# A model Earth-sized planet in the habitable zone of $\alpha$ Centauri A/B

Haiyang S. Wang ETH Zürich, Institute for Particle Physics and Astrophysics,
Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland  National Center for
Competence in Research PlanetS (www.nccr-planets.ch)  Charles H. Lineweaver
Research School of Astronomy and Astrophysics, Australian National University,
Canberra, ACT 2611, Australia  Research School of Earth Sciences, Australian
National University, Canberra, ACT 2601, Australia  Sascha P. Quanz ETH
Zürich, Institute for Particle Physics and Astrophysics, Wolfgang-Pauli-
Strasse 27, CH-8093 Zürich, Switzerland  National Center for Competence in
Research PlanetS (www.nccr-planets.ch)  Stephen J. Mojzsis Origins Research
Institute, Research Centre for Astronomy and Earth Sciences, Konkoly Thege
Miklós út 15-17, H- 1121 Budapest, Hungary.  Department of Lithospheric
Research, University of Vienna, UZA 2, Althanstraße 14, A-1090 Vienna,
Austria.  Department of Geological Sciences, University of Colorado, 2200
Colorado Avenue, Boulder, CO 80309-0399, USA.  Trevor R. Ireland School of
Earth and Environmental Sciences, University of Queensland, St Lucia QLD 4072,
Australia  Research School of Earth Sciences, Australian National University,
Canberra, ACT 2601, Australia  Paolo A. Sossi ETH Zürich, Institute of
Geochemistry and Petrology, Sonneggstrasse 5, CH-8092 Zürich, Switzerland.
Fabian Seidler  ETH Zürich, Institute for Particle Physics and Astrophysics,
Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland  Thierry Morel Space
sciences, Technologies and Astrophysics Research (STAR) Institute, Université
de Liège, Quartier Agora, Allée du 6 Août 19c, Bât. B5C, 4000 Liège, Belgium.

(Received October 24, 2021; Revised January 16, 2022; Accepted January 23,
2022)

###### Abstract

The bulk chemical composition and interior structure of rocky exoplanets are
of fundamental importance to understanding their long-term evolution and
potential habitability. Observations of the chemical compositions of the solar
system rocky bodies and of other planetary systems have increasingly shown a
concordant picture that the chemical composition of rocky planets reflects
that of their host stars for refractory elements, whereas this expression
breaks down for volatiles. This behavior is explained by devolatilization
during planetary formation and early evolution. Here, we apply a
devolatilization model calibrated with solar system bodies to the chemical
composition of our nearest Sun-like stars – $\alpha$ Centauri A and B – to
estimate the bulk composition of any habitable-zone rocky planet in this
binary system (“$\alpha$-Cen-Earth”). Through further modeling of likely
planetary interiors and early atmospheres, we find that compared to Earth,
such a planet is expected to have (i) a reduced (primitive) mantle that is
similarly dominated by silicates albeit enriched in carbon-bearing species
(graphite/diamond); (ii) a slightly larger iron core, with a core mass
fraction of $38.4_{-5.1}^{+4.7}$ wt% (cf. Earth’s 32.5 $\pm$ 0.3 wt%); (iii)
an equivalent water-storage capacity; and (iv) a CO2-CH4-H2O-dominated early
atmosphere that resembles that of Archean Earth. Further taking into account
its $\sim$ 25% lower intrinsic radiogenic heating from long-lived
radionuclides, an ancient $\alpha$-Cen-Earth ($\sim$ 1.5-2.5 Gyr older than
Earth) is expected to have less efficient mantle convection and planetary
resurfacing, with a potentially prolonged history of stagnant-lid regimes.

Theoretical models(2107) – Extrasolar rocky planets(511) – Planetary
interior(1248) – Atmospheric composition(2120) – Exoplanet dynamics(490)

##  1 Introduction

To date, over 4900 exoplanets have been confirmed (NASA Exoplanet Archive,
2022)111Accessed on 2022-01-16 at 18:00. and exoplanet statistics suggest that
close to 100% of Sun-like (FGK) stars harbor planetary systems (Cassan et al.,
2012; Lineweaver & Chopra, 2012; Winn & Fabrycky, 2015; Zhu & Dong, 2021). The
occurrence of planets with radii between 0.5 and 1.5 $R_{\oplus}$ orbiting in
the conservative habitable zone (HZ) (Kopparapu et al., 2013) of stars with
effective temperatures between 4800 and 6300 K, $\eta_{\oplus}$, is estimated
to be at least $0.37_{-0.21}^{+0.48}$ (Bryson et al., 2021). Discoveries
continue with legacy data from missions like Kepler, ongoing space
observations by TESS, and ground-based radial velocity surveys (e.g., HARPS,
CARMENES). Available data for presumably rock-dominated exoplanets, however,
are typically limited to mass and/or radius, and orbital parameters. The James
Webb Space Telescope (JWST), launched in December 2021, may be able to detect
the atmospheres of a few transiting terrestrial exoplanets orbiting within the
HZ of nearby M-dwarf stars (Koll et al., 2019). Towards the end of the 2020s,
mid-infrared instruments installed on the 30-40 m Extremely Large Telescope
(ELT) are expected to be able to directly image terrestrial, HZ exoplanets
around the very nearest FGK stars (Quanz et al., 2015; Bowens et al., 2021).
In anticipation of these observations and to guide the development of even
more ambitious future space mission concepts, such as HabEx (Gaudi et al.,
2020), LUVOIR (The LUVIOR team, 2019), and LIFE (Quanz et al., 2021), we must
focus on modeling efforts for predictions of rocky exoplanet bulk compositions
and interiors.

Observations of the chemical compositions of rocky bodies in the Solar System
(Wang et al., 2019a; Sossi & Fegley, 2018; Carlson et al., 2014; Grossman &
Larimer, 1974) and of polluted white dwarfs (Harrison et al., 2021, 2018;
Doyle et al., 2019) lend support to the idea that the chemical composition of
“terrestrial” (silicate+metal dominated) planets generally reflects that of
their host stars for refractory elements, whereas this expression breaks down
for volatile elements (Schulze et al., 2021; Adibekyan et al., 2021). This
discrepancy can be explained by devolatilization processes (Wang et al.,
2019a; Sossi et al., 2019; Norris & Wood, 2017; Hin et al., 2017) that
occurred during the formation and early evolution of the terrestrial planets
of our best star-planet sample, the Solar System. Analysis shows that a
variety of both stochastic and non-stochastic physical processes account for
the overall devolatilization outcome. Importantly, the average effect of these
processes is generally non-random (Wang, 2018) and follows a trend that
reflects the variation of elemental abundances with elemental volatilities
(Fegley et al., 2020; Wang et al., 2019a; Sossi & Fegley, 2018). The first
quantitative model of devolatilization (Wang et al., 2019a) is being
increasingly adopted in the modeling of rocky exoplanetary bulk compositions
and interiors (Wang et al., 2019b; Acuña, 2019; Spaargaren et al., 2020) or as
a reference for linking star-planet elemental relations (Dorn et al., 2019;
Liu et al., 2020; Cowley et al., 2021; Clark et al., 2021; Schulze et al.,
2021). Here, we apply this technique to a key target for exoplanet surveys –
the $\alpha$ Centauri AB System (hereafter, $\alpha$-CenA/B) – our nearest
Sun-like stellar neighbors.

###  1.1 The status of the search for an $\alpha$-CenA/B planet

Figure 1: (a) Trajectories of $\alpha$-Cen A (red) and B (blue) around their
barycenter (“$\times$”). The two stars are positioned at their approximate
present-day separation. The Hill spheres (dashed circles) and habitable zones
(nested green circles) of A and B are drawn to scale at periapsis. (b)
Apparent trajectory of B centered on A, with indications of their apparent
separation on the sky over the period from CE 2020 to 2050. The part of
trajectory in yellow indicates the coming observational window (CE 2022-2035),
when the apparent separation between A and B is larger than 6′′ and the search
for planets around A or B can be conducted without suffering significant
contamination from the respective companion star.

The binary stars of the system – $\alpha$-Cen A (spectral type G2) and B
(spectral type K1) – are on an inclined ($\sim 79^{\circ}$), eccentric ($\sim
0.5$), $\sim 80$ year orbit with a separation varying from 35.6 AU to 11.2 AU
(Pourbaix & Boffin 2016; Fig. 1) and have an estimated age of $\sim$ 6–7 Gyr
(Salmon et al., 2021; Morel, 2018). The binary shares a gravitationally-bound
companion star – the red dwarf $\alpha$-Cen C (Proxima Centauri; spectral type
M5), which orbits the barycentre of the A/B system with a period of $\sim$ 550
kyr (Kervella et al., 2017). Proxima Cen is confirmed to host at least one
planet (Anglada-Escudé et al., 2016; Damasso et al., 2020) whereas such
confirmation remains elusive for $\alpha$-CenA/B. The ostensible detection of
an Earth-mass exoplanet orbiting $\alpha$-Cen B (Dumusque et al., 2012) was
later found to be an artifact of the observational technique (Rajpaul et al.,
2016). However, owing to its immediate proximity to our Solar System,
$\alpha$-CenA/B continues to generate interest in the search for Earth-like
planets (Zhao et al., 2018; Kasper et al., 2019; Beichman et al., 2020; Wagner
et al., 2021; Akeson et al., 2021). Radial-velocity measurements put the
following detection limits on the masses of planets in the habitable zones of
A and B, respectively: $M_{A}\sin i<53M_{\oplus}$ and $M_{B}\sin
i<8.4M_{\oplus}$ (Zhao et al., 2018). Recent attempts to directly image low-
mass planets in $\alpha$-CenA/B with the NEAR experiment at the Very Large
Telescope (VLT) observatory have ruled out Jupiter-sized planets (Wagner et
al., 2021). A candidate signal that may be consistent with an exoplanet of
$R\sim 3.3-7R_{\oplus}$ around $\alpha$-Cen A awaits confirmation (Wagner et
al., 2021).

Simultaneously, numerical simulations continue to support the idea that over
geological timescales (i.e. $>10^{9}$ yr) stable planetary orbits can persist
within the habitable zones of both $\alpha$-Cen A and B (Andrade-Ines &
Michtchenko, 2014; Quarles & Lissauer, 2016; Quarles et al., 2020). Such
stability is also bolstered by the non-overlapping Hill spheres of the binary
stars at their periapsis (Fig. 1a). The interval between the years 2022–2035
will be the next ideal observational timeframe (Fig. 1b), during which
searching for planets around A or B with, e.g., JWST/MIRI (Beichman et al.,
2020) and ELT/METIS (Quanz et al., 2015; Carlomagno, 2020), will benefit from
lower levels of contamination from the other component. It is therefore timely
to predict what kind of planets to expect in the $\alpha$-CenA/B system based
on theoretical models, and thus provide guidance for future observations. For
this study, we focus our analysis on a hypothetical, Earth-sized planet in the
habitable zone around either A or B.

##  2 Data, methods, and analysis

###  2.1 Stellar chemical compositions

Figure 2: Comparison of the elemental abundances of $\alpha$-Cen A and B. A
$\chi^{2}$-test shows that $\chi^{2}/\mathbf{\nu}=0.72$ and
$P(\geq\chi^{2},\mathbf{\nu})=0.19$, where the degrees of freedom
$\mathbf{\nu}=20$ (i.e., the number of elements whose abundances are available
in both A and B). The data sources are from Morel (2018) and Wang et al.
(2020a) and are also listed in Table 1.

Both $\alpha$-Cen A and B are among the Gaia FGK “benchmark stars”, for which
the stellar properties have been carefully calibrated (Heiter et al., 2015;
Jofré et al., 2017). The chemical compositions of the two companions have also
been determined in detail with high-quality spectra for up to 22 elements
(Morel, 2018; Wang et al., 2020a). The datasets of (Morel, 2018; Wang et al.,
2020a) are selected for (i) their completeness, high precision and homogeneity
for all elements of interest to our study and (ii) their large consistency
with other reported results in the literature for $\alpha$ Cen A/B (e.g.
Neuforge-Verheecke & Magain, 1997; Koch & Edvardsson, 2002; Guiglion et al.,
2018). We do not compare the different literature analyses here, and such
comparisons have been discussed in detail in our refereed sources.

