# Early Habitability and Crustal Decarbonation of a Stagnant-Lid Venus

###### Abstract

Little is known about the early evolution of Venus and a potential habitable
period during the first one billion years. In particular, it remains unclear
whether or not plate tectonics and an active carbonate-silicate cycle were
present. In the presence of liquid water but without plate tectonics,
weathering would have been limited to freshly produced basaltic crust, with an
early carbon cycle restricted to the crust and atmosphere. With the
evaporation of surface water, weathering would cease. With ongoing volcanism,
carbonate sediments would be buried and sink downwards. Thereby, carbonates
would heat up until they become unstable and the crust would become depleted
in carbonates. With CO2 supply to the atmosphere the surface temperature rises
further, the depth below which decarbonation occurs decreases, causing the
release of even more CO2.

We assess the habitable period of an early stagnant-lid Venus by employing a
coupled interior-atmosphere evolution model accounting for CO2 degassing,
weathering, carbonate burial, and crustal decarbonation. We find that if
initial surface conditions allow for liquid water, weathering can keep the
planet habitable for up to 900 Myr, followed by evaporation of water and rapid
crustal carbonate depletion. For the atmospheric CO2 of stagnant-lid
exoplanets, we predict a bimodal distribution, depending on whether or not
these planets experienced a runaway greenhouse in their history. Planets with
high atmospheric CO2 could be associated with crustal carbonate depletion as a
consequence of a runaway greenhouse, whereas planets with low atmospheric CO2
would indicate active silicate weathering and thereby a habitable climate.

Journal of Geophysical Research: Planets

Origins Center, Nijenborgh 7, 9747 AG Groningen, The Netherlands Department of
Earth- and Life Sciences, Vrije Universiteit Amsterdam, Amsterdam, The
Netherlands Institute of Planetary Research, German Aerospace Center (DLR),
Berlin, Germany Department of Astronomy and Astrophysics, Berlin Institute of
Technology, Berlin, Germany NASA Goddard Institute for Space Studies, New
York, USA GSFC Sellers Exoplanet Environments Collaboration Theoretical
Astrophysics, Department of Physics and Astronomy, Uppsala University,
Uppsala, SE-75120, Sweden Dennis<EMAIL_ADDRESS>
Stagnant-lid model scenarios of early Venus tuned to reproduce present-day
observations suggest an early habitable period of up to 900 Myr

After runaway greenhouse, ongoing volcanism and crustal burial on stagnant-lid
planets cause rapid crust decarbonation and raise of atmospheric CO2

Stagnant-lid planets have bimodal distribution of atmospheric CO2: abundance
is low on habitable worlds and high after runaway greenhouse

## Plain Language Summary

Today, Venus has a thick atmosphere mainly composed of CO2 and a surface that
is too hot for any liquid water to exist. However, four billion years ago, the
Sun was much fainter, and if Venus’ atmosphere contained much less CO2 than
today, liquid water may have existed. Small amounts of atmospheric CO2 are
commonly associated with plate tectonics because of its ability to recycle
carbon into the interior. It is not clear, however, whether or not early Venus
possessed plate tectonics. Here, we simulate the evolution of Venus as a
planet without plate tectonics, and show that weathering processes can keep
the atmospheric CO2 low enough to maintain liquid surface water for almost one
billion years. During this time, weathering ensures that most of the CO2
degassed from the interior via volcanism gets stored in the crust in the form
of carbonates. Yet, part of the degassed CO2 keeps accumulating in the
atmosphere causing the surface temperature to rise because of the greenhouse
effect. Ultimately, the liquid water on the surface evaporates and weathering
stops. As soon as this happens, the crust becomes rapidly depleted in
carbonates, thereby building up Venus’ CO2-thick atmosphere that is observed
today.

##  1 Introduction

The evolution of Venus is still in many ways a mystery. Despite its similarity
to Earth in terms of size and bulk composition [<]e.g.,¿Lecuyer2000, the
atmospheric CO2 mass of Venus is larger by more than five orders of magnitude
[Donahue Pollack (1983)]. Whether Venus’ atmosphere was CO2-rich early in its
evolution, or whether - and how - it diverged from Earth’s atmosphere later in
its evolution is a matter of debate
[<]e.g.,¿gillmann2020,gillmann2016,lammer2018,lammer2009.

What makes assessing Venus’ early evolution very challenging is its relatively
young surface. Most of Venus’ surface has an age of $\approx$500 Ma [Turcotte
. (1999), McKinnon . (1997)], or even less [Bottke . (2016)]. Regarding its
early history, both an Earth-like scenario with a temperate climate and liquid
water [Grinspoon Bullock (2007)] as well as a hothouse have been discussed
[<]see¿taylor2018.

A main requirement for habitability is the existence of liquid water
[<]e.g.,¿cockell2016. An important constraint for liquid water on early Venus
is a slow rotation enabling the formation of high-level reflective clouds,
which increase the planetary albedo [Yang . (2014), Way . (2016), Way Del
Genio (2020)]. The preservation of liquid water on a planetary surface over an
extended time interval is commonly associated with the presence of plate
tectonics and an active carbonate-silicate cycle [Southam . (2015), Foley
(2015), Kasting Catling (2003), Sleep Zahnle (2001)]. If plate tectonics
regulated Venus’ climate in its early history, carbonates may have entered the
mantle following a shallow temperature-depth gradient, and Venus may have been
habitable over an extensive period of time [Way Del Genio (2020)]. However,
apart from limited surface features that have been associated with plume-
induced subduction [Davaille . (2017)], there is no sign of active plate
tectonics on Venus today [Smrekar . (2018)]. The tectonic state of early Venus
remains unclear, and in the absence of plate tectonics, an accumulation of CO2
in Venus’ atmosphere would clearly have reduced its habitable time span.

Besides plate tectonics, a major factor that is required for climate
regulation is the existence of liquid water on the planetary surface. Liquid
water enables silicate weathering, which forms the basis for Earth’s long-term
carbonate-silicate cycle [Walker . (1981), Kasting Catling (2003), Graham
Pierrehumbert (2020), Höning (2020)]. In fact, the existence of liquid water
is likely to be more important for climate regulation than plate tectonics: On
stagnant-lid planets, freshly produced basaltic crust in the presence of water
could be subject to silicate weathering [Foley Smye (2018), Foley (2019),
Höning . (2019)]. Carbonate sediments would be buried by new volcanic
eruptions and thereby move downwards. Since the stability of carbonates is
strongly temperature-dependent, decarbonation would occur at depth, thereby
releasing CO2 [Foley Smye (2018), Kerrick Connolly (2001)]. At shallow depth,
migration of CO2 to the surface may occur through cracks in porous media. Any
CO2 that does not migrate through cracks would sink further down as the crust
is buried by new lava flows. However, the formation of partial melt below the
lid and its rise towards the surface could also enable CO2 to make it to the
surface. The fraction of released CO2 that makes it to the surface is
difficult to estimate and likely depends on decarbonation depth, temperature,
porosity, and crustal burial rate. Future work is required to constrain this
fraction. In this paper, we assume that all released CO2 makes its way to the
surface, yielding the minimum habitable period. As shown by honing:2019, a
stabilising feedback cycle consisting of silicate weathering, burial, and
decarbonation can regulate the climate on stagnant-lid planets to some extent,
although this is likely to be less efficient compared to a cycle with plate
tectonics that recycle substantial amounts of carbon back into the mantle.

