LavAtmos An opensource chemical equilibrium vaporization code for lava worlds

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LavAtmos: An open-source chemical equilibrium vaporization code for lava worlds
Christiaan P. A. van BUCHEM
1
*, Yamila MIGUEL
1,2
, Mantas ZILINSKAS
1
, and
Wim van WESTRENEN
3
1
Leiden Observatory, Leiden University, Leiden, The Netherlands
2
SRON Netherlands Institute for Space Research, Leiden, The Netherlands
3
Faculty of Science, Earth Sciences, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
*Correspondence
Christiaan P. A. van Buchem, Leiden Observatory, Leiden University, Leiden, The Netherlands.
Email: vbuchem@strw.leidenuniv.nl
(Received 28 November 2022; revision accepted 17 April 2023)
Abstract–To date, over 500 short-period rocky planets with equilibrium temperatures above
1500 K have been discovered. Such planets are expected to support magma oceans,
providing a direct interface between the interior and the atmosphere. This provides a unique
opportunity to gain insight into their interior compositions through atmospheric
observations. A key process in doing such work is the vapor outgassing from the lava
surface. LavAtmos is an open-source code that calculates the equilibrium chemical
composition of vapor above a dry melt for a given composition and temperature. Results
show that the produced output is in good agreement with the partial pressures obtained
from experimental laboratory data as well as with other similar codes from literature.
LavAtmos allows for the modeling of vaporization of a wide range of different mantle
compositions of hot rocky exoplanets. In combination with atmospheric chemistry codes,
this enables the characterization of interior compositions through atmospheric signatures.
INTRODUCTION
With an ever-growing catalog of newly discovered
exoplanets, we have moved from the discovery phase well
into the characterization phase. An emerging category of
specific interest is that of the so-called hot rocky
exoplanets.
These planets are exposed to extreme stellar
irradiation that leads to surface temperatures hot enough
to prevent the planet from cooling and creating a crust
(Boukar´
e et al., 2022; Henning et al., 2018), exposing the
silicate mantle directly to the atmosphere. Furthermore,
since the atmosphere is a direct product of the outgassing
from the magma ocean and is in equilibrium with it, the
atmospheric compositions of these planets are directly
influenced by the interior composition (Dorn &
Lichtenberg, 2021; Ito et al., 2015; Kite et al., 2016,2020;
Miguel et al., 2011; Nguyen et al., 2020). This provides a
unique opportunity to derive interior properties from
atmospheric observations. In addition, there is growing
evidence that planetesimals, as well as the rocky planets
and moons that form from their accretion, were covered
by magma early in their evolution (Elkins-Tanton, 2012;
Greenwood et al., 2005; Hin et al., 2017; Norris &
Wood, 2017; Schaefer & Elkins-Tanton, 2018). Therefore,
constraints on the atmospheric products of interior–
atmosphere interactions on hot rocky exoplanets might
also provide us with a window to the conditions in the
early solar system and early Earth (Hirschmann, 2012).
Hot rocky planets have been the targets of several
observing programs throughout the past several years on
a range of different ground- and space-based telescopes
(Deibert et al., 2021; Demory et al., 2011; Esteves et al.,
2017; Keles et al., 2022). Conclusions drawn from
these observations remain uncertain and have yet to
give definitive proof of an atmosphere. However, some
Meteoritics & Planetary Science 58, Nr 8, 1149–1161 (2023)
doi: 10.1111/maps.13994
1149 Ó2023 The Authors. Meteoritics & Planetary Science
published by Wiley Periodicals LLC on behalf of The Meteoritical Society.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use,
distribution and reproduction in any medium, provided the original work is properly cited.
tentative evidence has been given for K2-141 b (Zieba
et al., 2022) and 55 Cnc e (Angelo & Hu, 2017; Demory
et al., 2016; Zilinskas et al., 2020,2021), and the advent
of the new generation of telescopes, such as JWST and
Ariel, may allow for the characterization of the chemical
composition of hot rocky-exoplanet atmospheres in the
near future (Ito et al., 2021; Zilinskas et al., 2022).
To know what to look for in such observations and
to interpret the data once it arrives, accurate atmospheric
models are required. For atmospheres on hot rocky
exoplanets, this involves modeling the degassing from
lava at the surface of the planet. Since we yet have to gain
a good understanding of the possible types of rocky-
exoplanet compositions, we do not yet know what kind
of compositions we should expect for these melts. Recent
work (Brugman et al., 2021; Putirka et al., 2021; Putirka
& Rarick, 2019) indicates that we should expect a wide
range of different possible silicate compositions. Hence,
open-source vaporization codes that can work with a
wide range of compositions are necessary to enable
modeling potential atmospheres as our understanding of
hot rocky planets develops.
