# 00178\. The evolutionary divergence of Mars, Venus and Earth

Keiko Hamano  Cedric Gillmann  Gregor J. Golabek  Diogo Lourenço  Frances
Westall

###### Abstract

Mars, Venus and Earth are expected to have started in a hot molten state.
Here, we discuss how these three terrestrial planets diverged in their
evolution and what mechanisms could be the cause. We discuss that early-on
after magma ocean crystallization the mantle/surface redox state and water
inventory may already differ considerably, depending on planetary mass and
orbital distance from the Sun. During the subsequent internal evolution, the
three planets also diverged in terms of their tectonic regime, affecting the
long-term planetary evolution via heat flux and outgassing rate, and possibly
the physical state of their respective core and the onset and end of a
planetary dynamo. We discuss how, throughout the evolution of these rocky
planets, the dominant process for atmospheric loss would shift from
hydrodynamic escape and impact erosion to non-thermal escape, where small
terrestrial planets like Mars are here more vulnerable to volatile loss.

###### keywords:

atmosphere evolution , comparative planetology , Earth , habitability , life ,
magma ocean , mantle dynamics , Mars , planetary evolution , Solar System ,
terrestrial planets , Venus , volatile cycles , volcanism

††journal: Treatise on Geochemistry, 3rd

[inst1]organization=Earth-Life Science Institute, Tokyo Institute of
Technology, addressline=2-12-1-IE-1 Ookayama, city=Meguro-ku,
postcode=152-8550, state=Tokyo, country=Japan

[inst2]organization=ETH Zürich, Institute of Geophysics,
addressline=Sonneggstrasse 5, postcode=8092, city=Zürich, country=Switzerland

[inst3]organization=Bayerisches Geoinstitut, University of Bayreuth,
addressline=Universitätsstrasse 30, postcode=95440, city=Bayreuth,
country=Germany

[inst4]organization=CNRS-Centre de Biophysique Moléculaire, addressline=Rue
Charles Sadron CS 80054, postcode=45071, city=Orléans, country=France

Key points/objectives box

  * 1.

We describe characteristics and processes that played a role for the
divergence among the three planets Mars, Venus and Earth.

  * 2.

We discuss how the primitive magma ocean phase could cause the divergence
early on.

  * 3.

We investigate long-term interior, surface and atmosphere processes that can
enhance those early established differences.

##  1 Introduction

Earth, Mars and Venus are all classified as “terrestrial planets", as opposed
to gaseous planets. They have solid surfaces and are composed mostly of
silicate rocks and metals with a relatively thin outer atmospheric layer of
liquids and gas trapped by gravity. Their building blocks are generally
considered to be of similar origin (Smrekar et al., 2018; Lammer et al.,
2018), coming from the planetary accretion disc, but their respective present-
day states are remarkably different.

The characteristics in the past and present on each planet are described in
detail in other chapters, thus here, we briefly compare the three planets.
Venus and Earth share similarities in their sizes, masses, and densities, and
their orbits are rather close to each other (Table 1). These characteristics
make it possible for Venus to have a comparable structure to Earth, although
measurements are currently not precise enough to fully resolve the question
(e.g. Dumoulin et al., 2017). Comparatively, Mars is smaller and less dense
than the two other planets and orbits further away from the Sun.

The most obvious differences between the three planets are readily observable
in their atmospheres and surface conditions. Earth has a mild climate with an
average temperature of 288 K, and harbors stable liquid water at its surface.
It currently has a 1 bar atmosphere mainly composed of nitrogen and oxygen
with minor species including noble gases and carbon dioxide. By contrast,
Venus and Mars have similar atmosphere compositions dominated by CO2 and N2.
SO2 can be observed on Venus (150 ppmv), but very little water (20 ppmv). Mars
offers a wide range of species with O2 (0.16%), CO (0.06%), H2O and NO.
Compared to Earth’s atmosphere, Venus has an atmosphere that is about 100
times more massive ($\sim$4.8 $\times~{}$ 1020 kg), while the Martian
atmosphere is about 100 times less massive ($\sim$2.5 $\times~{}$ 1016 kg).
Surface temperatures also cover a wide range, between Mars’ chilly 210 K
average (with large variations) and Venus’ hellish 737 K. It is interesting to
note that, due to its thick atmosphere, Venus boasts a larger atmospheric mass
of N2 than the Earth, despite it making up a much smaller percentage of the
total surface pressure. Additionally, much of Earth’s superficial carbon
inventory is stored in carbonates rather than in the planet’s atmosphere. This
inventory is estimated to be similar to the amount of CO2, present in the
atmosphere of Venus (Donahue and Pollack, 1983; Wedepohl, 1995; LÃ©cuyer et
al., 2000; Hartmann, 2012).

Table 1: Main characteristics of the present Earth, Venus and Mars

|  unit |  Earth |  Venus |  Mars
---|---|---|---|---
Radius |  (Earth=1) |  1 |  0.949 |  0.532
Mass |  (Earth=1) |  1 |  0.815 |  0.107
Mean density |  (Earth=1) |  1 |  0.951 |  0.714
Semi-major axis |  au |  1 |  0.723 |  1.52
Mean surface temperature |  K |  288 |  737 |  210
Average surface pressure |  bar |  1 |  92 |  6.36$\times 10^{-3}$
Atmospheric composition |  vol.% |  |  |
|  |  |  $\mathrm{N_{2}(78.08)}$, $\mathrm{O_{2}(20.95)}$, with noble gases and $\mathrm{CO_{2}}$ |  $\mathrm{CO_{2}}(96.5)$, $\mathrm{N_{2}}(3.5)$, and $\mathrm{SO_{2}}(0.015)$ |  $\mathrm{CO_{2}}(95.1)$, $\mathrm{N_{2}}(2.59)$, $\mathrm{O_{2}}(0.16)$, CO(0.06) with $\mathrm{H_{2}O}$ and NO
H2O inventory |  |  |
|  surface+atmosphere |  |  1 ocean |  $<2\times 10^{-4}$ ocean |  20-30 mGEL (polar caps and permafrost)
|  interior |  |  0-6 oceans |  - |  100-1000 ppm
Redox state in the upper mantle |  IW+1–5 |  - |  IW+0–1
Magnetic field |  |  |
|  Surface field |  T |  $5\times 10^{-5}$ |  $<10^{-8}$ |  $10^{-9}-10^{-4}$ (patchy but locally strong)
|  Interpretation |  |  Core dynamo |  No dynamo |  Remanent crustal field
Tectonic mode |  Plate tectonics |  Single plate/ Stagnant lid |  Stagnant lid

Data sources: Radius, mass, mean density, semi-major axis, mean surface
temperature, surface pressure and atmospheric composition are from from
Planetary Fact Sheet
(https://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html). H2O
inventory from Peslier et al. (2017) for Earth and Scheller et al. (2021) for
Mars. H2O inventory in Venus’s atmosphere was estimated from concentration of
water vapor obtained by Venus Express ($\sim$30 ppmv, Marcq et al., 2017). The
unit “ocean” represents the Earth’s ocean mass, 1.4$\times 10^{21}$ kg, and
“GEL” represents global equivalent layer. Redox state in the upper mantle from
Righter et al. (2016). For Earth, the redox state shows a large variation,
depending on the rock samples (xenoliths, peridotites, MORB, and Kilauea lava
samples). Magnetic field informations from Stevenson (2003).

Going deeper than surface observation and delving into the interior
characteristics of the planets is hampered by the relative paucity of data
available beyond Earth. Samples from Mars and in-situ measurements provide
some constraints (i.e. water inventory, redox state, isotopic measurements,
core size - see Table 1) that are still unavailable for Venus, which implies
that a large part of our understanding of Venus relies on educated guesses
based on Earth observations and the consequences of common mechanisms. The
present Earth is known for having an oxidized upper mantle, reflected by its
oxygen fugacity (a measure of the oxidation state of the mantle, from the
ratio of the relative abundance of iron (III) ions to total iron, and
depending on pressure and temperature; see also Section 2). In Earth’s
present-day upper mantle, oxygen fugacity relative to the iron-wüstite (IW)
buffer is estimated to be about IW+1$\sim$IW+5 (Righter et al., 2016;
Hirschmann, 2022, and references therein), that is between 1 and 5 logarithmic
units above the IW buffer. Higher values (up to IW+8) also have been measured
in oxidized samples possibly due to processes in the crust or metasomatism.
These values are several orders of magnitude higher than the value estimated
from FeO content in the upper mantle based on the assumption that mantle
material was in equilibrium with Fe metal during core formation ($\sim$
IW-2)(e.g. Frost et al., 2008). Earth’s upper mantle oxygen fugacity appears
to have been stable over the last $\approx$2 Gyr (Hirschmann, 2023; Stagno and
Aulbach, 2021). Some heterogeneity is expected depending on the source region
of the samples and their evolution (Hirschmann, 2023). Based on Martian
meteorites, the Martian upper mantle seems to have an oxygen fugacity of
IW+0$\sim$IW+1(Righter et al., 2016, and references therein). This value is
also larger than the level set by metal-silicate equilibrium ($\sim$ IW-1)
based on FeO content in the Martian mantle, but the difference is much smaller
than Earth’s. The redox state of the Venusian mantle remains unknown.
Calculations based on the equilibration during core formation yield a range of
values for oxygen fugacity similar to Earth’s (Righter et al., 2016), that
would then have probably evolved toward more oxidized values. Venus’s surface
may be highly oxidized as suggested by thermodynamic calculations and
spectroscopic data (Fegley et al., 1997).

It is known that Venus shows no signs of a self-generated magnetic field at
present-day, even though it has been speculated that remanent magnetisation
may still exist in the crust (O’Rourke et al., 2018). On the contrary, Earth
sustains an intrinsic magnetic field at present-day and possibly since the
Hadean (Tarduno et al., 2015), while Mars shows signs of a past magnetic
dynamo in patches of remanently magnetized ancient crustal material (AcuÃ±a et
al., 1999; Plattner and Simons, 2015).

Observation of the three planets has also led to hypotheses regarding their
internal dynamics. Earth’s mantle convection regime is known as plate
tectonics (i.e Wessel and MÃ¼ller, 2015), where the strong lithosphere is
broken into distinct mobile plates with deformation mostly localized at the
plate boundaries and subduction of oceanic plates being the dominant mechanism
for driving plate tectonics (e.g. Forsyth and Uyeda, 1975). As a result, very
little ancient crust still remains at the surface of the Earth. In contrast,
Mars exhibits a so-called stagnant-lid regime, where a thick rigid lithosphere
is decoupled from the convective mantle and mostly immobile on top of the
mantle (e.g. Solomatov, 1995). Most of Mars’ surface is thus ancient (billions
of years old), but shows a specific pattern: a dichotomy between the southern
highlands and the northern lowlands, with a $\sim$5 km difference in
elevation. Venus is located somewhere in the middle. Its surface shows no sign
of (i) global plate tectonics, (ii) localized subduction zones and (iii) a
clear topographic dichotomy between oceanic and continental crust as observed
on Earth. However, its surface is on average relatively young and signs of
deformation have been noted. Several explanations have been proposed, such as
episodic activity (Turcotte, 1993) or lithospheric weakening by magma
intrusion (the so-called plutonic squishy lid; Rozel et al., 2017; LourenÃ§o
et al., 2018). The offset between the center of mass and the center of figure
of a planet (CM-CF offset) indicates differences in interior dynamics, since
they would emerge from substantial large scale density anomalies in the solid
planet, possibly due to interior temperature or topography (King, 2018). The
CM-CF offset has been estimated to be smaller on Venus (280 m, Bindschadler et
al. (1994)) than for Earth (2.1 km, Yoder and Ahrens (1995)) and Mars (3.3 km,
Wieczorek (2015)). The martian offset has been suggested to be caused by the
crustal dichothomy and the Tharsis province (Wieczorek, 2015). The difference
between Earth and Venus is more difficult to explain, with no uniquely
identified mechanism that could act as a cause. It has been suggested that the
small CM-CF on Venus could be indicative of the lack of substantial
downwellings during the last tens to hundreds of million years of the planet
evolution and possible lack of a mobile lid regime (King, 2018).

In this chapter, we attempt to provide an overview of recent efforts to
clarify what factors and processes make the current state of the three planets
so diverse. We focus on physical and chemical processes that occurred after
their formation stage, while it should be noted that diversification of
terrestrial planets may also originate during their accretion stage (e.g.
Jacobson et al., 2017; Rubie et al., 2015a). Section 2 describes what
differences are expected to arise as a result of the formation of deep magma
oceans. In Section 3, we address the diversity in tectonic regime of the three
planets during the subsequent internal evolution and its consequences on the
long-term planetary evolution. How the dominant process for atmospheric loss
would shift throughout the evolution of these rocky planets is discussed in
Section 4. In Section 5, we review the unique features in the history of Mars,
Venus and Earth that arose from their diverging evolutionary pathways.
Finally, we conclude this chapter, with some perspectives in Section 6.

##  2 Diversity originating during a magma ocean stage

Terrestrial planets, especially Earth, likely undergo a single or multiple
global melting by giant impacts (e.g. Canup, 2012; Tucker and Mukhopadhyay,
2014; Nakajima and Stevenson, 2015; Lock et al., 2018). The energy imparted
into the planet during a succession of major collision events can be large
enough to melt a thick silicate outer layer, possibly down to the core-mantle
boundary, producing a deep magma ocean (e.g. Wetherill, 1976; Drake, 2000;
Nakajima et al., 2021). The planetary characteristics originated during
crystallization of a magma ocean would set initial conditions for the
subsequent long-term evolution of planetary interior and atmosphere. Here, we
focus on two processes that could occur during a magma ocean phase, iron redox
disproportionation and appearance of threshold flux of hot steam atmospheres.
Recent studies on these two processes highlight the importance of the
planetary mass and the orbital distance from the Sun as potential causes of
planetary diversity originated during their magma ocean stages, as described
in details in this section. We address the proposed mechanisms and predicted
characteristics of planets that evolved from a hot molten state.