Figure 2 compares the elemental abundances between $\alpha$-Cen A and B
(Columns 2-3, Table 1), which are found to be statistically consistent with
each other ($\chi^{2}/\nu=0.72$ and $P(\leq\chi^{2},\nu)=0.19$), supporting
the idea that A and B have a common origin (Beech, 2015). For consistency and
simplicity of discussion, we calculate the weighted-average elemental
abundances of A and B (Column 4, Table 1). The exceptions to the approach are
that (i) since the A and B abundances of Co and Y are inconsistent, we compute
unweighted averages and use their abundance spread as uncertainties; (ii) the
abundances of Mn and Ce are only available for $\alpha$ Cen A and are thus
adopted directly for the averaged AB system. We then use the protosolar
abundances (Wang et al., 2019a) to convert the differential abundances to the
absolute abundances (normalized to Al = 100; Column 5, Table 1). We did not
consider the effects of microscopic diffusion in $\alpha$ Cen A and B, but as
noted in Morel (2018) any changes arising from diffusion can probably be
accommodated by the abundance uncertainties.

Table 1:  The elemental abundances of $\alpha$ Cen A, $\alpha$ Cen B, and the average AB system. For details see Sect. 2.1. Element | [X/H]${}_{\textrm{A}}$ (dex) | [X/H]${}_{\textrm{B}}$ (dex) | [X/H]${}_{\textrm{AB}}$ (dex) | (X/Al)${}_{\textrm{AB}}$ (Al=100)
---|---|---|---|---
C | $0.262\pm 0.018$ | $0.220\pm 0.045$ | $0.256\pm 0.017$ | 9514 | $\,{}_{-1106}^{+1251}$
O | 0.191 $\pm$ 0.014 | 0.147 $\pm$ 0.040 | 0.186 $\pm$ 0.013 | 14735 | $\,{}_{-1683}^{+1900}$
Na | 0.331 $\pm$ 0.010 | 0.339 $\pm$ 0.036 | 0.332 $\pm$ 0.010 | 72 | $.7\,_{-4.8}^{+5.1}$
Mg | 0.250 $\pm$ 0.023 | 0.265 $\pm$ 0.041 | 0.254 $\pm$ 0.020 | 1192 | $\,{}_{-85}^{+318}$
Al | 0.281 $\pm$ 0.013 | 0.298 $\pm$ 0.031 | 0.284 $\pm$ 0.012 | 100 | $\,\pm 6$
Si | 0.261 $\pm$ 0.009 | 0.255 $\pm$ 0.018 | 0.260 $\pm$ 0.008 | 1153 | $\,{}_{-38}^{+39}$
Ca | 0.217 $\pm$ 0.010 | 0.222 $\pm$ 0.030 | 0.218 $\pm$ 0.009 | 64 | $.2\,_{-3.2}^{+3.4}$
Sc | 0.266 $\pm$ 0.014 | 0.257 $\pm$ 0.018 | 0.263 $\pm$ 0.011 | 0 | $.042\,_{-0.005}^{+0.016}$
Ti | 0.253 $\pm$ 0.011 | 0.284 $\pm$ 0.033 | 0.256 $\pm$ 0.010 | 2 | $.86\,_{-0.17}^{+0.18}$
V | 0.256 $\pm$ 0.017 | 0.294 $\pm$ 0.050 | 0.260 $\pm$ 0.016 | 0 | $.32\,\pm 0.02$
Cr | 0.248 $\pm$ 0.011 | 0.264 $\pm$ 0.033 | 0.250 $\pm$ 0.010 | 14 | $.8_{-0.7}^{+0.8}$
Mn | 0.271 $\pm$ 0.019 | – | 0.271 $\pm$ 0.019 | 10 | $.5\,\pm 0.7$
Fe | 0.237 $\pm$ 0.007 | 0.221 $\pm$ 0.016 | 0.234 $\pm$ 0.006 | 959 | $\,{}_{-37}^{+38}$
Co | 0.288 $\pm$ 0.019 | 0.202 $\pm$ 0.044 | $0.245\;_{-0.087}^{+0.062}$ | 2 | $.57\,_{-0.47}^{+0.41}$
Ni | 0.286 $\pm$ 0.009 | 0.278 $\pm$ 0.019 | 0.285 $\pm$ 0.008 | 59 | $.6\,_{-3.4}^{+3.6}$
Cu | 0.295 $\pm$ 0.020 | 0.291 $\pm$ 0.034 | 0.294 $\pm$ 0.017 | 0 | $.62\,\pm 0.06$
Zn | 0.266 $\pm$ 0.027 | 0.296 $\pm$ 0.031 | 0.279 $\pm$ 0.020 | 1 | $.48\,\pm 0.09$
Y | 0.203 $\pm$ 0.013 | 0.268 $\pm$ 0.029 | $0.236\;_{-0.046}^{+0.062}$ | 4 | $.78\,_{-0.52}^{+0.77}\;\times 10^{-3}$
Zr | 0.270 $\pm$ 0.053 | 0.343 $\pm$ 0.060 | 0.302 $\pm$ 0.040 | 0 | $.014\pm 0.001$
Ba | 0.185 $\pm$ 0.025 | 0.179 $\pm$ 0.025 | 0.182 $\pm$ 0.018 | 4 | $.50\,_{-0.27}^{+0.29}\;\times 10^{-3}$
Ce | 0.172 $\pm$ 0.055 | – | 0.172 $\pm$ 0.055 | 1 | $.09\,_{-0.13}^{+0.15}\;\times 10^{-3}$
Eu | 0.127 $\pm$ 0.040 | 0.081 $\pm$ 0.060 | 0.113 $\pm$ 0.033 | 8 | $.36\,_{-0.66}^{+0.71}\;\times 10^{-5}$

###  2.2 Devolatilization

We employ the fiducial model of devolatilization (Wang et al., 2019a), which
is quantified by the bulk elemental abundance differences between the proto-
Sun and the Earth (Wang et al., 2018, 2019a) as a function of 50% condensation
temperature ($T_{c}$50; Lodders, 2003), to devolatilize the averaged AB system
abundances. This process results in the devolatilized host stellar abundances
(Column 2, Table 2) as the proxy for the elemental composition of any rocky
planet in the HZ of the system (i.e. “$\alpha$-Cen-Earth”). The justification
and limitations of applying such a Sun-to-Earth model to other Solar-like
planetary systems are presented in Wang et al. (2019b) and also recapped
later. Further, since we are interested in how the model $\alpha$-Cen-Earth is
different from the bulk Earth by analyzing primarily the individual elements
or their ratios, the residuals of the devolatilization model for individual
elements (Column 3, Table 2) – i.e. the differences between the bulk Earth
composition (Wang et al., 2018) and the model Earth composition as
devolatilized from the protosolar abundances (Wang et al., 2019a) – are added
onto the devolatilized AB average stellar abundances to obtain the final bulk
elemental composition of the model $\alpha$-Cen-Earth (Columns 4-5, Table 2).

Table 2:  Estimates of the chemical composition of the model $\alpha$-Cen-Earth. For details see Sect. 2.2. Element | (X/Al)${}_{\textrm{devol}}$ (Al=100) | (X/Al)${}_{\textrm{residual}}$ | (X/Al)${}_{\textrm{bulk}}$ (Al=100) | (X/Fe)${}_{\textrm{bulk}}$ (Fe=100)
---|---|---|---|---
C | 35 | $.9\,_{-7.7}^{+9.0}$ | 0 | .3 | 36 | $.2\,_{-7.7}^{+9.0}$ | 4 | $.12\,_{-0.87}^{+1.03}$
O | 2674 | $\,{}_{-335}^{+377}$ | 13 |  | 2687 | $\,{}_{-335}^{+377}$ | 306 | $\,{}_{-38}^{+43}$
Na | 18 | $.4\,_{-1.4}^{+1.6}$ | 0 | .3 | 18 | $.7\,_{-1.4}^{+1.6}$ | 2 | $.13\,_{-0.16}^{+0.18}$
Mg | 1025 | $\,{}_{-81}^{+276}$ | -15 |  | 1010 | $\,{}_{-81}^{+276}$ | 115 | $\,{}_{-9}^{+31}$
Al | 100 | $\,\pm 6$ | 0 |  | 100 | $\;\pm 6$ | 11 | $.4\,_{-0.6}^{+0.7}$
Si | 923 | $\,{}_{-43}^{+47}$ | 19 |  | 941 | $\,{}_{-43}^{+47}$ | 107 | $\,\pm 5$
Ca | 64 | $.2\,_{-3.2}^{+3.4}$ | -1 | .8 | 62 | $.4\,_{-3.2}^{+3.4}$ | 7 | $.11\,_{-0.36}^{+0.38}$
Sc | 0 | $.042\,_{-0.005}^{+0.016}$ | -0 | .003 | 0 | $.039\,_{-0.004}^{+0.015}$ | 0 | $.004\,_{-0.001}^{+0.002}$
Ti | 2 | $.9\,\pm 0.2$ | -0 | .2 | 2 | $.7\,\pm 0.2$ | 0 | $.31\,\pm 0.02$
V | 0 | $.32\,\pm 0.02$ | -0 | .01 | 0 | $.31\,\pm 0.02$ | 0 | $.036\,_{-0.002}^{+0.003}$
Cr | 11 | $.4\,\pm 0.7$ | 0 | .7 | 12 | $.1\,\pm 0.7$ | 1 | $.38\,\pm 0.08$
Mn | 5 | $.3\,\pm 0.4$ | 0 | .1 | 5 | $.4\,\pm 0.4$ | 0 | $.62\,_{-0.04}^{+0.05}$
Fe | 820 | $\,{}_{-42}^{+46}$ | 57 |  | 877 | $\,{}_{-42}^{+46}$ | 100 | $\,\pm 5$
Co | 2 | $.3\,\pm 0.4$ | 0 | .0 | 2 | $.3\,\pm 0.4$ | 0 | $.26_{-0.05}^{+0.04}$
Ni | 53 | $.7\,_{-3.6}^{+3.9}$ | -0 | .8 | 52 | $.9_{-3.6}^{+3.9}$ | 6 | $.03\,_{-0.41}^{+0.44}$
Cu | 0 | $.21\,\pm 0.02$ | -0 | .02 | 0 | $.19\,\pm 0.02$ | 0 | $.022\,_{-0.002}^{+0.003}$
Zn | 0 | $.14\,\pm 0.01$ | -0 | .01 | 0 | $.12\,\pm 0.01$ | 0 | $.014\,_{-0.001}^{+0.002}$
Y | 4 | $.77\,_{-0.52}^{+0.77}\;\times 10^{-3}$ | 0 | $.03\;\times 10^{-3}$ | 4 | $.81\,_{-0.52}^{+0.77}\;\times{10}^{-3}$ | 5 | $.48\,_{-0.59}^{+0.87}\;\times 10^{-4}$
Zr | 0 | $.014\,\pm 0.001$ | 0 | .000 | 0 | $.014\,\pm 0.001$ | 1 | $.54\,_{-0.15}^{+0.17}\;\times 10^{-3}$
Ba | 4 | $.50\,\pm_{-0.27}^{+0.29}\;\times 10^{-3}$ | -0 | $.34\;\times 10^{-3}$ | 4 | $.16\,_{-0.25}^{+0.27}\;\times 10^{-3}$ | 4 | $.75\,_{-0.31}^{+0.33}\;\times 10^{-4}$
Ce | 1 | $.09\,_{-0.13}^{+0.15}\;\times 10^{-3}$ | -0 | $.03\;\times 10^{-3}$ | 1 | $.06\,_{-0.13}^{+0.15}\;\times 10^{-3}$ | 1 | $.21\,_{-0.15}^{+0.17}\;\times 10^{-4}$
Eu | 7 | $.59\,_{-0.65}^{+0.71}\;\times 10^{-5}$ | 0 | $.41\;\times 10^{-5}$ | 8 | $.01\,_{-0.65}^{+0.71}\;\times 10^{-5}$ | 9 | $.1_{-0.7}^{+0.8}\;\times 10^{-6}$

###  2.3 Key geochemical ratios

The stellar abundance ratios of carbon to oxygen (C/O) and magnesium to
silicon (Mg/Si) are diagnostic indicators, as widely adopted in the literature
(e.g. Bond et al., 2010; Delgado Mena et al., 2010; Fortney, 2012; Thiabaud et
al., 2015; Brewer & Fischer, 2016; Suárez-Andrés et al., 2018; Zhao et al.,
2018; Spaargaren et al., 2020; Clark et al., 2021) (we also use them later),
of the plausible composition of any rocky planet around the host star.
However, upon the application of our devolatilization approach, both carbon
and oxygen are severely depleted in rocky planets relative to their host star
and therefore, a planetary (not a stellar) C/O is no longer a valid indicator
of rocky planets’ dominant mineral types (silicates vs. carbides). Due to the
near-refractory nature (and similar $T_{c}$50; Lodders 2003; Wood et al. 2019)
of Mg and Si, their ratio in a star is not significantly altered through the
devolatilization process (Wang et al., 2019a) and thus is still a good first-
order proxy for Mg/Si in a rocky planet around the host star (Schulze et al.,
2021; Adibekyan et al., 2021; Thiabaud et al., 2014; Delgado Mena et al.,
2010; Bond et al., 2010).

