# The Missing Link: Testing Galactic Chemical Evolution Models with the First
Multi-Isotopic Abundances in Solar Twin Stars

David R. Coria Department of Physics $\&$ Astronomy, University of Kansas,
Lawrence, KS, USA  Ian J. M. Crossfield  Department of Physics $\&$ Astronomy,
University of Kansas, Lawrence, KS, USA  Joshua Lothringer  Department of
Physics $\&$ Astronomy, Johns Hopkins University, Baltimore, MD, USA  Becky
Flores  Department of Physics $\&$ Astronomy, Georgia State University,
Atlanta, GA, USA  Nikos Prantzos  Institut d’Astrophysique de Paris, Paris, FR
Richard Freedman  SETI Institute, Mountain View, CA, USA

###### Abstract

We present the first isotopic abundances of both 13CO and C18O in solar twin
stars and test the results against several galactic chemical evolution (GCE)
models with different nucleosynthesis prescriptions. First, we compare M-band
spectra from IRTF/iSHELL to synthetic spectra generated from custom solar
atmosphere models using the PHOENIX atmosphere code. Next, we compare our
calculated abundances to GCE models that consider isotopic yields from massive
stars, asymptotic giant branch (AGB) stars and fast-rotating stars. The
12C/13C ratios determined for this sample of solar twins are consistent with
predictions from the selected GCE models; however, the 16O/18O ratios
tentatively contradict these predictions. This project constitutes the first
in a stellar chemical abundance series seeking to: (1) support the James Webb
Space Telescope (JWST) as it characterizes exoplanet atmospheres, interiors,
and biosignatures by providing host star abundances (2) identify how
unexplored stellar abundances reveal the process of galactic chemical
evolution and correlate with star formation, interior, age, metallicity, and
activity; and (3) provide improved stellar ages using stellar abundance
measurements. By measuring elemental and isotopic abundances in a variety of
stars, we not only supply refined host star parameters, but also provide the
necessary foundations for complementary exoplanet characterization studies and
ultimately contribute to the exploration of galactic, stellar, and planetary
origins and evolution.

Solar analogs — Isotopic abundances — Galactic Chemical Evolution — Late-type
stars

##  1 Introduction

In stellar and planetary astrophysics, one of the most important areas of
study is the chemical composition of the object in question. Until recently,
large-scale photometric surveys could determine only the most fundamental
stellar parameters such as mass, radius, luminosity, and temperature. While
these parameters are important, they do not provide the context necessary for
examining the chemical evolution of our galaxy, nor do they provide a baseline
for exploring planet formation mechanisms, exoplanet atmospheres, and
exoplanet interiors. For this, we need spectroscopy and stellar chemical
abundances. Since generations of stars produce different elements, elemental
and isotopic abundance ratios provide information on the age of a system and
can be used as a sort of “cosmic clock”. These measurements are used to
perform key tests of mixing mechanisms inside stars and serve as powerful
diagnostic tools to constrain chemical enrichment, galaxy formation and
evolution models when used alongside accurate stellar ages, distances, and
kinematics (Jackson et al., 2021; Romano et al., 2017).

On the larger, galactic scale, abundance surveys have revealed interesting
trends between particular stellar elemental abundances, stellar age, and
various stellar populations throughout the galaxy (Brewer & Fischer, 2016;
Adibekyan et al., 2018; Botelho et al., 2020; Nissen, 2015; Nissen et al.,
2020; Delgado-Mena et al., 2019, 2021). Other studies use stellar abundances
to reconstruct the chemical history of the Milky Way (Jofré et al., 2017;
Jackson et al., 2021) and to track down our Sun’s long-lost siblings
(Adibekyan et al., 2018). Some stellar abundances can even be used to
distinguish exoplanet host stars from the general galactic stellar population
(Brewer et al., 2016; Swastik et al., 2022; Delgado-Mena et al., 2021; Teske
et al., 2019). Although galactic chemical evolution (GCE) models have already
successfully reproduced present-day cosmic abundances of many elements (e.g.
Kobayashi et al. (2011); Prantzos et al. (2018); Romano et al. (2017)), new
stellar abundance measurements allow for modelers to test the adopted stellar
nucleosynthetic yields for which there is little observational data. Doing so
will reveal whether the current understanding of stellar yields and chemical
evolution models is truly accurate or simply appears accurate by coincidence.
The 12C/13C ratio is most commonly observed in giant stars where it is well
known that various phenomena alter the initial 12C/13C ratio. However, such
comparisons also depend on stellar evolution and interior models. To
complement these data, GCE model predictions should also be compared to
12C/13C ratios measured in unevolved stars, like FGKM dwarf stars, that have
preserved the initial isotope ratio in their envelopes. All of the GCE model
studies mentioned in this paper (Kobayashi et al., 2011; Romano et al., 2017;
Prantzos et al., 2018) issue a call for dwarf star isotopic abundance ratios,
particularly for those isotope ratios (e.g. CNO (Romano, 2022), Mg, Si, Ti)
that we cannot trust from giant stars. Since these publications, the 12C/13C
ratio has been measured in solar twin stars (Botelho et al., 2020), M-dwarf
stars (Crossfield et al., 2019), and even in sub-stellar objects like brown
dwarfs and directly imaged exoplanets (Zhang et al., 2021a, b).

On a smaller, planetary-system scale, stellar elemental abundances provide a
glimpse into planetary formation and migration mechanisms as well as planetary
chemical composition. Since stellar atmospheres evolve slowly, the elemental
abundances of exoplanet hosts tend to reflect the composition of their planet-
forming disks (Brewer & Fischer, 2016) and have the potential to yield
constraints on planet formation processes and, in turn, even the physical
properties of exoplanets themselves (Bedell et al., 2018). These chemical
signatures, observed in the photospheres of stars, can be traced back to a
planet’s sequestration of heavy elements during planet formation or later in
the system’s history when a host star accretes planetary material. Thus, the
presence, absence, and composition of planets could ideally be inferred from
minute differences in the abundances between stars (Gaidos, 2015).

Recent chemical abundance surveys explore the implications for planet
formation of refractory element abundance (including C, O, Mg, and Si) and
overall metallicity for thousands of solar analog stars and others within the
local solar neighborhood (Fortney, 2012; Brewer & Fischer, 2016; Bedell et
al., 2018; Teske et al., 2019; Nibauer et al., 2021; Swastik et al., 2021).
Studying the chemical composition of carbonaceous chondrites within our own
solar system (Anders & Grevesse, 1989; Braukmüller et al., 2018) and the
photospheres of nearby polluted white dwarfs (Harrison et al., 2018; Bonsor et
al., 2021; Putirka & Xu, 2021) provide another means of indirectly inferring
the composition of planetary material and reinforce the link between stellar
abundances and exoplanet composition.

Other studies explore the possibility of using elemental abundance ratios like
the carbon-to-oxygen ratio (Öberg et al., 2011; Reggiani et al., 2022;
Seligman et al., 2022), refractory-to-volatile ratios (Hands & Helled, 2021;
Lothringer et al., 2021; Welbanks et al., 2019), or isotopic abundance ratios
like 12C/13C (Zhang et al., 2021a, b) to constrain a planet’s formation
location relative to stellar “snowlines”. As we enter the era of the space-
based James Webb Space Telescope and ground-based ELTs, we also prepare to
observe exoplanet atmospheres in unprecedented detail: from massive, accreting
super-Jupiters like TYC 8998-760-1 b down to super-Earths and smaller
terrestrial planets like those in the TRAPPIST-1 system. Contemporary and
future researchers use these planetary and stellar abundances to model
exoplanet atmospheres, to infer the structure and composition of the
exoplanet’s interior, and to understand how atmospheres and interiors co-
evolve over time (Madhusudhan, 2012; Unterborn et al., 2014; Brewer & Fischer,
2016; Unterborn et al., 2017; Lincowski et al., 2018, 2019).

Clearly, there is plenty of work being done to derive stellar elemental
abundances and explore their relationship to planet formation and galactic
chemical evolution, however, the same cannot be said for isotopic abundances.
The present-day isotopic abundance database contains only a handful of
measurements from giant stars and even fewer from dwarf stars and is currently
barring progress to test isotopic abundances against GCE models and planet
formation mechanisms.

In this paper, we present the first 12C/13C and 16O/18O ratio measurements
made in solar twin stars using infrared fundamental CO band features. By
developing a body of precise stellar isotopic abundance profiles, we aim to
identify the “missing link” between GCE model predictions and observations,
and to reveal the physical phenomena responsible for present-day abundances in
the process.

In Section 2, we provide an overview of CO isotopic abundances including:
isotope production in AGB stars, archival isotope measurements in giant stars,
pilot studies in dwarf stars and the challenges faced, the potential of
isotopic abundances to act as stellar chronometers, and also their role in
constraining GCE models. In Section 3, we present our solar twin sample
(including fundamental stellar parameters and elemental abundances), describe
our observations using IRTF/iSHELL Rayner et al. (2016) and spectral
reduction. Section 4 contains a description of our PHOENIX stellar models and
our isotopic abundance analysis methodology. In Section 5, we present our
12C/13C and 16O/18O ratio measurements for our solar twin sample and compare
them to GCE models (Kobayashi et al., 2011; Romano et al., 2017; Prantzos et
al., 2018) and archival 12C/13C measurements (Botelho et al., 2020). Finally,
in Section 6 we provide a brief commentary of our infrared, CO-based isotopic
abundance analysis and present an overview of future stellar targets and other
isotopic abundance ratios of interest.

##  2 Background & Motivation

###  2.1 Carbon and Oxygen Isotope Production Mechanisms

As low-to-intermediate mass stars (1 $\leq M_{\odot}\leq$ 8) enter the late
stages of their evolution, they play an important role in the chemical
enrichment of the ISM, particularly in regard to minor isotope production.
Asymptotic Giant Branch stars, or AGB stars, constitute the late phase in the
evolution of these low-to-intermediate mass stars. Depending on time and
location within the galaxy, up to 50% of the material returned to the ISM by
dying stars comes from AGB stars, (Goswami, 2014) and the many grain species
formed in their cool circumstellar envelopes contribute greatly to the dust
population of the ISM (Tielens & Allamandola, 1989). Therefore, understanding
the nucleosynthetic processes and yields from these stars is crucial to
chemical evolution modeling efforts. AGB star isotopic abundance ratios are
great probes of internal mixing processes and their effect on stellar
nucleosynthesis as different dredge-up events mix the burning material within
the stellar envelope. During their red giant branch (RGB) phase, stars undergo
a convective mixing process called the first dredge-up (FDU). This process
carries nuclei from internal layers to the stellar surface. Because these
internal layers are affected by partial CNO cycling which produces minor CNO
isotopes like 13C, this leads to a decrease in the atmospheric 12C/13C ratio
with respect to main sequence values of $\sim 90$ down to $\sim 20-30$. The
FDU leaves 16O abundances unaltered, increases the 17O abundance by about 50%,
and slightly reduces 18O (Abia et al., 2017). A second dredge-up event occurs
during the early-AGB phase of the more massive stars (M $\geq 4M_{\odot}$)
where 4He and 14N are brought to the surface, but this does not modify the CNO
isotope ratios significantly. The third dredge-up (TDU) event that occurs
during the star’s main AGB phase, however, mixes products of He burning into
the envelope. Since 12C is the main product of He burning, the stellar surface
becomes enriched in 12C and the 12C/13C ratio increases past the previous FDU
value (Abia et al., 2017). The amount of carbon in the envelope may eventually
exceed the amount of oxygen, and so the AGB star becomes an AGB carbon star.

