnas.2110427118. https://www.pnas.org/content/118/45/e2110427118

Litasov KD, Ohtani E (2007) Effect of water on the phase relations in Earth's mantle and deep water cycle. In: Ohtani E (ed) Special paper of the geological society of America, vol 421. Geol. Soc. Am., Boulder, pp 115–156. https://doi.org/10.1130/2007.2421(08)

Liu B, Johansen A, Lambrechts M, Bizzarro M, Haugbølle T (2022) Natural separation of two primordial planetary reservoirs in an expanding solar protoplanetary disk. Sci Adv 8(16):eabm3045. https://doi.org/10.1126/sciadv.abm3045

Liu B, Raymond SN, Jacobson SA (2022b) Early solar system instability triggered by dispersal of the gaseous disk. Nature 604(7907):643–646. https://doi.org/10.1038/s41586-022-04535-1

Lugaro M, Ott U, Kereszturi Á (2018) Radioactive nuclei from cosmoschronology to habitability. Prog Part Nucl Phys 102:1–47. https://doi.org/10.1016/j.ppnp.2018.05.002

Luger R, Barnes R (2015) Extreme water loss and abiotic $O_2$ buildup on planets throughout the habitable zones of M dwarfs. Astrobiology 15(2):119–143. https://doi.org/10.1089/ast.2014.1231

Lugmair GW, Shukolyukov A (1998) Early solar system timescales according to 53Mn-53Cr systematics. Geochim Cosmochim Acta 62(16):2863–2886. https://doi.org/10.1016/S0016-7037(98)00189-6

Lupu RE, Zahnle K, Marley MS, Schaefer L, Fegley B, Morley C, Cahoy K, Freedman R, Fortney JJ (2014) The atmospheres of earthlike planets after giant impact events. Astrophys J 784(1):27. https://doi.org/10.1088/0004-637X/784/1/27

Maas C, Hansen U (2015) Effects of Earth's rotation on the early differentiation of a terrestrial magma ocean. J Geophys Res, Solid Earth 120(11):7508–7525. https://doi.org/10.1002/2015JB012053

Maas C, Hansen U (2019) Dynamics of a terrestrial magma ocean under planetary rotation: a study in spherical geometry. Earth Planet Sci Lett 513:81–94. https://doi.org/10.1016/j.epsl.2019.02.016

Maas C, Manske L, Wünnemann K, Hansen U (2021) On the fate of impact-delivered metal in a terrestrial magma ocean. Earth Planet Sci Lett 554:116680. https://doi.org/10.1016/j.epsl.2020.116680
Mackwell SJ, Zimmerman ME, Kohlstedt DL (1998) High-temperature deformation of dry diabase with application to tectonics on Venus. J Geophys Res, Solid Earth 103(B1):975-984. https://doi.org/10.1029/97JB02671

Malavergne V, Bureau H, Raepsaet C, Gaillard F, Poncet M, Surblé S, Sifré D, Shcheka S, Fourdrin C, Deldicque D, Khodja H (2019) Experimental constraints on the fate of H and C during planetary core-mantle differentiation. Implications for the Earth. Icarus 321:473-485. https://doi.org/10.1016/j.icarus.2018.11.027

Malkus WVR (1954) Discrete transitions in turbulent convection. Proc R Soc Lond, Ser A, Math Phys Eng Sci 225(1161):185-195. https://doi.org/10.1098/rspa.1954.0196

Mallmann G, O'Neill HSC (2009) The crystal/melt partitioning of V during mantle melting as a function of oxygen fugacity compared with some other elements (Al, P, Ca, Sc, Ti, Cr, Fe, Ga, Y, Zr and Nb). J Petrol 50(9):1765-1794. https://doi.org/10.1093/petrology/egp053

Mao HK, Bell PM (1977) Disproportionation equilibrium in iron-bearing systems at pressures above 100 Kbar with applications to chemistry of the Earth's mantle. In: Saxena SK, Bhattacharji S, Annersten H, Stephansson O (eds) Energetics of geological processes. Springer, Berlin, pp 236-249. https://doi.org/10.1007/978-3-642-86574-9_12

Marcq E, Salvador A, Massol H, Davaille A (2017) Thermal radiation of magma ocean planets using a 1-D radiative-convective model of H₂O-CO₂ atmospheres. J Geophys Res, Planets 122(7):1539-1553. https://doi.org/10.1002/2016JE005224