The oxidation state of a planet is crucial to understand planetary chemistry
and internal fractionation of materials (Wade & Wood, 2005; Unterborn et al.,
2014) and it is usually recorded by oxygen fugacity ($f\textrm{O}_{2}$) – i.e.
the nonideal partial pressure of oxygen. It may, for convenience, be expressed
relative to a mineral buffer, such as Iron-Wüstite (IW) and Quartz-Fayalite-
Magnetite (QFM) (O’Neill, 1987; Ballhaus et al., 1990; Doyle et al., 2019). In
an exoplanetary context, however, the $f\textrm{O}_{2}$ is difficult to
estimate, because it changes in response to mineralogy, pressure and
temperature (Woodland & Koch, 2003; O’Neill et al., 2006; Armstrong et al.,
2019), all of which are unknown in the first place for our model $\alpha$-Cen-
Earth. We therefore opt for a proxy – that may be constrained directly from
the estimated planetary bulk composition – for the planetary nominal
$f\textrm{O}_{2}$. Considering that O, Mg, Si, and Fe are the most abundant
elements in a silicate planet (Wang et al., 2018; Yoshizaki & McDonough, 2020)
and that MgO and SiO2 are the major oxides while FeO content heavily depends
on the planet’s oxidation state, we propose the bulk (O-Mg-2Si)/Fe as a proxy
for the oxidation state of such a planet. For example, if a negative value is
found for (O-Mg-2Si)/Fe (indeed for our case as shown in Table 3), it
implicitly reveals a reduced nature of the mantle.

Furthermore, since Mg and Si are expected to be the dominant lithophile
elements in a silicate mantle (Palme & O’Neill, 2014; Wang et al., 2018;
Yoshizaki & McDonough, 2020) while Fe is the major constituent for a rocky
planet’s core (McDonough, 2003; Wang et al., 2018), (Mg+Si)/Fe is adopted as a
proxy for the potential core size of a rocky planet. Along these lines, since
Eu is also a lithophile element and by following (Wang et al., 2020a) it is a
preferred proxy for long-lived radionuclides 235,238U and 232Th in
terrestrial-type planets, we therefore adopt Eu/(Mg+Si) as a proxy for
indicating the concentration of these long-lived isotopes and the budget of
the resultant radiogenic heating production over geologic timescales. A
similar approach awaits formulation, however, to estimate 40K abundance
(Gastis et al., 2020). Following Frank et al. (2014), we assume that the
$\alpha$-CenA/B system has an initial value of 40K as that of the Solar
System, but we also note that due to the age of the stars in the
$\alpha$-CenA/B system (Morel, 2018; Salmon et al., 2021), 40K is considerably
depleted in the modern mantle of our model $\alpha$-Cen-Earth (Wang et al.,
2020a).

###  2.4 Software package and implementation

To carry out the analysis, three sets of software are employed: ExoInt (Wang
et al., 2019b) for both devolatilization and first-principal interior
modeling; Perple$\\_$X (Connolly, 2009) for a detailed modeling of the mantle
mineralogy and interior structure; and FactSage 8.0 (Bale et al., 2016) for
calculating the gas speciation from the modeled interiors. The details of the
software package and its implementation for the study are presented in
Appendix A.

##  3 Results

###  3.1 The chemical composition of the average AB system

Figure 3: Elemental abundances ([X/H], dex) of $\alpha$-Cen A and B and of the
averaged AB system, in comparison with the protosolar abundances (Wang et al.,
2019a). The dotted line indicates the mean enrichment ($\sim 1.72$) in
metallicity (Fe/H) in the averaged AB system compared to the Sun. Elements are
plotted from left to right in order of decreasing solar abundance. For more
details see Sects. 2.1 and 3.1.

Figure 3 compares the chemical composition of the average AB system with that
of the Sun. First of all, the average AB system is super-solar in metallicity
([Fe/H]), with an enrichment of iron to hydrogen by $\sim$ 72%. The enrichment
of other elements, except O, Ba, Ce, and Eu, to hydrogen ([X/H]) are either
equivalent or higher. The variation in the hydrogen-normalised enrichments for
major rock-forming elements (e.g., O, Mg, Si, Fe, Al, Ca, and Na) will have a
profound influence, as demonstrated later, on the geochemistry of the model
$\alpha$-Cen-Earth.

To first order, C/O affects the availability of rock-forming elements such as
Mg and Si to bond with O (e.g. Mg2SiO4) or C (e.g. SiC), while Mg/Si modulates
the silicate mineral assemblages (e.g. olivine vs. pyroxene; Mg2SiO4 vs.
MgSiO3). A calculation of C/O and Mg/Si in $\alpha$-CenA/B (Fig. 4) reveals
that both of these ratios are consistent with the solar values (within
uncertainties), although the C/O ($0.65\pm 0.11$) of $\alpha$-CenA/B is closer
– than that ($0.55\pm 0.09$) of the Sun (Wang et al., 2019a) – to the
threshold (0.8) (Bond et al., 2010; Delgado Mena et al., 2010) for forming a
carbide (rather than silicate) planet. With such a relatively higher value in
C/O, the $\alpha$-CenA/B planet is expected to develop a silicate mantle just
like terrestrial planets in our system, whereas the carbon-bearing phases
(e.g. graphite and diamond) in its exo-mantle may be slightly more abundant –
cf. (Zhao et al., 2018). An approximately equal Mg/Si between $\alpha$-CenA/B
and the Sun ($1.03^{+0.28}_{-0.08}$ vs. $1.04^{+0.28}_{-0.07}$) suggests a
mineralogy similar to that of the Earth, in accord with earlier studies (e.g.
Zhao et al., 2018; Morel, 2018). We also note that the most recent solar
photospheric abundances (Asplund et al., 2021) are consistent with our adopted
protosolar abundances (Wang et al., 2019a) within uncertainties in terms of
C/O vs. Mg/Si (Fig. 4), while a normalization to the former would lead to a
relatively higher C/O that favors our suggestion of the enrichment of carbon-
bearing phases in the silicates-dominated mantle of the model planet.

Figure 4: The comparison of $\alpha$ Cen AB with the Sun on the C/O–Mg/Si
diagram, with two different sets of solar abundances for references: dots in
yellow – Wang et al. (2019a); dots in grey – Asplund et al. (2021). The dashed
vertical and horizontal lines indicate the canonical boundaries for the
mineralogy of HZ rocky planets in a Sun-like star system (Bond et al., 2010;
Delgado Mena et al., 2010), while the dotted horizontal line indicates a lower
limit of C/O, above which carbon-bearing species is enriched in a silicate-
dominated mantle (Brewer & Fischer, 2016).

###  3.2 The chemical composition of the model $\alpha$-Cen-Earth

Figure 5: Estimates of bulk elemental composition of the model $\alpha$-Cen-
Earth, as devolatilized from the chemical composition of the average AB
system. The elemental compositions (by number) are normalized to Fe and bulk
Earth (Wang et al., 2018). The particularly large uncertainties for C, Mn, and
Cu in the bulk Earth composition are caused by their large uncertainties in
core composition (Wang et al., 2018). Elements are ordered by decreasing
abundance in the bulk Earth composition. For more details see Sects. 2.2 and
3.2.

Applying the fiducial model of devolatilization (Wang et al., 2019a) to the
averaged elemental abundances of the $\alpha$-CenA/B system provides an
estimate of the bulk elemental composition of the model $\alpha$-Cen-Earth
(Table 2). To focus the discussion on the relative abundances of individual
elements in the model $\alpha$-Cen-Earth compared to Earth, all elemental
abundances are normalized to iron, and by doing so, the $\sim$ 72% relative
enrichment of metallicity is removed (Fig. 5). Similar to the findings shown
in Fig. 3, the model $\alpha$-Cen-Earth has equivalent or relatively higher
concentrations of most elements (relative to Fe) and lower concentrations of
O, Ba, Ce, and Eu. The implications of such a bulk composition for the
interior chemistry, structure and dynamics of the planet are firstly analyzed
with the aforementioned key geochemical ratios, the values of which for the
model planet (relative to Earth) are listed in Table 3.

Table 3:  Estimates of key geochemical ratios of the model $\alpha$-Cen-Earth (normalized to Earth, by number; Wang et al. 2018)a. [Mg/Si] |  | [(Mg+Si)/Fe] |  | [(O-Mg-2Si)/Fe] |  | [Eu/(Mg+Si)] |
---|---|---|---|---|---|---|---
$0.98\,_{-0.11}^{+0.28}$ |  | $1.04\,_{-0.08}^{+0.16}$ |  | $-0.79\,_{-1.74}^{+1.56}$ |  | $0.73\,_{-0.13}^{+0.09}$ |
a [X/Y] = (X/Y)${}_{\alpha\textrm{-Cen-Earth}}$ / (X/Y)${}_{\textrm{Earth}}$,
where X and Y respectively denotes the numerator and denominator in any of the
listed key ratios in brackets.

Overall, the model $\alpha$-Cen-Earth’s [Mg/Si] of $0.98^{+0.28}_{-0.11}$ and
[(Mg+Si)/Fe] of $1.04^{+0.16}_{-0.08}$ resemble Earth’s values, whereas a
[(O-Mg-2Si)/Fe] of $-0.79^{+1.56}_{-1.74}$ and a [Eu/(Mg+Si)] of
$0.73^{+0.09}_{-0.13}$ are relatively lower than those of Earth. Note that the
uncertainties of these relative ratios include the uncertainties of these
ratios in Earth. A cross-check of these key geochemical ratios, as shown in
Fig. 6, helps understand better the geological properties of the model
$\alpha$-Cen-Earth than with individual ratios. For example, in panel (i) of
Fig. 6, the approximately equal [Mg/Si] reveals a silicate mantle composed of
the relatively similar fractions of olivine (main formula: (Mg, Fe)2SiO4) and
pyroxene (main formula: (Mg, Fe)SiO3), which in turn may be used to argue that
they have similar mantle viscosity and thus convection rate (Spaargaren et
al., 2020). In the [(Mg+Si)/Fe] vs. [(O-Mg-2Si)/Fe] panel, a slightly higher
[(Mg+Si)/Fe] alludes to a sub-equal or smaller core for the model
$\alpha$-Cen-Earth, whereas a lower [(O-Mg-2Si)/Fe] points to an FeO/Fe ratio
that is lower, thus resulting in an increased core size (the relative
importance of these competing effects are vetted by the subsequent
quantitative interior modeling). In panel (iii), a significantly lower
[Eu/(Mg+Si)] – a proxy for the concentration of the long-lived radionuclides –
that occurs in a mantle with mineralogy similar to the Earth’s (suggested by
[Mg/Si] above) implies that the mantle convection of the model $\alpha$-Cen-
Earth may be weakened by $\sim$ 1/4 less intrinsic radiogenic heating over its
geological history (assuming its gravitational energy to be similar to that of
Earth; to be discussed further). Finally, a combination of panels (iv) and
(ii) implies that the heat extraction from the Earth-sized core may be more
efficient due to the potentially increased core-mantle temperature differences
caused by the lower intrinsic radiogenic heating in the mantle (Wang et al.,
2020a; Nimmo et al., 2020), but also subject to the tectonic regime of the
planet (to be discussed later).