###  2.1 Iron disproportionation in silicate liquid

Early planetary mantles could have a redox state which reflects O partitioning
among interior reservoirs, affecting the composition of subsequently outgassed
volcanic gases and thus long-term climate. One of the mechanisms proposed to
affect the redox state in a planetary mantle is iron redox disproportionation,

$\displaystyle 3\mathrm{Fe^{2+}}$ $\displaystyle=$
$\displaystyle\mathrm{Fe^{0}}+\mathrm{2Fe^{3+}}.$ (1)

The original idea is that crystallization of Fe3+-rich solid phases such as
bridgmanite (the dominant mineral in the Earth’s lower mantle) produces Fe
metal by this reaction. Segregation of the produced Fe metal into the core
enriches the lower mantle in Fe3+. Then, the later mantle convection
homogenizes the Fe3+-rich lower mantle with the upper mantle, and raises the
Fe3+ content in the upper mantle gradually (e.g. Frost et al., 2008). If the
same iron disproportionation occurs and produces Fe metal directly in liquid
silicate, segregation of Fe metal and homogenization of the remaining Fe3+
melt can occur very quickly, possibly increasing the Fe3+ abundance in the
whole part of the magma ocean (Armstrong et al., 2019).

Under metal-saturated conditions, the partitioning of O between metal and
silicate melt determines the oxygen fugacity ($f_{\mathrm{O_{2}}}$).

$\displaystyle\mathrm{Fe^{met}}+\frac{1}{2}\mathrm{O_{2}}$ $\displaystyle=$
$\displaystyle\mathrm{FeO^{sil}}$ (2)

where the superscripts ‘met’ and ‘sil’ indicate a molten metallic phase and a
silicate liquid phase, respectively. Ferric iron in silicate melt is also set
by the reaction.

$\displaystyle\mathrm{FeO^{sil}}+\frac{1}{4}\mathrm{O_{2}}$ $\displaystyle=$
$\displaystyle\mathrm{FeO_{1.5}^{sil}}.$ (3)

The molar ratio of Fe3+ to total Fe (Fe3+/$\Sigma$Fe) in silicate melt
increases with the oxygen fugacity, and also varies with pressure, because of
the difference in partial molar volumes $\Delta v$ between the ferric and
ferrous oxide components (e.g. Kress and Carmichael, 1991; O’Neill et al.,
2006; Hirschmann, 2012) 111At an oxygen fugacity fixed relative to a specific
oxygen buffer, the pressure effect depends on $\Delta v$ relative to a change
in partial molar volumes associated with the buffer reaction (Hirschmann,
2022).. This suggests that the Fe3+/$\Sigma$Fe ratio in a magma ocean may
depend on the planetary mass, since pressures in a magma ocean increase with
the planetary mass.

The pressure dependence of $\Delta v$ and Fe3+/$\Sigma$Fe ratios was explored
recently by high-pressure experiments (Zhang et al., 2017; Armstrong et al.,
2019; Kuwahara et al., 2023) and first principle calculations (Deng et al.,
2020). Fe3+/$\Sigma$Fe decreases with pressure up to about 10 GPa owing to the
large volume of FeO1.5 compared to that of FeO (Kress and Carmichael, 1991;
O’Neill et al., 2006; Zhang et al., 2017). However, this trend reverses at
higher pressures because FeO1.5 has a larger compressibility than FeO
(Armstrong et al., 2019; Deng et al., 2020). Accordingly, Fe3+ is more stable
at pressures higher than around 10 GPa, possibly up to 90 GPa. These studies
show that silicate melt with a higher Fe3+/$\Sigma$Fe ratio can be in
equilibrium with Fe metal at higher pressure, suggesting that the
disproportionation could occur in silicate melt. The increasing stability of
Fe3+ at high pressures is also reported for basaltic and peridotitic melts
based on high pressure experiments by Kuwahara et al. (2023). Pressures in a
magma ocean would be higher for larger planets. Therefore, the enhanced
stability of Fe3+ suggests that larger planets have a higher abundance of Fe3+
in their magma ocean under the same oxygen fugacity and the presence of Fe
metal.

###  2.2 Potential correlation between planetary mass and atmospheric
composition

Fe metal produced by the disproportionation could sink quickly in the magma
ocean (e.g. Ichikawa et al., 2010). If the segregated Fe metal ponds and
equilibrates with the magma ocean at its base, then reaction (2) sets the
$f_{\mathrm{O_{2}}}$ at the base of the magma ocean. Due to the pressure
dependence of $\Delta v$ as described above, the $f_{\mathrm{O_{2}}}$ in the
silicate melt can vary as it ascends along a geotherm in the metal-free magma
ocean (Hirschmann, 2012), when the Fe3+/$\Sigma$Fe ratio is assumed to be
constant in a highly turbulent magma ocean. The $f_{\mathrm{O_{2}}}$ at the
top of a magma ocean is likely higher than that at its base, when the base
pressure exceeds roughly 10 GPa (Armstrong et al., 2019; Deng et al., 2020;
Kuwahara et al., 2023), though some differences exist among these studies. In
short, on small planets like the Moon and Mercury, the oxygen fugacity would
monotonically decrease from the base of the magma ocean towards the surface
(Zhang et al., 2017), while relatively large planets on Earth and Mars the
shallow part would be more oxidized than its base (Armstrong et al., 2019;
Deng et al., 2020), when the FeO-FeO1.5 reaction (3) buffers the oxygen
fugacity in the magma ocean.

Figure 1: The proposed trend in atmospheric compositions formed above a deep
magma ocean. The atmospheric composition reflects the surface redox state and
the partitioning of C-H-O-N-S elements between a magma ocean and its
atmosphere. The oxygen fugacity at the surface is estimated to be
IW-2$\sim$-1.5 for the Moon, IW-1$\sim$+1 for Mars, and IW+3$\sim$+5 for Earth
based on the assumption of metal-silicate equilibrium at the base of the magma
ocean (Deng et al., 2020). The difference in oxygen fugacity affects the gas
speciation and the volatile partitioning. H2O is highly soluble in silicate
melt so that its majority is dissolved in the magma ocean. Modified from Deng
et al. (2020) under CC by 4.0 license
(http://creativecommons.org/licenses/by/4.0/), based on numerical results by
Gaillard et al. (2022).

Based on the assumption that metal-silicate equilibration occurred at the base
of the magma ocean, these recent findings suggest that a larger planet
features more Fe3+ in the silicate melt and a more oxidized surface during its
deep magma ocean stage. Deng et al. (2020) proposed a trend between the Fe3+
abundance, the surface redox state, the speciation of atmospheres, and the
planetary mass (Figure 1). As the authors used FeO content in the present
upper mantle of Earth, Mars and Moon, the $f_{\mathrm{O_{2}}}$ at the base of
the magma ocean also differs among the planets, but the overall trend would be
similar even if the same $f_{\mathrm{O_{2}}}$ is imposed at the base: a larger
planet has an oxidizing surface above a Fe3+-rich magma ocean.

The oxygen fugacity at the surface controls the speciation of volatile
elements in the gas phase (Schaefer and Fegley, 2017; Gaillard et al., 2021).
Because volatile solubility in silicate melt strongly depends on gas
speciation (see Lichtenberg et al., 2021, and references therein), it also
affects the partitioning behaviour of volatile elements between a magma ocean
and its atmosphere. A gas species having a lower solubility is preferentially
outgassed into the atmosphere. The composition of atmospheres formed above a
magma ocean also depends on the pressure and temperature, relative abundance
of volatile elements, as well as the depth of a magma ocean. Gaillard et al.
(2022) modeled the partitioning of C-H-O-N-S elements between a deep magma
ocean and its atmosphere at 1,500 ∘C using volatile inventories on the present
Earth. According to the scenario proposed by Deng et al. (2020) and the
numerical results by Gaillard et al. (2022), large planets like Earth could
have an oxidizing atmosphere consisting of CO2, SO2, and N2 during its deep
magma ocean stage (Figure 1). Although we have little information about the
Venusian mantle, Venus could be expected to have had an oxidizing atmosphere
by analogy, if Venus experienced metal-silicate equilibration at high
pressures as well. Intermediate-sized planets like Mars might have a weakly
reducing atmosphere consisting of CO, CO2, and N2. And if planets as small as
the Moon formed with C-H-O-N-S whose relative abundance is as the same as that
of the Earth, the shallow magma ocean might produce a highly reducing
atmosphere consisting of CO and H2.

The oxidation mechanism involving the high stability of Fe3+ in silicate melt
at high pressures seems a promising way to oxidize a large part of the
silicate portion of planets rapidly. On the other hand, the Fe3+ abundance in
the magma ocean estimated for each planet relies on the simplified assumption
of perfect equilibration between silicate melt and metal at the base of the
magma ocean. For Earth, the estimated Fe3+/$\Sigma$Fe ratios show significant
differences among studies and do not necessarily coincide with the
observations (Section 5.3). The cause for the differences between the
predicted and observed Fe3+/$\Sigma$Fe ratios in the mantle requires further
investigation.

The solubility of volatile elements also depends on the chemical composition
of silicate melts and temperature, as well as cross-interaction among
dissolved volatiles, and much remains to be determined especially for extreme
conditions relevant to deep magma oceans (e.g. ultramafic compositions and
high temperatures). Under more reducing conditions, the formation and
flotation of graphite also would be an important factor on the C budget by
controlling the oxygen fugacity and limiting the amount of outgassed C
(Keppler and Golabek, 2019). On planets like Earth, another C-bearing phase,
namely diamonds, possibly forms due to the reducing condition at greater
depths (Armstrong et al., 2019). Keeping C as diamonds in the interior could
cause the atmosphere and surface to be C-depleted (Dasgupta, 2013). The
precipitation and stability of diamonds in a deep magma ocean remains to be
investigated.

Note that the atmospheric compositions predicted for a deep magma ocean stage
in Figure 1 would be different from those finally remaining at the end of the
magma ocean stage. Later outgassing processes along with magma ocean
crystallization can alter the mass and composition of atmospheres (see the
next section). The redox state in a magma ocean can also vary due to changes
in Fe3+/$\Sigma$Fe as crystallization proceeds (e.g. Boujibar et al., 2016;
Davis and Cottrell, 2021). According to recent modeling results by Maurice et
al. (2023), the Fe3+/$\Sigma$Fe ratio and the oxygen fugacity in the
crystallizing magma ocean can increase by several orders of magnitude
throughout magma ocean crystallization. Although this would not change the
total amount of Fe3+ in the mantle, the significant oxidation in the shallow
part could cause a transition from a reducing atmosphere towards an oxidizing
atmosphere during the solidification process.

###  2.3 Runaway threshold as a lower limit of thermal radiation from hot
steam atmospheres

Following core formation, a magma ocean crystallizes by convective heat
transport. At high degrees of melting, ultramafic melts are known to have a
very low viscosity (Liebske et al., 2005; Posner et al., 2018). Rayleigh
numbers of a planetary-scale magma ocean are extremely high, ranging from
$10^{20}$ to $10^{30}$ (e.g. Solomatov, 2007), thus the convection in a deep
magma ocean is supposed to be highly turbulent. At the early stage of
solidification, volatile species close to the surface are expected to dissolve
in the surface magma and to be transported downwards and homogenized by the
vigorous convection. As solidification proceeds, dissolved volatiles would be
released towards the surface, forming an overlying atmosphere. The outgassed
atmosphere insulates the surface and slows the cooling of a magma ocean.
Recently, such an interplay between a magma ocean and planetary atmosphere has
been modeled and investigated numerically by several groups (e.g. Elkins-
Tanton, 2008; Hamano et al., 2013, 2015; Lebrun et al., 2013; Schaefer et al.,
2016; Salvador et al., 2017; Katyal et al., 2019; Bower et al., 2019, 2022;
Lichtenberg et al., 2021). According to theoretical studies, the effectiveness
of thermal blanketing depends on the mass and composition of overlying
atmospheres. In particular, if a steam-dominated atmosphere forms during magma
ocean crystallization, terrestrial planets could experience different
evolutionary paths despite the same initial state, where the path is being
controlled by the orbital distance from the Sun (Hamano et al., 2013; Lebrun
et al., 2013; Salvador et al., 2017).

Figure 2: Thermal radiation from steam atmospheres. For these radiative
transfer calculations, the atmospheric pressure ($P_{\mathrm{atm}}$) is given
by the saturation vapor pressure of water at surface temperature below the
critical point of water, and set to 260 bar above it. As the surface
temperature increases, the thermal radiation increases and then levels off at
about 280 W/m2 (radiation limit or runaway threshold), thus the runaway
threshold is an upper limit in thermal radiation from water-saturated steam
atmospheres. Above the critical point of water, the thermal radiation
gradually starts to increase from the radiation limit with increasing surface
temperature, owing to thermal emissions from the hot surface and the hot and
dry (unsaturated) lower atmosphere. Under these hot surface conditions, the
threshold flux corresponds to a lower limit in the thermal radiation from
steam atmospheres. Modified from Hamano et al. (2015).

Why is the formation of a steam-dominated atmosphere important for the
possible divergent evolution of terrestrial planets? This is because it can
limit the thermal radiation from hot molten planets to a certain value.
Thermal radiation from steam atmospheres has been extensively explored
especially regarding conditions of the formation of liquid water ocean
(Komabayasi, 1967; Ingersoll, 1969; Rasool and De Bergh, 1970; Pollack, 1971;
Abe and Matsui, 1988; Kasting, 1988; Goldblatt et al., 2013; Kopparapu et al.,
2013). Radiative transfer calculations show that moist (water-saturated)
atmospheres have an upper limit for the outgoing infrared flux that can be
emitted from its top. If any energy input exceeds this limit, the surface
temperature increases until a new radiative equilibrium state is reached and
all liquid water completely evaporates from the surface. This is called a
runaway greenhouse state.

The physical mechanism behind the radiation limit was elucidated by Nakajima
et al. (1992) as follows. The thermal radiation from the top of the atmosphere
$F_{\mathrm{pl}}$ is given by

$\displaystyle F_{\mathrm{pl}}$ $\displaystyle=$ $\displaystyle\int
F_{\lambda}~{}d\lambda$ (4)

and

$\displaystyle F_{\lambda}$ $\displaystyle=$
$\displaystyle\int_{0}^{\tau_{\lambda,s}}\pi
B_{\lambda}(\tau^{\prime})\exp{[-\tau^{\prime}]}d\tau^{\prime}+\pi
B_{\lambda}(\tau_{\lambda,s})\exp{[-\tau_{\lambda,s}]}$ (5)

where $\tau$ is the effective optical depth at the top of the atmosphere, and
$F_{\lambda}$ and $B_{\lambda}$ is the spectral irradiance and the Planck
function emitted at wavelength $\lambda$. The subscript $s$ represents the
planetary surface. The first term at the right hand side of eq.(5) represents
contributions of thermal emission from atmospheric layers and the second term
is the emission from the planetary surface. The thermal radiation is most
sensitive to the temperature around $\tau\sim 1$.