Margot JL, Campbell DB, Giorgini JD, Jao JS, Snedeker LG, Ghigo FD, Bonsall A (2021) Spin state and moment of inertia of Venus. Nat Astron 5(7):676-683. https://doi.org/10.1038/s41550-021-01339-7

Marsh BD (1981) On the crystallinity, probability of occurrence, and rheology of lava and magma. Contrib Mineral Petrol 78(1):85-98. https://doi.org/10.1007/BF00371146

Martin RG, Livio M (2012) On the evolution of the snow line in protoplanetary discs. Mon Not R Astron Soc Lett 425(1):L6-L9. https://doi.org/10.1111/j.1745-3933.2012.01290.x

Marty B (2012) The origins and concentrations of water, carbon, nitrogen and noble gases on Earth. Earth Planet Sci Lett 313-314:56-66. https://doi.org/10.1016/j.epsl.2011.10.040

Marty B, Yokochi R (2006) Water in the early Earth. Rev Mineral Geochem 62(1):421-450. https://doi.org/10.2138/rmg.2006.62.18

Marty B, Avice G, Sano Y, Altwegg K, Balsiger H, Hässig M, Morbidelli A, Mousis O, Rubin M (2016) Origins of volatile elements (H, C, N, noble gases) on Earth and Mars in light of recent results from the Rosetta cometary mission. Earth Planet Sci Lett 441:91-102. https://doi.org/10.1016/j.epsl.2016.02.031

Marty B, Altwegg K, Balsiger H, Bar-Nun A, Bekaert DV, Berthelier JJ, Bieler A, Briois C, Calmonte U, Combi M, De Keyser J, Fiethe M, Fuselier SA, Gasc S, Gombosi TI, Hansen KC, Hässig M, Jäckel A, Kopp E, Korth A, Le Roy L, Mall U, Mousis O, Rême H, Owen T, Rubin M, Sémon T, Tzou CY, Waite JH, Wurz P (2017) Xenon isotopes in 67P/Churyumov-Gerasimenko show that comets contributed to Earth's atmosphere. Science 356(6342):1069-1072. https://doi.org/10.1126/science.aal3496

Massol H, Hamano K, Tian F, Ikoma M, Abe Y, Chassefière E, Davaille A, Genda H, Güdel M, Hori Y, Leblanc F, Marcq E, Sarda P, Shematovich VI, Stökl A, Lammer H (2016) Formation and evolution of protoatmospheres. Space Sci Rev 205:153-211. https://doi.org/10.1007/s11214-016-0280-1

Mathez EA (1984) Influence of degassing on oxidation states of basaltic magmas. Nature 310(5976):371-375. https://doi.org/10.1038/310371a0

Matrà L, MacGregor MA, Kalas P, Wyatt MC, Kennedy GM, Wilner DJ, Duchene G, Hughes AM, Pan M, Shannon A, Clampin M, Fitzgerald MP, Graham JR, Holland WS, Panić O, Su KYL (2017) Detection of exometary CO within the 440 Myr old fomalhaut belt: a similar CO + CO₂ ice abundance in exocomets and solar system comets. Astrophys J 842(1):9. https://doi.org/10.3847/1538-4357/aa71b4

Matrà L, Öberg KI, Wilner DJ, Olofsson J, Bayo A (2019) On the ubiquity and stellar luminosity dependence of exometary CO gas: detection around M dwarf TWA 7. Astron J 157(3):117. https://doi.org/10.3847/1538-3881/aaff5b

Matsui T, Abe Y (1984) The formation of an impact-generated H₂O atmosphere and its implications for the early thermal history of the Earth. In: Lunar and planetary science XV, pp 517-518. https://ui.adsabs.harvard.edu/abs/1984LPI....15..517M

Matsui T, Abe Y (1986a) Formation of a 'magma ocean' on the terrestrial planets due to the blanketing effect of an impact-induced atmosphere. Earth Moon Planets 34(3):223-230. https://doi.org/10.1007/BF00145081

Matsui T, Abe Y (1986b) Impact-induced atmospheres and oceans on Earth and Venus. Nature 322(6079):526-528. https://doi.org/10.1038/322526a0

Matsui T, Abe Y (1986c) Origin of the Moon and its early thermal evolution. In: Hartmann W, Phillips R, Taylor G (eds) Origin of the Moon, Lunar and Planetary Institute, pp 453-468. https://ui.adsabs.harvard.edu/abs/1986ormo.conf..453M/abstract
Matthews CN, Minard RD (2006) Hydrogen cyanide polymers, comets and the origin of life. Faraday Discuss 133:393–401. https://doi.org/10.1039/B516791D