12C, the main carbon isotope, is a primary product of the triple-$\alpha$
process that occurs during a star’s helium-burning phase and drives mixing
between the processed core and outer envelope in low to intermediate-mass AGB
stars. 12C from the hydrogen-burning shell in intermediate and massive stars
is responsible for producing all of the nuclei involved in the CNO cycle: 13C,
15N, and 17O. While 12C is significantly produced by low mass stars (1-4 M⊙),
13C is produced mainly in intermediate mass stars and massive stars via three
main production mechanisms: (1) the CNO cycle resulting from H-burning; (2)
12C burning in low metallicity, fast-rotating massive stars; and (3) proton-
capture nucleosynthesis in AGB stars (Botelho et al., 2020). State-of-the-art
GCE models investigate the connection between stellar rotation and internal
mixing mechanisms by implementing nucleosynthetic yields from massive, fast-
rotating stars (Prantzos et al., 2018; Romano et al., 2019).

Synthesis of the primary oxygen isotope, 16O, is well understood since it is a
primary product of stellar evolution. It is produced exclusively by massive
stars from 12C via $\alpha$-capture at the end of a star’s helium burning
phase. Lower mass stars eject only the initial 16O of their envelope and thus
do not contribute to the 16O enrichment of the galaxy. In fact, both the 16O
and 18O stellar yields are often negative in intermediate-mass asymptotic
giant branch (AGB) stars because they are destroyed by proton-capture
nucleosynthesis during CN burning (Kobayashi et al., 2011). Production of the
secondary oxygen isotopes, 17O and 18O, depends on pre-existing seed nuclei.
The lighter of the two, 17O, is mainly produced through CNO burning of
hydrogen into helium via the reaction: 17F $\rightarrow$ 17O + e+ \+ neutrino,
followed by 17O + 1H $\rightarrow$ 14N + 4He. The latter reaction leads to the
production of the next heavier oxygen isotope. The heavy oxygen isotope, 18O,
is primarily produced from $\alpha$-captures on 14N, left over from CNO
cycling, which occurs during the initial stages of helium burning (Meyer et
al., 2008; Nittler & Gaidos, 2012). 18O is also secondary product of the CNO
cycle and explosive nucleosynthesis (T $\sim$ 109 K) in massive stars. It is
also worth noting that more massive stars contribute significantly to the
production of 16O and 18O since these isotopes require helium burning for
production whereas low-mass stars contribute more to 17O synthesis which only
requires hydrogen burning (Meyer et al., 2008; Nittler & Gaidos, 2012). The
evolution of the minor oxygen isotope abundances is not well understood.
Specifically, the balance between 18O depletion via CNO cycling and 18O
production during helium burning is not well studied.

###  2.2 Isotopic CNO Abundances

####  2.2.1 Giant Star CNO Isotopic Abundances

CNO isotopic abundances have previously been measured in several red giant
stars and AGB carbon stars. Observations show that 16O/17O/18O ratios are in
agreement with evolutionary model predictions (Tsuji, 2006; Abia et al., 2017)
which confirms that oxygen ratios are well established using post-FDU values.
Although the observed 12C/13C ratios in these stars appear fairly diversified
in the range of $\sim$5-50 with a majority in the $\sim$10-20 range, most
appear lower than theoretical predictions and much closer to the CNO cycle
equilibrium 12C/13C ratio of $\sim 3.5$ (Tsuji, 2006; Takeda et al., 2019).
These low 12C/13C ratios could, in theory, be explained by extra mixing
processes during the RGB and AGB evolution phases, however this would also
imply extreme oxygen and nitrogen isotope ratios of 16O/17O $\geq$ 1000,
16O/18O $\geq$ 2000, and 14N/14N $\geq$ 104 (Tsuji, 2006; Abia et al., 2017).
Puzzling observations of AGB carbon stars with very low 12C/13C ratios do not
show these high oxygen and nitrogen ratios. Moreover, the stars that do
demonstrate extreme oxygen and nitrogen ratios have normal 12C/13C ratios
(Abia et al., 2017).

Carbon and oxygen isotope ratio measurements in giant stars are not as helpful
to GCE models as dwarf star measurements. This is because giant-star
nucleosynthesis significantly alters the initial ratio throughout the star’s
evolution whereas dwarf stars tend to preserve their initial isotopic ratios
in their atmospheres (Meyer et al., 2008; Nittler & Gaidos, 2012; Prantzos et
al., 2018). Thus, dwarf star abundances better reflect the chemical
composition of their birth clusters and are overall a better gauge of chemical
evolution over time.

####  2.2.2 Challenges to Isotopic Abundance Measurements in Dwarf Stars

Until recently, it has been notoriously difficult to detect isotopes in cool
dwarf stars, hence the inadequate isotopic abundance catalog. Isotopic effects
are prominent only in molecular, not atomic, lines; therefore, spectral
molecular features are most prominently observed in stars such as M-dwarfs
whose photospheres are cool enough to allow the formation of various molecular
species (Tsuji, 2016). However, molecular observations come with some
challenges due to telluric absorption and the sheer density of absorption
lines throughout the optical and infrared. This includes strong molecular
absorption due to metal oxides and hydrides (Koizumi et al., 2020) such as TiO
in the optical band or H2O in the NIR band (Souto et al., 2018) and the
opacity due to millions of other molecular absorption lines that dominate an
M-dwarf’s observed spectrum. These spectral features have hampered past
efforts to identify desired isotopic lines necessary for a detailed chemical
analysis and accurate atmospheric models (Veyette & Muirhead, 2018). In
addition, determining isotopic abundance ratios in stars requires very high-
resolution and high signal-to-noise spectra (Adibekyan et al., 2018; Romano et
al., 2017). It is rather difficult to detect isotopologue features in dwarf
star spectra, and so the database of isotopic carbon and oxygen abundances is
rather small.

####  2.2.3 Dwarf Star Carbon and Oxygen Isotopic Abundance Ratios

Despite these challenges, a few isotopolgue detections have been made in dwarf
stars ranging from F-type stars down to M dwarfs. A pilot study used medium-
resolution (R $\sim 20,000$) near-infrared spectra to measure the 12C/13C
ratio in a sample of M dwarf stars (Tsuji, 2016). The medium resolution
observations could not resolve the faint 13C16O from stronger 12C16O, but
evidence for 13C16O in these M dwarf spectra was reported for the first time.
This study demonstrates the need for very high-resolution spectra, otherwise
CO isotopologue lines become too blended to measure precise abundances.

With this caveat in mind, later studies successfully measured the 12C/13C in
solar twins using 12CH and 13CH features in the optical band (Adibekyan et
al., 2018; Botelho et al., 2020). These efforts relied on high-resolution (R
$\sim$120,000) and high S/N optical HARPS spectra to make their measurements.
This high resolution allowed them to discern weaker 13CH lines from the
predominant 12CH lines. The 12C/13C is used to look for stars from the same
birth cluster as the Sun (Adibekyan et al., 2018) and also to identify 12C/13C
trends with stellar isochrone age (Botelho et al., 2020).

For cooler stellar and sub-stellar objects, the preferred method is to target
the 12CO/13CO ratio instead since this carbon isotope ratio is more readily
detectable and attained from the ground using near- and mid-infrared
observations (Mollière & Snellen, 2019). Recent observations show that
infrared observations of the CO fundamental rovibrational band at high
resolution allow the observation of rarer isotopologues, even in dwarf stars,
by resolving individual lines in the spectrum and providing sensitivity to
much lower abundances of 13CO and C18O (Crossfield et al., 2019). This
approach was used to measure the first multiple isotopic abundances of
M-dwarfs in the mid-infrared at high resolution (R $\sim 60,000$): not merely
the common 12C16O but also the rarer species 13C12O and 12C18O (Crossfield et
al., 2019). Since CO is an oxygen-bearing molecule, unlike CH used in earlier
studies, these CO isotopologue features allow us to measure the 16O/18O in
addition to the 12C/13C ratio. This result shows that isotopic abundance
analysis is not only possible via high resolution spectroscopy, but it is also
the next logical step for many stellar targets.

In the following sections, we go into further detail describing our present
understanding of elemental and isotopic abundances and how they may provide
the “missing link” between stellar photospheres and galactic chemical
evolution.

###  2.3 Chemical Abundances as Stellar Chronometers

Investigations into the mechanisms responsible for chemical enrichment of the
galaxy have led to the study of elemental abundances as “stellar chronometers”
that have the potential to be used to determine stellar ages. It is assumed
that the chemical composition of low-mass dwarf stars remains unchanged
throughout stellar lifetimes , and instead chemical abundances evolve in time
through inheritance between stellar generations. Because older stellar
populations synthesize metals and release them back into the ISM to be
recycled into new stars, elemental abundances increase over time (da Silva et
al., 2012). Past observational data has shown that there is no tight
correlation between stellar ages and metallicities (Holmberg et al., 2007;
Casagrande et al., 2011), therefore we have to delve beyond and explore the
relation between individual elemental abundances and stellar age. Core-
collapse (Type II) supernovae enriched the early galaxy with $\alpha$-process
elements (C, O, Ne, Mg, Si, S, Ar, Ca, Ti) on a faster timescale than Type Ia
supernovae could enrich the galaxy in iron-peak elements (e.g. Cr, Mn, Fe, Ni)
(Kobayashi et al., 2020). This delay in iron-peak element enrichment produces
chemical signatures like [$\alpha$/Fe] that serve as a good proxy for stellar
age and a probe for the history of galactic chemical evolution (Haywood et
al., 2013; Delgado-Mena et al., 2019; Kobayashi et al., 2020). In general, the
[$\alpha$/Fe] abundance ratios and others formed mostly by Type II supernova
increase with the age of a star (Nissen, 2015; Bedell et al., 2018; Delgado-
Mena et al., 2019). The ratios of s-process elements (Sr, Ba, Zr, Y, La),
primarily produced in low-mass AGB stars, over Fe follow trends similar to the
iron-peak elements and show a negative correlation with stellar age (Delgado-
Mena et al., 2019). The first major study of elemental abundances and their
relation to age by da Silva et al. (2012) identified [Y/Mg], [Sr/Mg], [Y/Zn]
and [Sr/Zn] as having significant trends as a function of age in a large
sample of solar twins. Since this study, several other abundance ratios have
been identified as potential chemical clocks and we discuss them in more
detail below.