Figure 6: Key geochemical ratios of the model $\alpha$-Cen-Earth (black dots)
normalized to the Earth ($\oplus$, with normalized values indicated by dotted
lines; Wang et al. 2018). Earth’s uncertainties for these geochemical ratios
have been propagated to the error bars shown for the model $\alpha$-Cen-Earth.
Values are also reported in Table 3. For more details see Sect. 3.2 and
Appendix 2.3.

###  3.3 The interior composition and structure of the model $\alpha$-Cen-
Earth

Table 4 shows the results of the modeling of first-order mantle and core
composition as well as core mass fraction with ExoInt (Wang et al., 2019b,
also see Appendix A.1). It is found that the model $\alpha$-Cen-Earth has a
mantle composition similar to that of Earth, except for its FeO content that
is significantly depleted and native carbon species (graphite/diamond) that
may be relatively enriched. Some portion of carbon may be fractionated into
the core, but our model is unable to constrain that yet (to be discussed
later). The results are nonetheless consistent with the qualitative analysis
above, respectively with [(O-Mg-2Si)/Fe] in the planet and with C/O in its
host star. A further calculation of the Mg number (Mg# = MgO / (MgO + FeO), in
molar ratio; converted from the weight fractions in Table 4) – an indicator
for mantle chemistry and the degree of melting – for the (primitive) mantle of
the model planet reveals a much higher Mg#, $0.987^{+0.010}_{-0.020}$,
compared to $0.890\pm 0.001$ of the Earth’s primitive mantle (Palme & O’Neill,
2014; Wang et al., 2018)).

Table 4:  Estimates of mantle and core compositions as well as core mass fraction of the model $\alpha$-Cen-Earth, in comparison with those of Earth. | Mantle composition (wt%)
---|---
| MgO | SiO2 | FeO | Al2O3 | CaO | Na2O | NiO | C
$\alpha$-Cen-Earth | $44.8\,_{-7.0}^{+10.4}$ | $43.9\,_{-10.0}^{+6.4}$ | $1.0\,_{-0.8}^{+1.2}$ | $5.4\pm 0.7$ | $3.7\pm 0.5$ | $0.6\pm 0.1$ | $0.1\pm 0.1$ | $0.5\pm 0.1$
Eartha | 37.8 | 45.0 | 8.05 | 4.45 | 3.55 | 0.36 | 0.25 | 0.01
| Core composition (wt%) |  | Core mass fraction (wt%) |
| Fe | Ni | Si |  |  |  |  |
$\alpha$-Cen-Earth | $83.3\,_{-7.5}^{+9.0}$ | $5.3\,_{-0.6}^{+0.5}$ | $11.4\,_{-6.3}^{+6.4}$ |  | $38.4\,_{-5.1}^{+4.7}$ |
Earthb | $82.8\pm 2.9$ | $5.1\pm 0.2$ | $12.1\pm 3.0$ |  | $32.5\pm 0.3$ |
a Refer to the silicate Earth composition (without uncertainties) of McDonough
& Sun (1995).
b Refer to the core composition and core mass fraction of Wang et al. (2018);
silicon composition in the core is rescaled to represent the total estimate of
light elements in the core in Wang et al. (2018).

For the core composition of a presumed Fe-Ni-Si alloy, the model $\alpha$-Cen-
Earth is statistically consistent with Earth. However, the model planet has a
relatively higher core mass fraction ($38.4^{+4.7}_{-5.1}$ wt%) than that of
Earth ($32.5\pm 0.3$ wt%; Wang et al. 2018). It is noteworthy that, owing to
the lack of sulfur abundance measurements in $\alpha$-Cen A and B and the
model restrictions on considering other candidate light elements (e.g. C and
H), we have only modeled the concentration of Si as the sole light element in
the core. Hence, our modeled Si concentration ($11.4^{+6.2}_{-6.5}$ wt%)
should be seen as an upper limit of Si and of light elements, overall.

Figure 7: The comparison of the best-fit mineralogies (in volume fraction,
vol%) and density profiles (solid curves) between the model $\alpha$-Cen-Earth
(left panel) and the Earth (right panel). Earth’s density profile is
replicated as the dashed curve on the left panel for reference. The various
layers of the internal structure are noted, including the upper to lower
mantle transition zone (MTZ) and the lowermost-mantle layer
($D^{\prime\prime}$). The abbreviated mineral assemblages in the mantle are ol
– olivine, plg – plagioclase, opx – orthopyroxene, cpx – clinopyroxene, hp-cpx
– high-pressure clinopyroxene, wad – wadsleyite, ring – ringwoodite, gt –
garnet, aki – akimotoite, stv – stishovite, wus – magnesiowüstite
(ferropericlase), mg-pv – magnesium perovskite (brigdemanite), mg-postpv –
magnesium postperovskite, cf – calcium-ferrite structured phase, and ca-pv –
calcium perovskite. For more details see Sect. 3.3 and Appendix A.2.

With detailed interior modeling results shown in Fig. 7, we find that the
model $\alpha$-Cen-Earth has a broadly similar mantle mineralogy to that of
the Earth. Specifically, the upper mantle is enriched in olivine (‘ol’) over
pyroxene assemblages (‘cpx’, ‘opx’, etc.), with the mantle transition zone
(MTZ) being dominated by wadsleyite (‘wad’) and ringwoodite (‘ring’). The
lower mantle is dominated by the magnesium end-member perovskite (‘mg-pv’;
(Mg,Fe)SiO3; bridgmanite), except for the lowermost mantle (so-called
$D^{\prime\prime}$ zone) that is dominated by the higher-pressure perovskite
phase (magnesium post-perovskite, ‘mg-postpv’).

In particular, compared to Earth, the olivine/pyroxene ratio (by volume) in
the upper mantle of the model $\alpha$-Cen-Earth is equivalent ($2.2\pm 1.5$
vs. $\sim 1.9$). This highlights the importance of Mg/Si in modulating the
dominant mineral assemblages in the upper mantle. Likewise, the sum of
wadsleyite and ringwoodite in the MTZ is consistent with that of Earth, while
the trace phases such as akimotoite (‘aki’) and stishovite (‘stv’) vanish in
this zone. However, there is a slight increase in the wadsleyite/ringwoodite
ratio (by volume) in the model planet relative to Earth ($1.2\pm 0.1$ vs.
$\sim 0.7$). The implications of this will be discussed later. Further, the
modeled thickness of the $D^{\prime\prime}$ zone in the lower mantle of the
$\alpha$-Cen-Earth is noticeably thinner, with a decreased amount of the high-
pressure ‘mg-postpv’ phase ($2.9^{+1.7}_{-1.6}$ vs. $\sim 4.9$). This is
expected from the slightly enlarged core size and thus elevated core-mantle
boundary. A higher Mg# as revealed above may also suggest that the solid
solution in magnesiowüstite (‘wus’) should be dominated by the periclase (MgO)
endmember (instead of FeO).

Since the lower [(O-Mg-2Si)/Fe] of the planet (relative to Earth) frees a
larger fraction of Fe from being oxidized in the mantle ($1.1^{+1.1}_{-0.8}$
wt% vs. $\sim$ 8 wt% as for FeO; Table 4), thus segregating into the core, the
mantle density is slightly but systematically lower and vice-versa for the
core density. The relatively elevated core-mantle boundary implies a lower
pressure at the boundary, which in turn may lead to less effective Fe2+
disproportionation at time of core formation (Frost et al., 2004).

Importantly, these results should be understood in the context of the yet-
large uncertainty of the interior modeling (Fig. A1). Overall, the model
$\alpha$-Cen-Earth has a broadly Earth-like mineralogy and structure.

##  4 Discussion

###  4.1 A reduced primitive mantle and its outgassing

The modeled mass fractions of FeO in mantle rocks and Fe in the core (Table
4), permit calculation of the model $\alpha$-Cen-Earth’s nominal
$f\textrm{O}_{2}$ relative to IW ($\Delta$IW), which presumes equilibrium
between the mantle and core:

$\Delta\textrm{IW}=2\log(\frac{x^{\textrm{mantle}}_{\textrm{FeO}}}{x^{\textrm{core}}_{\textrm{Fe}}})+2\log(\frac{\gamma^{\textrm{mantle}}_{\textrm{FeO}}}{\gamma^{\textrm{core}}_{\textrm{Fe}}})$
(1)

where $x^{\textrm{mantle}}_{\textrm{FeO}}$ and
$x^{\textrm{core}}_{\textrm{Fe}}$ are mole fractions of FeO in mantle rocks
and Fe in the core, respectively (converted from their corresponding mass
fractions given in Table 4) and $\gamma^{\textrm{mantle}}_{\textrm{FeO}}$ and
$\gamma^{\textrm{core}}_{\textrm{Fe}}$ are activity coefficients for these
components. To facilitate comparison, we set the activity coefficient ratio
($\gamma^{\textrm{mantle}}_{\textrm{FeO}}/\gamma^{\textrm{core}}_{\textrm{Fe}}$)
to unity, which is expected to be valid at the high-temperature conditions of
the primitive mantle of Earth (Inoue et al., 2010; Doyle et al., 2019; Sossi
et al., 2020). As such, $\Delta$IW depends largely on
$x^{\textrm{mantle}}_{\textrm{FeO}}/x^{\textrm{core}}_{\textrm{Fe}}$, which
can be estimated for our model planet.

This leads to an $\Delta$IW value of $-4.0^{+0.6}_{-1.4}$, compared to the
terrestrial $\Delta$IW value of -2.2 upon core formation (Frost et al., 2004).
Namely, the primitive mantle of the model $\alpha$-Cen-Earth is $\sim 2$
logarithmic units more reduced than that of Earth. We emphasize that the
calculated $\Delta$IW value could not be an exact reflection of the planetary
fO2, which changes over the depth of the planet and also over time due to
planetary internal processes (e.g. disproportionation reactions occurring at
high pressures; Frost et al. 2004).

Oxygen fugacity at the planetary surface plays a critical role in determining
the composition of the outgassed C-O-H species from a magma ocean prior to and
during its crystallization (Hirschmann, 2012; Ortenzi et al., 2020). Such a
magma ocean may have been created in the history of the model $\alpha$-Cen-
Earth following extensive heating, presuming it also accreted partially
through energetic impacts of precursor planetesimals and planetary embryos, in
a manner analogous to the Earth. In order to understand the potential
diversity of the early atmospheric compositions produced, its H/C ratio and
$f\textrm{O}_{2}$ are required (Sossi et al., 2020). There is no direct
constraint on the H/C ratio of the model $\alpha$-Cen-Earth. Given a stellar
nebula of [C/H] = $0.256\pm 0.017$ dex (i.e. $\sim$ 2 times higher than the
solar C/H; Column 4, Table 1) and a relatively higher C/O (Fig. 4), we deduce
that H/C in a nascent $\alpha$-Cen-Earth should be considerably lower than
that in the early Earth, and hence adopt a value of
$\log(\textrm{(H/C)}_{\textrm{BSE}}/2)=0.53$, where bulk silicate Earth
(BSE)’s molar H/C is $\sim$ 6.8 (Hirschmann & Dasgupta, 2009; Marty, 2012).
Oxygen fugacity estimates are adopted from presumed core-mantle equilibration
conditions, although oxygen fugacity changes as the planet evolves, and as a
function of depth (as observed on Earth). Given these caveats, we consider two
end-member scenarios of atmosphere formation on the model $\alpha$-Cen-Earth.
The first presumes the atmospheric H/C is unfractionated from the primitive
mantle H/C of the model planet, and in the second, we adopt the model of Sossi
et al. (2020) to calculate solubilities of individual gas species using
basaltic melts as analogues for the magma ocean, presuming an Earth-like
mantle mass (see Sect. A.3). We note that the importance of H/C over the gross
atmospheric chemistry may be worth exploring in further (e.g. Liggins et al.,
2021).