The carbon cycle for stagnant-lid planets outlined above (including
weathering, burial, and decarbonation) features a positive feedback, a fact
that has received little attention in the literature so far: The equilibrium
partial pressure of CO2 in the atmosphere depends upon the equilibrium between
silicate weathering on the one hand, and mantle degassing plus crustal
decarbonation on the other hand. The decarbonation flux depends on the rate at
which carbonates reach the decarbonation depth, and therefore on the sum of
(1) the rate at which carbonated crust is buried, and (2) the rate at which
the decarbonation depth moves upwards. The decarbonation depth is controlled
by the temperature profile in the crust, and therefore by both the mantle
temperature and the surface temperature. With increasing surface temperature,
the decarbonation depth moves upwards, and the decarbonation flux increases.
As a result, the atmospheric CO2 increases, and the surface temperature rises
further (see Fig. 1).

Figure 1: Left: Simplified flowchart of the carbon cycle considered in the
model. Weathering only occurs if liquid water is present on the surface.
Right: Illustration of the positive feedback associated with decarbonation.

With increasing solar luminosity, the close proximity of Venus to the Sun
makes it difficult for liquid water to be preserved on Venus’ surface. With
increasing surface temperature, stronger water evaporation will lead to even
stronger increases in surface temperature as more water vapour is loaded into
the atmosphere [Driscoll Bercovici (2013), Kasting (1988), Pollack (1971),
Ingersoll (1969)]. The inner boundary of the habitable zone is commonly
associated with the so-called moist-greenhouse effect, where the stratosphere
becomes loaded with water vapor [Kasting . (1993), Kopparapu . (2013)]. At the
runaway greenhouse limit, the oceans evaporate entirely [Kopparapu . (2013)].

Once the inventory of liquid water has evaporated, silicate weathering would
cease, so that CO2 would accumulate in the atmosphere. If Venus was already in
a stagnant-lid convection mode early in its history, this accumulation of CO2
would have been particularly rapid and self-accelerating: as volcanism
proceeds, CO2 continues to be supplied to the atmosphere by both mantle
degassing and crustal decarbonation. Once silicate weathering stops, no carbon
can be recycled from the atmosphere back into the crust. With the resulting
rapid increase of atmospheric CO2, the surface temperature then rises further
whereupon crustal decarbonation speeds up (Fig. 1b) until all available carbon
has been removed from the crust and a new equilibrium state is reached. We
propose that this feedback led to a sharp rise in Venus’ atmospheric CO2
budget and its surface temperature. In the following text, we explore the
habitable period of early Venus and the subsequent self-accelerating
decarbonation feedback. We also elaborate on the difference with the
traditional runaway greenhouse feedback, and discuss consequences for the
atmospheric evolution of stagnant-lid exoplanets.

##  2 Model

In order to assess the early evolution of Venus, we combine a thermal
evolution model of the mantle with a model of carbon outgassing, weathering,
burial, and metamorphic release. We assume that weathering follows the same
functional dependence on crustal production and atmospheric CO2 as seafloor
weathering on Earth and that all carbon that is subject to metamorphic
decarbonation is released back into the atmosphere. We consider CO2 and water
vapour as greenhouse gases and assume that weathering is active as long as
liquid water is present on the surface. We test different combinations of the
initial mantle temperature and mantle oxidation state and use a combination
that yields Venus’ observed atmospheric CO2 as our reference model scenario.
In the following, we provide details of all model parts.

The thermal evolution of the mantle is calculated using a parameterized model
of mantle convection for stagnant-lid planets [Grott . (2011), Morschhauser .
(2011), Tosi . (2017), Godolt . (2019)]. The model calculates interior heat
fluxes by solving the energy-conservation equations of the core, mantle, and
stagnant lid, with the convective heat flux parameterized using boundary layer
theory [Schubert . (2001)]. We note that parameterized thermal evolution
models commonly feature scaling laws used to calculate the heat flux which are
derived from numerical models of mantle convection assuming a steady state.
Although no direct comparison is available for Venus-like planets, detailed
comparisons for the Moon, Mars and Mercury [Thiriet . (2019)] suggest that a
good agreement between fully numerical calculations and parameterized models
can be obtained. This indicates that our parameterized approach captures well
the average characteristics of the long-term evolution of a Venus-like planet.

The mantle viscosity is calculated following Stamenkovic:2012 as a function of
temperature and pressure. The crustal production rate is calculated from the
melt volume assuming solidus and liquidus of dry peridotite [Katz . (2003)]
and from the convection speed, assuming that a constant surface fraction of 1%
is covered by hot plumes in which partial melting takes place [Grott Breuer
(2010), Tosi . (2017)]. We note that this value is poorly constrained,
however, it does not qualitatively impact our results: A smaller (larger)
fraction would result in a linear decrease (increase) of the outgassing rate,
and other parameter values of our reference model affecting the outgassing
rate (such as the oxygen fugacity) would be adapted in a way that Venus’
observed CO2 is still obtained. Outgassing of CO2 is based on a model of redox
melting [Grott . (2011), Hirschmann Withers (2008)]. For a detailed
description of the thermal evolution and outgassing model, including all
relevant equations, see Tosi:2017.

Following honing:2019, weathering is calculated dependent on atmospheric CO2
partial pressure ($P_{CO_{2}}$) as follows (see A for details):

$F_{w}=\frac{X_{E}\xi_{E}}{f_{E}}\left(\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}\right)\left(\frac{P_{CO_{2}}}{P_{CO_{2},E}}\right)^{\alpha},$
(1)

where $\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}$ is the crustal production rate,
$P_{CO_{2},E}$ is the atmospheric CO2 partial pressure of present-day Earth
and $\alpha\approx 0.23$ is a scaling exponent [Brady Gislason (1997)]. The
other constants in Eq. (1) follow from the assumption of an equilibrium
between carbon degassing and recycling on present-day Earth [Höning . (2019)]:
$f_{E}$ is the present-day Earth fraction of buried carbonates that enter the
mantle, $X_{E}$ is the present-day Earth mid-ocean ridge CO2 concentration in
the melt, and $\xi_{E}$ is the present-day Earth fraction of seafloor
weathering (see Tab. 1 and A). As in honing:2019, we track buried carbonated
crust until decarbonation occurs at a depth

$z_{decarb}=\frac{T_{s}-B}{A-\displaystyle\frac{T_{m}-T_{s}}{D_{l}+\delta_{m}}},$
(2)

where $T_{s}$ and $T_{m}$ are the surface and mantle temperatures, $D_{l}$ and
$\delta_{m}$ are the lid thickness and upper thermal boundary layer thickness,
respectively. For the decarbonation constants $A$ and $B$ we follow Foley:2018
and assume that the bulk metamorphic decarbonation takes place from the
breakdown of dolomite (Tab. 1). We assume that the released CO2 makes it to
the surface via cracks in the crust or with uprising melt. If CO2 enclosed in
buried crust does not come into contact with uprising melt, it might
eventually make it back into the mantle, which is a process not included in
our model. For details of the model for weathering, carbonate burial, and
decarbonation, we refer to honing:2019 and A.

We consider water vapour and CO2 as greenhouse gases. In order to obtain a
first order estimate of the habitability of early Venus, we adopt a simple
two-stream radiative gray atmospheric box model to calculate greenhouse
heating [Catling Kasting (2017)]. This assumes that the atmosphere is
transparent to visible and other shortwave radiation, but can absorb
preferentially in the infrared. This absorption is assumed to be wavelength-
independent. Thereby, we neglect absorption of incoming shortwave radiation in
the UV and visible by e.g. hazes and ozone. Despite these simplifications, the
model reasonably well reproduces surface temperatures during Venus’ early
evolution as obtained by a comprehensive global climate model, as will be
shown later (see Section 3).