Among stellar chronometer candidates, the most widely discussed is perhaps the
[Y/Mg] ratio. In the context of stellar nucleosynthesis, it makes sense that
this abundance ratio is sensitive to stellar age. Massive stars produce and
expel Mg into the ISM on a different timescale than intermediate-mass AGB
stars produce and expel Y. [Y/Fe] notably decreases with stellar age contrary
to other s-process elements with a rather steep negative slope (slope = -0.033
dex Gyr-1) and [Mg/Fe] increases with stellar age (slope = +0.009 dex Gyr-1)
(Nissen, 2015) and so [Y/Mg] acts as a sensitive probe of stellar age.
Multiple studies have confirmed the trend of [Y/Mg] with age (Nissen, 2015;
Maia et al., 2016), and their equations can determine a stellar age with
$\sim$0.8 Gyr precision (for solar twin stars aged 0-10 Gyr) given a precise
measurement of [Y/Mg] ($\pm 0.02$). The best stellar chronometer candidates
are often ratios of light s-process elements (Sr, Ba, Zr, Y, La) over $\alpha$
elements (C, O, Ne, Mg, Si, S, Ar, Ca, Ti plus Zn and Al) (Delgado-Mena et
al., 2019) because of the drastically different “enrichment timescales”. For
more information on elemental abundance ratios that demonstrate a trend with
stellar age in solar twin samples, refer to Nissen (2015); Maia et al. (2016);
Nissen (2016); Spina et al. (2017); Delgado-Mena et al. (2019); Jofré et al.
(2020); Nissen et al. (2020).

Since the enrichment timescales for major and minor isotope are analogous to
those for the best stellar chronometer candidates, ratios of major to minor
isotopes must also be considered. In fact, Botelho et al. (2020) have recently
reported that the 12C/13C ratio in solar twin stars seems to have a tentative
correlation with metallicity but not quite with stellar age. It remains
unknown how the 16O/18O ratios behave with stellar age or metallicity solar
twin stars because of the difficulty in detecting faint C18O. In this paper,
we finally explore how both the 12C/13C and 16O/18O ratio correlate with
stellar age in a small sample of solar twin stars, but ultimately more dwarf
star observations are necessary to test carbon and oxygen isotope ratios’
performance as chemical clocks.

####  2.3.1 Solar Twin Galactic Chemical Evolution

Solar twin stars also exhibit peculiar abundance signatures that divide the
solar twin population into distinct age groups and help trace their origin
within the galaxy. Examination of solar twin stars in the solar vicinity show
that the ages of these stars are widely distributed from 0-10 Gyr (Tsujimoto,
2021). Stars of similar ages share elemental abundance patterns as anticipated
by the chemical evolution individual elements over time (Bedell et al., 2018).
The oldest group of solar twins (ages $\sim 8.7$ Gyr) has abundance patterns
(C to Dy) quite similar to solar-metallicity galactic bulge stars. The super-
solar abundances of this older group of solar twins is likely a result of the
faster chemical enrichment that occurs closer to the galactic center. These
abundance patterns further suggest that the oldest solar twins have migrated
to the local solar neighborhood from birthplaces within the galactic bulge
(Tsujimoto, 2021). The second group of solar twins with ages $\sim 5.9$ Gyr
demonstrate abundance patterns nearly identical to the Sun, and this
association of the Sun with slightly older solar twins reinforces the notion
of a common birthplace much closer to the galactic center. The 12C/13C and
16O/18O ratios, if proven to have a significant trend with stellar age, would
be powerful chemical clocks and stellar formation location tracers since they
also exhibit prominent gradients with galactocentric radius (Romano et al.,
2019).

Clearly there is plenty to explore in galactic chemical evolution and
exoplanet systems using elemental and isotopic abundances. However, dwarf star
isotopic abundance measurements are quite scarce despite being more reliable
than giant star measurements. Currently, isotopic abundance analyses focus on
solar twin stars of near-solar metallicity. It is crucial we expand the
database to probe low-mass and low-metallicity stars where GCE models lack
observational constraints. Therefore, we present an isotopic carbon and oxygen
abundance analysis of six bright, well-studied solar twins. This paper serves
as a pilot study using infrared (M band) CO features to derive 12C/13C and
16O/18O ratios. Once applied to solar twin stars, the technique could be
extended to K and M dwarf stars as well as low-metallicity stars to bridge the
‘observational’ gap in GCE models.

Table 1: Solar Twin Parameters

Stellar | Spectral | Brightness | Radius | Age | *Teff | Stellar | *Model | *Model
---|---|---|---|---|---|---|---|---
ID | Type | K Mag | (R☉) | (Gyr) | (K) | log g | Teff | log g
Sun | G2V | 5.08 | 1.0 | 4.567 $\pm\ $0.11 | 5780 | 4.44 | 5780 | 4.44
HIP 29432 | G4V | 5.301 | 0.95 | 5.51 $\pm\ $0.71 | 5758 $\pm\ $5 | 4.44 | 5780 | 4.44
HIP 42333 | G8V | 5.223 | 1.0 | 1.01 $\pm\ $0.52 | 5848 $\pm\ $8 | 4.50 | 5870 | 4.49
HIP 77052 | G2V | 4.300 | 0.96 | 3.67 $\pm\ $0.91 | 5683 $\pm\ $5 | 4.48 | 5690 | 4.39
HIP 79672 | G2V | 4.190 | 1.03 | 3.09 $\pm\ $0.40 | 5814 $\pm\ $3 | 4.45 | 5780 | 4.44
HIP 85042 | G3V | 4.686 | 1.04 | 6.66 $\pm\ $0.62 | 5694 $\pm\ $5 | 4.41 | 5690 | 4.39
HIP 102040 | G5V | 4.921 | 0.96 | 2.42 $\pm\ $0.91 | 5838 $\pm\ $6 | 4.48 | 5870 | 4.49

Note. — Stellar Parameters. Stellar ID from the Hipparcos Catalogue (ESA
1997); Spectral type and K band magnitude from 2MASS (Cutri et al., 2003);
Stellar radius from Gaia DR2 (Brown et al., 2018); Stellar age, Stellar
effective temperature *Teff, and stellar surface gravity (log g) from dos
Santos et al. (2016); Solar K Mag from Willmer (2018); Solar age from Bonanno
et al. (2002); Jacobsen et al. (2008). The final two columns contain the
stellar effective temperature and surface gravity parameters adopted for each
set of PHOENIX model spectra.

Table 2: Observational Parameters

Parameter | HIP 29432 | HIP 42333 | HIP 77052 | HIP 79672 | HIP 85042 | HIP 102040
---|---|---|---|---|---|---
Date [UT] | 2019-02-02 | 2019-03-29 | 2019-05-16 | 2019-05-16 | 2019-05-16 | 2019-05-16
Time [UT] | 07:48 - 08:23 | 06:14 - 06:52 | 07:44 - 08:01 | 08:25 - 08:53 | 10:53 - 11:30 | 14:31 - 15:03
iSHELL Mode | M1 | M1 | M1 | M1 | M1 | M1
Slit | 0.375” × 15” | 0.375” × 15” | 0.375” × 15” | 0.375” × 15” | 0.375” × 15” | 0.375” × 15”
Integration Time [s] | 48.65 | 63.94 | 48.65 | 48.65 | 48.65 | 48.65
Co-adds | 3 | 3 | 3 | 3 | 3 | 3
Exposures | 40 | 34 | 20 | 32 | 42 | 32
Median S/N | 16.6 | 36.2 | 32.5 | 45.3 | 36.4 | 22.0

Note. — Observational parameters for the six solar twins on IRTF/iSHELL
(Rayner et al., 2016)

Figure 1: A small section of the normalized spectra for the Sun from the ACE-
FTS Solar Atlas (Frank L.M. Hase, 2010) and our six solar twins from
IRTF/iSHELL (Rayner et al., 2016). The spectra have been shifted to the same
wavelength frame. The black dotted lines show the location of some 13CO
features used in our abundance analysis.

##  3 Sample and Observations

###  3.1 Solar Twin Sample

We selected a sample of six bright solar twin stars with near-solar spectral
types, radii, effective temperatures, metallicities, carbon abundances, and
oxygen abundances (See Tables 1 and 3). The stellar ages used in this analysis
are taken from (dos Santos et al., 2016) and originally obtained by Maia et
al. (2016) using Yonsei-Yale isochrones (Yi et al., 2001). The solar twin ages
range from 1-7 Gyr, but the metallicities are all within 0.15 dex from solar.
The solar twin ages cover a large portion of the “GCE vs. Time” space;
however, as our sample is nearly solar in [Fe/H], the low-metallicity ([Fe/H
$<-0.2$]) space remains unexamined by this sample.

Three out of the six solar twins in this sample appear in multi-star systems:
HIP 77052 is in a binary (Hirsch et al., 2021), HIP 85042 is in a triple
system (Riddle et al., 2015), and HIP 102040 has three optical companions
(Riddle et al., 2015). Out of the six solar twins, HIP 29432 is the only
confirmed exoplanet host. HIP 29432 hosts a modestly-irradiated Neptune-mass
planet with a semimajor axis of 0.55 AU (Fulton et al., 2016).

###  3.2 Observations

We observed the six solar twins listed in Table 2 during the 2019A semester
using the iSHELL spectrograph (Rayner et al., 2016) on the NASA Infrared
Telescope Facility. Table 2 lists the technical details of these observations.
We obtained spectra at R = 70,000 (4.3 km/s) and mostly-continuous coverage
from 4.52–5.24 $\mu$m. We reduced the raw iSHELL data using the SpeXTool Data
Reduction package (Cushing et al., 2004) which corrects for pixel-to-pixel
variations and produces the wavelength calibration. We then compute spatial
profiles and extract two one-dimensional spectra (one at each nod position).
These two spectra are combined to produce a single spectrum for each star.