At surface temperatures lower than the critical point of water, the amount of
H2O is roughly governed by the saturation water vapor pressure. At low surface
temperatures, the atmosphere is optically thin so the planetary radiation
comes mainly from the surface. As the surface temperature increases, more
water evaporates from the surface so the atmosphere becomes dominated by water
vapor. The emission from the surface attenuates within the opaque atmosphere,
while the infrared thermal radiation at the top of the atmosphere mainly comes
from a moist convective region (troposphere), in which the optical depth
becomes $\sim$ 1.

Assuming that the steam-rich atmosphere is saturated with water vapor, its
thermal structure (a pressure-temperature relation) in the moist convective
region approaches asymptotically the saturation vapor pressure curve of water
vapor. The pressure level at which the optical depth is equal to unity also
lies on the saturated vapor pressure curve. Consequently, the thermal
radiation from the top of the atmosphere also approaches a certain value
(radiation limit or runaway threshold) as the surface temperature increases
(Figure 2).

If the absorbed solar flux exceeds the critical flux, the surface temperature
increases until the outgoing thermal flux balances with the net solar
insolation. Above the critical point of water, the thermal radiation starts to
increase again as surface temperature increases (Figure 2). This is because
the thermal emissions from the hot surface and the hot and water-unsaturated
lower atmosphere escape through atmospheric windows, thus increasing both the
first and second terms at the right hand side of Eq.(5) (Goldblatt et al.,
2013; Hamano et al., 2015). When the mass of the steam atmosphere increases,
the thermal radiation starts to increase above the radiation limit, but never
falls below the runaway threshold. In short, under hot surface conditions,
like those during magma ocean crystallization, the radiation limit corresponds
to a lower limit for the outgoing thermal radiation of steam atmospheres. It
can be speculated that the presence of such a limit affects the energy budget
of solidifying terrestrial planets, depending on whether the net incoming flux
from the young Sun exceeds the lower limit or not. In a runaway greenhouse
state, the surface temperature could exceed the solidus temperature of rocks
(e.g. Kasting, 1988). A 30 bar steam atmosphere is sufficient for surface
temperature to exceed the solidus temperature of peridotite rocks with the
Earth’s gravity (e.g. Hamano, 2020).

###  2.4 Two distinctive cooling paths depending on the distance from the Sun

The effect of the radiation limit was first incorporated into a coupled model
of a magma ocean and its overlying atmosphere by Hamano et al. (2013) and
Lebrun et al. (2013). In both studies, the authors calculated the thermal
evolution of molten terrestrial planets along with the formation of outgassed
atmospheres. Hamano et al. (2013) considered a simple gray model of a pure H2O
atmosphere overlying a magma ocean and also incorporated loss of water
associated with hydrodynamic escape of hydrogen in their model. In the Lebrun
et al. (2013) model, the escape process of atmospheres was neglected, while
radiative transfer of H2O–CO2(–N2) atmospheres was treated in a more realistic
way with non-gray gas opacities.

Figure 3: Two types of evolutionary paths during magma ocean solidification.
Both paths start at the same initial condition at 3,000 K. On a planet at 1 au
(“Type I"), the atmosphere monotonically grows during cooling. In contrast, a
planet at 0.7 au (“Type II") loses its atmosphere after the planetary
radiation reaches the net stellar radiation at the orbit. Calculation results
from Hamano et al. (2013). Figure 4: Evolutionary dichotomy for terrestrial
planets. Beyond the critical distance (see text for its definition), an Earth-
sized planet solidifies on the order of 106 years or less, keeping its water
(Type I). In contrast, inside the critical distance, a magma ocean could last
longer for a larger inventory of water, and moreover, its solidification time
is well approximated by the time required for total loss of the primordial
water (Type II), indicated with thin dotted curves in the top panel. In short,
a Type II planet is desiccated during the slow solidification process.
Modified from Hamano et al. (2013)

Hamano et al. (2013) and Lebrun et al. (2013) assumed that volatiles, which
are initially dissolved in a deep magma ocean are exsolved at the surface as
solidification proceeds. They evaluated the thermal blanketing effect by an
overlying atmosphere, whose mass and composition also evolve by volatile
outgassing from the interior and atmospheric escape to space. The results for
a pure steam atmosphere are shown in Figure 3. The evolutionary paths of
solidifying Earth-sized planets formed at 1 au (Type I) and 0.7 au (Type II)
are imposed on results of radiative transfer calculations. Based on the
assumption of dissolution equilibrium between the magma ocean and the
overlying atmosphere, both planets start out with an about 40 bar steam
atmosphere with a total H2O inventory of 5 Earth’s ocean masses. At a surface
temperature of 3,000 K, the initial thermal radiation at the top of the
atmosphere amounts to approximately 1,500 W/m2.

On the Type I planet, the absorbed solar flux is lower than the radiation
limit. As the thermal radiation drops due to a decrease in surface
temperature, the planet moves in this diagram from right to left until it
reaches the threshold flux. The subsequent cooling heat flux is given by a
flux difference between the radiation limit and the absorbed solar flux, and
is high enough for the outgassing of water to overwhelm the escape. Therefore,
the curve for the Type I planet bends upward along the radiation limit due to
a net growth of the steam atmosphere. The resulting crystallization timescale
is on the order of 1 Myr or less. Due to the short duration, most water
remains at the end of the crystallization of the magma ocean (Figure 4). The
remaining dense steam atmosphere condenses and forms an ocean immediately
after the end of the magma ocean phase (Lebrun et al., 2013).

In contrast to the Type I planet, the solar radiation absorbed by the Type II
planet exceeds the radiation limit due to the proximity to the young Sun. In
this diagram, the Type II planet starts at the same position as the Type I and
moves from right to left as well. However, it reaches the absorbed solar flux,
prior to the threshold flux. The Type II planets cannot move further to the
left, otherwise the absorbed flux exceeds the outgoing thermal radiation, thus
leading to an increase in the surface temperature and the thermal radiation.
As all surface H2O is present as water vapor that can be rapidly lost by
photodissociation and followed by hydrogen escape to space. The net loss of
the steam atmosphere allows the planet to lose its heat by making the
atmosphere optically thin enough to emit the thermal radiation slightly larger
than the absorbed solar flux. This is why the curve for the Type II planet
sharply bends downward approximately along the value of the insolation. As a
result, the Type II planet is desiccated and much less water is left on the
surface when it completely solidifies (Figure 4). In the case that internal
heat flux from a magma ocean is extremely low, surface temperature may also
decrease due to structural changes in steam atmospheres, possibly leading to a
shorter-lived magma ocean (Selsis et al., 2023). This possibility remains to
be examined further, with a coupled magma-ocean-atmosphere model, which
includes outgassing processes.

A similar dichotomy was also reported for CO2-H2O atmospheres by Lebrun et al.
(2013), Salvador et al. (2017) and Massol et al. (2023). A critical condition
that separates these two evolutionary paths is given by the balance of
absorbed solar flux and the critical threshold for a runaway greenhouse. This
condition can be expressed as a critical orbital distance $a_{\mathrm{cr}}$
from the Sun222The expression for $a_{\mathrm{cr}}$ is re-scaled with the
critical flux for Earth-sized planets obtained by Goldblatt et al. (2013) and
Kopparapu et al. (2013) (about 280 W/m2). (Hamano et al., 2013),

$\displaystyle a_{\mathrm{cr}}$ $\displaystyle\approx$ $\displaystyle
0.77~{}\left(\frac{F_{\mathrm{lim}}}{280~{}\mathrm{W/m^{2}}}\right)^{-1/2}\left(\frac{S}{0.7~{}S_{\mathrm{sun}}}\right)^{1/2}\left(\frac{1-\alpha_{\mathrm{pl}}}{1-0.3}\right)~{}\mathrm{[au]}$
(6)

where $S$ and $S_{\mathrm{sun}}$ are the past and present solar constants,
$\alpha_{\mathrm{pl}}$ is the planetary albedo, and $F_{\mathrm{lim}}$ is the
radiation limit, which depends on the planetary gravity. The threshold value
obtained from non-gray cloud-free radiative transfer calculations is about 280
W/m2 for the Earth’s gravity and about 250 W/m2 for the Mars’ gravity
(Goldblatt et al., 2013; Kopparapu et al., 2014). Therefore, the critical
distance for Mars-sized planets is about 6 % larger than that for Earth-sized
planets. According to the value of the critical distance (Eq. 6), Earth and
Mars are categorized as Type I. If they had acquired abundant water during
formation, both planets would have formed oceans soon after their
solidification period on timescales of $\sim$106 years or less. By contrast,
it is not obvious which planetary type Venus belongs to. Three different
scenarios that Venus might have followed are discussed in Section 5.2.

The critical distance is identical to the inner edge of the habitable zone,
which is set by the onset of a runaway greenhouse state (the so-called runaway
greenhouse limit). According to recent 3D simulations, the onset condition for
a runaway greenhouse also depends on the initial state of the planetary
atmosphere due to different cloud feedbacks (Way and Del Genio, 2020; Turbet
et al., 2021). If Venus started from an extremely hot condition (magma ocean)
like Earth, the Type II scenario seems more probable (Turbet et al., 2021). In
our solar system $a_{\mathrm{cr}}$ lies in the middle of the formation region
of the terrestrial planets. This is simply because the critical flux of steam
atmospheres is comparable to the typical net insolation at these orbits. The
concept of a runaway greenhouse itself is applicable to atmospheres dominated
by other condensable gas species such as CO2 and CH4. However, the critical
flux estimated for these gas species is much smaller than that for water vapor
(Pierrehumbert, 2010; McKay et al., 1999), making the location of the runaway
greenhouse limit for other gas species irrelevant for the terrestrial planet
region.

In reality, planets would acquire not only water vapor, but also other gas
species during accretion. Many modeling studies have treated C-O-H
atmospheres, especially oxidizing atmospheres consisting of CO2–H2O, in a more
general case (Elkins-Tanton, 2008; Lebrun et al., 2013; Salvador et al., 2017;
Bower et al., 2019, 2022). Sossi et al. (2020) found that early atmospheres
are depleted in H-bearing components because most H is dissolved in the magma
ocean as H2O and the main component for the Earth’s earliest atmosphere could
be CO. The similar feature of the H-depleted atmosphere and the hydrous magma
ocean is seen in calculations of the C-H-O partitioning (Bower et al., 2022)
and the C-H-O-N-S partitioning (Gaillard et al., 2022) between a deep magma
ocean and its atmosphere in a wide range of surface oxygen fugacity. Gaillard
et al. (2022) also found that, under highly reducing conditions with oxygen
fugacity less than IW-4, most H is present in the atmosphere as H2 and the
atmosphere is C-depleted owing to the formation of graphite at the surface. At
a fixed $f_{\mathrm{O_{2}}}$, Bower et al. (2022) also calculated the change
in the mass and composition of the atmospheres by outgassing processes. They
showed that later outgassing of H2O and CO2, as well as a decrease in surface
temperature, increases the amount of H-bearing species such as H2O and H2, and
the CO2/CO ratio in the atmosphere.

The formation of H2O-dominated atmospheres would depend on the outgassing
efficiency at the late stage of solidification, as well as the volatile
inventories and the evolution of the surface redox state. As long as the melt
fraction in the surface magma is high enough for it to behave like a liquid,
water dissolved in the magma ocean likely outgases fast enough to keep the
system nearly at dissolution equilibrium (Pahlevan et al., 2019; Hamano et
al., 2013). The efficient outgassing would occur by coalescence and ascent of
bubbles in a low viscosity magma flow (Massol et al., 2016) or the diffusion
of water molecules through a surface thermal boundary layer, which can be as
thin as on the order of centimeters with a low liquid-like magma viscosity
(Solomatov, 2007). On the other hand, when the melt fraction drops along with
crystallization so that rheological transition from liquid-like to solid-like
behavior occurs, the outgassing rate of water may decrease. At this stage, a
highly viscous boundary layer would start to grow at the top of the magma
ocean. Although melt percolation seems to transport volatiles efficiently
upwards(e.g. Lebrun et al., 2013), its velocity decrease as the melt fraction
decreases. Some of the volatiles including water might be trapped in the
highly viscous crystal mush under the thick rigid surface layer. Bower et al.
(2022) suggest that the outgassing efficiency at late stage of a magma ocean
period would depend on the style of crystallization, i.e. fractional
crystallization or equilibrium crystallization. The outgassing efficiency may
also depend on the vigor of convection and the water abundance in the magma
ocean (Salvador and Samuel, 2023). Even if the oxygen fugacity is extremely
low at an early stage so that most of H is present as H2 in the atmosphere,
subsequent fractionation of Fe2+ and Fe3+ during the crystallization process
may gradually oxidize the surface magma ocean, converting H2 into H2O,
possibly leading to the transition to a steam-dominated atmosphere (Maurice et
al., 2023).

##  3 Post-magma ocean internal evolution

The long-term evolution of a planet’s interior profoundly impacts surface
conditions through the release of volatile species from the mantle into the
atmosphere. Here, we examine how terrestrial planets in the Solar System could
diverge during their long-term post-magma ocean internal evolution.
Furthermore, we discuss the current knowledge regarding the differences in
interior evolution for Mars, Earth and Venus. The interior evolution of
terrestrial planets is governed by heat transport in the mantle and its loss
at the surface. Heat is generated by the decay of radioactive elements
incorporated into the planet during formation, plus any residual
accretion/differentiation heat. This determines the dynamics of the planet’s
mantle and temperature field, but also partial melting of mantle material and
magmatism/volcanism, mantle structure, topography, and even possible magnetic
field generation (e.g. Schubert et al., 2001). Heat can be transported through
convection, which is the more efficient mechanism, or through conduction.

###  3.1 Convection regimes

A convection (or tectonic) regime is the surface expression of interior
dynamics. In general, various primary convection dynamic regimes are
considered: mobile lid (with plate tectonics being a specific subset),
stagnant lid, heat pipe, and plutonic-squishy lid (see Figure 5).

The mobile lid regime is characterized by its surface mobility, as the
lithosphere is part of the convecting cell and surface velocities are equal to
or greater than those of the underlying mantle. In the specific case of plate
tectonics, the surface is broken into a small number of plates exhibiting
differing relative motion, with deformation highly concentrated along the
narrow boundaries between these plates. Plate tectonics is further
characterized by long-term continuous subduction processes (e.g. Tackley,
2000; Stein et al., 2004; Rolf et al., 2022).