For both cases at magmatic temperatures, the reducing conditions are such that
the principal gases are H2 and CO, with the former predominating in high H/C
atmospheres (Fig. 8a) and vice-versa (Fig. 8b). These species are, however,
not stable in a cooling atmosphere and react to form CH4 through hydrogenation
below about 700 to 800 ∘C leading to an atmosphere dominated by H2O, CH4 and
CO2 (Fig. 8). Carbon dioxide can be generated through graphite precipitation
(H2 \+ 3CO $\rightarrow$ CO2 \+ H2O + 2C) and the relative proportions of CO2
to CH4 depend on the $f\textrm{O}_{2}$ and the H/C in the atmosphere (Sossi et
al., 2020). Hence, the primitive mantle-derived case (Fig. 8a) produces more
CH4 at low temperatures than does the magma ocean-derived scenario (Fig. 8b)
that is expected to be richer in CO2. This behavior is a consequence of the
higher solubility of H relative to C in magmatic liquids (except under
extremely reducing conditions; Sossi et al. 2020; Bower et al. 2021), giving
rise to complementary low H/C ratios and thus lower CH4 production rates in
magma ocean-generated atmospheres. At $\Delta$IW = -4, about 79 % of the H
budget, but only 1.5 % of the C budget, is expected to be dissolved in the
magma ocean, resulting in a much thinner gaseous envelope than in the nominal
‘primitive mantle’ case in which all H is presumed to be in the atmosphere.
Importantly, the fraction of H dissolved scales inversely with
$f\textrm{O}_{2}$, it is $\sim 86$ % dissolved at $\Delta$IW = -3.5 but only
55 % at $\Delta$IW = -5.3, owing to the higher H2/H2O ratio in the gas phase
and the low solubility of H2 relative to H2O (Hirschmann, 2012; Moore et al.,
1998). Methane is therefore likely to be a ubiquitous gas considering the
reduced nature of the model $\alpha$-Cen-Earth mantle. Nonetheless, in both
cases, the overall CO2-CH4-H2O-dominated early atmospheres (upon cooling)
resemble that of Archean Earth (Gaudi et al., 2020; Catling & Zahnle, 2020).
The subsequent evolution of the Earth, especially by the rising of oxygen 2.5
Gyr ago (known as “Great Oxidation Event”; Lyons et al. 2014; Luo et al. 2016)
slowly but radically reshaped Earth’s atmosphere, which eventually leads to a
modern atmosphere dominated by N2 and O2. Of course, we have no argument to
prescribe a ‘life-existent’ nascent $\alpha$-Cen-Earth, nor can we determine
the atmospheric evolution pathway for the planet (beyond what we have modeled
for the ’first-generation’ early atmospheres). At the extreme and by
considering the preferable photolytic destruction to CH4 and H2O (Lasaga et
al., 1971; Guo, 2019; Johnstone, 2020), we may suspect that a dry,
CO2-dominated atmosphere is a likely evolution outcome for such a planet. We
will return to this point when we are discussing the stagnant-lid regime for
the model planet.

Figure 8: Calculated model atmospheric compositions, in which species are
expressed as mole fractions, for the $\alpha$-Cen-Earth using Gibbs Free
Energy minimization in the H-C-O system (see Sect. A.3). For the primitive
mantle-derived atmosphere (a), the H/C ratio of the atmosphere is presumed to
reflect that of the bulk silicate planet, with log(H/C) = 0.53 (molar). For
the magma ocean-generated case (b), the H/C ratio of the atmosphere is set by
the relative solubilities of the individual gas species in equilibrium with
the silicate melt (Sossi et al., 2020). The colored fields represent the range
of partial pressures owing to the variation of oxygen fugacity within its
uncertainty ($\Delta$IW of -3.4 to -5.4, with the lines showing the case for
$\Delta$IW = -4). Note that for the magma ocean-generated case, the log(H/C)
of the atmosphere also changes (-0.345, -0.144 and 0.186 at $\Delta$IW = -3.4,
-4 -5.4, respectively) because of the lower solubility of H2 relative to H2O,
and the increasing H2/H2O ratio as the atmosphere becomes more reducing. The
gray vertical dashed line shows the temperature of graphite saturation. For
more details see Sect. 4.1 and Appendix A.3.

###  4.2 Equivalent water-storage capacity of Earth

Mantle rocks may be hydrated (if water exists) to different degrees: (i) under
relevant upper mantle conditions ($P<$ $\sim 15$ GPa) pyroxene can hold up to
20 times more water in its crystalline structure than olivine (Warren & Hauri,
2014); (ii) the dominant MTZ minerals (wadsleyite & ringwoodite) can store
water in their crystal structures by about one order of magnitude more than
any of olivine, pyroxene, and perovskite (Fei et al., 2017; Pearson et al.,
2014; Bercovici & Karato, 2003; Murakami et al., 2002; Bolfan-Casanova et al.,
2000); (iii) between wadsleyite and ringwoodite, the former favors water twice
as much as the latter based on water partitioning experiments (Inoue et al.,
2010). Compared to Earth, the model $\alpha$-Cen-Earth’s equivalent amount of
wadsleyite + ringwoodite as well as its consistent ratio of olivine/pyroxene
dictates that this planet should have a water-storage capacity equivalent to
Earth. This capacity is further strengthened by the relatively higher ratio of
wadsleyite/ringwoodite ($1.2\pm 0.1$ vs. $\sim 0.7$). The model $\alpha$-Cen-
Earth must therefore be able to store, at least, as much water as in its
mantle as Earth. It is worth stressing, however, that “mantle water-storage
capacity” neither implies presence of water in a particular abundance (cf.
Dorn et al., 2015; Unterborn et al., 2018; Dencs & Regály, 2019; Shah et al.,
2020; Acuna et al., 2021), nor does it define the source of water (cf. Hallis
et al., 2015; Peslier et al., 2017; Wu et al., 2018; O’Brien et al., 2018;
Lichtenberg et al., 2019). A further investigation of these aspects is
important for understanding the potential hydrosphere of a rocky planet, but
is beyond what can be constrained with the model bulk elemental composition
only.

###  4.3 A Venus-like geodynamic regime?

According to Wang et al. (2020a), an $\alpha$-Cen-Earth with a significantly
lower Eu/(Mg+Si) relative to Earth (Fig. 6) has $\sim$ 1/4 and $\sim$ 1/2 less
in radiogenic heating from the decay of long-lived radionuclides than Earth at
its formation and at present-day, respectively. As calculated in Sect. 4.1,
the primitive mantle of this model planet is also considerably more reduced
(by two orders of magnitude) than that of Earth. The former is also modeled to
be relatively enriched in graphite/diamond (this should hold still even if
some portion of native carbon species has been segregated into the core;
Dasgupta et al. 2013; Li & Fei 2014; Fichtner et al. 2021), as shown in Table
4. Taken together, these factors preferentially impose a stagnant-lid tectonic
regime (Hakim et al., 2019; Dorn et al., 2018; Noack et al., 2017; Unterborn
et al., 2014).

In a stagnant-lid regime, volcanism and outgassing of the planet are generally
suppressed owing to an effective thermal boundary layer and curtailed
convection (Ballmer & Noack, 2021). For an Earth-sized, stagnant-lid planet,
the outgassing of CO2 (up to 50 bar) is permitted, however (Dorn et al., 2015,
Lena Noack, personal communication). Since Fe lowers the solidus temperature
of mantle peridodite (Hirschmann, 2000), a depleted Fe content in the model
$\alpha$-Cen-Earth’s mantle (with a significant higher Mg# of
$0.987^{+0.010}_{-0.020}$, versus $0.890\pm 0.001$ for Earth) further means
that partial melting (and hence volcanism) should be less prevalent on the
model planet. Over much of the history of the planet, mantle convection and
planetary resurfacing should have been moribund. This assessment however does
not consider the role of melting in heat transport and, particularly under a
stagnant lid, heat build-up (Driscoll & Bercovici, 2014). Furthermore, a
transient and periodic episode of mobile lids, and thus active volcanism and
surging degassing, may take place when accumulated heat beneath a stagnant lid
becomes enough to cause catastrophic resurfacing via lithospheric overturn –
i.e. resembling that proposed for the history of Venus: alternating active and
stagnant-lid (Turcotte 1993) (cf. localized resurfacing through lava flows;
Noack et al. 2012). Once the heat has been sufficiently released, however, the
mantle cools down and enters into another long-duration episode of stagnant
lid tectonics.

The evolution of planetary heat flux also has important implications for the
presence or absence of planetary dynamos. Low radiogenic heat production is
proposed to favor the generation of geodynamos due to the increased mantle-
core temperature difference and thus efficient heat extraction from the core
(Nimmo et al., 2020). However, the overlying stagnant-lid regime also
ultimately prevents heat extraction from the surface, consequently reducing
the mantle-core temperature differences – i.e. a negative feedback to the
generation of geodynamos. The generation and evolution of geodynamos are also
related to the planetary rotation (Zuluaga & Cuartas, 2012) and may also be
mechanically stirred by stochastic impacts (Jacobson et al., 2017), all of
which are beyond what we can constrain for the $\alpha$-Cen-Earth that is
modeled based on our predicted bulk composition only. As such, in spite of a
broadly Earth (and potentially Venus)-like interior composition and structure
as well as a lower radiogenic heating, it remains an open question if such an
$\alpha$-Cen planet would mirror the apparent lack of active dynamos in Venus
(Schubert & Soderlund, 2011; Phillips & Russell, 1987).

##  5 Conclusions

Starting with the measured host stellar abundances and a fiducial model of
devolatilization, we present an analysis of planetary bulk composition,
interiors and (early) atmospheres for a model Earth-sized planet in the
habitable zone of $\alpha$-Cen A/B. The detailed analysis offers a new
approach of investigation to what we may expect for Earth-sized planets in the
habitable zones in the solar neighborhood. Of course, the validity of our
analysis and thus conclusion is subject to our principal assumption that our
adopted devolatilization model (Wang et al., 2019a) may be applied to the
$\alpha$ Cen A/B system. Firstly, it is noteworthy that our findings for a HZ
rocky planet around the ”Sun-like” $\alpha$-Cen A/B should not be extrapolated
to its counterpart around Proxima Cen, which is a red dwarf and has a debated
origin from the binary companions (Kervella et al., 2017; Beech et al., 2017;
Feng & Jones, 2018). Second, although $\alpha$ Cen A and B are “Sun-like”
stars, their metallicities are $\sim 72$% higher than the solar metallicity
(Fig. 3). How this difference would affect the condensation/evaporation
process, and thus the devolatilization scale, is the subject of ongoing work
(Wang et al., 2020b). Third, we ignore any potential effect of the “binarity”
of the stars on their surrounding planetary bulk chemistry during planet
formation, even though we highlight that dynamically, the planetary orbits in
the habitable zone around either companion are stable. Finally, we have yet to
explore a larger parameter space, e.g. in mass and radius, but have only
benchmarked our analysis with an Earth-sized planet, which would otherwise
have an impact on the interior modeling (Unterborn et al., 2016; Dorn et al.,
2018; Hinkel & Unterborn, 2018). We nonetheless envisage that such an analysis
is readily replicable with different parameter settings (Wang et al. in
preparation) and is informative as presented to enable such an extension.

In addition, active research continues over whether a correlation exists
between stellar multiplicity on the occurrence rate of planets (Kraus et al.,
2016; Savel et al., 2020); this extends to the effect of stellar metallicity
and the occurrence rate of small/rocky planets (Mulders et al., 2016; Petigura
et al., 2018; Lu et al., 2020; Emsenhuber et al., 2020). For the calculation
of gas speciation, we presume an H/C ratio for the primitive mantle of the
model $\alpha$-Cen-Earth by scaling from the Earth’s value with the difference
in C/H between $\alpha$-Cen AB and Sun. This approach, however, may be
oversimplified. Furthermore, we do not consider any catastrophic impact at a
scale that may destabilize/remove the mantle or atmosphere of an Earth-sized
planet, which may radically alter the geodynamic regimes of the planet
including its mantle convection (O’Neill et al., 2017), dynamo (Jacobson et
al., 2017), and even atmosphere (Lupu et al., 2014). With all of these caveats
in mind, we conclude with caution in the following:

  1. 1.

An $\alpha$-Cen-Earth as modeled should have a reduced (primitive) mantle that
is similarly dominated by silicates albeit likely enriched in native carbon
species (e.g. graphite/diamond);

  2. 2.