The surface temperature can be expressed in terms of the slanted optical depth
$\tau$ of the atmosphere and the equilibrium temperature $T_{e}$:

$T_{s}^{4}=T_{e}^{4}\left(1+\frac{3\tau}{4}\right)\quad\text{with}\hskip
6.00006ptT_{e}^{4}=\frac{(1-A)S_{\odot}}{4\sigma},$ (3)

where $S_{\odot}$ is the incident insolation at the top of the atmosphere,
$\sigma$ is the Stefan-Boltzmann constant, and $A$ is the planetary albedo. As
a reference model, we mimic reflective clouds from Venus’ slow rotation by
adopting a planetary albedo of 0.6 [<]consistent with¿way2020, but also test
the influence of other values for $A$. The net incident insolation is assumed
to increase by a factor of 1.4 in 4.5 Gyr [Gough (1981)].

We note that Eq. 3 calculates the ground temperature, which is then used to
calculate surface water evaporation. Equilibrium between the ground
temperature and the atmospheric temperature will be reached quickly via
convection, forming an adiabatic temperature profile [Pierrehumbert (2010)].
The difference between the ground temperature and near-surface atmospheric
temperatures [<]commonly defined as the temperature at 2 m, see e.g.¿deque2005
is up to $\approx$5 K [<]e.g.,¿zeng1998. Following abe1985 and pujol2003, the
optical depth of the atmosphere in the infrared is given by:

$\tau=\sum_{i}{\tau_{i}}=\sum_{i}{\frac{3K^{\prime}_{i}P_{i}}{2g}},$ (4)

where $g$ is the gravitational acceleration, $P_{i}$ is the partial pressure
of a given atmosphere species $i$, and $K^{\prime}_{i}$ is the absorption
coefficient corresponding to this pressure. $K^{\prime}_{i}$ can be expressed
using the absorption coefficient $K_{0,i}$ at standard atmospheric pressure
$P_{0}$

$K^{\prime}_{i}=\left(\frac{K_{0,i}g}{3P_{0}}\right)^{1/2},$ (5)

where $K_{0,w}$ and $K_{0,c}$ are the absorption coefficients of H2O and CO2,
respectively, as given in Tab. 1.

Since the hydrological cycle is not well constrained on early Venus, we make
the rather straightforward assumption in our model that the atmosphere is
always fully saturated in water vapour. On modern Earth, the global mean
surface relative humidity is 78% [Manabe Wetherald (1967)] and large regions
in the Tropics remain close to saturation. Therefore, our approach is
conservative in this respect, and may underestimate the habitable period of
early Venus. We calculate the saturation pressure with a vapor pressure curve
from alduchov1997. Water in the atmosphere and the ocean are assumed to be in
equilibrium, with the ocean acting as a buffer to supply water to the
atmosphere as the surface temperature and pressure start to increase. As soon
as all surface water is evaporated, we set the weathering rate (Eq. 1) to be
equal to zero.

As a simplification, we neglect water outgassing from the mantle which we
assume to be dry. Due to the high viscosity of a dry mantle, our successful
model scenarios (that are model runs that yield outgassed CO2 abundances that
fit present-day observations) have higher initial mantle temperatures;
otherwise our results will not be affected in any significant way (discussed
in Section 4.2). We test initial surface ocean masses of $10^{18}$ kg
($\approx$ 2.2 m Water Equivalent Layer, WEL) and $10^{19}$ kg ($\approx$ 22 m
WEL), which correspond to a fraction of $\approx 0.1\%$ and $\approx 1\%$ of
Earth’s oceans and are within the bounds provided by Pioneer Venus in-situ D/H
measurements [Donahue . (1982), Donahue Russell (1997)]. We note that
persson2020 extrapolated the present-day escape rate of oxygen ions backwards
in time (assuming present-day atmospheric composition and structure) and their
results suggested that this mechanism could lead to a modest total escape of
up to about 0.6 m WEL. However, additional water sink mechanisms have been
proposed (discussed in Section 4.3).

The initial atmosphere in our model is composed of a background surface
pressure of 1 bar N2, which has been assumed for early Venus [Way Del Genio
(2020)], for stagnant-lid planets in general [Tosi . (2017)], and for other
habitability studies [Kasting . (1993)]. This value is also similar to that
found on Earth today and to what has been used for climate models of the
Archean Earth [<]e.g.,¿charnay2013. Raindrop fossils indicate a surface
atmospheric pressure 2.7 Gyr ago smaller than today, although this value
likely fluctuated significantly [Som . (2012), Som . (2016)]. All boundary
parameters and initial conditions of the atmosphere and carbon cycle model are
summarised in Tab. 1. Tab. 2 summarises parameter values used in the thermal
evolution model (see Tosi:2017 for a full description).

Table 1: Parameter values and initial conditions used in the atmosphere and carbon cycle model. [1] from Sleep:2001 [2] from Foley:2018 [3] from Foley:2015 [4] from Burley:2015 [5] from pujol2003 Symbol | Description | Value
---|---|---
$A$ | Planetary albedo (reference) | 0.6
$D$ | Orbital distance (reference) | 0.72 AU
$\alpha$ | Weathering exponent | 0.23 [1]
$A$ | Decarbonation constant | 3.125 $\times 10^{-3}$ K [2]
$B$ | Decarbonation constant | 8.355 $\times 10^{2}$ K m -1 [2]
$M_{o}(0)$ | Initial water ocean mass |  $10^{18}$ kg, $10^{19}$ kg
$f_{E}$ | Earth’s fraction of buried carbonates that enter the mantle | 0.45
$\xi_{E}$ | Earth’s fraction of seafloor weathering | 0.1 [3]
$X_{E}$ | Earth’s mid-ocean ridge concentration of CO2 in the melt | 125 ppm [4]
$K_{0,w}$ | Absorption coefficient water vapour | 0.01 m2 kg-1 [5]
$K_{0,c}$ | Absorption coefficient CO2 | 0.05 m2 kg-1 [5]
Table 2: Parameter values used in the thermal evolution model described in Tosi:2017 with a pressure- and temperature dependent viscosity as described in Stamenkovic:2012 [1]. Symbol | Description | Value
---|---|---
$R_{p}$ | Planet Radius | 6050 km
$R_{c}$ | Core Radius | 3110 km
$g$ | Surface gravity | 9.0 m s-2
$T_{m}(0)$ | Initial mantle temperature | 1700 K to 2000 K
$\Delta f_{O_{2}}$ | Mantle oxygen fugacity | IW-1 to IW+1
$D_{lid}(0)$ | Initial lid thickness | 50 km
$T_{c}(0)$ | Initial core temperature | 2760 K
$Ra_{crit}$ | Critical Rayleigh Number | 450
$k_{m}$ | Thermal conductivity (mantle) | 4 W (m K)-1
$k_{cr}$ | Thermal conductivity (crust) | 3 W (m K)-1
$c_{c}$ | Heat capacity (core) | 800 J K-1
$c_{m}$ | Heat capacity (mantle) | 1100 J K-1
$E$ | Activation energy |  $3\times 10^{5}$ J mol-1 [1]
$V$ | Activation volume |  $2.5\times 10^{-6}$ m3 mol-1 [1]
$\eta_{ref}$ | Reference viscosity |  $10^{21}$ Pa s [1]
$T_{ref}$ | Reference temperature | 1600 K [1]

##  3 Results

###  3.1 Early evolution of Venus

Figure 2: Early evolution of a Venus-like stagnant-lid planet at a solar
distance of 0.72 AU, with an assumed planetary albedo of 0.6, a mantle oxygen
fugacity equal to the iron-wüstite buffer, and an initial mantle temperature
of 1900 K. (a) Distribution of carbon between atmosphere (blue) and crust
(yellow) from a model scenario that considers weathering; the dashed purple
line depicts the sum of both reservoirs. The green line depicts the total
degassed CO2 for a model scenario that neglects weathering. (b) Surface
temperature for models with and without weathering. (c) Carbon fluxes for the
scenario that considers weathering. (d) Water vapour for scenarios with and
without weathering. (e) Lid and crustal thicknesses and decarbonation depth
for the scenario that considers weathering. (f) Mantle, lid, and crustal base
temperatures for a scenario with weathering.