We correct for telluric absorption in our spectra following the approach of
(Crossfield et al., 2019), using the following A0V standard stars (V
Magnitude): HR 7891 (4.82), HR 2133 (6.075), HR 3314 (3.90), HR 5881 (3.53),
HR 5881 (3.53), HR 6629 (3.75). Finally, we remove parts of the spectrum with
obvious bad pixels and wherever S/N $<$ unity. In practice, the choice of S/N
cut-off is not especially significant since low-S/N parts of the spectrum are
appropriately de-weighted when we calculate our weighted-mean line profile for
each isotopologue (see Section 4).

##  4 Measuring Isotopic Abundances

###  4.1 Model Spectra

To measure CO isotopologue abundances in our solar twin sample, we compare our
observed spectra to synthetic spectra generated from custom solar atmosphere
models derived from the PHOENIX atmosphere code (Version 16; Husser et al.,
2013)(Hauschildt et al., 1999). Our PHOENIX model atmospheres contain 64
vertical layers, spaced evenly in log-space on an optical depth grid from
$\tau$ = 10${}^{-8}-1000$ spanning $1.0-10^{6}$ nm. In our observed wavelength
range, the models were sampled at least every 0.01 nm. In contrast to the
M-dwarf synthetic spectra from our similar analysis Crossfield et al. (2019),
the solar-like models for this analysis were only run with H I, He I, and He
II in NLTE to reduce computation time. For both the 13CO and the C18O
analysis, we generate synthetic spectra with 13C and 18O enrichments of
3$\times$, 1.78$\times$, 1$\times$, 0.56$\times$, 0.3$\times$, and 0$\times$
solar. We use a CO line list (Goorvitch, 1994) that contains lines for 12C16O,
13C16O, 12C18O, and other CO isotopologues. This older line list is in good
agreement with newer line lists of the CO fundamental band. These models are
run for effective temperatures (in K) of 5690, 5780, and 5870 and logg (cgs)
of 4.39, 4.44, and 4.49 respectively. Each solar twin’s isotopologue abundance
analysis is performed with the set of model spectra that best fits that star’s
effective temperature and log g (refer to Table 1).

###  4.2 Line Selection

We measured our isotopic abundances following the process described in
Crossfield et al. (2019). In this study, we use relatively strong, isolated
13CO and C18O lines to determine 13C and 18O isotopic abundances. Identifying
these lines requires a focus on the highest S/N regions of the stellar spectra
around 4.6–4.7 microns. Here, tellurics are relatively weak and the stellar
spectra are dominated by 12C16O, 13C16O, and 12C18O lines from the CO
fundamental rovibrational band. We have compiled a list of the strongest 13CO
and C18O lines within our desired wavelength range using the HITRAN database
(Gordon et al., 2017). The HITRAN line lists used for CO line identification
are based on data from Goorvitch (1994) line lists used in our PHOENIX models.
In this wavelength range, there are 41 12CO Lines, 34 13CO Lines, and 32 C18O
lines, but not all of them are included in the abundance calculation. Some
lines are obscured by strong telluric absorption lines, some fall beyond
outside the wavelength coverage in our IRTF/iSHELL spectra, and some weaker
isotopologue lines are overshadowed by stronger absorption from 12C16O and
other molecular species. Please refer to our machine-readable line lists and
the associated README file for more details on our line selection process.

Figure 2: Stacked 13CO line profiles for our sample. The line profiles
represent the weighted average of several M-band 13CO lines for the observed
stellar spectrum (in blue) and multiple PHOENIX model spectra of varying 13CO
abundances. We interpolate between these models using $\chi^{2}$ minimization
to determine the stellar 13CO abundance relative to solar (See analysis
example in Fig. 4; results shown in Table 3). Figure 3: Stacked C18O line
profiles for our sample. The line profiles represent the weighted average of
several M-band C18O lines for the observed stellar spectrum (in blue) and
multiple PHOENIX model spectra of varying C18O abundances. We interpolate
between these models using $\chi^{2}$ minimization to determine the stellar
C18O abundance relative to solar ($\chi^{2}$ minimization shown in Fig. 4;
results shown in Table 3).

###  4.3 Abundance Calculation

Atomic abundances are often calculated using only a few absorption lines with
relatively high S/N. In our case, however, it is important to note that most
of these spectral lines belonging to the isotopologues of interest have low
statistical significance and are barely visible by eye when considered
individually. We thus create a single line profile of each CO isotopologue,
for each solar twin in our sample by taking all useable absorption lines for
each isotopologue and combining them into a single, high S/N line profile. We
create the single line profile by taking the weighted mean, after continuum-
normalizing, of each spectral line. This produces the stacked absorption
profiles shown in Fig. 2 and Fig. 3. We then create corresponding line
profiles for the synthetic stellar models detailed above, using the same set
of lines. The isotopic abundances for each CO isotopologue are then determined
by comparing the stacked absorption lines from the observed spectrum to the
those of the synthetic models.

We measure the 13C/H and 18O/H abundance ratios for each solar twin by a
$\chi^{2}$ analysis, which represents how well the model line profile fits the
observed solar twin line profile. We calculate $\chi^{2}$ over the velocity
range $\Delta V$ ($6<\Delta V<12$) km/s centered at the line profile center V
= 0. Because we want to minimize $\chi^{2}$ to identify the best fit abundance
value, the set of $\chi^{2}$ values (only including values $\leq 175$) is fit
with a parabola and the minimum is then calculated, giving the best-fit
isotopologue abundance. We infer 1$\sigma$ confidence intervals using the
region where $\Delta\chi^{2}\leq 1$ (Avni, 1976). Fig. 4 shows an example of
this approach for the Sun (further described below). The final 13CO and C18O
abundances are shown in Table 3.

To test the accuracy of our 13C/H and 18O/H measurements within our solar twin
sample and the consistency across different CO line lists, we also repeat this
analysis using an infrared spectrum of the Sun from the ACE-FTS Solar Atlas
(Frank L.M. Hase, 2010). Ideally, if we measure the 13CO and C18O abundances
relative to solar in a spectrum of the Sun, our analysis should find an
abundance of 1.0 x Solar for each CO isotopologue. This is, nearly, what we
observe. Using this solar spectrum with uncertainties adopted from our highest
S/N spectrum (HIP 79672; see Table 2), we measure $1.10\pm 0.04$ and $1.03\pm
0.42$ x Solar abundances for 13CO and C18O respectively. The slight 13CO
overestimate appears in the solar twin analysis even after the $\chi^{2}\leq
175$ cutoff. These results indicate that our systematic and modeling errors
are $\leq 10\%$ for both isotopologues. We discuss this issue further in
Section 5.4.

Figure 4: Example of our analysis approach for the infrared solar spectrum
from the ACE-FTS Solar Atlas (Frank L.M. Hase, 2010). Here we show the six
$\chi^{2}$ values calculated between the solar line profile and each model of
varying 13CO and C18O abundances. We fit a parabola to the $\chi^{2}$ values
($\leq 175$) and assign the minimum as the best-fit isotopologue abundance
relative to solar. We measure $1.10\pm 0.10$ and $1.03\pm 0.42$ x Solar
abundances for 13CO and C18O respectively.

##  5 Results

Our 13CO, C18O, 12C/13C, and 16O/18O measurements are summarized in Table 3
for our six-solar-twin sample and the Sun. Similar to the analysis in Botelho
et al. (2020), we calculate a weighted least-squares linear fit for our
12C/13C ratios to identify tentative trends. The fit demonstrates a decrease
in the 12C/13C ratio over metallicity (slope = -157 $\pm$ 82 dex-1).
Similarly, we see the 12C/13C ratio decrease over time with a slope of -6.65
$\pm$ 2.15 Gyr-1. A weighted linear fit of our oxygen ratios demonstrates an
increasing trend over both metallicity and time: slope = +2438 $\pm$ 713 dex-1
and +75.55 $\pm$ 56.8 Gyr-1 respectively. Although the Botelho et al. (2020)
data suggest a systematic increase in 12C/13C with [Fe/H] but not with time,
our sample does not seem to significantly favour either an increase or
decrease.

We will now discuss how our new carbon and oxygen isotope ratios compare to
various GCE models. We will also examine how these solar twin carbon isotope
ratio measurements compare to archival measurements. A visual comparison of
our measurements to several GCE models is shown in Fig. 5. The top two panels
show 12C/13C vs. [Fe/H] (left) and 16O/18O vs. [Fe/H] (right). The bottom two
panels show 12C/13C vs. Time (left) and 16O/18O vs. Time (right).

Figure 5 shows our solar twin 12C/13C and 16O/18O ratio measurements compared
to GCE models and archival measurements (13CO only). The top four panels show
the predicted evolution of 12C/13C (left) and 16O/18O (right) ratios over
stellar metallicity using GCE models from Kobayashi et al. (2011); Prantzos et
al. (2018). Similarly, the bottom two panels show the predicted evolution of
12C/13C (left) and 16O/18O (right) ratio over time using GCE models from
Romano et al. (2017). The orange circle represents Solar values from Ayres et
al. (2013) and the gray points represent the values of the Botelho et al.
(2020) solar twin sample. The red points represent the solar twin abundances
measured in this paper. Our measurements agree somewhat with GCE predictions
for 12C/13C, but are less obvious for 16O/18O. We elaborate on these GCE
models and the comparison below.

Table 3: 12C/13C and 16O/18O Abundances

| Age | [Fe/H] | [C/H] | [O/H] |  13CO/H | C18O/H | Measured | Measured
---|---|---|---|---|---|---|---|---
ID | (Gyr) | (dex) | (dex) | (dex) | (x Solar) | (x Solar) |  12C/13C |  16O/18O
Sun | *4.603 | 0.0 | 0.0 | 0.0 | 1.10 $\pm$ 0.10 | 1.03 $\pm$ 0.42 | $*91.4\pm 1.3$ | $*511\pm 10$
HIP 29432 | 5.51 | -0.096 | -0.103 | -0.092 | 1.03 $\pm$ 0.28 | 5.36 $\pm$ 1.08 | $70\pm 26$ | $77\pm 26$
HIP 42333 | 1.01 | 0.138 | -0.047 | -0.130 | 1.88 $\pm$ 0.18 | 1.24 $\pm$ 0.84 | $59\pm 10$ | $558\pm 426$
HIP 77052 | 3.67 | 0.036 | 0.048 | 0.104 | 1.07 $\pm$ 0.09 | 1.10 $\pm$ 0.41 | $77\pm 13$ | $344\pm 177$
HIP 79672 | 3.09 | 0.056 | 0.037 | 0.078 | 1.25 $\pm$ 0.10 | 0.80 $\pm$ 0.42 | $84\pm 13$ | $811\pm 499$
HIP 85042 | 6.66 | 0.015 | 0.081 | 0.131 | 0.97 $\pm$ 0.09 | 1.43 $\pm$ 0.36 | $103\pm 17$ | $428\pm 148$
HIP 102040 | 2.42 | -0.093 | -0.056 | -0.134 | 0.75 $\pm$ 0.27 | 0.63 $\pm$ 1.50 | $107\pm 48$ | $596\pm 1504$

Note. — Ages from dos Santos et al. (2016). [Fe/H] $\pm\ 0.005$ from Brewer et
al. (2016). [C/H] $\pm\ 0.07$ and [O/H] $\pm\ 0.09$ abundances from Rice &
Brewer (2020) and Polanski et al. (in prep.); *Solar age and isotope ratios
from (Ayres et al., 2013)

Figure 5: Comparison of our six solar twin 12C/13C and 16O/18O ratios to GCE
models (Kobayashi et al., 2011; Romano et al., 2017; Prantzos et al., 2018)
and archival solar twin measurements (Botelho et al., 2020).