To date, a limited number of codes have been used to
calculate the chemical composition of vapors degassing
from lava at a given temperature and the composition of
an atmosphere in equilibrium with lava of a given
temperature. The MAGMA code (Fegley & Cameron,
1987) was written to study the fractional vaporization of
Mercury. The same code was used for the study of other
solar system bodies (Schaefer & Fegley, 2007; Schaefer &
Fegley Jr., 2004) and exoplanets (Kite et al., 2016; Miguel
et al., 2011; Schaefer & Fegley, 2009; Schaefer et al.,
2012; Visscher & Fegley, 2013). This code makes use of
the Ideal Mixing of Complex Components (IMCC)
model, developed by Hastie and co-authors (Hastie &
Bonnell, 1985,1986; Hastie et al., 1982), to calculate the
activity of the oxide components in the melt.
In more recent years, the MELTS code (Ghiorso &
Sack, 1995) has seen increased use for modeling the
thermodynamics for outgassing codes (Ito et al., 2015,
2021;J
¨
aggi et al., 2021; Wolf et al., 2023). Wolf and co-
authors have developed the code named VapoRock
which has been used to model the early atmosphere of
Mercury (J¨
aggi et al., 2021) and to explore how relative
abundances of SiO and SiO
2
could be used to infer the O
2
fugacity of a volatile-depleted mantle (Wolf et al., 2023).
The main difference between VapoRock and LavAtmos
is the manner in which the O
2
partial pressure is
determined. In the discussion (“Discussion” Section), we
include a more in-depth comparison of the two codes.
Other approaches that calculate the condensate
compositions from an initial gas composition, as opposed
to calculating vaporization reactions from an existing melt
reservoir, have also been developed in the literature
(Herbort et al., 2020,2022).
In this paper, we present a new open-source code,
which we named LavAtmos, that calculates the
equilibrium composition of a vapor above a melt of a
given composition, at a given temperature and at a given
melt–vapor interface pressure. As shown in the graphical
table of contents, a general overview of the workflow
of the code is presented. Just as the abovementioned
previous works (Ito et al., 2015,2021; Wolf et al., 2023),
we use MELTS to calculate the oxide component
properties of a melt. These properties are then combined
with thermochemical data available in the JANAF
tables (Chase, 1998) to perform gas–melt equilibrium
calculations. The oxygen fugacity (fO
2
) is derived from
the law of mass action, similarly to the approach used for
thermodynamic calculations for pure silica and alumina
(Krieger, 1965a,1965b) and for the MAGMA code
(Fegley & Cameron, 1987). LavAtmos currently takes 9
oxide species into account (SiO
2
, MgO, Al
2
O
3
, TiO
2
,
Fe
2
O
3
, FeO, CaO, Na
2
O, and K
2
O), 31 different vapor
species with corresponding vaporization reactions (shown
in Table 1) and is suitable for calculations between 1500
and 4000 K. LavAtmos is written in Python for ease of
use and integration with the MELTS Python wrapper
named Thermoengine.
1
It is released as an open-source
code under the GNU General Public License version 3.
2
LavAtmos is available on https://github.com/cvbuchem/
LavAtmos.
In this paper, we provide an in-depth look at the
methods used in “Methodology” Section. We compare its
performance to laboratory data and the results calculated
by other similar codes where those are available in
the public domain in “Validation” Section. Finally, we
discuss assumptions made in the method, the advantages
and limitations of the code, and highlight a set of
potential applications in “Discussion” Section, rounding
off with a conclusion in “Conclusion” Section.
METHODOLOGY
In this section, we cover how the partial pressures of
included species are calculated. Consider the generalized
form of a vaporization reaction of a liquid oxide j,
gaseous O
2
, and the resulting vapor species i:
cijXxjOyjlðÞþdijO2gðÞ,Xxjcij Oyjcijþ2dij gðÞ (1)
Xis the cation of the species, x
j
the number of cation
atoms, y
j
the number of oxygen atoms, and c
ij
and d
ij
are the stoichiometric coefficients for this reaction. The
gaseous species (atmosphere) are indicated using (g) and
the liquid species (melt) using (l). As an example, the
1150 C. P. A. van Buchem et al.
19455100, 2023, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/maps.13994 by University Of Leiden, Wiley Online Library on [15/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
vaporization reaction of liquid SiO
2
to form gaseous
SiO can be written as:
SiO2lðÞ1
2O2gðÞ,SiO gðÞ (2)
Assuming that the reaction is in equilibrium, the partial
pressure of the vapor species ican be calculated by
adhering to the law of mass action as follows:
Pij ¼Krij acij
jPdij
O2(3)
where P
ij
is the partial pressure of vapor species ias
formed from liquid species j,Krij is the chemical
equilibrium constant of the reaction, a
j
is the activity of
liquid oxide j, and PO2is the partial pressure of O
2
(also
known as the oxygen fugacity fO
2
). Some more
elaboration on the derivation is shown in the appendix
(“Deriving the Partial Pressure Equation” Section). For
the example reaction shown in Equation (2), the partial
pressure of SiO can be determined using:
PSiO ¼KraSiO2P1=2
O2(4)
The variables that must be known to calculate the
partial pressure of a vapor species are the stoichiometric
coefficients c
i
and d
i
, the chemical equilibrium constant
of reaction Krifor the vapor species i, the chemical
activity a
j
of the oxide jinvolved in the reaction, and
the oxygen partial pressure PO2. Stoichiometric coefficients
are determined by writing out balanced reaction equations
(see Table 1). The chemical equilibrium constant of each
reaction Krij is determined using the data available in the
JANAF tables (Chase, 1998).