Venus’ initial mantle temperature and mantle oxidation state are not well
constrained. From magma ocean solidification, initial mantle temperatures of
up to 2000 K have been considered [Foley . (2014)]. Since rock samples
delivered from Venus have not yet been identified on Earth, the mantle
oxidation state remains poorly known and may lie between reduced [<]as on the
Moon and Mars,¿Wadhwa:2008 and oxidized (as on Earth). Surface measurements by
the Venera 13, 14, and Vega 2 missions suggest that the mean FeO/MnO ratio,
which strongly depends on the oxidation state, likely lies between the values
of Earth and Mars [Schaefer Fegley Jr (2017)]. Fig. 2 depicts results of our
reference model, for which we chose an initial mantle temperature of 1900 K
and an oxygen fugacity equal to the iron-wüstite (IW) buffer. The motivation
of the choice of this parameter combination will be addressed in Section 3.2,
where we will also test other combinations of parameter values. All model runs
start with an initially habitable scenario using an atmosphere without any
CO2, but initial abundances of CO2 will be tested in Section 4.4. Time 0
refers to the solidification of the magma ocean. In Fig. 2, panel (a) shows
the early evolution of carbon in Venus’ atmosphere and crust, (b) the
corresponding surface temperature, (c) the carbon fluxes, (d) the water
vapour, and (e) and (f) various interior evolution parameters. The green
curves in Fig. 2 depict the evolution of the atmospheric CO2 (Fig. 2a),
surface temperature (Fig. 2b), and water vapour (Fig. 2d) in a scenario where
weathering is neglected so that all degassed CO2 accumulates in the
atmosphere. In contrast, all other curves in Fig. 2 correspond to a scenario
where weathering, carbonate burial and decarbonation are accounted for. The
yellow curve in Fig. 2a depicts the evolution of the crustal carbon reservoir,
which technically also includes a minor part of volatile CO2 in the crustal
matrix, introduced in order to ensure numerical stability [Höning . (2019)].
Note that the total amount of degassed CO2 in the scenario that neglects
weathering (green) is larger than in the scenario that includes weathering
(purple dashed), since the runaway greenhouse sets in earlier, and the
corresponding higher surface temperature causes a higher degassing rate during
this time interval.

Fig. 2 shows that including weathering considerably extends the period of time
for stagnant-lid planets to remain habitable. With ongoing mantle degassing
and weathering, the crustal reservoir becomes enriched in carbon whereas the
atmospheric CO2 only slowly increases with time during the first 900 Myr. With
ongoing volcanism, buried carbonate sediments move downwards, and thereby heat
up. At $\approx$900 Myr, buried carbonates become unstable. Since we assume
that all CO2 released by decarbonation makes it via cracks or with uprising
melt to the surface, atmospheric CO2 increases, and thereby the surface
temperature. Liquid water evaporates and weathering stops, while the crust
continues to release its carbon into the atmosphere - the planet becomes
uninhabitable. However, in a scenario without weathering, the oceans evaporate
already at $\approx$400 Myr. Therefore, introducing the weathering mechanism
extends the potential habitable time span of a stagnant-lid Venus by
$\approx$500 Myr.

It is interesting to note that in Fig. 2a the slope of the blue curve is
steeper than that of the green curve at the respective time when the runaway
greenhouse is triggered. This is because mantle degassing is accompanied by
decarbonation while weathering has ceased. Note also that the exact value of
the surface temperature directly after the runaway greenhouse (here:
$\approx$430 K) follows from the (arbitrary) choice of the surface water
budget. Our results however suggest that the point in time at which a planet
becomes uninhabitable is not sensitive to the initial water ocean budget
(shown below).

The decarbonation flux curve in Fig. 2c has several inflection points. At
$\approx$ 0.92 Gyr, carbonated crust reaches the decarbonation depth (compare
panel e) where carbonates become unstable. As a result, the decarbonation flux
sharply increases and thereby the surface temperature, such that the surface
water evaporates and weathering stops. The accompanying sharp rise of the
surface temperature results in a decrease of the decarbonation depth, so that
the decarbonation flux becomes particularly high. After this event, the
decarbonation flux qualitatively follows the weathering flux with some delay
($\approx$0.9 Gyr), since the model tracks carbonated crust on its way to the
decarbonation depth. However, since the decarbonation depth steadily decreases
with time, variations in the decarbonation flux occur on a shorter timescale
compared to variations in the weathering flux. In this example, variations of
the decarbonation flux occur between $\approx$0.9 and $\approx$1.12 Gyr while
variations of the weathering flux occur between 0 and $\approx$0.9 Gyr. At
$\approx$1.12 Gyr, all carbonates have become unstable, and the decarbonation
flux approaches zero. It does not however instantaneously approach zero,
because of the volatile CO2 reservoir introduced into the crustal matrix,
which releases a constant fraction to the atmosphere at each timestep.

As long as the combined outgassing flux does not vary significantly with time
and weathering is active, an equilibrium between outgassing and weathering is
expected, since weathering is controlled by atmospheric CO2
[<]e.g.,¿berner1997need. In Fig. 2c (black dashed line), we however observe
that the total carbon flux is not always equal to zero and therefore the
system is not always in steady state. In the early evolution (0.1 Gyr),
equilibrium between degassing and weathering is not reached and CO2 in the
atmosphere builds up. Later in the evolution (0.6 Gyr), degassing
substantially increases, which is a result of the assumed dry mantle of high
viscosity and the thereby increasing mantle temperature (compare Fig. 2f). Due
to the increasing degassing rate, the atmospheric CO2 subsequently increases.
As a result, the weathering rate also increases, but with some delay since
some CO2 has accumulated in the atmosphere. Once weathering has ceased,
atmospheric CO2 rapidly increases.

Figure 3: Comparison between an initial ocean mass of $10^{19}$ kg (top) and
$10^{18}$ kg (bottom) and different planetary albedos A. The diamonds in (a)
and (c) represent combinations of incident insolation and atmospheric CO2
obtained from our reference model, which were used as an input for the 3D
global climate model assuming a water equivalent layer of 10m [Way Del Genio
(2020)]. The resulting average surface temperatures are plotted as diamonds in
(b) and (d), and the resulting albedos are used as inputs for additional runs
of our parameterized atmosphere-interior model, which are plotted as red,
yellow, purple, and green curves. See text for further explanation.

In Fig. 3, we compare the early evolution of the atmospheric CO2 and surface
temperature using initial ocean masses of $10^{19}$ kg (top) and $10^{18}$ kg
(bottom). As expected, the effect of the initial ocean mass on the early
evolution before the runaway greenhouse is negligible, whereas the temperature
increase during the runaway greenhouse is more pronounced with a larger ocean
reservoir. The slight decrease of CO2 partial pressure in Fig. 3a before the
sharp inflection is a result of the rapid water evaporation, which reduces the
atmospheric volume fraction of CO2 to a greater extent than it increases the
total mass of the atmosphere. In Fig. 3c however, the water mass added to the
atmosphere is one order of magnitude smaller, hence this effect is not
apparent here.

In addition, Fig. 3 depicts the effect of the planetary albedo. With an Earth-
like albedo of 0.3 (dotted curves), the runaway greenhouse is triggered
directly in the early stages as soon as a relatively small amount of CO2 is
released into the atmosphere. In particular an initial atmospheric CO2
reservoir would cause a direct transition from the magma ocean phase to a
runaway greenhouse. However, slow rotation in Venus’ early evolution could
have favoured the formation of a global, reflective cloud layer, increasing
the planetary albedo to a value between 0.5 and 0.6 [Way . (2016), Way Del
Genio (2020)]. Fig. 3 shows that this can lead to an extended early habitable
period, even in a stagnant-lid regime. In addition to the point in time where
the runaway greenhouse effect is triggered, the planetary albedo influences
the surface temperature before and after this event.