###  5.1 Kobayashi et al. (2011) Model

This model includes nucleosynthetic yields from Type Ia supernovae (Nomoto et
al., 1997), updated yields from Type II supernovae and hypernovae (Kobayashi
et al., 2006), and AGB stars (Campbell & Lattanzio, 2008; Karakas, 2010). As
is evident in this particular model, GCE models that neglect the yields of
massive, fast-rotating stars confirm a secondary production mechanism for 13C
which results in a very high ($\sim 10^{3}$) 12C/13C ratio at low metallicity
and is much higher than the solar value $\sim 90$ (Kobayashi et al., 2011).
Because the chemical enrichment timescale of the galactic halo is longer than
in the solar neighborhood, there is a higher 12C/13C ratio predicted in the
halo due to a significant contribution from low-mass AGB stars. In Figure 5
(top left panel), we see that this model accurately predicts the solar 12C/13C
ratio, but overestimates it for stars in the solar neighborhood like the solar
twins from the Botelho et al. (2020) sample. The 12C/13C ratio measured here
for HIP 85042 (101 $\pm$ 17) and HIP 102040 (105 $\pm$ 48) also fit the model
fairly well. The other four solar twins (HIP 29432, HIP 42333, HIP 77052, HIP
79672) demonstrate a significantly lower 12C/13C than model predictions as
well as the solar twins in the Botelho et al. (2020) sample. Overall, the
decreasing trend in 12C/13C over metallicity is consistent with this GCE
model.

All six of our solar twin 16O/18O measurements agree with the Kobayashi et al.
(2011) model predictions within the uncertainties, even HIP 102040 and HIP
29432 for which we report the lowest S/N measurements. See Figure 5 (top right
panel).

###  5.2 Prantzos et al. (2018) Model

All the major isotopes of the multi-isotopic elements up to Fe (12C, 14N, 16O,
20Ne, 28Si, 32S, 36Ar, 40Ca, 54Cr, 56Fe) are reproduced to better than 15%
and, in most cases, to better than 10% in this set of GCE models. Prantzos et
al. (2018) provides both a baseline model – which includes yields from low to
intermediate mass stars, massive stars, and rotating massive stars – and a
second model which considers yields from non-rotating massive and low-to-
intermediate mass stars only. These models use the metallicity-dependent
yields from Cristallo et al. (2015) and rotating and non-rotating stellar
yields from Limongi & Chieffi (2018). The inclusion of rotating star yields in
the baseline model significantly reduces the 12C/13C ratio at low
metallicities (12C/13C $<1000$ for [Fe/H] $>-2.0$). Even so, the 12C/13C
ratios observed in solar twins with near-solar metallicities are significantly
lower than the baseline model’s predictions. Therefore, in Figure 5
(top/bottom left panels) we plot only the secondary model, not the baseline
model. The observed solar twin 12C/13C ratios match the secondary model
slightly better. It is worth noting that the 12C/13C measurements presented
here show the same trend, decreasing over metallicity, as the GCE models,
contrary to the Botelho et al. (2020) solar twin sample. We will explore this
issue further in Section 6.4 by comparing the carbon isotope ratios in our six
solar twins (HIP 29432, HIP 42333, HIP 77052, HIP 79672, and HIP 102040) to
the Botelho et al. (2020) 12C/13C measurements of the same stars.

While these models slightly overestimate 12C/13C ratio observed in solar
twins, they demonstrate a slight underestimate for 16O/18O ratios. In the top
right and bottom right panels of Figure 5, we observe that five out of the six
solar twin measurements of the oxygen isotope ratio presented here, including
the Sun with 16O/18O $\sim 511$ (Ayres et al., 2013), show ratios greater than
the model predictions of 16O/18O $\sim 300$ for near-solar metallicity stars.
It is worth noting that this particular GCE model set would still
underestimate the 16O/18O ratio even if we eliminate the lowest SNR
measurements in our sample.

###  5.3 Romano et al. (2017) Model

The four carbon isotope ratio models incorporate different combinations of
stellar yields. Models 1 and 2 use the same nucleosynthetic prescription for
low- to intermediate-mass stars (LIMS) and massive stars (Karakas, 2010;
Nomoto et al., 2013); however, Model 2 additionally includes super-AGB star
yields (Doherty et al., 2014a, b). Model 3 keeps LIMS yields from Karakas
(2010) but pulls the massive star nucleosynthesis prescription from multiple
sources (Meynet & Maeder, 2002; Hirschi et al., 2005; Hirschi, 2006; Ekström
et al., 2008). Finally, Model 4 adds super-AGB star yields (Doherty et al.,
2014a, b) to the other nucleosynthesis prescriptions from Model 3. In the
bottom left panel of Figure 5, notice that Models 1 and 3 best reproduce solar
data (Ayres et al., 2013), while inclusion of super-AGB star carbon synthesis
(Models 2 and 4) results in an underestimate of the solar 12C/13C ratio.
Nonetheless, all four models predict the current 12C/13C ratios in the solar
neighborhood, in agreement with local ISM values, within the errors. Any
discrepancies between solar abundances and the local ISM values are typically
attributed to the Sun’s migration to its current position from a birthplace
closer to the galactic center.

If we consider only the 12C/13C ratios from our six solar twin sample, we
observe that Models 1 and 2, without fast-rotator yields, perform better and
predict the carbon isotope ratios of the entire sample within the errors.
Although Models 3 and 4 could, potentially be used to describe the isotopic
abundance evolution of younger of solar twins (Age $<6$ Gyr) particularly
those in the Botelho et al. (2020) sample, they do not quite agree with the
measurements made in our oldest star (HIP 85042, Age $=6.66$ Gyr) nor in the
youngest (HIP 42333, Age $=1.01$ Gyr).

In terms of the isotopic oxygen ratio (Figure 5, bottom right panel), Models 1
and 2 also reproduce the 16O/18O ratios measured in the Sun and along the
Galactic disc. These two models produce the same 16O/18O evolution as they
only differ in the treatment of super-AGB stars, and oxygen is mainly produced
in massive stars, not in AGB stars. Older stars (Age $>6$ Gyr) are predicted
to be more 18O- poor than the Sun while younger stars (Age $<6$ Gyr) are
expected to have little 18O enrichment relative to the Sun. The older stars in
the sample, HIP 85042 and HIP 29432, appear to be enriched in 18O relative to
solar values with 16O/18O ratios lower than the youngest star, HIP 42333,
which has a near-solar ratio.

###  5.4 Comparing Carbon Isotope Ratios

The slight 13CO overestimate (recall we measure $1.10\pm 0.04$ and $1.03\pm
0.42$ x Solar abundances for 13CO and C18O respectively in a solar spectrum;
see Section 4.3) mentioned previously led us to compare our solar twin 12C/13C
ratios to archival measurements (Botelho et al., 2020). Using this archival
sample, we compare our 12C/13C measurements to a sample of stars 10x larger,
with isotopic abundance measurements made with optical CH features rather than
infrared CO. This allows us to examine 12C/13C trends across different sample
sizes and examine the efficiency of this isotopic abundance analysis using
optical (Botelho et al., 2020) vs. infrared spectra (this paper).

In Fig. 6, all 12C/13C measurements agree within the uncertainties except the
one for HIP 42333. Although a mismatch in one out of six stars may not be
unexpected, this discrepancy with the Botelho et al. (2020) measurement of the
same star is surprising: disagreement may be expected for our lower signal-to-
noise measurements such as HIP 29432 with S/N = 16.6, but not for HIP 42333
with a higher signal-to-noise ratio (S/N = 36.2) and a well-behaved line
profile. After applying a 13CO correction of -0.1 x Solar to our overestimated
abundances, we recalculate the 12C/13C ratios and plot them in Fig. 6. The
correction brings our four sub-solar 12C/13C ratios closer to archival values.
Our two stars with super-solar 12C/13C ratios move further from archival
values but still agree within the uncertainties.

The smaller uncertainties for the Botelho et al. (2020) sample are likely due
to the higher resolution and S/N of their solar twin spectra. Their sample of
solar twins uses HARPS spectra which cover 3780-6910 Å at a resolution R $\sim
115,000$ and reach a S/N of approximately 800 per pixel. These values are
significantly higher than what we obtain in the M band with IRTF/iSHELL at a
resolution of R $\sim 60,000$: We achieve S/N of just $\sim 20-40$ per pixel.
It appears that the 12C/13C ratio may be easier to measure, both in efficiency
and precision, using CH spectral features contained in optical spectra.
However, there are no ideal oxygen-bearing molecules with spectral features
accessible at optical wavelengths. Therefore, measuring the 16O/18O ratio
remains possible only using infrared CO features.

In the Botelho et al. (2020) solar twin study, they report that the linear fit
of 12C/13C as a function of metallicity shows a positive slope of +56.5 $\pm$
7.2 dex-1. The GCE models discussed above, surprisingly, follow an opposite
trend with [Fe/H]. Our solar twin sample demonstrates a weak hint of negative
trend for the 12C/13C ratio over metallicity (slope = -157 $\pm$ 82 dex-1)
that is in accordance with the steady 13C enrichment predicted by GCE models.
However, this is still consistent with the trend of Botelho et al. (2020) at
the $3\sigma$ level.

The archival sample also explores trends between the 12C/13C ratio as a
function of the isochrone stellar age. They show that 12C/13C ratio is
marginally correlated with age (slope of +0.614 $\pm$ 0.250 Gyr-1). In our
sample, we observe a positive correlation between the 12C/13C ratio and
isochrone age with a slope of +6.65 $\pm$ 2.15 Gyr-1 that is again consistent
with that of Botelho et al. (2020) at $3\sigma$. Both samples are consistent
with an overall decrease of the 12C/13C ratio over time.