Maurice M, Tosi N, Samuel H, Plesa AC, Hüttig C, Breuer D (2017) Onset of solid-state mantle convection and mixing during magma ocean solidification. J Geophys Res, Planets 122(3):577–598. https://doi.org/10.1002/2016JE005250

Maurice M, Dasgupta R, Hassanzadeh P (2023) Redox evolution of the crystallizing terrestrial magma ocean and its influence on the outgassed atmosphere. Planet Sci. J. 4(2):31. https://doi.org/10.3847/PSJ/acb2ca

McCammon C (1997) Perovskite as a possible sink for ferric iron in the lower mantle. Nature 387(6634):694–696. https://doi.org/10.1038/42685

McCammon C (2005a) The paradox of mantle redox. Science 308(5723):807–808. https://doi.org/10.1126/science.1110532

McCammon CA (2005b) Mantle oxidation state and oxygen fugacity: constraints on mantle chemistry, structure, and dynamics. In: Earth’s deep mantle: structure, composition, and evolution. Am. Geophys. Union, Washington, pp 219–240. https://doi.org/10.1029/160GM14

McCollom TM (2013) Miller-urey and beyond: what have we learned about prebiotic organic synthesis reactions in the past 60 years? Annu Rev Earth Planet Sci 41(1):207–229. https://doi.org/10.1146/annurev-earth-040610-133457

McCord TB (1968) The loss of retrograde satellites in the solar system. J Geophys Res 73(4):1497–1500. https://doi.org/10.1029/JB073i004p01497

McKenzie D (2011) Compaction and crystallization in magma chambers: towards a model of the skaergaard intrusion. J Petrol 52(5):905–930. https://doi.org/10.1093/petrology/egr009

McKinnon WB, Zahnle KJ, Ivanov BA, Melosh HJ (1997) Cratering on Venus: models and observations. In: Bougher SW, Hunten DM, Phillips RJ (eds) Venus II: geology, geophysics, atmosphere, and solar wind environment, p 969

Meech K, Raymond S (2020) Origin of Earth’s water: sources and constraints. In: Meadows VS, Arney GN, Schmidt BE, Des Marais DJ (eds) Planetary astrobiology. University of Arizona Press, Tucson, p 325. https://doi.org/10.2458/azu_uapress_9780816540068

Mei S, Kohlstedt DL (2000) Influence of water on plastic deformation of olivine aggregates: 2. Dislocation creep regime. J Geophys Res, Solid Earth 105(B9):21471–21481. https://doi.org/10.1029/2000JB90180

Melosh HJ (1990) Giant impacts and the thermal state of the early Earth. In: Newsom HE, Jones JH (eds) Origin of the Earth, Lunar and Planetary Institute, pp 69–83

Melosh H, Vickery A (1989) Impact erosion of the primordial atmosphere of Mars. Nature 338(6215):487–489

Menou K (2013) Water-trapped worlds. Astrophys J 774(1):51. https://doi.org/10.1088/0004-637X/774/1/51

Merk R, Breuer D, Spohn T (2002) Numerical modeling of $ ^{26}Al$-induced radioactive melting of asteroids considering accretion. Icarus https://doi.org/10.1006/icar.2002.6872

Miller SL (1953) A production of amino acids under possible primitive Earth conditions. Science 117(3046):528–529. https://doi.org/10.1126/science.117.3046.528

Miller SL (1955) Production of some organic compounds under possible primitive Earth Conditions. J Am Chem Soc 77(9):2351–2361. https://doi.org/10.1021/ja01614a001

Miller SL, Urey HC (1959) Organic compound synthesis on the primitive Earth. Science 130(3370):245–251. https://doi.org/10.1126/science.130.3370.245

Miyazaki Y, Korenaga J (2021) Inefficient Water Degassing Inhibits Ocean Formation on Rocky Planets: an Insight from Self-Consistent Mantle Degassing Models. Astrobiology. https://doi.org/10.1089/ast.2021.0126

Miyazaki Y, Korenaga J (2022) A wet heterogeneous mantle creates a habitable world in the Hadean. Nature 603(7899):86–90. https://doi.org/10.1038/s41586-021-04371-9

Miyazaki A, Hiyagon H, Sugiura N, Hirose K, Takahashi E (2004) Solubilities of nitrogen and noble gases in silicate melts under various oxygen fugacities: implications for the origin and degassing history of nitrogen and noble gases in the Earth. Geochim Cosmochim Acta 68(2):387–401. https://doi.org/10.1016/S0016-7037(03)00484-8