The planet is also expected to have a slightly larger iron core, with a core
mass fraction of $38.4^{+4.7}_{-5.1}$ wt% (cf. Earth’s $32.5\pm 0.3$ wt%);

  3. 3.

The planet should have an equivalent water-storage capacity of Earth;

  4. 4.

Such a planet may also have a CO2-CH4-H2O-dominated early atmosphere that
resembles that of Archean Earth; observationally, this may be tested with a
dry, CO2-dominated atmosphere considering the preferable photolytic
destruction to CH4 and H2O and the possibility that –

  5. 5.

the planet may be in a Venus-like stagnant-lid regime, with sluggish mantle
convection and planetary resurfacing, over most of its geological history.

We thank the reviewer for useful comments, which helped improve the quality of
the manuscript. We thank Lena Noack, Craig O’Neill, Kaustubh Hakim, Christoph
Mordasini, and Yann Alibert for useful discussion. This work has been carried
out within the framework of the National Centre of Competence in Research
PlanetS supported by the Swiss National Science Foundation (SNSF). H.S.W and
S.P.Q acknowledge the financial support of the SNSF. S.J.M. extends special
thanks to the University of Vienna, Department of Lithospheric Research
(Vienna, Austria) for the Ida Pfeiffer Guest Professorship at which time this
manuscript was completed. P.A.S acknowledges SNSF Ambizione Grant 180025. T.M.
acknowledges financial support from Belspo for contract PRODEX PLATO mission
development.

##  Appendix A Software and implementation

###  A.1 ExoInt

ExoInt (Wang et al., 2019b) is an open-access package for devolatilizing
stellar abundances and computing the mantle composition of major end-member
oxides, core composition of an Fe-Ni-Si-S alloy (other candidate light
elements such as C and H are not considered yet), as well as core mass
fraction. Here we employ an updated version of ExoInt
(v1.2)222https://github.com/astro-seanwhy/ExoInt, in which the important
updates are (i) SiO2 is moved to the end of lithophile oxides and ahead of
siderophile oxides (e.g. FeO and NiO), enabling Si to partially sink into the
core while the mantle is reduced; (ii) the probability of the valid output
from Monte Carlo simulations is computed together with the raw estimate of the
mass fraction of each entity in the mantle and core (for details see Table A1
as well as Appendix A of Wang et al. 2019b), and these probabilities are taken
as the weighting factors of these raw/unconstrained mass fractions to obtain
the final/constrained mantle and core compositions as reported in Table 4.

Table A1:  Unconstrained compositional outputs of the mantle and core and their corresponding probability values ($P$-values). The differences in these $P$-values come from the random draws of different sets of bulk elemental composition with the Monte Carlo simulations ($2\times 10^{4}$ times), which determine two competing scenarios (due to the modeling degeneracy): (i) Si may be partially in the core (i.e. the reduced case where Fe and Ni remain in their metallic phases and 100% sink into the core); (ii) Si is fully oxidized and thus is not segregated into the core (in such a case Fe and Ni may be partially oxidized in the mantle). As such, the raw outputs of two scenarios are weighted by their $P$-values to obtain the final (constrained) mantle and core compositions (renormalized to 100 wt%) as reported in Table 4.  | Mantle
---|---
| MgO | SiO2 | FeO | Al2O3 | CaO | Na2O | NiO | C
Composition (wt%) | $44.9\,_{-7.0}^{+10.0}$ | $44.0\,_{-9.8}^{+6.4}$ | $8.7\,_{-6.5}^{+10.4}$ | $5.4\pm 0.7$ | $3.7\pm 0.5$ | $0.6\pm 0.1$ | $0.7^{+0.6}_{-0.3}$ | $0.5\pm 0.1$
$P$-value | 1.00 | 1.00 | 0.12 | 1.00 | 1.00 | 1.00 | 0.12 | 1.00
| Core |  |
| Fe | Ni | Si |  |
Composition (wt%) | $83.0\,_{-7.2}^{+9.2}$ | $5.2\,_{-0.6}^{+0.5}$ | $12.9\,_{-7.3}^{+7.0}$ |  |
$P$-value | 1.00 | 1.00 | 0.88 |  |

###  A.2 PerPle$\\_$X

Figure A1: The uncertainties of the best-fit mineralogy and structure of the
model $\alpha$-Cen-Earth. The Earth’s best-fit mineralogy as well as density
and P-T profiles are shown in dashed curves for comparison. The modeling
starts from the base of the lithosphere (i.e. excluding crust/surface). The
core regime is partially shown in the gray area towards the left-end of each
panel, with the model $\alpha$-Cen-Earth’s core radius fraction and its
uncertainty labeled as “$R_{\textrm{core}}$” and with Earth’s core radius
fraction indicated by a vertical dashed line. The data for producing the plot
are available upon request.

Perple$\\_$X (Connolly, 2009) is a Gibbs free energy minimization package to
compute the mantle mineralogy given the chemical composition and the pressure
and temperature gradients. The mineral equations of state (EoS) and
thermodynamic parameters of the foremost oxides (SiO2, MgO, FeO, Al2O3, CaO
and Na2O) are adopted from Stixrude & Lithgow-Bertelloni (2011). Other less
important oxides (e.g. NiO, SO3, and CO2) and all reduced phases (e.g.
graphite/diamond and other mantle metals), which are also computable with
ExoInt, are neglected for the mineralogy modeling. The liquid EoS (Anderson &
Ahrens, 1994) is adopted for an Fe-Ni alloy core (with/without light
elements). We adopt an adiabatic thermal gradient as commonly practiced in the
literature for rocky exoplanets (Dorn et al., 2015; Unterborn et al., 2018;
Lorenzo, 2018). Integration of the gradient starts at the base of the
lithosphere (i.e. the top of the uppermost mantle), with an initial pressure
and temperature arbitrarily set at 3 Gpa and 1450 K – similar to the
conditions at Earth’s crust-mantle boundary (Anderson, 1982; Dziewonski &
Anderson, 1981). Then the best-fit values of our estimates of the mantle and
core compositions and core mass fraction with ExoInt for the model
$\alpha$-Cen-Earth (Table 4), along with the assumption of 1$M_{\oplus}$ and
$R_{\oplus}$, are input to Perple$\\_$X to obtain the self-consistent
mineralogy and density profile as shown in Fig. 7. Monte Carlo simulations
with the random values drawn from our mantle and core compositional estimates
(Table 4) are carried out to obtain the uncertainties of individual minerals
as shown in Fig. A1. For generating the best-fit mineralogy for Earth, the
input mantle and core compositions are from Table 4 (excluding NiO and C as
well as the uncertainties associated with the core compositions).

###  A.3 FactSage 8.0

FactSage 8.0 (Bale et al., 2016) is employed to calculate the gas speciation
as a function of temperature. The composition used is set in the H-C-O system
for a real gas and pure solid and liquid phases, and a nominal total pressure
of 1 bar. The mole fraction of O adjusted to yield the desired relative oxygen
fugacity at 2073 K. The calculations were then stepped in 100 K temperature
intervals down to 373 K and the equilibrium speciation and any condensing
solid or liquid phases resolved. In the magma ocean-generated cases, the
primitive mantle’s H/C was subjected to partitioning between a magma ocean and
its atmosphere at 2073 K, in order to calculate a new H/C ratio of the
atmosphere. To do so, the H abundance was fixed at the value of Earth’s mantle
(0.012 wt%) (Palme & O’Neill, 2014), and the C content increased to 0.043 wt%
to yield the desired molar log(H/C) ratio (0.53; see main text). Partial
pressures were then resolved according to mass balance given the mass of the
mantle (assumed to be that of the Earth’s, $4.01\times 10^{24}$ kg) and the
acceleration due to gravity. The mass balance must also satisfy the condition
of redox equilibrium, meaning that the H2/H2O and CO/CO2 ratios are uniquely
determined by the fixed temperature, pressure and oxygen fugacity. The partial
pressure of each species was then iteratively determined by considering the
solubility of H2O, H2, CO, and CO2 in basaltic melts as proxies for the magma
ocean (for details see Sossi et al. 2020 and references therein).