In order to compare our results for early Venus with output from comprehensive
3D climate models, we use the 3D General Circulation Model (GCM) ROCKE-3D [Way
Del Genio (2020), Way . (2017)]. We set the atmospheric composition to 1 bar
N2 and test four parameter combinations of atmospheric CO2 and incident
insolation that fit our reference model scenario during Venus’ early
evolution: (i) 0.112 bar surface CO2 and an insolation of 1886.1 W m-2, (ii)
0.132 bar CO2 and 1913.6 W m-2, (iii) 0.134 bar CO2 and 1935.4 W m-2, (iv)
0.206 bar CO2 and 1970.1 W m-2. In Fig. 3a and c, we plot these points as
diamonds. From the GCM, we obtain the following planetary albedos and average
surface temperatures (averaged over the last 50 years of each run after they
have reached radiative equilibrium): (i) an albedo of 0.523 and surface
temperature of 300.4 K, (ii) 0.531 and 302.3 K, (iii) 0.536 and 302.7 K, (iv)
0.549 and 306.4 K. Using these planetary albedos, we then re-run our
parameterized interior-atmosphere model and plot the results as (i) red, (ii)
yellow, (iii) purple, and (iv) green curves in Fig. 3. In Fig. 3b and d, we
plot the average surface temperatures obtained from the GCM model as diamonds.
We find that the results from our parameterized interior-atmosphere model
during the early evolution are in good agreement with the GCM model,
particularly on the plateau region in atmospheric CO2 and surface temperature
around $\approx$0.5 Gyr if the respective albedos derived from the GCM are
used. All four control points confirm our main finding of an early habitable
stagnant-lid Venus.

###  3.2 Influence of mantle oxidation state and initial mantle temperature

Figure 4: Evolution of the atmospheric CO2 for a stagnant-lid planet at 0.72
AU for model scenarios with (blue) and without (green) weathering and
different oxygen fugacities (top row: IW, middle row: IW-0.5, bottom row:
IW-1) and initial mantle temperatures (left column: 2000 K, middle column:
1900 K, right column: 1800 K).

The oxygen fugacity and the initial mantle temperature are major factors that
could strongly impact the atmospheric evolution of stagnant-lid planets for
models with [Höning . (2019)] and without weathering [Ortenzi . (2020), Tosi .
(2017), Godolt . (2019)], in particular in combination with the surface
pressure [Gaillard Scaillet (2014)]. Unfortunately, these parameter values are
poorly known for Venus. However, Venus’ present-day atmosphere contains
$\approx 10^{22}$ mol CO2, which may be used as a boundary condition.
Continuous volcanic degassing in a stagnant-lid regime is in agreement with
the observed argon mass in Venus’ atmosphere [O’Rourke Korenaga (2015)],
although we note that the use of argon to constrain the degassing history of
terrestrial planets is not straightforward and that the solutions are not
unique [Watson . (2007), Way Del Genio (2020)].

Fig. 4 shows the evolution of atmospheric CO2 for various parameter
combinations of the initial mantle temperature (2000 K, 1900 K, 1800 K) and
oxygen fugacity (iron-wüstite buffer IW, half a log unit below, IW-0.5, and
one log unit below, IW-1). The highest initial mantle temperature that we test
(2000 K) is motivated by considerations of magma ocean crystallisation [Foley
. (2014)]. The solar distance is 0.72 AU and the model accounts for the solar
flux evolution. Green curves again show model scenarios that neglect
weathering whereas blue curves show scenarios that consider weathering,
carbonate burial, and decarbonation.

Fig. 4 suggests that a high initial mantle temperature as well as a high
oxygen fugacity both favour a high atmospheric CO2 amount throughout the
entire evolution due to a high mantle degassing rate. This is the case for the
model scenarios with and without weathering. The point in time where the blue
curve approaches the green curve can be interpreted as the onset of the
runaway greenhouse of the model scenario with weathering: As soon as both
curves converge, the crust has lost all its carbon, which is a direct
consequence of the halt to weathering due to a lack of liquid water. It
therefore becomes apparent that the weathering feedback becomes particularly
important for maintaining habitability if the oxygen fugacity and the initial
mantle temperature are relatively low. Fig. 4i suggests that for a small
degassing rate throughout the entire evolution, weathering can keep the
atmospheric CO2 sufficiently low to avoid a runaway. This result is consistent
with way2020, who find that for low atmospheric CO2, Venus could have remained
habitable until today. The three local maxima in Fig. 4i reflect changes of
the decarbonation flux: As soon as crust with a higher carbon concentration
than that of the previous timestep reaches decarbonation depth, the
decarbonation flux increases, and thereby the weathering rate and the carbon
concentration of freshly formed crust. In combination with a steadily
increasing decarbonation depth, these events result in local maxima [<]see
also Fig. 2 of ¿honing:2019. We note, however, that the total amount of
degassed CO2 (green curve) at 4.5 Gyr is almost two orders of magnitude lower
than that observed for Venus today, indicating that the scenario depicted in
Fig. 4i is not representative of Venus’ evolution.

We note the different shapes of the blue curves in Fig. 4. For example, the
blue curve of the top centre model (IW+0, 1900 K, Fig. 4b) is approximately
constant until 900 Myr, which is the point in time where the runaway
greenhouse is triggered (compare with Fig. 2). In contrast, if the initial
mantle temperature is higher (for example 2000 K, IW-0.5), the atmospheric CO2
experiences a local maximum. This is because a hot mantle rapidly cools down
in the early evolution. A different behaviour can be seen for cases where the
initial mantle temperature is lower (for example IW-0.5, 1800 K, Fig. 4f).
Here, the atmospheric CO2 steadily increases.

It is interesting to note that a steadily increasing atmospheric CO2 is
contrary to what is assumed for Earth’s atmospheric evolution
[<]e.g.,¿Sleep:2001. The reason for this is twofold: First, plate tectonics
planets lack a thick, insulating lid, and therefore cool down relatively
quickly [<]e.g.,¿Schubert:2001,Honing:2016. As a result, the degassing rate on
planets with plate tectonics decreases with time, for example due to a
decreasing plate speed [Oosterloo . (2021)] or an increasing fraction of
subduction zones that avoid decarbonation [Höning . (2019)]. Second, we assume
that weathering on stagnant lid planets is a function of CO2 only, whereas
continental weathering on Earth is a function of both CO2 and temperature.
With increasing incident insolation, a smaller amount of CO2 is therefore
required for continental weathering to balance degassing and the atmospheric
CO2 partial pressure decreases with time.

Comparing the present-day atmospheric CO2 (t=4.5 Gyr) of each model run with
the present-day atmospheric CO2 of Venus ($\approx 10^{22}$ mol) provides a
first-order estimate of a reasonable initial mantle temperature and oxygen
fugacity of Venus. We find that an oxygen fugacity equal to the iron-wüstite
buffer and an initial mantle temperature of 1900 K fits the present-day
observation well. Therefore, we chose this parameter combination as a
reference case, which has been explored in more detail in Fig. 2. Note
however, that this solution is not unique; a higher initial mantle temperature
combined with a smaller oxygen fugacity, or vice versa, could also fit the
present-day observation of Venus’ atmospheric CO2 (see e.g. Fig. 4d).