Figure 6: Comparing 12C/13C ratio measurements for our solar twin sample with
archival measurements (Botelho et al., 2020). The closer measurements from
each study are to each other, the closer they lie to the blue dotted line. All
solar twin measurements are consistent within the uncertainties except for HIP
42333 for which we report a significantly lower 12C/13C ratio ($\sim 58$) than
in the previous study ($\sim 94$). Refer to Section 5.4 for more details.

##  6 Conclusions

Our high resolution spectra (R $\sim$ 60,000) from IRTF/iSHELL have made it
possible to successfully measure the 12C/13C and 16O/18O ratios in a sample of
solar twin stars, the latter of which have never been observed before.

Our analysis of 13CO and C18O in HIP 102040 and HIP 29432 in particular, the
solar twins with the lowest S/N spectra, exemplify the challenge of detecting
isotopologues in stellar photospheres. Low S/N spectra result in uncertainties
that rival the magnitude of the stellar line profiles themselves. We further
observe that the CO isotopologue lines are greatly deformed in these sub-
optimal spectra, and this leads to distorted stacked line profiles that do not
resemble the Gaussian shape of their stellar model counterparts. These effects
are visibly more pronounced in the weaker C18O lines (Fig. 3) and thus make
the C18O abundance measurements significantly more difficult to make than the
13CO.

We also find that both K band and M band spectra are amenable to CO
isotopologue analysis depending on the observing time available and the target
star’s brightness. In their pioneer analysis, Tsuji & Nakajima (2016) utilized
K band spectra to measure 12C/13C in a sample of M dwarf stars. Their study
was notably hindered by the low spectral resolution of their K band spectra
which resulted in significant blending of the inherently weak absorption lines
from the CO overtone band. Our analysis instead targeted the much stronger CO
absorption lines in the fundamental rovibrational band. M band spectra are
ideal because they provide access to the CO fundamental rovibrational band
that produces the strongest minor isotopologue signatures. This is more
practical for brighter targets, however, because M band observations require
much more observing time to attain the necessary S/N than K band observations.
K band observations may be the only practical choice for fainter stars, but
the weaker lines in CO overtone band make minor isotopologue detection more
difficult.

Nonetheless, the solar twin isotopic ratio measurements fit relatively well
compared to the GCE models, within the uncertainties. Since GCE models are
generally tailored to solar abundances, we do not expect much deviation from
GCE model predictions, at least not from a population of solar twin stars.
This isotopic abundance analysis in solar twin stars is a “pilot study” for
similar analyses in GKM-type dwarf stars. The truly interesting isotopic
abundance science lies in low metallicity stars.

###  6.1 Exploring Isotope Ratios in the Low-Metallicity Regime

While there has been some progress in measuring the 12C/13C ratio in near-
solar metallicity dwarf stars, the more interesting results come from low-
metallicity stars. Low metallicity stars provide us a glimpse into the
chemical composition of the early galaxy, and thus provide key observational
constraints to GCE models. Unfortunately, there are virtually no 12C/13C ratio
measurements in the literature for these metal-poor dwarf stars. However, a
recent measurement by Spite et al. (2021) shows a sub-solar 12C/13C ratio (27
$<$ 12C/13C $<$ 45) in metal-poor ([Fe/H] = -2.59) dwarf star HD 140283 (log g
= 3.70) suggests a much higher 13C abundance in the early galaxy than is
predicted by GCE models. This one carbon measurement, however, makes it
difficult to confirm the CNO isotopic composition of the early galaxy.
Measurements of the 18O abundance are significantly more difficult to make in
these metal-poor dwarf stars; however, a sufficiently high resolution and high
S/N spectrum may reveal the elusive C18O features. Regardless of the target or
method, we need a larger database of 12C/13C and 16O/18O ratios covering a
wide range of stellar metallicities to unveil the mysteries of stellar mixing
processes, stellar nucleosynthesis, and the isotopic composition of the early
galaxy.

Furthermore, inspection of the GCE models in Section 6 demonstrates that the
predicted evolution of major isotope abundances fits solar values quite well;
however, evolution of the minor isotopes does not fit solar abundances nearly
as well. Because minor isotopes are more fragile than their primary isotopes
and destroyed by typical stellar processes, it is difficult to predict minor
isotope evolution over time through GCE models. The only hope, then, is to
determine the correct [Fe/H] dependence of these minor isotopes. To better
explore the production of secondary carbon and oxygen isotopes, we need to
expand the isotopic abundance database beyond solar twin stars and measure
these isotope ratios in a sample of low-metallicity stars.

###  6.2 Isotope Ratios in the Low-Mass Regime

In addition to being good GCE model calibrators, isotopic carbon and oxygen
isotopes may also prove to be good tracers of planetary formation, migration,
and atmospheric evolution. Of the 5,044 exoplanets discovered to date (NASA
Exoplanet Archive), only one has a 12C/13C ratio measurement: TYC-8998-760-1
b, a young accreting super-Jupiter (Zhang et al., 2021b). While exciting, this
new sub-solar carbon isotope ratio does not have a complementary host star
measurement which makes it difficult to definitively identify a link between
host star abundances, planetary abundances, formation location, and migration
(Reggiani et al., 2022). It is also believed that the different formation
mechanisms between brown dwarfs and super-Jupiters (e.g. gravitational
collapse vs. core accretion) may produce distinct 12C/13C signatures in their
atmospheres (Zhang et al., 2021a). Thus, in addition to stellar and planetary
isotopic abundances, brown dwarf isotopic abundances introduce yet another
important piece of evidence in the planet formation puzzle.

The first exoplanetary and brown dwarf 12C/13C measurements (Zhang et al.,
2021b, a), are likely to be the first of many. Beyond these studies of such
giant, H-dominated bodies, CO and H2O isotopologue bands may be detectable
even in terrestrial exoplanet atmospheres (orbiting late-type M dwarfs like
TRAPPIST-1) using JWST transit transmission spectra throughout the near
infrared (1-8 µm), especially at 3-4 µm (Lincowski et al., 2019). JWST and
next-generation ELTs may therefore be capable of detecting isotopologues in
exoplanet atmospheres ranging from super-Jupiters down to terrestrial-size
planets (Lincowski et al., 2019). For now, however, planetary CNO isotope
measurements should focus on super-Jupiters and their host stars. Short-period
super-Jupiters close to their host stars will provide isotopic abundances
within the CO snowline using transmission spectroscopy while bright super-
Jupiters, like TYC-8998-760-1 b, provide isotopic abundances outside the CO
snowline using a combination of spectroscopy and direct imaging techniques.

###  6.3 Future Prospects for Other Isotopes

Other isotopic abundance ratios for nitrogen, magnesium, silicon, and titanium
have been measured previously in giant stars, but because internal processes
change these ratios throughout a giant star’s lifetime, they do not provide
the same constraints on GCE or planetary formation mechanisms as dwarf stars
do. Thus, the next important step in building an isotopic abundance database
is to go beyond CNO isotopes and measure those previously studied in giant
stars and those with the greatest implications for exoplanet formation and
composition. Elemental nitrogen abundances are routinely measured in dwarf
stars, but the 14N/15N ratio remains unstudied. Nitrogen isotopes would
complete the CNO isotopic abundance trifecta, but there are practically no
nitrogen isotope measurements for dwarf stars in the literature despite the
extensive research done by GCE modelers to predict the evolution of the
14N/15N (Romano et al., 2017). Optical 12C15N absorption features are
sensitive to the 15N abundance in giant stars (Hedrosa et al., 2013) and may
be useful in measuring the dwarf star 14N/15N ratios.

Past measurements of the (25Mg,26Mg)/24Mg ratios in cool dwarf stars show that
there is a decreasing trend over [Fe/H] which is in accordance with GCE models
(Yong et al., 2003). Further analysis of cool thick-disk and halo stars shows
a different trend over metallicity that requires increased 25Mg and 26Mg
production. This may be attributed to intermediate mass asymptotic giant
branch stars (Yong et al., 2003), and so GCE models can still gain important
constraints from Mg isotopes. Silicon abundance measurements in a sample of
evolved M-type stars also make good probes of the evolution of metallicity in
the ISM. There is a tentative correlation between the 29Si/30Si and the mass-
loss rates of these evolved stars which acts as a proxy of stellar age (Peng
et al., 2013). Mg and Si isotopes in exoplanet host stars also may provide
useful constraints for exoplanet composition (Suárez-Andrés et al., 2018) and
so they provide another key set of isotopes to target for the stellar and
planetary isotopic abundance database.

Titanium is also a good target for isotopic abundance studies with features
that can be measured in GKM dwarfs stars and potentially, exoplanet
atmospheres as well. Titanium has five stable isotopes (46-50Ti) with about
$25\%$ of its abundance partitioned among the minor isotopes–much greater than
the relative abundances of the minor H, C, and O isotopes (all $\sim 2\%$)
(Serindag et al., 2021). This makes Ti isotopes more accessible for
challenging observations due to their higher relative abundances compared to
other elements. Oxygen and silicon burning in massive stars is responsible for
the production of 46Ti and 47Ti while 48Ti, 49Ti, and 50Ti are produced mainly
in Type Ia and Type II supernovae (Hughes et al., 2008). This isotope
fractionation due to different production mechanisms makes dwarf star Ti
isotopes great candidates for testing GCE models. There have been previous
measurements of Ti isotope ratios in M dwarf stars of near-solar metallicity
with good GCE agreement (Chavez & Lambert, 2009), but as we have expressed in
this paper, the more interesting science lies in sub- and super-solar
metallicity stars. In terms of exoplanets, simulations of Ti isotope
measurements in exoplanet atmospheres show that an hour of observing time on
8-meter-class telescopes is sufficient to reveal Ti isotopes in the
atmospheres of wide-separation super-Jupiters (Serindag et al., 2021).

###  6.4 Concluding Remarks

In conclusion, this isotopic abundance analysis in solar twin stars served as
a “pilot study” for similar analyses in GKM-type dwarf stars of various ages,
metallicities, and even for exoplanet host stars. The agreement between the
12C/13C and 16O/18O measurements made in this paper and GCE model predictions
demonstrate the accuracy and precision of calculating isotopic abundances in
solar twin stars. The next important step is to fine-tune this process for M
dwarf and low-metallicity stars because these stars have the most to benefit
from new abundance-age relationships. Furthermore, as the predominant type of
exoplanet host stars, M dwarfs provide the best testing sites for abundance-
formation relations and planetary isotopic abundance measurements. Together,
these stellar and planetary isotopic abundances may eventually unveil “the
missing links” between exoplanet formation mechanisms and exoplanet
atmospheric evolution, chemical clocks and stellar ages, and the chemical
evolution of the galaxy.