Modirrousta-Galian D, Korenaga J (2023) The three regimes of atmospheric evaporation for super-earths and sub-neptunes. Astrophys J 943(1):11. https://doi.org/10.3847/1538-4357/ac9d34

Mojzsis SJ, Brasser R, Kelly NM, Abramov O, Werner SC (2019) Onset of giant planet migration before 4480 million years ago. Astrophys J 881(1):44. https://doi.org/10.3847/1538-4357/ab2c03

Monteux J, Ricard Y, Cottice N, Dubuffet F, Ulvrova M (2009) A model of metal-silicate separation on growing planets. Earth Planet Sci Lett 287(3-4):353–362. https://doi.org/10.1016/j.epsl.2009.08.020

Moore G (2008) Interpreting H$_2$O and CO$_2$ contents in melt inclusions: constraints from solubility experiments and modeling. Rev Mineral Geochem 69:333–361. https://doi.org/10.2138/rmg.2008.69.9
Morbidelli A, Chambers J, Lunine JI, Petit JM, Robert F, Valsecchi GB, Cyr KE (2000) Source regions and timescales for the delivery of water to the Earth. Meteorit Planet Sci 35(6):1309–1320. https://doi.org/10.1111/j.1945-5100.2000.tb01518.x

Morbidelli A, Lunine JI, O'Brien DP, Raymond SN, Walsh KJ (2012) Building terrestrial planets. Annu Rev Earth Planet Sci 40:251–275. https://doi.org/10.1146/annurev-earth-042711-105319

Morbidelli A, Nesvorny D, Laurenz V, Marchi S, Rubie DC, Elkins-Tanton L, Wieczorek M, Jacobson S (2018) The timeline of the lunar bombardment: revisited. Icarus 305:262–276. https://doi.org/10.1016/j.icarus.2017.12.046

Morbidelli A, Baillié K, Batygin K, Charnoz S, Guillot T, Rubie DC, Kleine T (2022) Contemporary formation of early Solar System planetesimals at two distinct radial locations. Nat Astron 6(1):72–79. https://doi.org/10.1038/s41550-021-01517-7

Moroz VI, Ekonomov AP, Moshkin BE, Revercomb HE, Sromovsky LA, Schofield JT, Spänkuch D, Taylor FW, Tomasko MG (1985) Solar and thermal radiation in the Venus atmosphere. Adv Space Res 5(11):197–232. https://doi.org/10.1016/0273-1177(85)90202-9

Mosenfelder JL, Asimow PD, Ahrens TJ (2007) Thermodynamic properties of Mg₂SiO₄ liquid at ultra-high pressures from shock measurements to 200 GPa on forsterite and wadsleyite. J Geophys Res, Solid Earth 112(B6). https://doi.org/10.1029/2006JB004364

Nakajima M, Stevenson DJ (2015) Melting and mixing states of the Earth's mantle after the Moon-forming impact. Earth Planet Sci Lett 427:286–295. https://doi.org/10.1016/j.epsl.2015.06.023

Nakajima S, Hayashi YY, Abe Y (1992) A study on the “runaway greenhouse effect” with a one-dimensional radiative-convective equilibrium model. J Atmos Sci 49(23):2256–2266. https://doi.org/10.1175/1520-0469(1992)049<2256:ASOTGE>2.0.CO;2

Nakajima M, Golabek GJ, Wünnemann K, Rubie DC, Burger C, Melosh HJ, Jacobson SA, Manske L, Hull SD (2021) Scaling laws for the geometry of an impact-induced magma ocean. Earth Planet Sci Lett 568:116983. https://doi.org/10.1016/j.epsl.2021.116983

Nesvorný D (2018) Dynamical evolution of the early solar system. Annu Rev Astron Astrophys 56(1):137–174. https://doi.org/10.1146/annurev-astro-081817-052028

Nesvorný D, Vokrouhlický D, Bottke WF, Levison HF (2018) Evidence for very early migration of the Solar System planets from the Patroclus–Menoetius binary Jupiter Trojan. Nat Astron 2(11):878–882. https://doi.org/10.1038/s41550-018-0564-3

Newman WI, Symbalisty EM, Ahrens TJ, Jones EM (1999) Impact erosion of planetary atmospheres: some surprising results. Icarus 138(2):224–240