In a stagnant lid, a rigid lithosphere shows no lateral mobility and little
deformation (Nataf and Richter, 1982; Christensen, 1984; Solomatov, 1995). The
lid sits on top of a convective mantle; the hot mantle and cold lithosphere
are decoupled. Stagnant lid naturally occurs when planetary lithospheres
cannot be broken or mobilized by mantle convection, either because the
lithosphere is too strong or the convective stresses are too low. Therefore,
planets with a thick lithosphere or sluggish convection, for example, would
fall into this regime (e.g. Sleep, 2000a; O’Neill et al., 2016; Stern et al.,
2018; Rolf et al., 2022). As a result, heat flux and volcanic production are
expected to be generally lower on stagnant lid than on mobile lid planets. For
small or old planets, stagnant lid appears to be the final regime as
geological activity dies down and the end-member toward which all terrestrial
planets ultimately evolve as they cool down.

However, for larger, younger planets, the stagnant lid can insulate the mantle
from the surface because heat transport by conduction through the lid is
inefficient. Reducing the heat loss from the mantle leads to increasing
interior temperatures that can cause substantial partial melting. A subset of
the stagnant lid is a direct result of this scenario and is called the heat
pipe regime, where heat is transported to the surface through erupting
silicate melt (Moore and Webb, 2013; Moore et al., 2017). This subset of the
stagnant lid regime has been suggested for young terrestrial planets and, at
present-day, for Io, one of Jupiter’s moons (O’Reilly and Davies, 1981). In
such cases, volcanic production and heat transport can be as high as in the
plate tectonics regime.

Plutonic-squishy lid has been suggested recently as an alternative to the
previous scenarios, where most of the melt produced by the planet is intruded,
and remains within the lithosphere rather than reaching the surface. This
leads to a warm ductile lithosphere that prevents plate tectonics (Rozel et
al., 2017; LourenÃ§o et al., 2018, 2020). However, the surface can be
moderately mobile (more so than in stagnant lid but less than in mobile lid
regime), but surface velocities are lower than the convective mantle’s.
Deformation is more localized than in stagnant lid but less than in a plate
tectonics, with generally small tectonic units. Heat is extracted from the
mantle more efficiently than in the stagnant lid regime. Isolated subduction
by lithospheric dripping is possible. Volcanic production would be relatively
low due to the high fraction of intruded melt, but the surface heat flux could
be close to that of the mobile lid regime (LourenÃ§o et al., 2018).

The regimes discussed above are possible end-members for what is likely closer
to a continuum of interior dynamics. Real-life is more complicated than these
ideal configurations and spatial and temporal variations are expected for each
given planet. It is also likely that terrestrial planets can switch from one
regime to the other during their evolution (Sleep, 2000b). An episodic lid
regime, for example, could correspond to a scenario with short occurrences of
mobile lid separated by long periods of stagnant lid (e.g. Armann and Tackley,
2012) or the other way around (Lenardic and Crowley, 2012). Finally, it is
likely that transition periods between regimes could last hundreds of millions
to billions of years (e.g. Weller and Kiefer, 2020; Rolf et al., 2022).

Figure 5: The three main end-member convection regimes: Plate tectonics,
Stagnant Lid and Plutonic-squishy lid. Two additional specific cases are also
highlighted: episodic lid, which is the transition between plate
tectonics/mobile lid and the stagnant lid end member, and heat pipe, a
stagnant lid with a large volcanic production (i.e., eruption). Schematic
views of the interior dynamics of the three main regimes are indicated as
cutaway illustrations of planetary interior structures, next to their
respective domains. Regimes are distinguished by possibly observable
characteristics of the planet. These axes should not be considered as the
causes of the regimes depicted and are not fully independent from each other.
Surface heat flux, the most readily available observable in the solar system,
depends on many factors, such as size, mass, age and composition of the
planet. The intrusion to extrusion ratio defines how much of the melt produced
in the upper mantle reaches the surface. It is not a direct proxy of total
volcanism and is likely to vary spatially. It could be a function of the
surface temperature, which is a more direct observable, but can change over
time. Surface yield stress is the convective stress caused by mantle
convection required to break the lithosphere. It varies with the age of the
planet and probably surface temperature. The presence of surface water and
other fluids, and processes such as erosion, are also known to facilitate
subduction and therefore lower the surface yield stress, which could introduce
additional points of divergence between Mars, Venus and Earth. Lithospheric
thickness could be considered as a first order observable for this parameter,
although it is also influenced, to a lesser extent, by the intrusion to
extrusion ratio. Convection regime figures are modified from LourenÃ§o and
Rozel (2023).

The interior of present-day Earth is convecting, and heat is lost efficiently
by plate tectonics. Evidence suggests that modern-day plate tectonics has
existed in its current form for at least 1 Gyr (Stern, 2005), with suggested
onsets at least 3-4 Gyr ago (e.g. Dhuime et al., 2015; Cawood et al., 2006;
Nutman et al., 2002). The clear topographic dichotomy between oceanic and
continental crust, with the majority of the volcanic activity localized at the
plate boundaries, is specific to plate tectonics. Earth’s tectonic regime is
also characterized by the subduction of oceanic lithosphere that enables the
large-scale recycling of surface material into the mantle. Earth’s tectonic
processes and erosion combined are also responsible for the small number of
impact craters to be found on Earth (see Figure 6, top panel).

This convection regime has not been observed anywhere else on present-day
terrestrial planets. Mars is currently in a stagnant-lid regime. On Mars, the
lack of tectonic activity and limited erosion due the thin atmosphere result
in a heavily cratered, mostly old surface (see Figure 6, middle panel). It
should be noted that stagnant lid does not mean geologically dead, since Mars
appears to have been operating in the stagnant-lid regime for billions of
years and still shows recent signs of activity (e.g. Hartmann, 2005; Hauber et
al., 2011). Other planets, like Mercury, could also be in stagnant lid, but
closer to being geologically dead bodies (see Grott et al., 2011).

The current convection regime active on Venus is uncertain: while Venus does
not display global plate tectonics, the planet shows signs of deformation,
volcanic and tectonic activity, and lateral variation (e.g. Basilevsky and
Head, 2003; Rolf et al., 2022; Herrick et al., 2023; Hanmer, 2023), which
would be out of place in a fully stagnant-lid regime, such as observed on
Mars. As a result, the term “single plate planet” rather than “stagnant lid
planet” has been used to describe Venus. It has been suggested that Venus
could be an episodic lid planet, with brief overturns of the lithosphere into
the mantle, separated by long stagnant periods (Turcotte, 1993; Armann and
Tackley, 2012). The “plutonic-squishy lid” regime has also been proposed, and
could possibly explain the relatively young surface age, deformation and heat
flux measurements better than relying on a “well timed” overturn (LourenÃ§o
and Rozel, 2023; Rolf et al., 2022). However, no definitive evidence has been
found yet to settle the question. Venus’ stronger tectonic activity compared
to Mars can be also seen in the relatively small number of impact craters on
its surface (see Figure 6, bottom panel) as erosion processes are negligible
on this planet.

Evidence for Mars’ or Venus’ ancient convection regimes is even more difficult
to identify. Mars’s surface is old and indicates that its most active phase
occurred during the first billion year of its evolution (Carr, 2007), however
the available evidence does not shed much light on what the planet’s early
dynamics looked like. Venus’ relatively young surface does not allow any
direct insight into its distant past, as older surfaces have been covered by
more recent basaltic material. Indirect evidence from the atmosphere of the
planet indicate that large-scale outgassing may have been required to generate
the current volatile inventory (Weller et al., 2022; Gillmann et al., 2022),
which could indicate an active regime like a mobile lid in the past. Such an
active phase may not be required when considering other sources of volatiles
like impact delivery (Sakuraba et al., 2019; Gillmann et al., 2020) or could
contradict 40Ar measurements unless outgassing occurs very early (Kaula, 1999;
Gillmann et al., 2022).

Figure 6: (top) Map of Earth impact craters larger than 5 km diameter together
with their respective ages coded by color. Filled yellow circles indicate an
uncertain age. (middle) Map of Mars impact craters larger than 20 km diameter.
Smaller impact craters are not shown for visibility. (bottom) Map of Venus
impact craters larger than 5 km diameter. Venus impact craters are thought to
be relatively young (less than 1 Ga) but relative and absolute ages are
uncertain. Earth topography credit: Copyright:©2013 National Geographic
Society, i-cubed, published by Esri for use in ArcGIS. Earth crater database
adapted from (Mazrouei et al., 2019) and (Spray, 2018). Mars MOLA topography
map: WMS server used for JMARS client by Arizona State University for Jmars
(Christensen et al., 2009), credit: ASU, NASA, Goddard. Mars crater database
from Robbins and Hynek (2012). Venus map Credit: Credit: USGS/NASA/JPL
Magellan Mission, http://planetarymaps.usgs.gov/cgi-
bin/mapserv?map=/maps/venus/venus_simp_cyl.map. Venus crater database is from
(Herrick et al., 1997), and available at
https://www.lpi.usra.edu/resources/vc/.

###  3.2 Volcanic production

While it is obvious that Earth is volcanically active at present-day, the same
cannot be said about Mars and Venus. However, dating of lava flows on Mars
indicates volcanic activity in specific areas in the last few hundred million
years (Neukum et al., 2004; Werner, 2009; Carr and Head, 2010; Niles et al.,
2010) and marsquakes in the Cerberus Fossa region indicate the presence of
magma in the martian underground (Stähler et al., 2022). On Venus, transient
IR anomalies localized close to identified lava flows and surface changes in
volcanic regions have been interpreted as current volcanic activity (Smrekar
et al., 2010; Herrick and Hensley, 2023). Global volcanic production rates are
estimated to be around 20-30 km3/yr for Earth and the extrusive volcanic
production to be about 4 km3/yr (Crisp, 1984; Morgan, 1998). In the case of
Venus, it has been estimated to range from 0.3 to 10 km3/yr (Fegley Jr and
Prinn, 1989; Bullock and Grinspoon, 2001) to $\leq$ 2 km3/yr (Head et al.,
1991). Estimates for Mars indicate lower production rates around 0.3 km3/yr
(Greeley and Schneid, 1991).

Past volcanic production is even more difficult to constrain, but all three
planets show signs of an active past. Mars boasts some of the largest
volcanoes in the solar system and multiple volcanic provinces. Venus’ surface
is mainly covered by basaltic plains, its mostly young surface indicates
active resurfacing, and extremely long lava flows have been observed (Fegley
Jr, 2014; Conrad and Nimmo, 2023).

It is likely that the three planets were more active during the first billion
years as they lost accretion heat. Furthermore, heating by short-lived 26Al
might have played a role in the early evolution of the growing planetary
embryos (Lichtenberg et al., 2019). Mars is considered to have completed
accretion and core formation already within $\sim$ 10 Myrs (Dauphas and
Pourmand, 2011; Mezger et al., 2013) and magma ocean crystallisation occurred
within $\sim$ 20 Myrs after the start of the solar system (Bouvier et al.,
2018). In comparison to Earth-like planets, smaller bodies such as Mars would
have lost heat more rapidly during their early stages of evolution. This could
explain differences in estimated volcanic production rates. However, once a
stagnant lid is in place, the planet loses heat inefficiently, which may be
why Mars’ core appears to still be mostly liquid (Irving et al., 2023). It
could also cause the mantle to heat up and cause widespread partial melting
(which is in turn countered by increasing thick lids; (O’Neill et al., 2014).
Differences between Venus and Earth may originate from other characteristics,
since their sizes are similar.

###  3.3 Outgassing as evidence for planetary history

The volcanic history of a terrestrial planet is critical to the evolution of
its atmosphere. Volcanic outgassing is one of the major sources of volatiles
for the fluid envelopes of a rocky planet. In general, a higher production of
volcanic material is expected to increase global volatile extraction from the
mantle, but transport from the interior to the atmosphere is modulated by
interior and surface conditions (see Gillmann et al., 2022). For example, the
specific composition and mass of outgassed species depends on interior
composition, redox state (Hirschmann and Withers, 2008; Ortenzi et al., 2020)
and $P$-$T$ conditions, both in the mantle (during melting) and at the surface
(upon release, Gaillard and Scaillet (2014)).

As a rule, due to their size and heat budget, Venus and Earth are expected to
produce more melt than Mars and possibly outgas more. Differences between
Earth and Venus would be caused by past history and mantle dynamics
differences: at present Venus is expected to experience less volcanism, but
precise estimates are difficult to make. Based on their atmosphere composition
all three planet would release CO2. Section 3.6 discusses the consequences for
the volatile inventory. Mars could outgas CO2 at low volatile concentrations
due to its composition and reduced interior (Hirschmann and Withers, 2008). It
is unknown what the composition of Venus’ outgassing is, but it is thought
that water may not be released into the atmosphere because the planet’s mantle
is dry and/or the surface pressure is high (Gaillard and Scaillet, 2014).

The concentration of radioactive Ar in the atmosphere has been suggested to be
a proxy for the volcanic history of a terrestrial planet. As potassium decays
into 40Ar, argon partitions into the liquid phase during partial melting and
is outgassed into the atmosphere. Based on assumed initial compositions for
the planet (i.e. K/U ratio), one can compare the relative outgassing of the
planets. Measurements for 40Ar suggest that Earth could be $\approx$ 50%
degassed, and Venus would have outgassed $\approx$ 25% of its volatiles,
making its atmosphere more primordial (less affected by outgassed volatiles,
at least after the end of the magma ocean phase, Kaula, 1999). The
uncertainties in initial compositions however, make this number poorly
constrained (Gillmann et al., 2022). Additionally, the timing of the
outgassing is important, as an early massive outgassing, when little 40Ar has
been produced, could possibly release large amounts of volatiles without being
mirrored by 40Ar measurements. Finally, especially in the case of Mars, losses
of Argon through atmospheric escape could be difficult to quantify (i.e.
Hutchins and Jakosky, 1996; Gillmann et al., 2011; Leblanc et al., 2012).
However, models that track the evolution of outgassing and 40Ar production
under a continuous stagnant lid regime throughout the simulated history of
Mars (O’Neill et al., 2007; Gillmann et al., 2011) produce volcanic fluxes
that are consistent with present-day 40Ar measurements (Pollack and Black,
1982). In the end, though qualitative, differences in the records of Earth and
Venus point at a different style of outgassing, which could be explained if
Earth operated mostly under mobile lid/plate tectonics (associated with larger
outgassing), while Venus has had an episodic regime (O’Neill et al., 2014), a
change in its regime (Gillmann and Tackley, 2014), or if its mobile-lid/plate-
tectonics regime is limited to its early evolution (Arkani-Hamed, 1993;
Gillmann and Tackley, 2014; Weller et al., 2022).