## References

  * Acuña (2019) Acuña, L. 2019, Master’s thesis, Lund University.  https://www.lunduniversity.lu.se/lup/publication/8976827
  * Acuna et al. (2021) Acuna, L., Deleuil, M., Mousis, O., et al. 2021, Astron. Astrophys., 647, 1, doi: 10.1051/0004-6361/202039885
  * Adibekyan et al. (2021) Adibekyan, V., Dorn, C., Sousa, S. G., et al. 2021, Science (80-. )., 374, 330, doi: 10.1126/science.abg8794
  * Akeson et al. (2021) Akeson, R., Beichman, C., Kervella, P., Fomalont, E., & Benedict, G. F. 2021.  https://arxiv.org/abs/2104.10086
  * Anderson (1982) Anderson, O. 1982, Phil. Trans. R. So. Lond. A, 306, 21
  * Anderson & Ahrens (1994) Anderson, W., & Ahrens, T. 1994, J. Geophys. Res., 99, 4273
  * Andrade-Ines & Michtchenko (2014) Andrade-Ines, E., & Michtchenko, T. A. 2014, Mon. Not. R. Astron. Soc., 444, 2167, doi: 10.1093/mnras/stu1591
  * Anglada-Escudé et al. (2016) Anglada-Escudé, G., Amado, P. J., Barnes, J., et al. 2016, Nature, 536, 437, doi: 10.1038/nature19106
  * Armstrong et al. (2019) Armstrong, K., Frost, D. J., McCammon, C. A., Rubie, D. C., & Ballaran, T. B. 2019, Science (80-. )., 365, 903, doi: 10.1126/science.aax8376
  * Asplund et al. (2021) Asplund, M., Amarsi, A., & Grevesse, N. 2021, Astron. Astrophys., 1, doi: 10.1051/0004-6361/202140445
  * Bale et al. (2016) Bale, C. W., Bélisle, E., Chartrand, P., et al. 2016, Calphad Comput. Coupling Phase Diagrams Thermochem., 55, 1, doi: 10.1016/j.calphad.2016.07.004
  * Ballhaus et al. (1990) Ballhaus, C., Berry, R. F., & Green, D. H. 1990, Nature, 348, 437, doi: 10.1038/348437a0
  * Ballmer & Noack (2021) Ballmer, M. D., & Noack, L. 2021.  https://arxiv.org/abs/2108.08385
  * Beech (2015) Beech, M. 2015, Alpha Centauri: unveiling the secrets of our nearest stellar neighbor (Springer).  https://www.springer.com/de/book/9783319093710
  * Beech et al. (2017) Beech, M., McCowan, C., & Peltier, L. 2017, Am. J. Astron. Astrophys., 5, 1, doi: 10.11648/j.ajaa.20170501.11
  * Beichman et al. (2020) Beichman, C., Ygouf, M., Sayson, J. L., et al. 2020, Publ. Astron. Soc. Pacific, 132, 15002, doi: 10.1088/1538-3873/ab5066
  * Bercovici & Karato (2003) Bercovici, D., & Karato, S. I. 2003, Nature, 425, 39, doi: 10.1038/nature01918
  * Bolfan-Casanova et al. (2000) Bolfan-Casanova, N., Keppler, H., & Rubie, D. C. 2000, Earth Planet. Sci. Lett., 182, 209, doi: 10.1016/S0012-821X(00)00244-2
  * Bond et al. (2010) Bond, J. C., O’Brien, D. P., & Lauretta, D. S. 2010, Astrophys. J., 715, 1050, doi: 10.1088/0004-637X/715/2/1050
  * Bowens et al. (2021) Bowens, R., Meyer, M. R., Delacroix, C., et al. 2021, Astron. Astrophys., 653, A8, doi: 10.1051/0004-6361/202141109
  * Bower et al. (2021) Bower, D. J., Hakim, K., Sossi, P. A., & Sanan, P. 2021.  https://arxiv.org/abs/2110.08029
  * Brewer & Fischer (2016) Brewer, J. M., & Fischer, D. A. 2016, Astrophys. J., 831, 1, doi: 10.3847/0004-637X/831/1/20
  * Bryson et al. (2021) Bryson, S., Kunimoto, M., Kopparapu, R. K., et al. 2021, Astron. J., 161, 36, doi: 10.3847/1538-3881/abc418
  * Carlomagno (2020) Carlomagno, B. 2020, J. Astron. Telesc. Instruments, Syst., 6, 1, doi: 10.1117/1.JATIS.6.3.035005
  * Carlson et al. (2014) Carlson, R. W., Garnero, E., Harrison, T. M., et al. 2014, Annu. Rev. Earth Planet. Sci., 42, 151, doi: 10.1146/annurev-earth-060313-055016
  * Cassan et al. (2012) Cassan, A., Kubas, D., Beaulieu, J. P., et al. 2012, Nature, 481, 167, doi: 10.1038/nature10684
  * Catling & Zahnle (2020) Catling, D. C., & Zahnle, K. J. 2020, Sci. Adv., 6, doi: 10.1126/sciadv.aax1420
  * Clark et al. (2021) Clark, J. T., Clerté, M., Hinkel, N. R., et al. 2021, Mon. Not. R. Astron. Soc., 504, 4968, doi: 10.1093/mnras/stab1052
  * Connolly (2009) Connolly, J. A. D. 2009, Geochemistry, Geophys. Geosystems, 10, doi: 10.1029/2009GC002540
  * Cowley et al. (2021) Cowley, C. R., Bord, D. J., & Yüce, K. 2021, Astron. J., 161, 142, doi: 10.3847/1538-3881/abdf5d
  * Damasso et al. (2020) Damasso, M., Sordo, F. D., Anglada-Escudé, G., et al. 2020, Sci. Adv., 6, 1, doi: 10.1126/sciadv.aax7467
  * Dasgupta et al. (2013) Dasgupta, R., Chi, H., Shimizu, N., Buono, A. S., & Walker, D. 2013, Geochim. Cosmochim. Acta, 102, 191, doi: 10.1016/j.gca.2012.10.011
  * Delgado Mena et al. (2010) Delgado Mena, E., Israelian, G., González Hernández, J. I., et al. 2010, Astrophys. J., 725, 2349, doi: 10.1088/0004-637X/725/2/2349
  * Dencs & Regály (2019) Dencs, Z., & Regály, Z. 2019, Mon. Not. R. Astron. Soc., 487, 2191, doi: 10.1093/mnras/stz1412
  * Dorn et al. (2018) Dorn, C., Bower, D. J., & Rozel, A. 2018, in Handb. Exopl. (Cham: Springer International Publishing), 1–25, doi: 10.1007/978-3-319-30648-3_66-1
  * Dorn et al. (2019) Dorn, C., Harrison, J. H., Bonsor, A., & Hands, T. O. 2019, Mon. Not. R. Astron. Soc., 484, 712, doi: 10.1093/mnras/sty3435
  * Dorn et al. (2015) Dorn, C., Khan, A., Heng, K., et al. 2015, Astron. Astrophys., 577, A83, doi: 10.1051/0004-6361/201424915
  * Doyle et al. (2019) Doyle, A. E., Young, E. D., Klein, B., Zuckerman, B., & Schlichting, H. E. 2019, Science, 366, 356, doi: 10.1126/science.aax3901
  * Driscoll & Bercovici (2014) Driscoll, P., & Bercovici, D. 2014, Phys. Earth Planet. Inter., 236, 36, doi: 10.1016/j.pepi.2014.08.004
  * Dumusque et al. (2012) Dumusque, X., Pepe, F., Lovis, C., et al. 2012, Nature, 1, 4, doi: 10.1038/nature11572
  * Dziewonski & Anderson (1981) Dziewonski, A. M., & Anderson, D. L. 1981, Phys. Earth Planet. Inter., 25, 297, doi: 10.1016/0031-9201(81)90046-7
  * Emsenhuber et al. (2020) Emsenhuber, A., Mordasini, C., Burn, R., et al. 2020.  https://arxiv.org/abs/2007.05562
  * Fegley et al. (2020) Fegley, B., Lodders, K., & Jacobson, N. S. 2020, Chemie der Erde, 80, 125594, doi: 10.1016/j.chemer.2019.125594
  * Fei et al. (2017) Fei, H., Yamazaki, D., Sakurai, M., et al. 2017, Sci. Adv., 3, 1, doi: 10.1126/sciadv.1603024
  * Feng & Jones (2018) Feng, F., & Jones, H. R. 2018, Mon. Not. R. Astron. Soc., 473, 3185, doi: 10.1093/mnras/stx2576
  * Fichtner et al. (2021) Fichtner, C. E., Schmidt, M. W., Liebske, C., Bouvier, A. S., & Baumgartner, L. P. 2021, Earth Planet. Sci. Lett., 554, 116659, doi: 10.1016/j.epsl.2020.116659
  * Fortney (2012) Fortney, J. J. 2012, Astrophys. J., 747, L27, doi: 10.1088/2041-8205/747/2/L27
  * Frank et al. (2014) Frank, E. a., Meyer, B. S., & Mojzsis, S. J. 2014, Icarus, 243, 274, doi: 10.1016/j.icarus.2014.08.031
  * Frost et al. (2004) Frost, D. J., Liebske, C., Langenhorst, F., et al. 2004, Nature, 428, 409, doi: 10.1038/nature02413
  * Gastis et al. (2020) Gastis, P., Perdikakis, G., Dissanayake, J., et al. 2020, arXiv.  https://arxiv.org/abs/2001.11600
  * Gaudi et al. (2020) Gaudi, B. S., Seager, S., Mennesson, B., et al. 2020, The Habitable Exoplanet Observatory (HabEx) Mission Concept Study Final Report, Tech. rep.  https://arxiv.org/abs/2001.06683
  * Grossman & Larimer (1974) Grossman, L., & Larimer, J. W. 1974, Rev. Geophys., 12, 71, doi: 10.1029/RG012i001p00071
  * Guiglion et al. (2018) Guiglion, G., De Laverny, P., Recio-Blanco, A., & Prantzos, N. 2018, Astron. Astrophys., 619, 1, doi: 10.1051/0004-6361/201833782
  * Guo (2019) Guo, J. H. 2019, Astrophys. J., 872, 99, doi: 10.3847/1538-4357/aaffd4
  * Hakim et al. (2019) Hakim, K., Spaargaren, R., Grewal, D. S., et al. 2019, Astrobiology, 19, 867, doi: 10.1089/ast.2018.1930
  * Hallis et al. (2015) Hallis, L. J., Huss, G. R., Nagashima, K., et al. 2015, Science (80-. )., 350, 795, doi: 10.1126/science.aac4834
  * Harrison et al. (2018) Harrison, J. H., Bonsor, A., & Madhusudhan, N. 2018, Mon. Not. R. Astron. Soc., 479, 3814, doi: 10.1093/mnras/sty1700
  * Harrison et al. (2021) Harrison, J. H., Shorttle, O., & Bonsor, A. 2021, Earth Planet. Sci. Lett., 554, 116694, doi: 10.1016/j.epsl.2020.116694
  * Heiter et al. (2015) Heiter, U., Jofré, P., Gustafsson, B., et al. 2015, Astron. Astrophys., 582, 1, doi: 10.1051/0004-6361/201526319
  * Hin et al. (2017) Hin, R. C., Coath, C. D., Carter, P. J., et al. 2017, Nature, 549, 511, doi: 10.1038/nature23899
  * Hinkel & Unterborn (2018) Hinkel, N. R., & Unterborn, C. T. 2018, Astrophys. J., 853, 83, doi: 10.3847/1538-4357/aaa5b4
  * Hirschmann (2000) Hirschmann, M. M. 2000, Geochemistry, Geophys. Geosystems, 1, doi: 10.1029/2000GC000070
  * Hirschmann (2012) —. 2012, Earth Planet. Sci. Lett., 341-344, 48, doi: 10.1016/j.epsl.2012.06.015
  * Hirschmann & Dasgupta (2009) Hirschmann, M. M., & Dasgupta, R. 2009, Chem. Geol., 262, 4, doi: 10.1016/j.chemgeo.2009.02.008
  * Inoue et al. (2010) Inoue, T., Wada, T., Sasaki, R., & Yurimoto, H. 2010, Phys. Earth Planet. Inter., 183, 245, doi: 10.1016/j.pepi.2010.08.003
  * Jacobson et al. (2017) Jacobson, S. A., Rubie, D. C., Hernlund, J., Morbidelli, A., & Nakajima, M. 2017, Earth Planet. Sci. Lett., 474, 375, doi: 10.1016/j.epsl.2017.06.023
  * Jofré et al. (2017) Jofré, P., Das, P., Bertranpetit, J., & Foley, R. 2017, Mon. Not. R. Astron. Soc., 467, 1140, doi: 10.1093/mnras/stx075
  * Johnstone (2020) Johnstone, C. P. 2020, Astrophys. J., 890, 79, doi: 10.3847/1538-4357/ab6224
  * Kasper et al. (2019) Kasper, M., Arsenault, R., Zins, G., et al. 2019, The Messenger, 178, 5, doi: 10.18727/0722-6691/5163
  * Kervella et al. (2017) Kervella, P., Thévenin, F., & Lovis, C. 2017, Astron. Astrophys., 598, L7, doi: 10.1051/0004-6361/201629930
  * Koch & Edvardsson (2002) Koch, A., & Edvardsson, B. 2002, Astron. Astrophys., 381, 500, doi: 10.1051/0004-6361:20011578
  * Koll et al. (2019) Koll, D. D., Malik, M., Mansfield, M., et al. 2019, arXiv, 140, doi: 10.3847/1538-4357/ab4c91
  * Kopparapu et al. (2013) Kopparapu, R. K., Ramirez, R., Kasting, J. F., et al. 2013, Astrophys. J., 765, doi: 10.1088/0004-637X/765/2/131
  * Kraus et al. (2016) Kraus, A. L., Ireland, M. J., Huber, D., Mann, A. W., & Dupuy, T. J. 2016, Astron. J., 152, 8, doi: 10.3847/0004-6256/152/1/8
  * Lasaga et al. (1971) Lasaga, A. C., Holland, H. D., & Dwyer, M. J. 1971, Science (80-. )., 174, 53, doi: 10.1126/science.174.4004.53