Newsom HE, Ross Taylor S (1989) Geochemical implications of the formation of the moon by a single giant impact. Nature 338(6210):29–34. https://doi.org/10.1038/338029a0

Ni H, Zhang L, Guo X (2016) Water and partial melting of Earth's mantle. Sci China Earth Sci 59(4):720–730. https://doi.org/10.1007/s11430-015-5254-8

Nicklas RW, Puchtel IS, Ash RD (2018) Redox state of the Archean mantle: evidence from V partitioning in 3.5–2.4 Ga komatiites. Geochim Cosmochim Acta 222:447–466. https://doi.org/10.1016/j.gca.2017.11.002

Nikolaou A, Katyal N, Tosi N, Godolt M, Lee Grenfell J, Rauer H (2019) What factors affect the duration and outgassing of the terrestrial magma ocean? Astrophys J 875:11. https://doi.org/10.3847/1538-4357/ab08ed

Nimmo F, Kleine T (2015) Early differentiation and core formation. In: Badro J, Walter M (eds) The early Earth: accretion and differentiation. AGU, Washington DC, pp 83–102. https://doi.org/10.1002/9781118860359.ch5

Noack L, Godolt M, Von Paris P, Plesa AC, Stracke B, Breuer D, Rauer H (2014) Can the interior structure influence the habitability of a rocky planet? Planet Space Sci 98:14–29. https://doi.org/10.1016/j.pss.2014.01.003

Noack L, Kislyakova KG, Johnstone CP, Güdel M, Fossati L (2021) Interior heating and outgassing of proxima centauri b: identifying critical parameters. Astron Astrophys 651:1–17. https://doi.org/10.1051/0004-6361/202040176

Noda S, Ishiwatari M, Nakajima K, Takahashi YO, Takehiro S, Onishi M, Hashimoto GL, Kuramoto K, Hayashi YY (2017) The circulation pattern and day-night heat transport in the atmosphere of a synchronously rotating aquaplanet: dependence on planetary rotation rate. Icarus 282:1–18. https://doi.org/10.1016/j.icarus.2016.09.004

Nomura R, Ozawa H, Tateno S, Hirose K, Hernlund J, Muto S, Ishii H, Hiraoka N (2011) Spin crossover and iron-rich silicate melt in the Earth/'s deep mantle. Nature 473(7346):199–202. https://doi.org/10.1038/nature09940

Nomura R, Hirose K, Uesugi K, Ohishi Y, Tsuchiyama A, Miyake A, Ueno Y (2014) Low core-mantle boundary temperature inferred from the solidus of pyrolite. Science 343(6170):522–525. https://doi.org/10.1126/science.1248186
Nyquist LE, Reese YD, Wiesmann H, Shih CY, Takeda H (2001) Live <sup>53</sup>Mn and <sup>26</sup>Al in an unique cumulate eucrite with very calcic feldspar (An~ 98). Meteorit. Planet. Sci. Suppl. 36:A151–A152

Nyquist LE, Kleine T, Shih CY, Reese YD (2009) The distribution of short-lived radioisotopes in the early solar system and the chronology of asteroid accretion, differentiation, and secondary mineralization. *Geochim Cosmochim Acta* 73(17):5115–5136. https://doi.org/10.1016/j.gca.2008.12.031

O'Brien DP, Walsh KJ, Morbidelli A, Raymond SN, Mandell AM (2014) Water delivery and giant impacts in the ‘Grand Tack’ scenario. *Icarus* 239:74–84. https://doi.org/10.1016/j.icarus.2014.05.009

O'Brien DP, Izidoro A, Jacobson SA, Raymond SN, Rubie DC (2018) The delivery of water during terrestrial planet formation. *Space Sci Rev* 214(1):47. https://doi.org/10.1007/s11214-018-0475-8

Odert P, Lammer H, Erkaev N, Nikolaou A, Lichtenegger H, Johnstone C, Kislyakova K, Leitzinger M, Tosi N (2018) Escape and fractionation of volatiles and noble gases from Mars-sized planetary embryos and growing protoplanets. *Icarus* 307:327–346. https://doi.org/10.1016/j.icarus.2017.10.031

Ohtani E (2020) The role of water in Earth's mantle. *Nat Sci Rev* 7(1):224–232. https://doi.org/10.1093/nsr/nwz071

Okuchi T (1997) Hydrogen partitioning into Molten iron at high pressure: implications for Earth's core. *Science* 278(5344):1781–1784