The generation (or not) of a magnetic field in the planetary core is also a
clue pointing towards different evolutionary paths. Earth shows a self-
sustained magnetic field with a strength similar to present-day since at least
3.2 Ga, possibly 3.45 Ga (Tarduno et al., 2014). Mars, however, sustains no
dynamo at present-day but traces of ancient remanent magnetisation of its
crust exist and date back to the first 600 Myr of its evolution (Steele et
al., 2023). Finally, Venus shows no sign of a global self-sustained magnetic
field at present-day (Phillips and Russell, 1987) and no remanent
magnetisation has been observed so far. A magnetic dynamo is generated by
convection in the liquid layer of the metallic core. It can be thermal
(sufficient heat is lost at the core mantle boundary to drive core convection)
and/or chemical (iron solidifies and sinks towards the solid inner core, thus
stirring the liquid core), but it is always related to heat extraction by
mantle convection and core cooling. The lack of a dynamo is thus indicative of
either a completely frozen core, a stably stratified core (Jacobson et al.,
2017) or a too low heat flux out of the core (insufficient to cause core
convection, thus no thermal dynamo).

The lack of a dynamo on Venus is especially puzzling if one assumes that Earth
and Venus share a similar core composition and characteristics, as simulations
would predict that slow rotating present-day Venus could generate a detectable
magnetic field (i.e. O’Rourke et al., 2018). The current estimates for the
tidal Love number on Venus are not precise enough to discriminate between a
solid and liquid core (Dumoulin et al., 2017). It has been suggested that
Venus did not experience giant collisions such as Earth’s moon-forming impact,
and therefore retained a stratified core (Jacobson et al., 2017), thus
explaining the lack of magnetic field. In that case, the slow retrograde
rotation observed for Venus would be caused by tidal interaction (Dobrovolskis
and Ingersoll, 1980; Correia and Laskar, 2003; Leconte et al., 2015), not
impact despinning. However, it has also been proposed that impacts were the
cause of the peculiar Venus rotation (i.e. McCord, 1968; Alemi and Stevenson,
2006; Raymond et al., 2013). If the core is unstratified, the lack of a
present-day magnetic field would suggest near-complete solidification or that
the thermal conductivity of Venus’ core material is higher than generally
assumed (O’Rourke et al., 2018).

###  3.4 The role of impacts in interior evolution

Impacts have also been suggested to affect the interior dynamics of
terrestrial planets. During a collision, the kinetic energy of the impactor
can be transferred to the target planet’s mantle as thermal energy. If the
impact is energetic enough and large enough (so that the heated volume extends
beyond the lithosphere and into the mantle, typically for impactors above 100
km radius), then the mantle dynamics can be affected by the collision
(Gillmann et al., 2016).

Such large impacts have been shown to cause temporary subduction events in
numerical simulations of Venus and Earth (Gillmann et al., 2016; O’Neill et
al., 2017; Borgeat and Tackley, 2022) and to increase lithosphere mobility.
However, their consequences in simulations are relatively short-term (a few
hundred million years at most) and any mobile lid regime they cause would have
naturally emerged within the simulation parameters (Borgeat and Tackley,
2022).

Simulations of Mars’ largest recorded impacts have also failed to result in
any lasting change for both climate or internal state (Turbet et al., 2020;
Ruedas and Breuer, 2019). Only early-on ($\geq$ 4 Ga) impactors are likely to
be large enough (above a few hundred kilometer radius, in order to
significantly penetrate into the mantle) to have affected the interior and
climate significantly on the long-term. Finally, it is unclear how different
the impact flux would have been on the three terrestrial planets and what
marker would allow us to distinguish between possible scenarios (e.g. Gillmann
et al., 2020).

###  3.5 Modelling efforts and governing parameters

While numerical models are now capable of simulating Earth-like single sided
plate tectonics, where only one of the plates sinks back into the mantle even
when both are oceanic plates (i.e. Crameri and Tackley, 2014, 2015), the
actual conditions for a planet to develop this regime are more difficult to
assess. In essence, it requires the lithosphere to be brittle enough so it can
break rather than flow in a ductile way, and not so strong that convective
stress can never break it. In terms of modelling, this means that the yield
strength should be low (a few tens of MPa - see for example LourenÃ§o and
Rozel, 2023). However, these values do not fit with laboratory measurements
for Earth materials, which are reportedly much higher, potentially because
these experiments also do not account for localized weak zones, faults and
lateral material variations occurring on larger length scales.

Temperature is a major parameter that affects rheology. It has been shown that
surface temperature variations, due to the evolution of the climate, could
have direct consequences on the convection regime. For example, Lenardic et
al. (2008) have shown that a surface temperature increase of about 100 K could
shut down existing plate tectonics in an Earth-like model by reducing the
viscosity of the convective mantle below the lithosphere. Because of the
exponential dependence of the viscosity upon temperature, increasing
temperature by 100 K reduces the viscosity by about one order of magnitude
(Kohlstedt et al., 1995). In turn, lower viscosities would reduce convective
stresses upon the lithosphere (Moresi and Solomatov, 1998). If convective
stress drops below the yield strength of the lithosphere, plate tectonics
stops (Moresi and Solomatov, 1998). Models of Venus (Gillmann and Tackley,
2014) indicate that water abundance variations in the atmosphere of Venus
could change surface temperatures by several 10s to 100s K and cause a switch
from a mobile to a episodic lid regime as partial pressure of water evolves
towards its present-day value. Noack et al. (2012) highlight that particularly
high surface temperatures (higher than at present-day) could reduce
lithosphere viscosity enough to allow it to be dragged by the mantle and
become mobile. Such high temperatures (and possibly present-day Venus
temperatures) could also lead to a relatively ductile lithosphere and prevent
a plate-like behaviour by allowing faults to “heal” more easily (Bercovici and
Ricard, 2014). It is still unclear whether any of those scenarios occurred
during the evolution of Venus.

The temperature within the lithosphere can also be affected by intrusive
volcanism, in turn possibly favored by high surface temperatures (LourenÃ§o et
al., 2020). The phenomenon can be local and generate weak zones or be more
widespread and lead to a warm and soft lithosphere.

Water has also been suggested to play an important role in the rheology of the
mantle and lithosphere of terrestrial planet due to its effect on the friction
mechanisms and pore pressure (Korenaga, 2013). Through the dependence of
viscosity on water, the water cycle affects mantle dynamics. The correlation
between plate tectonics and liquid surface water in the solar system has
motivated this line of thought. If water is needed for plate tectonics (i.e.
Solomatov, 2004), a dry early state, as described before, would favor the
single plate/episodic lid regime as suggested for present-day Venus. On the
other hand, low water abundances may lead to a higher mantle viscosity (Xie
and Tackley, 2004), which could, for example, improve the coupling between the
mantle and lithosphere. Because the abundance of water in the mantle is also
dependent on mantle dynamics, a feedback mechanism would exist between thermal
evolution and the water cycle (Crowley et al., 2011).

In the end, despite important advances in our understanding of different
regimes and mechanisms at work in planetary mantles, the lack of actual
knowledge regarding the state and conditions inside solar system terrestrial
planets prevents us from proposing a definitive explanation for the
differences we observe. This is in part because we have little direct
knowledge of the rheology and water content of both Mars and Venus. In recent
years, partly in preparation for future exoplanet atmosphere characterization,
efforts have been made to use atmosphere composition to investigate interior
evolution, by using the consequences of outgassing integrated over the
planets’ history e.g. (Gillmann et al., 2020; Krissansen-Totton et al., 2021a;
Ortenzi et al., 2020; Weller et al., 2022; Warren and Kite, 2023).

###  3.6 Consequences on volatile inventory

The convection regime of all three terrestrial planets had important
consequences for their whole evolution and surface conditions. On Earth, the
composition of the atmosphere is the result of many processes, collectively
referred to as volatile cycles (see Dasgupta and Hirschmann, 2010). Over
geological timescales, surface solid-gas reactions, the effect of life and the
recycling flux at the subduction zones governs, for example, the abundance of
CO2 in the atmosphere, with complex and uncertain feedbacks (e.g.
Friedlingstein et al., 2006), while on short timescales, ocean-atmosphere-
biosphere interaction would dominate.

Comparatively, volatile exchanges are likely to be much simpler on Mars and
Venus (e.g. Van Thienen et al., 2007). The long-term stagnant lid on Mars
makes any recycling of gaseous species into the mantle unlikely. Same applies
for Venus, at least since the time of the formation of the present-day surface
and atmosphere. Additionally, at present-day Venus surface conditions,
carbonates are not stable and, due to the lack of surface water, can not form
(Fegley Jr, 2014). A limited form of volatile storage can act as a temporary
sink even on stagnant lid planets. However, with no volatile cycle and no
pathway back into the mantle, it can be easily destabilized. HÃ¶ning et al.
(2021) have described such an evolution and suggest that volatiles would be
released back into the atmosphere during the first billion year as temperature
increases either at the surface or at the depth where the material is buried.

In the absence of a stabilizing feedback, volatiles would accumulate in the
atmosphere when not lost by escape processes, which would be the situation we
observe for Mars and Venus relative to Earth (Bean et al., 2017; Turbet et
al., 2019). The nature and amount of gases produced by partial melting and
volcanism, then released into the atmosphere, are primarily dependent on the
composition and redox state of the mantle, which both remain uncertain, even
for Earth. The redox state of the mantle can be expressed using the oxygen
fugacity measured as the ratio between the abundances of the different iron
ions relative to a buffer, like the IW buffer (see also Section 2). Earth’s
upper mantle is, despite some heterogeneities, rather oxidized at present-day,
at approximately IW+1 to IW+5 (e.g. Ballhaus et al., 1990; Hirschmann, 2022),
while Mars is more reduced, around IW+0 to IW+1 (Herd et al., 2002; Shearer et
al., 2006; Karner et al., 2007; Hirschmann and Withers, 2008), and Venus
remains unconstrained, possibly close to Earth (Schaefer and Fegley, 2017). As
a result, outgassing on Mars may be characterized by lower CO2 concentrations
in the magma than on Earth and, possibly, Venus (Hirschmann and Withers,
2008).

However, it has also been suggested that surface conditions, such as surface
pressure, may affect the composition of the outgassing into the atmosphere.
For example, surface pressure affects the gas-gas and gas-melt equilibria,
which modifies volatile speciation during release (i.e. Gaillard and Scaillet,
2014). As a result, high surface pressures (above $\approx$10 bar) may inhibit
part of water outgassing into the atmosphere, increasing its solubility in the
lava. Gaillard and Scaillet (2014) suggest $\approx$90$\%$ of the initial
water content of lava could be trapped. Instead, more Earth-like surface
pressures would lead to water being the dominant outgassed species. On the
other hand, CO2 can outgas even at pressures of $\approx$100 bar. Venus-like
surface pressures would prevent most H2O from reaching the atmosphere under
present-day Venus conditions, and possibly in the past, as long as surface
pressures remain high (above a few bar). Earth may thus occupy a niche where
the mantle is oxidized enough and the surface pressure low enough to allow for
the outgassing of both CO2 and water. Under Mars- or Venus-like conditions,
either the mantle or at the surface, respectively, could stifle the release of
one or both of those species (Gillmann et al., 2022).

Episodic volcanic outgassing is also often suggested for Venus. Based on the
most recent resurfacing event that covered most of the surface with basalt (or
the equivalent production under the equilibrium hypothesis; Phillips et al.
(1992); see also Smrekar et al. (2018), Lopez et al. (1998) estimate that 9-10
such events would be required to build up the present-day CO2 atmosphere,
assuming an Earth-like lava composition. This corresponds to a total amount of
extrusive lava of about 5$\times$1010 km3 (based on possibly generous
estimates from (Bullock and Grinspoon, 2001)), which would translate into a
total volume of melt of 2.5-5$\times$1011 km3. As a reference, the volume of
Venus’ mantle is about 7.8$\times$1011 km3. Therefore, episodic production of
the atmosphere requires massive outgassing, which could be in conflict with
40Ar measurements, unless it occurred early or a large fraction of the
atmosphere was already acquired during accretion or from other sources
(impacts, destabilization of surface material).

Based on a detailed survey of the surface, Head et al. (2022) suggest that
80-100 (likely smaller scale) resurfacing events would be required and that
the atmosphere of Venus is therefore ancient, which seems to be supported by
40Ar measurements. Simulations that reproduce episodic evolution (Armann and
Tackley, 2012; Gillmann and Tackley, 2014; Gillmann et al., 2020; Weller et
al., 2022) require multiple billions of years to generate enough volcanic
episodes to produce Venus’ 90 bar CO2 atmosphere, or fail to generate enough
large events, due to the large amount of heat required for such large melting
episodes - heat that is extracted from the mantle during the process.

Additionally, if CO2 would outgas easily (provided the mantle is oxidized
enough), water may have been unable to reach the atmosphere for a large part
of the Venus evolution due to high surface pressures (Gaillard and Scaillet,
2014; Gaillard et al., 2022). Way et al. (2022a) propose that such large-scale
volcanism (possibly akin to Earth’s Large Igneous Provinces) may have
contributed to the present harsh venusian climate. However, little is known
about the ancient volcanic production and outgassing on Venus, and modelling
based on existing constraints, like 40Ar, noble gases, D/H ratio is an active
and promising avenue of research (Noack et al., 2012; Gillmann et al., 2020;
Krissansen-Totton et al., 2021a).

##  4 Atmospheric loss

Looking at the different atmosphere masses on Earth, Mars and Venus, signs of
volatile losses can for instance be inferred from the fractionation of non-
radiogenic gases and the deuterium to hydrogen ratio (D/H). Indeed, Mars has
been observed to be more enriched in deuterium by a factor of 5 than Earth
(Owen et al., 1988) and Venus by a factor of 150 (Donahue et al., 1997). The
preferential loss of the lighter isotope compared to the heavier one affects
the ratio between the two isotopes - the more a sample deviates from the
primordial ratio, the stronger the loss. One should however remember that this
is not true for all loss mechanisms (impact erosion of the atmosphere or
intense hydrodynamic escape would not fractionate H, for example), and that
quantifying that loss (Pahlevan et al., 2019; Kurokawa et al., 2018; Zahnle
and Kasting, 2023) or how the ratio is affected by other processes is still
uncertain (Grinspoon, 1993; Avice et al., 2022).

Generally speaking, three main categories of escape are considered and
discussed below: hydrodynamic escape (or thermal escape, as it is due to
heating of the atmosphere), non-thermal escape (chemical reactions and
collisions with particles from the solar wind) and impact erosion (caused by
meteoritic collisions).