  * Li & Fei (2014) Li, J., & Fei, Y. 2014, in Treatise on Geochemistry, 2nd edn., ed. R. W. Carlson, Vol. 3 (Elsevier), 527–557, doi: 10.1016/B978-0-08-095975-7.00214-X
  * Lichtenberg et al. (2019) Lichtenberg, T., Golabek, G. J., Burn, R., et al. 2019, Nat. Astron., 3, 307, doi: 10.1038/s41550-018-0688-5
  * Liggins et al. (2021) Liggins, P., Jordan, S., Rimmer, P. B., & Shorttle, O. 2021, 1.  https://arxiv.org/abs/2111.05161
  * Lineweaver & Chopra (2012) Lineweaver, C. H., & Chopra, A. 2012, Annu. Rev. Earth Planet. Sci., 40, 597, doi: 10.1146/annurev-earth-042711-105531
  * Liu et al. (2020) Liu, F., Yong, D., Asplund, M., et al. 2020, Mon. Not. R. Astron. Soc., 495, 3961, doi: 10.1093/mnras/staa1420
  * Lodders (2003) Lodders, K. 2003, Astrophys. J., 591, 1220, doi: 10.1086/375492
  * Lorenzo (2018) Lorenzo, A. J. 2018, Master’s thesis, Arizona State University.  https://repository.asu.edu/items/51736
  * Lu et al. (2020) Lu, C. X., Schlaufman, K. C., & Cheng, S. 2020, Astron. J., 160, 253, doi: 10.3847/1538-3881/abb773
  * Luo et al. (2016) Luo, G., Ono, S., Beukes, N. J., et al. 2016, Sci. Adv., 2, 1, doi: 10.1126/sciadv.1600134
  * Lupu et al. (2014) Lupu, R. E., Zahnle, K., Marley, M. S., et al. 2014, Astrophys. J., 784, doi: 10.1088/0004-637X/784/1/27
  * Lyons et al. (2014) Lyons, T. W., Reinhard, C. T., & Planavsky, N. J. 2014, Nature, 506, 307, doi: 10.1038/nature13068
  * Marty (2012) Marty, B. 2012, Earth Planet. Sci. Lett., 313-314, 56, doi: 10.1016/j.epsl.2011.10.040
  * McDonough (2003) McDonough, W. 2003, in Treatise on Geochemistry, 1st edn., ed. R. W. Carlson, Vol. 2 (Elsevier), 547–568, doi: 10.1016/B0-08-043751-6/02015-6
  * McDonough & Sun (1995) McDonough, W., & Sun, S.-s. 1995, Chem. Geol., 120, 223, doi: 10.1016/0009-2541(94)00140-4
  * Moore et al. (1998) Moore, G., Vennemann, T., & Carmichael, I. 1998, Am. Mineral., 83, 36
  * Morel (2018) Morel, T. 2018, Astron. Astrophys., 615, A172, doi: 10.1051/0004-6361/201833125
  * Mulders et al. (2016) Mulders, G. D., Pascucci, I., Apai, D., Frasca, A., & Molenda-Żakowicz, J. 2016, Astron. J., 152, 187, doi: 10.3847/0004-6256/152/6/187
  * Murakami et al. (2002) Murakami, M., Hirose, K., Yurimoto, H., Nakashima, S., & Takafuji, N. 2002, Science (80-. )., 295, 1885, doi: 10.1126/science.1065998
  * NASA Exoplanet Archive (2022) NASA Exoplanet Archive. 2022, Planetary Systems, Version: 2022-01-16 18:00, NExScI-Caltech/IPAC, doi: 10.26133/NEA12
  * Neuforge-Verheecke & Magain (1997) Neuforge-Verheecke, C., & Magain, P. 1997, Astron. Astrophys., 328, 261
  * Nimmo et al. (2020) Nimmo, F., Primack, J., Faber, S. M., Ramirez-Ruiz, E., & Safarzadeh, M. 2020, Astrophys. J., 903, L37, doi: 10.3847/2041-8213/abc251
  * Noack et al. (2012) Noack, L., Breuer, D., & Spohn, T. 2012, Icarus, 217, 484, doi: 10.1016/j.icarus.2011.08.026
  * Noack et al. (2017) Noack, L., Rivoldini, A., & Van Hoolst, T. 2017, Phys. Earth Planet. Inter., 269, 40, doi: 10.1016/j.pepi.2017.05.010
  * Norris & Wood (2017) Norris, C. A., & Wood, B. J. 2017, Nature, 549, 507, doi: 10.1038/nature23645
  * O’Brien et al. (2018) O’Brien, D. P., Izidoro, A., Jacobson, S. A., Raymond, S. N., & Rubie, D. C. 2018, Space Sci. Rev., 214, doi: 10.1007/s11214-018-0475-8
  * O’Neill et al. (2017) O’Neill, C., Marchi, S., Zhang, S., & Bottke, W. 2017, Nat. Geosci., 10, 793, doi: 10.1038/ngeo3029
  * O’Neill (1987) O’Neill, H. 1987, Am. Mineral., 72, 67
  * O’Neill et al. (2006) O’Neill, H. S. C., Berry, A. J., McCammon, C. C., et al. 2006, Am. Mineral., 91, 404, doi: 10.2138/am.2005.1929
  * Ortenzi et al. (2020) Ortenzi, G., Noack, L., Sohl, F., et al. 2020, Sci. Rep., 10, 1, doi: 10.1038/s41598-020-67751-7
  * Palme & O’Neill (2014) Palme, H., & O’Neill, H. 2014, in Treatise on Geochemistry, 2nd edn., ed. R. W. Carlson, Vol. 3 (Elsevier), 1–39, doi: 10.1016/B978-0-08-095975-7.00201-1
  * Pearson et al. (2014) Pearson, D. G., Brenker, F. E., Nestola, F., et al. 2014, Nature, 507, 221, doi: 10.1038/nature13080
  * Peslier et al. (2017) Peslier, A. H., Schönbächler, M., Busemann, H., & Karato, S. I. 2017, Space Sci. Rev., 212, 743, doi: 10.1007/s11214-017-0387-z
  * Petigura et al. (2018) Petigura, E. A., Marcy, G. W., Winn, J. N., et al. 2018, Astron. J., 155, 89, doi: 10.3847/1538-3881/aaa54c
  * Phillips & Russell (1987) Phillips, J. L., & Russell, C. T. 1987, Adv. Sp. Res., 7, 291, doi: 10.1016/0273-1177(87)90232-8
  * Pourbaix & Boffin (2016) Pourbaix, D., & Boffin, H. M. 2016, Astron. Astrophys., 586, 4, doi: 10.1051/0004-6361/201527859
  * Quanz et al. (2015) Quanz, S. P., Crossfield, I., Meyer, M. R., Schmalzl, E., & Held, J. 2015, Int. J. Astrobiol., 14, 279, doi: 10.1017/S1473550414000135
  * Quanz et al. (2021) Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2021.  https://arxiv.org/abs/2101.07500
  * Quarles et al. (2020) Quarles, B., Li, G., Kostov, V., & Haghighipour, N. 2020, Astron. J., 159, 80, doi: 10.3847/1538-3881/ab64fa
  * Quarles & Lissauer (2016) Quarles, B., & Lissauer, J. J. 2016, Astron. J., 151, 111, doi: 10.3847/0004-6256/151/5/111
  * Rajpaul et al. (2016) Rajpaul, V., Aigrain, S., & Roberts, S. 2016, Mon. Not. R. Astron. Soc. Lett., 456, L6, doi: 10.1093/mnrasl/slv164
  * Salmon et al. (2021) Salmon, S. J., Van Grootel, V., Buldgen, G., Dupret, M. A., & Eggenberger, P. 2021, Astron. Astrophys., 646, doi: 10.1051/0004-6361/201937174
  * Savel et al. (2020) Savel, A. B., Dressing, C. D., Hirsch, L. A., et al. 2020, Astron. J., 160, 287, doi: 10.3847/1538-3881/abc47d
  * Schubert & Soderlund (2011) Schubert, G., & Soderlund, K. M. 2011, Phys. Earth Planet. Inter., 187, 92, doi: 10.1016/j.pepi.2011.05.013
  * Schulze et al. (2021) Schulze, J. G., Wang, J., Johnson, J. A., et al. 2021, Planet. Sci. J., 2, 113, doi: 10.3847/psj/abcaa8
  * Shah et al. (2020) Shah, O., Alibert, Y., Helled, R., & Mezger, K. 2020, 162.  https://arxiv.org/abs/2012.06455
  * Sossi et al. (2020) Sossi, P. A., Burnham, A. D., Badro, J., et al. 2020, 1
  * Sossi & Fegley (2018) Sossi, P. A., & Fegley, B. 2018, Rev. Mineral. Geochemistry, 84, 393, doi: 10.2138/rmg.2018.84.11
  * Sossi et al. (2019) Sossi, P. A., Klemme, S., O’Neill, H. S. C., Berndt, J., & Moynier, F. 2019, Geochim. Cosmochim. Acta, 260, 204, doi: 10.1016/j.gca.2019.06.021
  * Spaargaren et al. (2020) Spaargaren, R., Wang, H., Ballmer, M., Mojzsis, S., & Tackley, P. 2020, in Eur. Sci. Congr. 2020 (https://doi.org/10.5194/epsc2020-745), doi: 10.5194/epsc2020-745
  * Stixrude & Lithgow-Bertelloni (2011) Stixrude, L., & Lithgow-Bertelloni, C. 2011, Geophys. J. Int., 184, 1180, doi: 10.1111/j.1365-246X.2010.04890.x
  * Suárez-Andrés et al. (2018) Suárez-Andrés, L., Israelian, G., González Hernández, J. I., et al. 2018, Astron. Astrophys., 614, A84, doi: 10.1051/0004-6361/201730743
  * The LUVIOR team (2019) The LUVIOR team. 2019, LUVOIR Final Report, Tech. rep.  https://arxiv.org/abs/1912.06219
  * Thiabaud et al. (2014) Thiabaud, A., Marboeuf, U., Alibert, Y., et al. 2014, Astron. Astrophys., 562, A27, doi: 10.1051/0004-6361/201322208
  * Thiabaud et al. (2015) Thiabaud, A., Marboeuf, U., Alibert, Y., Leya, I., & Mezger, K. 2015, Astron. Astrophys., 580, A30, doi: 10.1051/0004-6361/201525963
  * Unterborn et al. (2018) Unterborn, C. T., Desch, S. J., Hinkel, N. R., & Lorenzo, A. 2018, Nat. Astron., 2, 297, doi: 10.1038/s41550-018-0411-6
  * Unterborn et al. (2016) Unterborn, C. T., Dismukes, E. E., & Panero, W. R. 2016, Astrophys. J., 819, 32, doi: 10.3847/0004-637x/819/1/32
  * Unterborn et al. (2014) Unterborn, C. T., Kabbes, J. E., Pigott, J. S., Reaman, D. M., & Panero, W. R. 2014, Astrophys. J., 793, 124, doi: 10.1088/0004-637X/793/2/124
  * Wade & Wood (2005) Wade, J., & Wood, B. J. 2005, Earth Planet. Sci. Lett., 236, 78, doi: 10.1016/j.epsl.2005.05.017
  * Wagner et al. (2021) Wagner, K., Boehle, A., Pathak, P., et al. 2021, Nat. Commun., 12, 1, doi: 10.1038/s41467-021-21176-6
  * Wang (2018) Wang, H. 2018, Phd thesis, Australian National University, doi: 10.25911/5d5147caa0d1e
  * Wang et al. (2020a) Wang, H., T. Morel, Quanz, S., & Mojzsis, S. 2020a, Astron. Astrophys., 19, 1, doi: 10.1051/0004-6361/202038386
  * Wang et al. (2018) Wang, H. S., Lineweaver, C. H., & Ireland, T. R. 2018, Icarus, 299, 460, doi: 10.1016/j.icarus.2017.08.024
  * Wang et al. (2019a) —. 2019a, Icarus, 328, 287, doi: 10.1016/j.icarus.2019.03.018
  * Wang et al. (2019b) Wang, H. S., Liu, F., Ireland, T. R., et al. 2019b, Mon. Not. R. Astron. Soc., 482, 2222, doi: 10.1093/mnras/sty2749
  * Wang et al. (2020b) Wang, H. S., Sossi, P. A., & Quanz, S. P. 2020b, in Eur. Sci. Congr. 2020 (online: Europlanet Science Congress 2020), EPSC2020–874, doi: 10.5194/epsc2020-874
  * Warren & Hauri (2014) Warren, J. M., & Hauri, E. H. 2014, J. Geophys. Res. Solid Earth, 119, 1851, doi: 10.1002/2013JB010328
  * Winn & Fabrycky (2015) Winn, J. N., & Fabrycky, D. C. 2015, Annu. Rev. Astron. Astrophys., 53, 409, doi: 10.1146/annurev-astro-082214-122246
  * Wood et al. (2019) Wood, B. J., Smythe, D. J., & Harrison, T. 2019, Am. Mineral., 104, 844, doi: 10.2138/am-2019-6852CCBY
  * Woodland & Koch (2003) Woodland, A. B., & Koch, M. 2003, Earth Planet. Sci. Lett., 214, 295, doi: 10.1016/S0012-821X(03)00379-0
  * Wu et al. (2018) Wu, J., Desch, S. J., Schaefer, L., et al. 2018, J. Geophys. Res. Planets, 123, 2691, doi: 10.1029/2018JE005698
  * Yoshizaki & McDonough (2020) Yoshizaki, T., & McDonough, W. F. 2020, Geochim. Cosmochim. Acta, 273, 137, doi: 10.1016/j.gca.2020.01.011
  * Zhao et al. (2018) Zhao, L., Fischer, D. A., Brewer, J., Giguere, M., & Rojas-Ayala, B. 2018, Astron. J., 155, 24, doi: 10.3847/1538-3881/aa9bea
  * Zhu & Dong (2021) Zhu, W., & Dong, S. 2021, Annu. Rev. Astron. Astrophys., 59, 291, doi: 10.1146/annurev-astro-112420-020055
  * Zuluaga & Cuartas (2012) Zuluaga, J. I., & Cuartas, P. A. 2012, Icarus, 217, 88, doi: 10.1016/j.icarus.2011.10.014