## References

  * Abia et al. (2017) Abia, C., Hedrosa, R. P., Domí nguez, I., & Straniero, O. 2017, Astronomy $\&$ Astrophysics, 599, A39, doi: 10.1051/0004-6361/201629969
  * Adibekyan et al. (2018) Adibekyan, V., de Laverny, P., Recio-Blanco, A., et al. 2018, Astronomy$\&$ Astrophysics, 619, A130, doi: 10.1051/0004-6361/201834285
  * Anders & Grevesse (1989) Anders, E., & Grevesse, N. 1989, Geochimica et Cosmochimica Acta, 53, 197, doi: https://doi.org/10.1016/0016-7037(89)90286-X
  * Avni (1976) Avni, Y. 1976, ApJ, 210, 642, doi: 10.1086/154870
  * Ayres et al. (2013) Ayres, T. R., Lyons, J. R., Ludwig, H.-G., Caffau, E., & Wedemeyer-Böhm, S. 2013, The Astrophysical Journal, 765, 46, doi: 10.1088/0004-637x/765/1/46
  * Bedell et al. (2018) Bedell, M., Bean, J. L., Meléndez, J., et al. 2018, ApJ, 865, 68, doi: 10.3847/1538-4357/aad908
  * Bonanno et al. (2002) Bonanno, A., Schlattl, H., & Paternò , L. 2002, Astronomy $\&$ Astrophysics, 390, 1115, doi: 10.1051/0004-6361:20020749
  * Bonsor et al. (2021) Bonsor, A., Jofré, P., Shorttle, O., et al. 2021, Monthly Notices of the Royal Astronomical Society, 503, 1877–1883, doi: 10.1093/mnras/stab370
  * Botelho et al. (2020) Botelho, R. B., Milone, A. d. C., Meléndez, J., et al. 2020, MNRAS, 499, 2196, doi: 10.1093/mnras/staa2917
  * Braukmüller et al. (2018) Braukmüller, N., Wombacher, F., Hezel, D. C., Escoube, R., & Münker, C. 2018, Geochimica et Cosmochimica Acta, 239, 17, doi: https://doi.org/10.1016/j.gca.2018.07.023
  * Brewer & Fischer (2016) Brewer, J. M., & Fischer, D. A. 2016, ApJ, 831, 20, doi: 10.3847/0004-637X/831/1/20
  * Brewer et al. (2016) Brewer, J. M., Fischer, D. A., Valenti, J. A., & Piskunov, N. 2016, ApJS, 225, 32, doi: 10.3847/0067-0049/225/2/32
  * Brown et al. (2018) Brown, A. G. A., Vallenari, A., Prusti, T., et al. 2018, Astronomy $\&$ Astrophysics, 616, A1, doi: 10.1051/0004-6361/201833051
  * Campbell & Lattanzio (2008) Campbell, S. W., & Lattanzio, J. C. 2008, Astronomy $\&$ Astrophysics, 490, 769, doi: 10.1051/0004-6361:200809597
  * Casagrande et al. (2011) Casagrande, L., Schönrich, R., Asplund, M., et al. 2011, Astronomy $\&$ Astrophysics, 530, A138, doi: 10.1051/0004-6361/201016276
  * Chavez & Lambert (2009) Chavez, J., & Lambert, D. L. 2009, The Astrophysical Journal, 699, 1906, doi: 10.1088/0004-637x/699/2/1906
  * Cristallo et al. (2015) Cristallo, S., Straniero, O., Piersanti, L., & Gobrecht, D. 2015, The Astrophysical Journal Supplement Series, 219, 40, doi: 10.1088/0067-0049/219/2/40
  * Crossfield et al. (2019) Crossfield, I. J. M., Lothringer, J. D., Flores, B., et al. 2019, ApJ, 871, L3, doi: 10.3847/2041-8213/aaf9b6
  * Cushing et al. (2004) Cushing, M., Vacca, W., & Rayner, J. 2004, Astronomical Society of the Pacific.  http://irtfweb.ifa.hawaii.edu/~spex/Spextool.pdf
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, 2MASS All Sky Catalog of point sources.
  * da Silva et al. (2012) da Silva, R., de Mello, G. F. P., Milone, A. C., et al. 2012, Astronomy $\&$ Astrophysics, 542, A84, doi: 10.1051/0004-6361/201118751
  * Delgado-Mena et al. (2021) Delgado-Mena, E., Adibekyan, V., Santos, N. C., et al. 2021, Astronomy$\&$ Astrophysics.  https://arxiv.org/abs/2109.04844
  * Delgado-Mena et al. (2019) Delgado-Mena, E., Moya, A., Adibekyan, V., et al. 2019, Astronomy$\&$ Astrophysics, 624, A78, doi: 10.1051/0004-6361/201834783
  * Doherty et al. (2014a) Doherty, C. L., Gil-Pons, P., Lau, H. H. B., et al. 2014a, Monthly Notices of the Royal Astronomical Society, 441, 582, doi: 10.1093/mnras/stu571
  * Doherty et al. (2014b) Doherty, C. L., Gil-Pons, P., Siess, L., Lattanzio, J. C., & Lau, H. H. B. 2014b, Monthly Notices of the Royal Astronomical Society, 446, 2599, doi: 10.1093/mnras/stu2180
  * dos Santos et al. (2016) dos Santos, L. A., Meléndez, J., Nascimento, J.-D. d., et al. 2016, Astronomy $\&$ Astrophysics, 592, A156, doi: 10.1051/0004-6361/201628558
  * Ekström et al. (2008) Ekström, S., Meynet, G., Chiappini, C., Hirschi, R., & Maeder, A. 2008, Astronomy $\&$ Astrophysics, 489, 685, doi: 10.1051/0004-6361:200809633
  * Fortney (2012) Fortney, J. J. 2012, The Astrophysical Journal, 747, L27, doi: 10.1088/2041-8205/747/2/l27
  * Frank L.M. Hase (2010) Frank L.M. Hase, Sean D. McLeod, J. J. H. P. F. B. 2010, Journal of Quantitative Spectroscopy and Radiative Transfer, 111, 521.  http://www.ace.uwaterloo.ca/solaratlas.php
  * Fulton et al. (2016) Fulton, B. J., Howard, A. W., Weiss, L. M., et al. 2016, The Astrophysical Journal, 830, 46, doi: 10.3847/0004-637x/830/1/46
  * Gaidos (2015) Gaidos, E. 2015, The Astrophysical Journal, 804, 40, doi: 10.1088/0004-637x/804/1/40
  * Goorvitch (1994) Goorvitch, D. 1994, ApJS, 95, 535, doi: 10.1086/192110
  * Gordon et al. (2017) Gordon, I. E., Rothman, L. S., Hill, C., et al. 2017, Journal of Quantitative Spectroscopy and Radiative Transfer, 203, 3, doi: https://doi.org/10.1016/j.jqsrt.2017.06.038
  * Goswami (2014) Goswami, A. 2014, in Thirty Meter Telescope Science Forum, ed. M. Dickinson & H. Inami, 19
  * Hands & Helled (2021) Hands, T. O., & Helled, R. 2021, Monthly Notices of the Royal Astronomical Society, 509, 894, doi: 10.1093/mnras/stab2967
  * Harrison et al. (2018) Harrison, J. H. D., Bonsor, A., & Madhusudhan, N. 2018, Monthly Notices of the Royal Astronomical Society, 479, 3814–3841, doi: 10.1093/mnras/sty1700
  * Hauschildt et al. (1999) Hauschildt, P. H., Allard, F., Ferguson, J., Baron, E., & Alexander, D. R. 1999, The Astrophysical Journal, 525, 871, doi: 10.1086/307954
  * Haywood et al. (2013) Haywood, M., Matteo, P. D., Lehnert, M. D., Katz, D., & Gó mez, A. 2013, Astronomy $\&$ Astrophysics, 560, A109, doi: 10.1051/0004-6361/201321397
  * Hedrosa et al. (2013) Hedrosa, R. P., Abia, C., Busso, M., et al. 2013, The Astrophysical Journal, 768, L11, doi: 10.1088/2041-8205/768/1/l11
  * Hirsch et al. (2021) Hirsch, L. A., Rosenthal, L., Fulton, B. J., et al. 2021, The Astronomical Journal, 161, 134, doi: 10.3847/1538-3881/abd639
  * Hirschi (2006) Hirschi, R. 2006, Astronomy $\&$ Astrophysics, 461, 571, doi: 10.1051/0004-6361:20065356
  * Hirschi et al. (2005) Hirschi, R., Meynet, G., & Maeder, A. 2005, Astronomy $\&$ Astrophysics, 443, 581, doi: 10.1051/0004-6361:20053329
  * Holmberg et al. (2007) Holmberg, J., Nordström, B., & Andersen, J. 2007, Astronomy $\&$ Astrophysics, 475, 519, doi: 10.1051/0004-6361:20077221
  * Hughes et al. (2008) Hughes, G. L., Gibson, B. K., Carigi, L., et al. 2008, Monthly Notices of the Royal Astronomical Society, doi: 10.1111/j.1365-2966.2008.13870.x
  * Husser et al. (2013) Husser, T.-O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
  * Jackson et al. (2021) Jackson, H., Jofré, P., Yaxley, K., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 32–47, doi: 10.1093/mnras/staa4028
  * Jacobsen et al. (2008) Jacobsen, B., Yin, Q.-z., Moynier, F., et al. 2008, Earth and Planetary Science Letters, 272, 353, doi: 10.1016/j.epsl.2008.05.003
  * Jofré et al. (2020) Jofré , P., Jackson, H., & Maia, M. T. 2020, Astronomy $\&$ Astrophysics, 633, L9, doi: 10.1051/0004-6361/201937140
  * Jofré et al. (2017) Jofré, P., Das, P., Bertranpetit, J., & Foley, R. 2017, Monthly Notices of the Royal Astronomical Society, 467, 1140–1153, doi: 10.1093/mnras/stx075
  * Karakas (2010) Karakas, A. I. 2010, Monthly Notices of the Royal Astronomical Society, 403, 1413, doi: 10.1111/j.1365-2966.2009.16198.x
  * Kobayashi et al. (2020) Kobayashi, C., Karakas, A. I., & Lugaro, M. 2020, The Origin of Elements from Carbon to Uranium, arXiv, doi: 10.48550/ARXIV.2008.04660
  * Kobayashi et al. (2011) Kobayashi, C., Karakas, A. I., & Umeda, H. 2011, MNRAS, 414, 3231, doi: 10.1111/j.1365-2966.2011.18621.x