Atmospheric escape fluxes have been directly measured or calculated for the
three planets. Additionally, Mars and Venus appear drier than the Earth, and
water plays an important role in the long-term terrestrial planet evolution.
Therefore, it is no surprise that atmospheric loss processes have been
proposed as a possible cause of the diverging evolutionary pathways for
terrestrial planets in the Solar System.

Noble gases in the Venus atmosphere have been analyzed by mass spectrometers
and gas chromatographs on board the Pioneer Venus and Venera probes. Although
a similar pattern is observed for the three terrestrial planets, the 20Ne/36Ar
ratio is depleted by a factor of $\approx$ 3 in the Venus atmosphere relative
to Earth’s. Ne and Ar are more abundant in Venus’ atmosphere than in Earth’s
atmosphere, by at least factors of 10 and 50, respectively. 20Ne and 36Ar
abundances are close to chondritic for Venus, but depleted for Mars and Earth,
as are 84Kr and 130Xe for those two planets. In addition, 130Xe/84Kr is
measured at one order of magnitude below the chondritic ratio, indicating
further loss (Pepin, 1991). In the case of Venus, however, Kr and Xe are still
poorly constrained, thus so far it is not possible to assess whether or not
Venus follows the Earth-like pattern (Lammer et al., 2018). With the caveat of
Venus Xe measurements, all three planets are depleted in noble gases compared
to the solar composition. In general though, Venus’ noble gas elemental
spectrum is suggested to be more solar-like than those of Earth and Mars.

On Mars, the isotopic components of atmospheric Kr are close to those of the
solar wind and remained mainly unfractionated (e.g. Pepin, 1991; Becker et
al., 2003; Conrad et al., 2016). Xe isotopes in Earth’s and Mars’ atmosphere
are enriched in heavier isotopes. The case of Xe is still actively debated,
with the fractionation possibly attributed to long-term (4.5-2 Ga; Avice and
Marty (2020)) escape of ionized hydrogen dragging of Xe (Zahnle et al., 2019).

Neon is less fractionated (Wieler, 2002) in Venus atmosphere (20Ne/22N = 11.9
$\pm$ 0.7) than in Earth’s atmosphere (20Ne/22Ne = 9.8) with respect to solar
composition (20Ne/22Ne = 13.5). Because Ne is only slightly heavier than O,
hydrodynamic escape of Ne implies hydrodynamic escape of oxygen, and Ne may be
used as a tracer of oxygen escape at primitive stages (e.g. Gillmann et al.,
2009a). There is also no evidence of changes in Ne, Ar and Kr isotopic
compositions (non-radiogenic) during the past 3.5 Ga on Earth (Avice et al.,
2017). On all three planets it has generally been suggested that their lighter
noble gases were fractionated during an early hydrodynamic escape phase (the
first few hundred million years).

###  4.1 Hydrodynamic escape

Hydrodynamic (or thermal) escape occurs due to heating of the atmosphere by
intense EUV radiation from the Sun or by radiation from a primitive hot rocky
planet (Ginzburg et al., 2018, "core-powered"). It causes atoms in the upper
atmosphere to exceed the escape velocity, leading to very efficient escape of
the bulk gas of the upper atmosphere where the atmosphere remains a
collisional fluid as it passes through the transonic point (Chamberlain, 1963;
Chassefière, 1996; Fossati et al., 2017). Light species (especially H) are
also the most efficient at escaping via this process, as they require less
energy to reach bulk escape velocity.

Heavier species (such as helium, carbon or oxygen atoms) can undergo escape
via so-called hydrodynamic drag where they are carried along with the stream
of lighter hydrogen atoms (e.g. Hunten, 1973). Due to solar evolution (the
decrease in EUV flux with time (Claire et al., 2012), this implies the most
favourable conditions for such a process occur during the first few hundred
million years. At lower energy levels, a transition occurs from hydrodynamic
escape to the much less efficient Jeans escape, causing the loss of atoms
populating the high energy tail of a Maxwell distribution (Jeans, 1925;
Chamberlain, 1963), and still occurring at present-day on Earth, Mars and
Venus.

Hydrodynamic escape would have efficiently removed the primordial H/He
atmosphere that all three planets obtained from the solar nebula during their
formation (Lammer et al., 2018, 2020). Earth’s D/H seems to be incompatible
with oceans originating from the solar nebula (Marty, 2012). Then, during the
magma ocean phase, the ongoing thermal loss would have affected the water
vapor/CO2 atmosphere of Earth, Venus and Mars to various degrees, whether it
came from interaction of the atmosphere with the magma ocean or from
catastrophic outgassing during magma ocean solidification. Finally, if a
planet, such as Venus, entered a runaway greenhouse state, then hydrodynamic
escape would also have been a dominant factor for water loss. The loss of
water would have remained efficient but the presence of more abundant heavier
species would have led to diminished loss rates. Still, modelling efforts have
shown that a Mars-like body orbiting at Earth-like distance from the Sun would
lose its atmosphere (85 bar H2O and 11 bar CO2) in about 15 Myr (Odert et al.,
2018), and that Venus would only take 50 Myr to lose about 2 Earth ocean
equivalents (Gillmann et al., 2009b). Gravity, the composition of the
atmosphere and the proximity to the star all affect the loss rates, with
smaller or closer planets being more affected. Thus, Mars could have lost a
large part of its initial water inventory and even CO2 (Tian et al., 2009;
Odert et al., 2018). Mars being drier than Earth due to early escape ($\geq$ 4
Ga) is consistent with martian meteorites measurements (Cassata, 2017).

The planets are efficiently dried out, as long as a supply of water is
available in the atmosphere. Kasting and Pollack (1983) calculated that
hydrodynamic escape was the dominant process as long as the water mass mixing
ratio of water in the lower atmosphere exceeded 0.1, even during the later
evolution.

In short, factors that favor a strong hydrodynamic escape are (in order of
importance): (i) an H-rich atmosphere (water vapour for instance), (ii) a
strong EUV flux (for example during the first few hundred million years of the
evolution) and (iii) a small planet with low gravity (see also Catling and
Zahnle, 2009). Because of (i) and (ii) thermal escape is likely the dominant
process during the first few hundred million years of planetary evolution. The
escape of lighter species (H) is favored, but a strong enough flux can cause
the loss of heavier components. Conversely a CO2 atmosphere, low EUV flux and
stronger gravity would reduce escape rates, while magnetic fields do not
impede hydrodynamic escape.

###  4.2 Non-thermal escape

Non-thermal escape covers a few mechanisms that involve the interaction of the
upper atmosphere molecules (above the exobase) and ions with energy and
particles brought by the solar flux, such as: charge exchange, photochemical
dissociation, sputtering, polar wind, plasma clouds. In each case, the
interaction leads specific molecules to reach high enough velocities to escape
(Catling and Zahnle, 2009).

Over the last decades, a large number of studies have attempted to quantify
the escape rates of heavy ions (such as O+, O${}_{2}^{+}$ and CO${}_{2}^{+}$)
on Mars, Earth and Venus based on observations. (Ramstad and Barabash, 2021)
have summarized these results (their figure 5) and found that estimates for
Earth, Mars and Venus tend to be roughly similar, despite the large variations
in planetary size, atmosphere composition, presence (or absence) of a global
magnetic field. Mars’ heavy ion escape rates range between 2 $\times$ 1023 s-1
and 1025 s-1; for Venus reported rates cover 1-6 $\times$ 1024 s-1 (with an
outlier one order of magnitude above), while Earth’s escape fluxes are higher:
7 $\times$ 1024 to 1026 s-1. For O+ alone, rates ranges from 2-4 $\times$ 1024
s-1 for Mars, to 1-4 $\times$ 1024 s-1 for Venus and 5 $\times$ 1024 s-1 to 5
$\times$ 1025 s-1 for Earth (see Ramstad and Barabash, 2021, and references
therin).

These reported values also cast doubt on the previously accepted notion that
magnetic fields provide an efficient shield against atmospheric escape, which
in turn was used to explain why Earth was so different compared to Mars and
Venus, and retained its water. To explain the similar measured escape rates
reported above, it has been suggested that Earth’s magnetic field extends much
further into space than its atmosphere (a few Earth radii) and therefore
intercepts more energy from the Sun than both Mars or Venus (Brain et al.,
2012), leading to increased atmospheric escape.

It has also been suggested that magnetic fields could actually enhance
atmospheric escape (e.g. Gunell et al., 2018). This idea has been disputed by
Tarduno et al. (2014), for example for underestimating the return fluxes
(ionized molecules escaping following magnetic lines that reconnect to the
planet rather than open lines in the magnetotail). The current state of the
research indicates that the magnetic field affects escape mechanisms (a
magnetized planet will lose molecules at the cusps of the field rather than in
the tail of the induced field) and affect which mechanism can be dominant.
However, so far we are not able to explain exactly what the resulting escape
flux will be (Gronoff et al., 2020). As a consequence, it remains uncertain by
how much the presence of a past magnetic field could have affected the
respective evolution of Mars, Venus and Earth, although as discussed above
there may be hints that the presence of a magnetic field does not result in a
radically different volatile loss history.

###  4.3 Past escape reconstruction

Attempts have been made to reconstruct past escape rates (Hunten et al., 1989)
based on the present-day measurements for Mars (Chassefière and Leblanc, 2004;
Gillmann et al., 2009b), with the latest contributions being the MAVEN results
(Jakosky, 2021), and Venus (Gillmann and Tackley, 2014; Persson et al., 2020).
These are obtained by extrapolating the present-day escape rates obtained at
high and low solar EUV fluxes during a solar cycle. However, they ignore
changes in atmosphere composition and structure, or exosphere temperature and
remain dependent on other factors, such as the existence of a magnetic field
(Gronoff et al., 2020; Way et al., 2022b). Depending on the specific
conditions at a given time, escape rates caused by a given mechanism are
likely to vary and the dominant escape process would certainly change: water
vapour atmospheres would be defined by strong H loss from hydrodynamic escape,
while dry atmospheres would see non-thermal processes gain importance.
Generally speaking, the two types of atmospheres are often used to describe,
respectively, (1) the primitive phase of planetary evolution during magma
evolution or runaway greenhouse, and (2) the last $\approx$ 4 Gyr and present-
day.

For example, CO2 in the thermosphere radiates energy back to space, leading to
infrared cooling of the upper atmosphere and affecting the structure of the
atmosphere (Roble and Dickinson, 1989). This is why Venus’ exobase is both
cooler and occurs at a lower altitude than Earth’s. A hot, expanded
atmosphere, resulting from a switch from a CO2-rich atmosphere to a N2
atmosphere for example, could possibly lead to escape rates orders of
magnitude higher (Lammer et al., 2006; Way et al., 2022b, even though
estimates are very uncertain;). Past reconstructed escape rates should thus be
considered with caution, only as a first order approximation. They are
currently, however, our best shot at ancient loss rates, since we are not yet
able to predict a total escape rate from a given set of conditions.

Non-thermal escape is modulated by (i) a planet’s gravity, with weaker gravity
leaving planets more vulnerable to loss. Non-thermal escape is also a function
of (ii) the composition of the atmosphere, since most mechanisms depend on
chemistry. However the precise effects of different atmosphere composition on
loss rates is still uncertain. Finally, as a large part of the escape involves
ions, (iii) magnetic fields existence and configuration will affect non-
thermal escape. Non-thermal escape is dominant during late evolution and for
species such as O (all planets) or C, N, Ar (for Mars).

###  4.4 Loss of water and the fate of remnant oxygen

From observation, for non-thermal processes, the ratio of the escape of H and
O appears to be close to or below the stoichiometry of water (between 1.1 and
2.6 Persson et al., 2018, for instance, in the case of Venus). Such a ratio
leads to the full escape of water or a moderate loss of O relative to the
source water. On the other hand, thermal escape is expected to lead to a
relative accumulation of oxygen in the atmosphere due to the strong
differences in loss efficiencies for species of different masses. Oxygen,
being heavier, is lost at a much reduced rate compared to H. The ratio of the
loss of H to O would thus be much higher than that of their respective
abundance in the atmosphere (2 H for 1 O, assuming they come from the
photodissociation of water; Kasting and Pollack, 1983; Gillmann et al.,
2009a). As a result the atmosphere becomes more oxidized unless the excess O
can be removed through other processes such as oxidizing reducing gas species
and atmosphere-surface reactions. The fate of the remnant O has been
considered to be a constraint for the evolution of the Venusian atmosphere,
and is discussed in detail in Section 5.2. On Earth, reconstructed atmosphere
compositions dating back from before the Great Oxygenation Event (Lyons et
al., 2014; Catling and Zahnle, 2020) indicate that a long-lived O2-rich
atmosphere resulting from the process mentioned above is unlikely. Banded iron
formations (Canfield, 2005, and references therein), for example are on Earth
indicators of oxidation of iron in oceans under an atmosphere with low O2
concentrations and low seawater sulfates (and provide a link to the
consequences of life for planetary evolution, see below, Cloud Jr, 1968).

As mentioned above (see Section 4), signs for long-term water loss are
evidenced by the D/H measurements on Earth, Mars and Venus. Alsaeed and
Jakosky (2019), for example, reconstruct the evolution of water reservoirs
based on atmospheric escape on Mars and suggest that at 3.3 Ga, a global
equivalent layer of 40-120 m of water could have existed to explain the
present-day D/H ratio. Further, Mars’ atmosphere is enriched in 15N over 14N,
which has been suggested to result from non-thermal loss processes (Shizgal
and Arkos, 1996; Gillmann et al., 2011). On the other hand, non-thermal escape
on Mars is unable to account for the loss of a water equivalent above a few
100 mbar over 3-4 Gyr (Gillmann et al., 2009b, 2011). At the same time, the
cumulated water escape on Venus over the last 3.8 Gyr was recently estimated
to amount to a few centimeters to tens of centimeters only (Persson et al.,
2020).

It seems unlikely that non-thermal escape could, by itself, cause the
divergences observed in the solar system. However, it can critically influence
already thin atmospheres of low mass terrestrial planets like Mars’.
Additionally it remains a significant evolutionary process that shaped the
observed characteristics of thicker atmospheres like Earth’s and Venus’.