###  3.3 Bimodal distribution of atmospheric CO2

While the atmospheric CO2 on planets with active weathering remains low, a
halt to weathering would naturally lead to increasing atmospheric CO2 with
time, independent of the tectonic state of the planet. Since planets with
plate tectonics are anticipated to have higher degassing rates than stagnant-
lid planets, CO2 accumulation through mantle degassing would be particularly
rapid if plate tectonics keeps operating. In addition, the surface temperature
after a runaway greenhouse could become so high that carbonate sediments on
the surface become unstable, which would result in a particularly strong
increase in atmospheric CO2 [Graham Pierrehumbert (2020)]. As a consequence,
the atmospheric CO2 would show a bimodal distribution with low abundances as
long as weathering is active and higher abundances thereafter.

On stagnant-lid planets, the mechanisms described above would likely operate
less efficiently due to smaller degassing rates. Here, however, an additional
mechanism would come into play, leading to a bimodal distribution in
atmospheric CO2. Due to the lack of subduction zones, degassed CO2 would not
be recycled back into the mantle. Instead, as long as weathering is active,
the crust would be gradually enriched in carbonates (see Fig. 1, left, and
Fig. 2a), while atmospheric CO2 would remain low. As soon as weathering
ceases, ongoing crustal burial and decarbonation would rapidly deplete the
crust in carbonates. In Fig. 2a we observe an increase of atmospheric CO2 by
approximately one order of magnitude within 100 Myr.

Figure 5: Top: Atmospheric CO2 for a stagnant-lid planet at 0.72 AU with a
planetary albedo of 0.6 as a function of oxygen fugacity and time. Bottom:
Atmospheric CO2 of a stagnant-lid planet at 4.5 Gyr for an oxygen fugacity of
IW-1 as a function of solar distance and planetary albedo. All model runs have
an initial mantle temperature of 1900 K and assume active weathering as long
as liquid water is present on the surface.

An example of the aforementioned bimodal distribution is depicted in Fig. 5,
where we show the atmospheric CO2 partial pressure of a Venus-sized stagnant-
lid planet as a function of oxygen fugacity and time (top) and of planetary
albedo and solar distance (bottom). Note that for our rather straightforward
atmospheric model it is challenging to estimate the surface temperature and
thereby the transition to a runaway greenhouse for high CO2 abundances. With
this in mind, in Fig. 5 (bottom), we chose a combination of initial mantle
temperature (1900 K) and mantle oxidation state (IW-1) that results in a
relatively modest amount of atmospheric CO2 of up to a few bar at t=4.5 Gyr.
This range is comparable to habitable zone planets considered by Tosi:2017 and
kadoya2019.

The atmospheric CO2 dramatically varies depending on whether (green/yellow) or
not (blue boxes) the planet experienced a runaway greenhouse in its history,
with a difference of approximately one order of magnitude. For a planet at
Venus’ distance and an albedo of 0.6 (Fig. 5, top), atmospheric CO2 remains in
the order of 0.1 bar as long as weathering is active and increases to more
than 1 bar after weathering has ceased; this transition is only marginally
affected by the oxygen fugacity. For stagnant-lid planets with an oxygen
fugacity of IW-1 and an age of 4.5 Gyr (Fig. 5, bottom), we obtain a bimodal
distribution between 0.7 and 1.3 AU depending on the planetary albedo. The
difference in atmospheric CO2 between planets with and without weathering
remains in the order of at least one order of magnitude.

This finding has profound implications for future exoplanet observations. If
the CO2 absorption band retrieval were to indicate enhanced atmospheric
abundances for rocky planets lying closer to their host stars (assuming the
planets do not lie too close to the star so that escape of C and O atoms
becomes relevant) than for planets further away, then this might indicate that
an active weathering cycle operating on planets of the latter category, even
if these are in a stagnant-lid regime. A planet observed with a small
atmospheric CO2 budget could give an indication of liquid surface water and a
habitable climate. CO2 absorption may be one of the few observable spectral
signatures for favourable rocky exoplanetary targets with current and near-
future platforms [<]e.g.,¿[]wunderlich2021,Fauchez2019. For this reason the
interpretation of the CO2 abundances following a bimodal distribition could be
critical to assess exoplanet habitability since other variables relevant for
habitability such as the possible presence of additional greenhouse gases are
generally more challenging to determine [Fauchez . (2019)].

##  4 Discussion

We coupled a thermal evolution model for stagnant-lid planets with a model of
weathering, carbonate burial, and decarbonation, and applied this model to
early Venus and stagnant-lid exoplanets. Our main findings are twofold. First,
crustal weathering could yield an extensive habitable period for early Venus
even in a stagnant-lid regime, and second, stagnant-lid exoplanets may show a
bimodal distribution of their atmospheric CO2. Assumptions and uncertainties
in the model that could affect these conclusions are discussed below.

###  4.1 Limitations of the climate model

Since our coupled interior-atmosphere evolution model calculates reservoirs
and fluxes over billions of years, it was necessary to make substantial
simplifications regarding the atmospheric climate model. Instead of a
radiative-convective model as is commonly used for approximating the runaway
greenhouse [<]e.g.,¿kopparapu2013,kopparapu2017, we adopted a simple two-
stream radiative grey atmospheric box model [Catling Kasting (2017)]. Assuming
constant planetary albedo and opacity, results can only be seen as reliable if
changes in atmospheric CO2 and water vapour remain small. Nevertheless, the
early evolution of Venus is simulated reasonably well with our model. In Fig.
3, we show that the temperature difference obtained from our model compared
with results from a 3D global climate model at 4 control points during the
early habitable period is relatively small ($\approx$10 K if compared to a
model run with the respective albedo obtained from the GCM, and if compared to
a model run of a constant albedo of 0.6, only the first three control points
show a moderately higher temperature difference of $\approx$20 K). All four
control points confirm our main finding of early habitable conditions. We note
that our assumptions of constant albedo and opacity do not hold for predicting
the climate for the period after ocean water evaporation. However, in Fig. 4,
where we plot the complete evolution over 4.5 Gyr, we only show the
atmospheric reservoir. This reservoir is mainly an outcome of the interior
evolution and would therefore be affected by the climate to a much lesser
extent.

###  4.2 Parameterisation of weathering and CO2 degassing

On Earth, seafloor weathering is an important component of the long-term
carbonate-silicate cycle [Brady Gislason (1997), Krissansen-Totton Catling
(2017), Krissansen-Totton . (2018)]. Hydrothermal alteration of new basaltic
crust produces alkalinity, which favours precipitation and burial of
carbonates. This concept has been applied to stagnant-lid planets [Foley Smye
(2018), Foley (2019), Höning . (2019)]. However, even on Earth, the dependence
of the rate of seafloor weathering on atmospheric CO2, temperature, and/or
ocean pH is a matter of debate [Krissansen-Totton . (2018), Krissansen-Totton
Catling (2017), Coogan Dosso (2015), Sleep Zahnle (2001), Brady Gislason
(1997)]. The effect of different parameterizations for seafloor weathering on
the climate of stagnant-lid planets has been explored in honing:2019. These
authors find that a parameterization that neglects any direct dependence of
the weathering rate on atmospheric CO2 inevitably causes a removal of almost
the entire atmospheric reservoir as soon as the degassing rate approaches
zero, which appears to be unrealistic. Similarly, using a solely temperature-
dependent parameterisation for seafloor weathering, model results by
foley:2019 suggest a low abundance of atmospheric CO2 and an icy surface as
soon as outgassing ceases. We decided to use a direct dependence of basalt
weathering on atmospheric CO2 in our model, but note that additional
dependencies on surface temperature or ocean pH cannot be ruled out and might
affect the habitable time span of early Venus. In addition, depending on the
poorly constrained topography shifts of early Venus, a thermodynamic limit to
weathering [Graham Pierrehumbert (2020), Maher Chamberlain (2014)] might also
be worth to be considered in follow-up work.