The activity of the oxides in the melt is determined
using the MELTS code. Developed over the course of
the past two and a half decades, MELTS has been
consistently updated and expanded (Asimow & Ghiorso,
TABLE 1. Overview of the 31 vaporization reactions included in LavAtmos.
End-member # Reactants Vapor
–1 1/2O
2
(g) ↔O(g)
SiO
2
2 SiO
2
(l) O
2
(g) ↔Si(g)
3 2SiO
2
(l) 2O
2
(g) ↔Si
2
(g)
4 3SiO
2
(l) 3O
2
(g) ↔Si
3
(g)
5 SiO
2
(l) 1/2O
2
(g) ↔SiO(g)
6 SiO
2
(l) ↔SiO
2
(g)
Al
2
O
3
7 1/2Al
2
O
3
(l) 3/4O
2
(g) ↔Al(g)
8Al
2
O
3
(l) 3/2O
2
(g) ↔Al
2
(g)
9 1/2Al
2
O
3
(l) 1/4O
2
(g) ↔AlO(g)
10 Al
2
O
3
(l) O
2
(g) ↔Al
2
O(g)
11 1/2Al
2
O
3
(l) 1/2O
2
(g) ↔AlO
2
(g)
12 Al
2
O
3
(l) 1/2O
2
(g) ↔Al
2
O
2
(g)
TiO
2
13 TiO
2
(l) O
2
(g) ↔Ti(g)
14 TiO
2
(l) 1/2O
2
(g) ↔TiO(g)
15 TiO
2
(l) ↔TiO
2
(g)
Fe
2
O
3
16 1/2Fe
2
O
3
(l) 3/4O
2
(g) ↔Fe(g)
17 1/2Fe
2
O
3
(l) 1/4O
2
(g) ↔FeO(g)
Fe
2
SiO
4
18 1/2Fe
2
SiO
2
(l) 1/2O
2
(g) 1/2SiO
2
(l) ↔Fe(g)
19 1/2Fe
2
SiO
4
(l) 1/2SiO
2
(l) ↔FeO(g)
Mg
2
SiO
4
20 1/2Mg
2
SiO
4
(l) 1/2O
2
(g) 1/2SiO
2
(l) ↔Mg(g)
21 Mg
2
SiO
4
(l) O
2
(g) SiO
2
(l) ↔Mg
2
(g)
22 1/2Mg
2
SiO
4
(l) 1/2SiO
2
(l) ↔MgO(g)
CaSiO
3
23 CaSiO
3
(l) 1/2O
2
(g) SiO
2
(l) ↔Ca(g)
24 2CaSiO
3
(l) O
2
(g) 2SiO
2
(l) ↔Ca
2
(g)
25 CaSiO
3
(l) SiO
2
(l) ↔CaO(g)
Na
2
SiO
3
26 1/2Na
2
SiO
3
(l) 1/4O
2
(g) 1/2SiO
2
(l) ↔Na(g)
27 Na
2
SiO
3
(l) 1/2O
2
(g) SiO
2
(l) ↔Na
2
(g)
28 1/2Na
2
SiO
3
(l) +1/4O
2
(g) 1/2SiO
2
(l) ↔NaO(g)
KAlSiO
4
29 KAlSiO
4
(l) 1/4O
2
(g) 1/2Al
2
O
3
(l) SiO
2
(l) ↔K(g)
30 2KAlSiO
4
(l) 1/2O
2
(g) Al
2
O
3
(l) 2SiO
2
(l) ↔K
2
(g)
31 KAlSiO
4
(l) +1/4O
2
(g) 1/2Al
2
O
3
(l) SiO
2
(l) ↔KO(g)
Note: Reaction 1 is the gas to gas reaction of O
2
to O. The rest of the reactions (2–31) describes the vaporization reactions. Each vapor species
has a unique reaction that includes a MELTS end-member species, O
2
, and (if necessary) residue liquid metal oxides.
Vaporisation code for lava worlds 1151
19455100, 2023, 8, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/maps.13994 by University Of Leiden, Wiley Online Library on [15/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
摘要：

ReportLavAtmos:Anopen-sourcechemicalequilibriumvaporizationcodeforlavaworldsChristiaanP.A.vanBUCHEM1*,YamilaMIGUEL1,2,MantasZILINSKAS1,andWimvanWESTRENEN31LeidenObservatory,LeidenUniversity,Leiden,TheNetherlands2SRONNetherlandsInstituteforSpaceResearch,Leiden,TheNetherlands3FacultyofScience,EarthSci...

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