###  4.5 Atmosphere erosion by impacts

Impact-related erosion of the atmosphere can lead to volatile loss(Cameron,
1983; Melosh and Vickery, 1989). Four main mechanisms can cause escape (e.g.
Dehant et al., 2019): (i) direct ejection of the atmosphere by the shock wave,
(ii) the rising of the vaporized projectile and sediments in a vapor plume,
(iii) heating of the atmosphere by ejected particles and (iv) in the case of
very large collisions, ground motion of the planet can accelerate particles of
the atmosphere above escape velocities. That last process is deemed to be the
most efficient one. Genda and Abe (2003) estimate that such an impact ($R_{\rm
i}\sim$ 1000 km) could remove about 20% of a preexisting atmosphere and the
presence of a water ocean could even enhance the atmosphere loss (Genda and
Abe, 2005). More recent work (Schlichting et al., 2015), derives estimates
depending on relative mass of the impactor to the planet and its velocity.
Significant loss (above 10% of a preexisting atmosphere) requires the impactor
to be traveling at several times the planet’s escape velocity and/or to be of
a comparable mass to the target, which is more easily achieved for Mars than
for larger planets.

A key feature of impact erosion is that it generates bulk ejection of the
atmosphere and does not isotopically fractionate individual elements in the
planetary atmosphere, unlike other processes described above. It could,
however fractionate the volatile budget of two elements, in case those
elements are not distributed equally within the planet, for example if one
resides preferentially within the atmosphere while the other one is trapped in
the interior(e.g. Massol et al., 2016). Impact erosion of the atmosphere is
probably the main mean of removing Kr from the atmospheres of terrestrial
planets, since Kr (generally non-fractionated) is too heavy and difficult to
ionize to be significantly lost through the previously discussed thermal and
non-thermal processes (Pepin, 1994; Catling and Zahnle, 2009; Cassata et al.,
2022).

Smaller impactors ($R_{\rm i}$ $\leq$ 1000 km) individually remove less
atmospheric volatiles through processes (i)-(iii) than larger ones, however,
they are more efficient at atmospheric erosion per unit of mass. Schlichting
and Mukhopadhyay (2018) highlight that the much more numerous population of
smaller impactors (1 km $\leq$ $R_{\rm i}$ $\leq$ 20 km), as a whole, can
remove more volatiles than the few larger collisions (25 km $\leq$ $R_{\rm i}$
$\leq$ 1000 km). They argue that such a flux of small impactors would be able
to erode an Earth-like atmosphere within a few billion years. While this can
affect decisively thin atmospheres (such as Mars’), this escape rate makes
little difference, by itself, on a planet with a multi-bar atmosphere such as
present-day Venus.

In short, volatile loss is very dependent on the planetary mass and impact
velocity: less massive planets such as Mars are more vulnerable to erosion
than Earth or Venus (Pham et al., 2011) and faster impactors can drive a
greater loss. Furthermore, massive atmospheres would be only marginally
affected by erosion, relative to their total masses, in contrast to planets
with thinner atmospheres. Finally, impacts can also act as sources of
volatiles depending on their exact composition (Gillmann et al., 2020, for
example) and affect atmosphere chemistry (Schaefer and Fegley, 2017). While
erosion, from a relatively predictable population of impactors, averages out,
volatile deposition by collisions is much more susceptible to stochastic
events (such as a single large volatile-rich impact), which may cause drastic
changes in atmosphere bulk composition and chemistry.

##  5 Unique features of the history of Mars, Venus and Earth

###  5.1 Mars

As Mars is less massive than Earth, magma ocean pressures on Mars would have
been lower, compared to the Earth’s magma ocean pressures. Geochemical studies
on martian meteorites support core formation pressure of about 14 GPa to
explain the depletion in siderophile and chalcophile elements in the martian
mantle (e.g. Righter and Chabot, 2011). Therefore, the iron disproportionation
would have had a limited effect on Fe3+ abundance and a $f$O2 gradient in the
martian magma ocean. The estimated surface $f$O2 above the magma ocean is
about IW-1$\sim$IW+1 (Deng et al., 2020). This $f$O2 is high enough that a
large fraction of H would be dissolved in the magma ocean as H2O (Gaillard et
al., 2022). As the orbit of Mars is far enough to escape from the runaway
greenhouse state, Mars is expected to have crystallized rapidly, though the
predicted duration of magma ocean crystallization shows a large discrepancy
between thermal models ($<\sim$1 Myr, Elkins-Tanton, 2008; Lebrun et al.,
2013) and geochemical constraints (several to tens Myr after core formation,
Borg et al., 2016; Kruijer et al., 2017, 2020). Several processes such as late
differentiation caused by cumulate overturn (e.g. Elkins-Tanton et al., 2005)
and heating by late accretion(e.g. Marchi et al., 2018) have been proposed as
potential causes of the prolonged Martian magma ocean. Depending on its
outgassing efficiency, its water would remain at the surface or in its
interior (Odert et al., 2018).

Mars’ ancient surface shows a dichotomy between the southern highlands and the
northern lowlands. The dichotomy is considered to be the oldest geological
feature on Mars and was created within the first 400-500 Ma after the planet’s
formation (Nimmo and Tanaka, 2005; Carr and Head, 2010). Different processes
have been suggested as the origin of this topographic feature like (i) impact
excavation of the northern hemisphere (Wilhelms and Squyres, 1984; Frey and
Schultz, 1988; Andrews-Hanna et al., 2008; Marinova et al., 2008; Nimmo et
al., 2008), (ii) low degree convection (Zhong and Zuber, 2001; Roberts and
Zhong, 2006; Zhong, 2009; Keller and Tackley, 2009; Å rÃ¡mek and Zhong, 2010)
and (iii) an impact in the southern hemisphere forming a so-called impact
megadome (Reese and Solomatov, 2006, 2010; Reese et al., 2010; Golabek et al.,
2011; Ballantyne et al., 2023; Cheng et al., 2024). Also it has been suggested
that Mars could have developed short-term plate tectonics during its first few
hundred million years (Frey, 2006; Sautter et al., 2015).

In short, due to its relatively small mass, and possibly limited water
inventory, Mars would have transitioned from a possibly active first billion
year into a stagnant lid regime. At about the same time, it lost a large part
of its initial water inventory and its magnetic field. Details regarding the
climate on ancient Mars beyond increasing desiccation remain debated, and both
"warm and wet" and "cold and wet/snowy" origins have been proposed (Wordsworth
et al., 2015), as well as episodic warming by volcanism and reducing
greenhouse gases (Halevy and Head III, 2014).

Observations of the martian surface give an idea of the consequences that
hydrodynamic escape could have as Mars’ terrain age allows studying its
distant past. Fluvial features indicate a decline in water’s role in shaping
the surface of the planet, evolving from valley networks in the Noachian to
episodic outflow channels in the Hesperian towards the more arid planet since
the Amazonian (Carr, 2007). Based on mineral alteration in the presence of
diminishing amounts of water the subsurface mineralogy analysis suggests a
similar evolution from Phyllosian to Theikian to Siderikian (Bibring et al.,
2006).

Long-term evolution models suggest outgassing would be relatively limited,
possibly due to interior redox conditions inherited from its primitive history
(Hirschmann and Withers, 2008; Deng et al., 2020). A large portion of the
outgassing would have occurred during the first billion years of its evolution
(Lammer et al., 2018), before most of its interior heat was lost. However,
even such low volatile release rates could be sufficient to affect surface
conditions and the composition of the atmosphere. Based on the estimated lava
composition and simulated volcanic production over the evolution of Mars,
outgassing histories have been modelled (i.e. Gillmann et al., 2009b, 2011;
Grott et al., 2011; Leblanc et al., 2012; Morschhauser et al., 2011; Sandu and
Kiefer, 2012; Hu et al., 2015).

It is likely that water loss on Mars was stronger early in the evolution of
the planet, both for hydrodynamic and non-thermal escape (Lammer et al.,
2018), and that for most of the evolution, escape was limited to a fraction of
a bar. Some simulations indicate that ancient surface pressures on Mars,
around 3.5-4 Ga, may have been low (a few to a few hundred millibar) and that
much of present-day CO2 atmosphere could originate from late outgassing
(Gillmann et al., 2009b, 2011; Leblanc et al., 2012; Lammer et al., 2013).
Volcanic outgassing could also account for most of present-day water surface
inventory (up to a 100 m global equivalent layer, Alsaeed and Jakosky (2019)).
This is in line with work by Kite et al. (2014) suggesting an upper limit of
$\sim$1 bar atmospheric pressure $\sim$3.6 Ga ago. This thin atmosphere was
more prone to atmosphere loss than Earth’s and Venus’, accordingly over time
favourable conditions for the presence of liquid water at the martian surface
ceased.

###  5.2 Venus

####  5.2.1 Potential evolution paths

Compared to Earth and Mars, there is little information on the history of
Venus. This is, in a large part, due to the overall young apparent age of most
of the planetary surface, which limits observations regarding most of its
evolution. No definitive evidence for surface water exists in the case of
Venus, due to the lack of surface features dating back more than 300-1000 Ma.
Surface mineralogy of tesserae (8% of the present-day venusian crust) has been
proposed to indicate the presence of felsic material in unknown quantities
(Shellnutt, 2019). This would suggest that an uncertain amount of liquid water
could have existed on Venus for an unknown period of time. Most of the
constraints on Venus’ past are derived from its atmosphere that retains the
accumulated effects of every process affecting volatile inventories. Needless
to say, unraveling plausible scenarios is a complicated endeavour. Current
research has not yet managed to converge toward a single agreed succession of
events that would lead to present-day Venus.

If Venus and Earth formed in the same way from the same building blocks, the
apparent dryness of the Venus could have been caused by its proximity to the
Sun. Venus receives about 1.9 times more solar flux than Earth, and so it can
relatively easily enter a runaway greenhouse state (Zahnle et al., 2007).
However, while the atmosphere and surface of Venus are dry compared to Earth,
the presence of water inside Venus has not been ruled out. Three different
scenarios have been proposed to explain the lack of water at the surface of
Venus (Kasting, 1988; Hamano et al., 2013; Gillmann et al., 2022): (i) Venus
was once an ocean planet like Earth, and then, its climate was destabilized by
internal factors, and/or, as the Sun got brighter over time, the surface water
was evaporated and lost by photolysis and escape of hydrogen. (ii) Venus
evolved into a desiccated planet as it is today during its magma ocean
crystallization process. (iii) Water was never outgassed from the interior of
the planet and was trapped in its interior.

One-dimensional cloud-free climate calculations yield the radiation limit of
about 280 W/m2 considering a planetary albedo of about 0.2 for thick steam-
dominated atmospheres (Kopparapu et al., 2013; Goldblatt et al., 2013). Simply
substituting these values into equation (6) gives the critical orbital
distance of 0.82 au, seemingly suggesting that Venus was well inside the
critical distance and thus followed scenario (ii). However, planetary albedo
plays a critical role in defining the radiative balance of rocky planets. 1D
climate models cannot fully handle the effects of atmospheric circulation,
such as heat transport by winds and the distribution of relative humidity and
clouds, which may favor the formation of an ocean. Recent 3D simulations have
shown that the stability of water oceans on early Venus would depend on
starting conditions in its atmosphere. If all water on early Venus was
initially present as a liquid ocean in a moderate climate, clouds formed on
the dayside would have reflected sunlight efficiently and maintained the
surface water ocean considering a slow rotation rate of Venus (Yang et al.,
2013; Way et al., 2016). By contrast, if early Venus started out with a hot
steam atmosphere, it would have remained in a runaway greenhouse state due to
thermal blanketing by clouds formed on the nightside and strong absorption of
sunlight by abundant water vapor (Turbet et al., 2021). If Venus experienced a
giant impact at the end of its accretion, like Earth, the latter case seems
more plausible. On the other hand, there is a possibility that Venus had a
different initial thermal state when it formed in a much different way from
Earth (e.g. Jacobson et al., 2017). This topic is out of scope of this
chapter.

In scenarios (i) and (ii), water vapor is considered to be dissociated and
lost by extensive escape of hydrogen to space. If Venus started with a water
equivalent of one Earth’ ocean mass, a preferential escape of hydrogen might
have left about 240 bars of oxygen on Venus. Some fraction of oxygen may also
have escaped directly if the energy input is high enough (possible roughly
before 4 Ga). However, based on recent numerical results (Johnstone, 2020;
Johnstone et al., 2021; Saxena et al., 2019), the activity of the young Sun
was not strong enough to drive rapid oxygen escape, thus some oxygen would
have remained in the Venusian atmosphere.

The fate of the remnant oxygen has been considered to be a constraint for the
recent evolution of the Venusian atmosphere. If oxygen builds up, the mixing
ratio of water vapor drops so that oxygen could become less prone to escape
(Kasting and Pollack, 1983; Wordsworth and Pierrehumbert, 2014). It had long
been suggested that a mechanism that could explain the loss of oxygen from the
atmosphere of Venus (and other terrestrial planets) was long-term ongoing loss
of volatiles by non-thermal escape processes (see for example Gronoff et al.
(2020)). However, total loss of O through non-thermal escape processes is
estimated to be far less than those needed to explain the loss of an amount of
water comparable to one Earth ocean (Gillmann et al., 2020; Persson et al.,
2020). Rapid water loss requires additional oxygen sink(s) other than thermal
and non-thermal escape processes, which can efficiently dispose of the
remaining oxygen.

In scenario (i), some of the oxygen may have reacted with, for example, CO to
form CO2 (or reduced species outgassed at the time) and some of the oxygen may
have been consumed by oxidation of Venusian crustal material (experiments by
Berger et al. (2019) and Filiberto et al. (2020), models by Gillmann et al.
(2020); Warren and Kite (2023), and review by Gillmann et al. (2022)).
However, it is unclear whether a combination of all these processes could have
removed tens to hundreds of bars of O2 immediately without preventing hydrogen
from escaping. Generally speaking, current results suggest that only a
moderate amount of oxygen can be extracted from the atmosphere by solid-gas
reactions. Experiments and models currently suggest the total removal of O2
may be limited to amounts similar to those caused by non-thermal escape (about
a fraction of a bar to 1 bar at most). This does not outright make scenario
(i) implausible but rather limits the possible range of water inventories
(perhaps to a fraction of an Earth ocean, or arid conditions) and the
time/length of the "wet" period (during the first few hundred million years).
Recent studies suggest that a runaway greenhouse transition with enough water
in the atmosphere (a minimum of a few tens of bars) may have caused global
melting of the surface, which may become a volatile and oxygen sink (Gillmann
et al., 2022; Warren and Kite, 2023). However, no evidence of such an event
has been recorded due to the young age of the surface of Venus. This remains
an active research topic, but the lack of constraints and multiple processes
involved still make quantitative estimates unreliable.