The assumed direct dependence of the weathering rate on the crustal production
rate is fundamentally different than on Earth, where weathering proceeds
mainly via continental processes, which depend on mountain building and
erosion exposing fresh rock. Since we assume that on stagnant-lid planets
freshly produced basaltic crust is directly subject to weathering, it
inevitably follows that even if erosion takes place later in the evolution,
the crust exposed as a result would already have been carbonated at the time
it formed [<]see¿honing:2019. Therefore, we argue that on stagnant-lid
planets, weathering rates are likely to depend proportionally on crustal
production, even if the crust is not submerged. We however point out the
importance of liquid water for weathering of freshly formed crust. If part of
the surface of early Venus were emerged above sea-level, which is indeed
likely to be the case for the smaller assumed initial ocean reservoir (Fig. 3c
and d), this would require regular rainfall.

Assuming that weathering on early Venus has a similar functional dependence on
CO2 as seafloor weathering on Earth, we assumed that the mineralogy of Venus
is mainly basaltic. However, recent observations from the Venus Express
mission indicate that the mineralogy of Tessera Terrain, a region of high
topography, is more silica-rich or felsic [Gilmore . (2017)]. On the one hand,
weathering fluxes at a given CO2 for granites may be smaller than for basalts
[Hakim . (2021)], and therefore on average, the weathering exponent $\alpha$
(Eq. 1) might be smaller. On the other hand, for our reference model, we find
that the habitable period ends as soon as decarbonation of the crust occurs,
which weakens the dependence of our results upon the exact value of $\alpha$.
In model scenarios where the planet remains habitable after decarbonation sets
in (see Fig. 4), a smaller value of $\alpha$ would reduce the habitable
period. Altogether, a better knowledge of Venus’ mineralogy and a better
understanding of its crustal production history is needed in order to further
improve our understanding of its early habitability. A significant step
towards the determination of Venus’ surface mineralogy could be taken with the
recently approved VERITAS mission [Freeman . (2016)].

Whether or not weathering could have extended the habitable time span of an
early stagnant-lid Venus depends on its initial mantle temperature and oxygen
fugacity. If the combination of both parameters exceeds a certain threshold,
then rapid outgassing of CO2 inhibits efficient climate regulation (see Fig.
4). In particular an initial mantle temperature as high as 2000 K would
dramatically limit the habitable period. However, the combination of an
initial mantle temperature of 1900 K together with an oxygen fugacity equal to
the iron-wüstite buffer allows for a habitable period of 900 Myr while the
atmospheric CO2 amount obtained at 4.5 Gyr is in agreement with present-day
observations of Venus’ atmospheric CO2.

Figure 6: Evolution of atmospheric CO2 for a planet as in Fig. 4 but for an
initial mantle temperature of 1800 K (left column) and 1700 K (right column)
in combination with an oxygen fugacity of IW+1 (top row) and IW+0.5 (bottom
row).

In Fig. 4, we explored parameter combinations of an initial mantle temperature
of 1800 and 2000 K and an oxygen fugacity between the iron-wüstite Buffer and
one log-unit below it. However, since no rock samples from Venus have been
identified yet, its oxidation state is unknown, and an even higher oxidation
state - similar to Earth - cannot be ruled out. In Fig. 6, we show that a
combination of a smaller initial mantle temperature and a higher oxygen
fugacity (for example 1700 K and IW+0.5) yields an atmospheric CO2 partial
pressure similar to that obtained in the reference scenario (with 1900 K and
IW+0). However, the effect of weathering is negligible here, since the small
initial degassing rate caused by the low temperature results in low
atmospheric CO2 during the first $\approx$1 Gyr in both model scenarios. Later
in the evolution, the combination of a high degassing rate (from a hotter
mantle) and a high solar flux triggers a runaway independent of whether or not
weathering is active.

An additional simplification of our model is that it does not explicitly
calculate Venus’ mantle carbon inventory. Earth’s carbon inventory has been
estimated at $2.5\times 10^{22}$ mol [Sleep Zahnle (2001)], but could be as
high as $1\times 10^{23}$ mol [Dasgupta Hirschmann (2010)]. Assuming that
Venus’ initial mantle carbon inventory is similar to Earth’s, explicitly
modelling Venus’ mantle carbon reservoir would not significantly affect early
degassing during the habitable period. In the late evolution, our
simplification may overestimate degassing if mantle material previously
depleted in CO2 is brought to the melt region. Since our model assumes that
melting occurs within plumes, which are expected to sample deep primordial
mantle material, this is not necessarily the case, however. On the other hand,
we also neglected external sources that could have supplied carbon to the
atmosphere, for example during late accretion events [<]see for
example¿gillmann2020, however, these sources would not dominate the planetary
carbon budget [<]for Earth, see¿mikhail2019.

In addition to the initial mantle temperature and the oxygen fugacity, water
in the mantle would affect the interior evolution and the degassing rate.
First, it would reduce the viscosity, and thereby enhance the convection rate,
heat flow, and CO2 degassing. Second, it would reduce the melting temperature,
which further enhances degassing. In order to limit the complexity of our
model and to allow for a more straightforward way of studying relevant
feedbacks, we neglected water in the mantle and its degassing into surface
oceans. Calculating the mantle viscosity, we followed Stamenkovic:2012,
thereby neglecting the water-dependence of viscosity. As shown by Tosi:2017,
an initially wet mantle can significantly enhance early degassing of CO2 and
would thereby compete with a high initial mantle temperature in order to
successfully reproduce the atmospheric CO2 of present-day Venus. A wet mantle
would allow for an initial mantle temperature of 1700 K or lower to yield
early degassing of CO2 [Tosi . (2017)], although the cycle of weathering,
carbonate burial, and decarbonation as described above would likely operate
similarly.

###  4.3 Initial ocean mass

From analysis of large-probe neutral mass spectrometer data obtained from
Pioneer Venus, early Venus is thought to have a minimum water mass of
$10^{18}$ kg on its surface, which is two orders of magnitude more than its
present-day amount [Donahue Hodges Jr (1992)]. Some studies even suggest a
more massive water ocean on early Venus [Salvador . (2017)], but the low
present-day oxygen ion escape rate of Venus makes such a scenario challenging
to justify [Persson . (2020), Gillmann . (2020), Lammer . (2009)]. A
potentially significant water sink has been suggested by way2020: During the
global resurfacing event $\approx$ 500 Myr ago, a large volume of freshly
produced basaltic crust may have been an efficient oxygen sink [Way Del Genio
(2020)]. We note that a global resurfacing event has been associated with a
transition from plate tectonics to stagnant-lid [Solomatov Moresi (1996)],
which we do not assume in our model. However, numerical simulations show that
such a resurfacing event may also emerge from a stagnant-lid convection regime
[Noack . (2012)]. armann2012simulating and Gillmann:2014 find that simulations
with an episodic overturn can more readily explain surface observations such
as topography, gravity, surface age, and inferred crustal thickness, although
a continuous stagnant-lid regime cannot be excluded for specific model
parameter combinations. rolf2018inferences suggest that simulations and
observations best favour at least one global overturn event with ongoing
resurfacing. Altogether, continuous stagnant-lid convection with one or more
resurfacing events as efficient oxygen sinks in Venus’ late evolution remains
a valid option.

Modelling Venus’ early evolution (Fig. 2), we decided to use an initial
surface ocean reservoir of $10^{19}$ kg. This value is sufficiently high to
illustrate a significant runaway greenhouse effect, resulting in a surface
temperature increase of $\approx$100 K (see Fig. 2b). However, since our model
neglects a water sink, this high value would result in an overestimation of
the surface temperature and thereby mantle melting and degassing in the late
evolution. Therefore, when plotting the atmospheric CO2 in Fig. 4, we used for
this case an initial surface ocean reservoir of $10^{18}$ kg. The early
evolution before the runaway greenhouse and its onset is not sensitive to the
assumed ocean mass (see Fig. 3).