Olson P, Sharp ZD (2018) Hydrogen and helium ingassing during terrestrial planet accretion. *Earth Planet Sci Lett* 498:418–426. https://doi.org/10.1016/j.epsl.2018.07.006

Olson PL, Sharp ZD (2019) Nebular atmosphere to magma ocean: a model for volatile capture during Earth accretion. *Phys Earth Planet Inter* 294. https://doi.org/10.1016/j.pepi.2019.106294

O'Neill H (1991) The origin of the moon and the early history of the Earth—a chemical model. Part 2: the Earth. *Geochim Cosmochim Acta* 55(4):1159–1172. https://doi.org/10.1016/0016-7037(91)90169-6

O'Neill C, Marchi S, Zhang S, Bottke W (2017) Impact-driven subduction on the Hadean Earth. *Nat Geosci* 10(10):793–797. https://doi.org/10.1038/ngeo3029

Ormel CW (2017) The emerging paradigm of pebble accretion. In: Pessah M, Gressel O (eds) Formation, evolution, and dynamics of young solar systems. Springer, Cham, pp 197–228. https://doi.org/10.1007/978-3-319-60609-5_7

Oro J, Miller SL, Lazcano A (1990) The origin and early evolution of life on Earth. *Annu Rev Earth Planet Sci* 18(1):317–356. https://doi.org/10.1146/annurev.ea.18.050190.001533

O'Rourke JG (2020) Venus: a thick basal magma ocean may exist today. *Geophys Res Lett* 47(4):e86126. https://doi.org/10.1029/2019GL086126

Otonello G, Richet P, Papale P (2018) Bulk solubility and speciation of H₂O in silicate melts. *Chem Geol* 479:176–187. https://doi.org/10.1016/j.CHEMGEO.2018.01.008

Pahlevan K, Schaefer L, Hirschmann MM (2019) Hydrogen isotopic evidence for early oxidation of silicate Earth. *Earth Planet Sci Lett* 526:115770. https://doi.org/10.1016/j.epsl.2019.115770

Pan V, Holloway JR, Hervig RL (1991) The pressure and temperature dependence of carbon dioxide solubility in tholeiitic basalt melts. *Geochim Cosmochim Acta* 55(6):1587–1595. https://doi.org/10.1016/0016-7037(91)90130-W

Papale P (1997) Modeling of the solubility of a one-component H₂O or CO₂ fluid in silicate liquids. *Contrib Mineral Petrol* 126(3):237–251. https://doi.org/10.1007/s004100050247

Papale P (1999) Modeling of the solubility of a two-component H₂O + CO₂ fluid in silicate liquids. *Am Mineral* 84(4):477–492. https://doi.org/10.1007/s004100050247

Papale P, Moretti R, Barbato D (2006) The compositional dependence of the saturation surface of H₂O + CO₂ fluids in silicate melts. *Chem Geol* https://doi.org/10.1016/j.chemgeo.2006.01.013

Parfitt EA, Wilson L (2008) Fundamentals of physical volcanology. Blackwell, Malden. https://www.wiley.com/en-us/Fundamentals+of+Physical+Volcanology-p-9780632054435

Pasek M, Lauretta D (2008) Extraterrestrial flux of potentially prebiotic C, N, and P to the early Earth. *Orig Life Evol Biosph* 38(1):5–21. https://doi.org/10.1007/s11084-007-9110-5

Patočka V, Calzavarini E, Tosi N (2020) Settling of inertial particles in turbulent Rayleigh-Bénard convection. *Phys Rev Fluids* 5(11):114304. https://doi.org/10.1103/PhysRevFluids.5.114304

Patočka V, Tosi N, Calzavarini E (2022) Residence time of inertial particles in 3D thermal convection: implications for magma reservoirs. *Earth Planet Sci Lett* 591:117622. https://doi.org/10.1016/j.epsl.2022.117622

Pepin RO (1991) On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles. *Icarus* 92(1):2–79. https://doi.org/10.1016/0019-1035(91)90036-S

Peslier AH, Schönbächler M, Busemann H, Karato SI (2017) Water in the Earth's interior: distribution and origin. *Space Sci Rev* 212(1–2):743–810. https://doi.org/10.1007/s11214-017-0387-z

Pham LBS, Karatekin Ö Dehant V (2011) Effects of impacts on the atmospheric evolution: comparison between Mars, Earth, and Venus. *Planet Space Sci* 59(10):1087–1092. https://doi.org/10.1016/j.pss.2010.11.010