In scenario (ii) the remnant oxygen would have been immediately removed from
the atmosphere by oxidizing ferrous iron in the surface magma e.g. (Gillmann
et al., 2009a; Lammer et al., 2018). Compared with the solid rocky surface,
the surface magma over the vigorously convective magma ocean is expected to
react with the overlying atmosphere more efficiently, due to its higher
mobility and resurfacing rate. Furthermore, modeling results suggest that, in
scenario (ii), the planetary surface can remain molten until most of its water
is lost (Hamano et al., 2013). This is because the surface temperature could
exceed the solidus temperature ($\sim$ 1,340 K for peridotites) as far as a
few tens of bars of steam atmosphere remains (Hamano, 2020). On the other
hand, a recent numerical study (Selsis et al., 2023) suggest that, under some
conditions, a water-vapor atmosphere may see its structure dominated by
radiative rather than convective layers, leading to cooler surface
temperatures than for an adiabatic temperature profile. As a result, the
occurrence and/or lifetime of a magma ocean may be greatly reduced. The magma
ocean could solidify earlier than previously assumed, before the steam
atmosphere escapes, which would reduce its efficiency as a trap for volatile
species, including oxygen.

Nonetheless, if the magma ocean acts as a volatile sink, the oxygen buildup
associated with hydrodynamic escape would not have occurred when Venus
followed scenario (ii). One of the implications expected from this scenario is
that the Venus’ magma ocean may have a redox evolution different than Earth’s,
depending on the amount of the remnant oxygen reacted. The oxidation of the
magma ocean associated with extensive loss of water may affect the speciation
and partitioning of volatile elements. It may also explain an elevated
atmospheric N inventory on Venus, compared with Earth (Wordsworth, 2016). Due
to the lack of direct samples, the redox state of the present Venusian mantle
remains poorly constrained. As deduced from FeO contents of surfacial basalts,
the overall oxygen budget may be similar to Earth’s (e.g. Righter et al.,
2016), whereas thermodynamic calculations and spectroscopic data suggests that
the oxygen fugacity of Venus’ surface may be as high as the magnetite–hematite
phase boundary (Fegley et al., 1997).

Accumulation of oxygen is not an issue in scenario (iii) either, as water
would have only be a minor component of early outgassing in the first place.
Venus surface and atmosphere would be dry, but its interior may not be. The
potentially different dryness of the interior among the three scenarios might
affect the subsequent evolution of the interior. In such an evolution,
inefficient outgassing of the magma ocean (Ikoma et al., 2018; Solomatova and
Caracas, 2021; Salvador and Samuel, 2023) combined with high surface pressures
(increasing solubility of water in the magma ocean Gaillard and Scaillet,
2014), would have limited outgassing of water. Early loss of hydrogen could
have favored the oxidation of the magma ocean (Gaillard et al., 2022),
therefore an increased loss of H on Venus may help explain the divergent
evolution path of Venus. Later water outgassing related to volcanism would be
prevented by high surface pressures due to the thick CO2 atmosphere (Gaillard
and Scaillet, 2014).

####  5.2.2 The interior of Venus

Our understanding of the interior of Venus is very limited. Observations are
generally consistent with an approximately Earth-like internal structure and
composition, but error bars are large and accommodate a wide range of possible
configurations. In short, no direct observations strongly imply any radical
structural differences compared to Earth, despite the surface expressions of
interior dynamics diverging widely from what we can observe on Earth.

It is consensus that Venus displays no present-day global plate tectonics, but
is possibly (1) in a plutonic squishy lid regime because of its high surface
temperature or (2) in a quiet period of an episodic lid regime, or (3) in
stagnant-lid after a transition from mobile-lid regime. Specific sequences of
regime transitions have been discussed by Rolf et al. (2022) and Gillmann et
al. (2022) (and references therein), but so far the question remains unsolved.
The absence of a global self-generated magnetic field on Venus (Nimmo, 2002;
Smrekar et al., 2018), possibly caused by insufficient heat extraction out of
the core, is likely tied to the question of the mantle dynamics evolution
through time (O’Rourke et al., 2018). Further investigation into past evidence
of magnetic field generation may provide new constraints for the evolution of
Venus’ mantle thermal state and convection regime (O’Rourke et al., 2019).

Differences in the dynamics of the interior of Earth and Venus and convection
regimes may be related to the suspected dryness of the interior of Venus
(Kiefer et al., 1986; Grinspoon, 1993). Because water affects melting and the
mantle viscosity,it also affects mantle dynamics: for example, a dry mantle
produces less melt and has a higher viscosity; Green et al. (2014); Karato
(2015). However, the extent to which water can be a critical factor still
remains to be fully analysed and quantified. Additionally, some works
suggesting dry Venus (Kiefer et al., 1986; Grinspoon, 1993) made strong
assumptions on the processes at work on Venus. Kiefer et al. (1986), for
example, linked the correlation between Venus’ geoid and topography to the
absence of an asthenosphere, which could be due to dry conditions (and is now
questioned; Armann and Tackley (2012); Maia and Wieczorek (2022)). The dryness
of the interior inferred by Grinspoon (1993) relied on assumptions on the rate
of volcanic production and outgassing. However, volcanic production is poorly
constrained and highly debated (Herrick et al., 2023), while outgassing itself
would be affected by Venus’ high surface pressure and reduced water release
(see Section 3.6). As a result, whether Venus’ interior is dry or wet remains
uncertain.

So far, no measurement has allowed us to rule out a specific set of evolution
scenarios with any degree of certainty. We have no sample of volcanic rocks or
volatiles from Venus, to estimate its interior composition and conditions.
Data on the state of the core are consistent with a solid, liquid or stably
stratified core (Dumoulin et al., 2017). Models (O’Rourke et al., 2018)
suggest that if Venus had an Earth-like structure and composition, it would
likely generate a similar global magnetic field. Therefore, without a better
understanding of the interior of the planet, we are unable to decide whether
Venus lost its global magnetic field or never generated one in the first
place.

This need for more observations is driving the current Venus exploration
projects with multiple missions planned or selected: DaVinci (USA), VERITAS
(USA), EnVision (Europe), Venus Orbiter Mission (also known as Shukryaan-1)
(India), Venera-D (Russia) and VOICE (China). Those missions are set to
improve our knowledge of the interior structure of the planet, state of its
core, its subsurface structure, surface topography, geology and composition
and atmosphere structure and composition (both close to the ground and higher
up, with a special interest in volcanic production), with a focus on traces of
activity through time.

###  5.3 Earth

####  5.3.1 Oxidation of Earth’s magma ocean

Compared with other planetary bodies such as Mars and the Moon, Earth has a
highly oxidized mantle characterized by high Fe3+ abundance (e.g. Frost et
al., 2008). The evolution of the redox state of the Earth’s mantle is one of
the research fields actively explored (chapter 00008). Geochemical studies of
Hadean zircons suggest that the oxidation of the Earth’s mantle might have
occurred very early (Trail et al., 2011), possibly during its magma ocean
stage.

One of the mechanisms proposed to explain the oxidation of the terrestrial
magma ocean is hydrogen escape accompanying dissociation of water (Hamano et
al., 2013; Sharp et al., 2013). The present Earth’s upper mantle has a
Fe3+/$\Sigma$Fe of 0.02–0.06, which corresponds to the Fe2O3 content of
0.16–0.48 wt% (Hirschmann, 2022, and references therein). Using the simple
assumption of oxidation of FeO to Fe2O3, the amount of water required to raise
the Fe2O3 content from zero to the present level is equivalent to 0.5-1.5
Earth’s ocean masses for the whole mantle, and about 1/3 of this value (i.e.
0.2-0.5 ocean masses) for the upper mantle only. Earth is sufficiently far
from the critical orbital distance (6) discussed in Section 2.4, thus Earth’s
magma ocean would have crystallized rapidly on the order of 1 Myr or less
(Hamano et al., 2013; Lebrun et al., 2013; Salvador et al., 2017; Bower et
al., 2022). Hamano et al. (2013) estimated the total loss of water throughout
the Earth’s magma ocean stage to be about 0.2 ocean masses at most for a pure
steam atmosphere. Due to the low mixing ratio of H-bearing species in the
upper atmosphere, the loss of water would become probably lower if the early
atmosphere included large amounts of other gaseous species such as CO2. Thus,
water loss during the Earth’s magma ocean stage might have a partial
contribution to oxidation of the upper mantle, but the effect could be
marginal for the oxidation of the whole mantle.

An alternative mechanism is the redox disproportionation of Fe2+ to Fe3+ and
Fe0. This oxidation mechanism was originally proposed to be driven by
crystallization of a solid phase with affinity for Fe3+, such as perovskite.
However, it is unclear how quickly Fe metal formed by iron disproportionation
could sink to the core through the solid mantle. As described in section 2.1,
recent experimental and theoretical studies reported that redox
disproportionation could occur directly in a magma ocean owing to a high
stability of Fe3+ at high pressure (Armstrong et al., 2019; Deng et al., 2020;
Kuwahara et al., 2023). Metal silicate equilibration at the base of the magma
ocean can produce a high Fe3+/$\Sigma$Fe in the melt even at an oxygen
fugacity as low as IW-2. This oxidation mechanism requires that the base of
the magma ocean attains pressures as high as tens of GPa. This is in line with
estimations of terrestrial magma ocean depths caused by giant impacts during
the late stage of Earth’s formation (Nakajima et al., 2021). The Earth’s large
planetary mass and the accretion history involving giant impacts during the
late stage of formation may be key factors that set the different initial
condition for the redox evolution of its mantle.

This oxidation scenario seems promising for Earth, although the estimated
Fe3+/$\Sigma$Fe in the silicate melt shows significant differences among
studies. Based on the assumption of metal-silicate equilibration at 25-90 GPa,
Deng et al. (2020) computed the Fe3+/$\Sigma$Fe of about 0.01-0.02, which is
comparable to the value observed in the Earth’s upper mantle. On the other
hand, the Fe3+/$\Sigma$Fe estimated by Armstrong et al. (2019) and Kuwahara et
al. (2023) are much higher. Using a relatively low base pressure of 25-33 GPa,
Kuwahara et al. (2023) obtained a Fe3+/$\Sigma$Fe value of 0.2-0.5, which is
one order of magnitude higher than the Fe3+/$\Sigma$Fe in the upper mantle.
The cause of such differences remains unclear. If the excess in the
Fe3+/$\Sigma$Fe is confirmed, then it may suggest reduction processes such as
the late accretion of reducing material (Dauphas, 2017; Fischer-Gödde and
Kleine, 2017; Genda et al., 2017), which could form a transient reducing
surface environment, or may reflect incomplete metal-silicate equilibration,
rather than a single equilibration event at the base of the magma ocean (e.g.
Rubie et al., 2015b).

####  5.3.2 Earth’s most distinctive feature: Life affects planetary evolution
and volatile cycles

The discussion above has made abundantly clear the fact that the Earth today
is very different to present-day Venus and Mars. The present-day Earth is
characterised by an equable climate (from the point of view of life), stable
water at its surface, an oxidised atmosphere, and a robust plate tectonic
regime that links surface processes to those in the mantle, in the process
buffering the whole system Earth.

At present, Venus’ surface is dry and hot with a less oxidized atmosphere (and
H2SO4 clouds), and no plate tectonics. Mars is a dry cold planet with a CO2
atmosphere and a stagnant lid. Neither has life at its surface and the
question of whether Venus could host some form of life in its clouds, or Mars
in its subsurface, remains debated.

However, as the above discussions point out, the Earth did not start out as it
is today. Indeed, life could not have emerged on an oxidised planet since
abiogenesis (the emergence of life, as we know it) requires reduced organic
building bricks (e.g. Hudson et al. (2020). On the other hand, the oxidation
that is so characteristic of its surface is a product of biological processes.
Thus, while the early planets, Earth, Venus and Mars may have shared certain
characteristics that permitted life to emerge, their evolution paths diverged
significantly. As we understand the emergence of life, it was conceivable on
Mars but remains uncertain for Venus, due to the remaining uncertainties
regarding early surface conditions (see section 5.2.1). Since life is an
integral component of the Earth system, it is pertinent here to consider, in
the context of terrestrial geology and geophysics, how it appeared and evolved
through geological time. Since reconstructions of the past Earth’s atmosphere
composition do not highlight significant changes in bulk composition related
purely to long-term escape (Gronoff et al., 2020), the intimate interaction
between the effects of life at the surface, on internal processes, as well as
on the atmospheric envelope and vice versa, is of equal importance.

There are numerous theories about how and where life emerged, in deep ocean
hydrothermal vents (Baross and Hoffman, 1985; Russell and Hall, 1997; Martin
and Russell, 2003), shallow water hydrothermal vents (Westall et al., 2018),
subaerial hydrothermal vents (Damer and Deamer, 2020; Van Kranendonk et al.,
2021), in impact craters (Sasselov et al., 2020), in deep-seated fault systems
(Schreiber et al., 2012), in pumice rafts (Brasier et al., 2011) or in nuclear
sands (Maruyama and Ebisuzaki, 2023) to name but a few hypotheses (for a
review see (Westall et al., 2018)). Westall et al. (2023) briefly reviewed the
conditions that existed during the Hadean (4.5-4.0 Ga), and that were
apparently compatible with prebiotic processes and the emergence of life. They
included an anoxic atmosphere, (i) a high EUV flux reaching the surface of the
Earth that may or may not have been beneficial for early prebiotic processes,
depending upon the scenario preferred, (ii) a highly volcanic environment
including abundant hydrothermal activity, and (iii) a largely ocean-covered
planet with little exposed land mass. Modern-style plate tectonics did not
exist and there is still much debate as to what style of tectonic regime was
active during the Hadean (Capitanio et al., 2020; Gerya, 2022). A Hadean
initiation of plate tectonics has been hypothesised on the basis of an
andesitic source for zircons dating back to the Hadean (Turner et al., 2020),
while evidence for both vertical and horizontal deformation styles has been
documented in Paleo-Meso Archean formations (Heubeck et al., 2023), suggesting
some form of tectonic activity. Recent studies suggest that modern style plate
tectonics did not arise until much later in Earth’s history, towards the end
of the Proterozoic, about 800 Ma (see Figure 7, (Hawkesworth et al., 2020;
Stern, 2018), therefore the plutonic squishy lid might offer an alternative
explanation (Rozel et al., 2017; LourenÃ§o et al., 2018).

Figure 7: Indicators of crustal evolution and the gradual rise of modern style
plate tectonics, using zircon crystallization age distribution (lower serrated
yellow curves), throughout geological history. Vertical grey bars mark the
development of supercontinents/supercratons (see references in Hawkesworth et
al. (2020)). The crustal growth curve (brown) is adapted from modelling by
Dhuime et al. (2012). The crustal reworking curve is based on the Hf isotope
ratios of zircons in different time slices (Dhuime et al., 2012). Variations