###  4.4 Initial CO2-rich atmosphere

Figure 7: Early evolution with initial CO2 abundances between 0 and 1$\times
10^{20}$ mol, other parameter values as in Fig. 2.

For the sake of simplicity, our reference model assumes an initial atmosphere
only composed a background-pressure of 1 bar N2. However, magma ocean
solidification might degas a substantial amount of CO2 into the atmosphere
[Elkins-Tanton (2008), Lebrun . (2013), Salvador . (2017), Nikolaou . (2019)].
In order to assess to what extent early weathering can keep the planet
habitable despite an initial CO2-rich atmosphere, in Fig. 7 we test the
influence of an initial atmosphere reservoirs of CO2 up to 1020 mol ($\approx$
1 bar). We find that an initial atmosphere of 5$\times 10^{19}$ mol on early
Venus still allows for climate regulation and liquid water, while 1$\times
10^{20}$ mol directly triggers ocean evaporation. However, our model assumed a
constant planetary albedo of 0.6, and for higher initial CO2 abundances the
planetary albedo might increase. Altogether, if environmental conditions
allowed for liquid water on an early stagnant-lid Venus shortly after magma
ocean solidification, our finding of an extended early habitable period of
$\approx$0.9 Gyr should remain valid, even with an initial CO2-rich atmosphere
in combination with a higher initial albedo.

###  4.5 Plate tectonics on early Venus?

The idea that early Venus might have been habitable has extensively been
discussed in the literature [Way Del Genio (2020), Grinspoon Bullock (2007),
Salvador . (2017), Way . (2016)]. Most authors consider plate tectonics when
assessing a potential habitable period of early Venus. However, Venus’ early
tectonic regime is debated, since geological observations of Venus’ surface
only allow for an interpretation of the time after the global resurfacing
event $\approx$500 Myr ago, while a transition from a mobile to a stagnant lid
has been suggested [Weller Kiefer (2020), Gillmann Tackley (2014), Head
(2014)]. The likelihood of plate tectonics may also depend on the rheology of
the mantle [Noack Breuer (2014), O’Neill . (2007)], although a clear
conclusion as to whether or not plate tectonics occurred on early Venus cannot
be drawn. Our model assumes that the convective mode of Venus has been
stagnant-lid throughout its entire history. It is important to emphasise that
early plate tectonics would further enhance Venus’ habitability, since the
carbonate-silicate cycle operates more efficiently on planets where subduction
of carbonates into the mantle follows a shallow temperature-depth gradient.
However, our study suggests that plate tectonics is not required for extended
habitability of early Venus.

##  5 Conclusions

We assessed the atmospheric evolution and habitability of early Venus
accounting for weathering, carbonate burial, and decarbonation. In addition,
we applied our model to Venus-sized stagnant-lid exoplanets around a Sun-like
star. Our findings can be summarised as follows:

  * $\bullet$

As soon as weathering on stagnant-lid planets stops as a result of ocean
evaporation, the supply of CO2 to the atmosphere speeds up until the crust
becomes depleted in carbonates. This is a consequence of a positive feedback
involving atmospheric CO2, surface temperature, and the rate of change of the
decarbonation depth. This decarbonation feedback complements the runaway
greenhouse feedback, thereby causing a dramatic rise in the surface
temperature.

  * $\bullet$

A model with an initial mantle temperature of 1900 K and an oxygen fugacity
equal to the iron-wüstite buffer results in an atmospheric CO2 similar to that
observed on Venus today. If the initial atmospheric CO2 reservoir allows for
liquid surface water, our model accounting for weathering, burial, and
decarbonation indicates a habitable time period of 900 Myr, which is 500 Myr
longer than obtained from a model without weathering.

  * $\bullet$

Stagnant-lid exoplanets should show a bimodal distribution of their
atmospheric CO2: Planets close to their host star should have a crust depleted
in carbonates and an atmosphere abundant in CO2, while planets further away
from their host star could still possess an active carbon cycle restricted to
their atmosphere and crust, which would efficiently regulate their surface
temperature. An observation of this bimodal distribution e.g. by successfully
retrieving the strong CO2 fundamental band could therefore be used as a first
proxy of habitability which is easier to observe than other potentially
relevant factors such as additional greenhouse gases in the atmosphere.

###### Acknowledgements.

We thank two anonymous reviewers for helpful comments and suggestions. DH was
supported through the NWO StartImpuls. PB, NT and JLG acknowledge support from
the DFG Priority Program SPP 1992 “Exploring the Diversity of Extrasolar
Planets” (TO 704/3-1 and GO 2610/2-1). PB and NT also acknowledge support from
the DFG Research Unit FOR 2440 “Matter under planetary interior conditions”.
MJW was supported by NASA’s Nexus for Exoplanet System Science (NExSS).
Resources supporting this work were provided by the NASA High-End Computing
(HEC) Program through the NASA Center for Climate Simulation (NCCS) at Goddard
Space Flight Center. MJW acknowledges support from the GSFC Sellers Exoplanet
Environments Collaboration (SEEC), which is funded by the NASA Planetary
Science Division’s Internal Scientist Funding Model. All relevant equations
for the interior evolution model are explained in Tosi:2017 and all model
additions that adequately support reproducibility of our results are given in
this paper. The GCM model is explained in way2017. Produced data are available
in honing:2021.

##  Appendix A Weathering and decarbonation on stagnant-lid planets

The global rate of seafloor weathering on Earth is usually described as the
product of carbonatization per crustal volume and the global crustal
production rate [<]e.g.,¿Sleep:2001. Applying this functional dependence to
stagnant-lid planets, we assume that the silicate weathering rate of these
planets $F_{w}$ (in mol yr-1) depends on the atmospheric CO2 partial pressure
$P_{CO_{2}}$ and the production rate of basaltic crust
$\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}$ in the same manner as seafloor
weathering on Earth:

$\frac{F_{w}}{F_{sfw,E}}=\frac{\left(\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}\right)}{\left(\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}\right)_{E}}\left(\frac{P_{CO_{2}}}{P_{CO_{2},E}}\right)^{\alpha},$
(6)

where the index $E$ denotes present-day Earth values. We can relate the
present-day Earth seafloor weathering rate $F_{sfw,E}$ to the carbon ingassing
rate $F_{in,E}$ into Earth’s mantle:

$F_{in,E}=F_{sfw,E}\frac{f_{E}}{\xi_{E}},$ (7)

where $\xi_{E}$ is the fraction of seafloor weathering rate relative to the
total weathering rate and $f_{E}$ is the fraction of buried carbonates that
enters the mantle. We now assume that on present-day Earth carbon ingassing
equals outgassing, which in turn is given by the product of the
CO2-concentration of mid-ocean ridge melt $X_{E}$ and the crustal production
rate:

$F_{in,E}=X_{E}\left(\frac{\mathrm{d}M_{cr}}{\mathrm{d}t}\right)_{E}.$ (8)

Combining Eqs. 6–8, we arrive at Eq. 1 [<]for details, see¿honing:2019.

As in honing:2019, we track carbonated crust that is buried by new lava flows
and thereby sinks downward. Neglecting heat sources in the crust, we calculate
the temperature $T(z)$ at depth $z$ assuming a linear temperature profile:

$T(z)=T_{s}+\frac{z(T_{m}-T_{s})}{D_{l}+\delta_{m}},$ (9)

where $T_{s}$ and $T_{m}$ are the surface and mantle temperatures, and
$\delta_{m}$ and $D_{l}$ are the thicknesses of the thermal boundary layer and
of the stagnant lid, respectively. The decarbonation temperature is assumed to
increase linearly with depth:

$T_{decarb}=Az+B,$ (10)

where $A$ and $B$ are constants from Foley:2018. Combining Eqs. 9 and 10, we
arrive at Eq. 2.

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