  * Kobayashi et al. (2006) Kobayashi, C., Umeda, H., Nomoto, K., Tominaga, N., & Ohkubo, T. 2006, The Astrophysical Journal, 653, 1145, doi: 10.1086/508914
  * Koizumi et al. (2020) Koizumi, Y., Kuzuhara, M., Omiya, M., et al. 2020, Publications of the Astronomical Society of Japan, 73, 154–173, doi: 10.1093/pasj/psaa112
  * Limongi & Chieffi (2018) Limongi, M., & Chieffi, A. 2018, The Astrophysical Journal Supplement Series, 237, 13, doi: 10.3847/1538-4365/aacb24
  * Lincowski et al. (2019) Lincowski, A. P., Lustig-Yaeger, J., & Meadows, V. S. 2019, AJ, 158, 26, doi: 10.3847/1538-3881/ab2385
  * Lincowski et al. (2018) Lincowski, A. P., Meadows, V. S., Crisp, D., et al. 2018, The Astrophysical Journal, 867, 76, doi: 10.3847/1538-4357/aae36a
  * Lothringer et al. (2021) Lothringer, J. D., Rustamkulov, Z., Sing, D. K., et al. 2021, The Astrophysical Journal, 914, 12, doi: 10.3847/1538-4357/abf8a9
  * Madhusudhan (2012) Madhusudhan, N. 2012, The Astrophysical Journal, 758, 36, doi: 10.1088/0004-637x/758/1/36
  * Maia et al. (2016) Maia, M. T., Ramí rez, I., Meléndez, J., et al. 2016, Astronomy $\&$ Astrophysics, 590, A32, doi: 10.1051/0004-6361/201527848
  * Meyer et al. (2008) Meyer, B. S., Nittler, L. R., Nguyen, A. N., & Messenger, S. 2008, Reviews in Mineralogy and Geochemistry, 68, 31, doi: 10.2138/rmg.2008.68.4
  * Meynet & Maeder (2002) Meynet, G., & Maeder, A. 2002, Astronomy $\&$ Astrophysics, 390, 561, doi: 10.1051/0004-6361:20020755
  * Mollière & Snellen (2019) Mollière, P., & Snellen, I. A. G. 2019, Astronomy $\&$ Astrophysics, 622, A139, doi: 10.1051/0004-6361/201834169
  * Nibauer et al. (2021) Nibauer, J., Baxter, E. J., Jain, B., et al. 2021, The Astrophysical Journal, 907, 116, doi: 10.3847/1538-4357/abd0f1
  * Nissen (2015) Nissen, P. E. 2015, Astronomy $\&$ Astrophysics, 579, A52, doi: 10.1051/0004-6361/201526269
  * Nissen (2016) —. 2016, Astronomy $\&$ Astrophysics, 593, A65, doi: 10.1051/0004-6361/201628888
  * Nissen et al. (2020) Nissen, P. E., Christensen-Dalsgaard, J., Mosumgaard, J. R., et al. 2020, Astronomy$\&$ Astrophysics, 640, A81, doi: 10.1051/0004-6361/202038300
  * Nittler & Gaidos (2012) Nittler, L. R., & Gaidos, E. 2012, Meteoritics $\&$ Planetary Science, 47, 2031, doi: 10.1111/j.1945-5100.2012.01410.x
  * Nomoto et al. (1997) Nomoto, K., Iwamoto, K., Nakasato, N., et al. 1997, Nuclear Physics A, 621, 467, doi: 10.1016/s0375-9474(97)00291-1
  * Nomoto et al. (2013) Nomoto, K., Kobayashi, C., & Tominaga, N. 2013, Annual Review of Astronomy and Astrophysics, 51, 457, doi: 10.1146/annurev-astro-082812-140956
  * Peng et al. (2013) Peng, T.-C., Humphreys, E. M. L., Testi, L., et al. 2013, Astronomy $\&$ Astrophysics, 559, L8, doi: 10.1051/0004-6361/201322466
  * Prantzos et al. (2018) Prantzos, N., Abia, C., Limongi, M., Chieffi, A., & Cristallo, S. 2018, MNRAS, 476, 3432, doi: 10.1093/mnras/sty316
  * Putirka & Xu (2021) Putirka, K. D., & Xu, S. 2021, Nature Communications, 12, doi: 10.1038/s41467-021-26403-8
  * Rayner et al. (2016) Rayner, J., Tokunaga, A., Jaffe, D., et al. 2016, NASA IRTF.  http://irtfweb.ifa.hawaii.edu/~ishell/iSHELL_SPIE2016_10jun16.pdf
  * Reggiani et al. (2022) Reggiani, H., Schlaufman, K. C., Healy, B. F., Lothringer, J. D., & Sing, D. K. 2022, The Astronomical Journal, 163, 159, doi: 10.3847/1538-3881/ac4d9f
  * Rice & Brewer (2020) Rice, M., & Brewer, J. M. 2020, The Astrophysical Journal, 898, 119, doi: 10.3847/1538-4357/ab9f96
  * Riddle et al. (2015) Riddle, R. L., Tokovinin, A., Mason, B. D., et al. 2015, The Astrophysical Journal, 799, 4, doi: 10.1088/0004-637x/799/1/4
  * Romano (2022) Romano, D. 2022, The Astronomy and Astrophysics Review, 30, doi: 10.1007/s00159-022-00144-z
  * Romano et al. (2019) Romano, D., Matteucci, F., Zhang, Z.-Y., Ivison, R. J., & Ventura, P. 2019, Monthly Notices of the Royal Astronomical Society, 490, 2838–2854, doi: 10.1093/mnras/stz2741
  * Romano et al. (2017) Romano, D., Matteucci, F., Zhang, Z.-Y., Papadopoulos, P. P., & Ivison, R. J. 2017, Monthly Notices of the Royal Astronomical Society, 470, 401–415, doi: 10.1093/mnras/stx1197
  * Seligman et al. (2022) Seligman, D. Z., Rogers, L. A., Cabot, S. H. C., et al. 2022, The Volatile Carbon to Oxygen Ratio as a Tracer for the Formation Locations of Interstellar Comets, arXiv, doi: 10.48550/ARXIV.2204.13211
  * Serindag et al. (2021) Serindag, D. B., Snellen, I. A. G., & Molliè re, P. 2021, Astronomy $\&$ Astrophysics, 655, A69, doi: 10.1051/0004-6361/202141941
  * Souto et al. (2018) Souto, D., Unterborn, C. T., Smith, V. V., et al. 2018, ApJ, 860, L15, doi: 10.3847/2041-8213/aac896
  * Spina et al. (2017) Spina, L., Meléndez, J., Karakas, A. I., et al. 2017, Monthly Notices of the Royal Astronomical Society, 474, 2580, doi: 10.1093/mnras/stx2938
  * Spite et al. (2021) Spite, M., Spite, F., & Barbuy, B. 2021, Astronomy $\&$ Astrophysics, 652, A97, doi: 10.1051/0004-6361/202141741
  * Suárez-Andrés et al. (2018) Suárez-Andrés, L., Israelian, G., González Hernández, J. I., et al. 2018, Astronomy$\&$ Astrophysics, 614, A84, doi: 10.1051/0004-6361/201730743
  * Swastik et al. (2022) Swastik, C., Banyal, R. K., Narang, M., et al. 2022, Galactic chemical evolution of exoplanet host stars: Are high-mass planetary systems young?, arXiv, doi: 10.48550/ARXIV.2205.15793
  * Swastik et al. (2021) —. 2021, The Astronomical Journal, 161, 114, doi: 10.3847/1538-3881/abd802
  * Takeda et al. (2019) Takeda, Y., Omiya, M., Harakawa, H., & Sato, B. 2019, Publications of the Astronomical Society of Japan, doi: 10.1093/pasj/psz104
  * Teske et al. (2019) Teske, J. K., Thorngren, D., Fortney, J. J., Hinkel, N., & Brewer, J. M. 2019, The Astronomical Journal, 158, 239, doi: 10.3847/1538-3881/ab4f79
  * Tielens & Allamandola (1989) Tielens, A. G. G. M., & Allamandola, L. J. 1989, Interstellar dust: contributed papers. Proceedings.
  * Tsuji (2006) Tsuji, T. 2006, Proceedings of the International Astronomical Union, 2, 307, doi: 10.1017/s1743921307000622
  * Tsuji (2016) —. 2016, Publications of the Astronomical Society of Japan, 68, 84, doi: 10.1093/pasj/psw076
  * Tsuji & Nakajima (2016) Tsuji, T., & Nakajima, T. 2016, Publications of the Astronomical Society of Japan, 68, 13, doi: 10.1093/pasj/psv119
  * Tsujimoto (2021) Tsujimoto, T. 2021, The Astrophysical Journal Letters, 920, L32, doi: 10.3847/2041-8213/ac2c75
  * Unterborn et al. (2017) Unterborn, C. T., Hull, S. D., Stixrude, L. P., et al. 2017, Stellar Chemical Clues As To The Rarity of Exoplanetary Tectonics.  https://arxiv.org/abs/1706.10282
  * Unterborn et al. (2014) Unterborn, C. T., Kabbes, J. E., Pigott, J. S., Reaman, D. M., & Panero, W. R. 2014, The Astrophysical Journal, 793, 124, doi: 10.1088/0004-637x/793/2/124
  * Veyette & Muirhead (2018) Veyette, M. J., & Muirhead, P. S. 2018, ApJ, 863, 166, doi: 10.3847/1538-4357/aad40e
  * Welbanks et al. (2019) Welbanks, L., Madhusudhan, N., Allard, N. F., et al. 2019, The Astrophysical Journal Letters, 887, L20, doi: 10.3847/2041-8213/ab5a89
  * Willmer (2018) Willmer, C. N. A. 2018, The Astrophysical Journal Supplement Series, 236, 47, doi: 10.3847/1538-4365/aabfdf
  * Yi et al. (2001) Yi, S., Demarque, P., Kim, Y.-C., et al. 2001, The Astrophysical Journal Supplement Series, 136, 417, doi: 10.1086/321795
  * Yong et al. (2003) Yong, D., Lambert, D. L., & Ivans, I. I. 2003, The Astrophysical Journal, 599, 1357, doi: 10.1086/379369
  * Zhang et al. (2021a) Zhang, Y., Snellen, I. A. G., & Molliè re, P. 2021a, Astronomy $\&$ Astrophysics, 656, A76, doi: 10.1051/0004-6361/202141502
  * Zhang et al. (2021b) Zhang, Y., Snellen, I. A. G., Bohn, A. J., et al. 2021b, Nature, 595, 370, doi: 10.1038/s41586-021-03616-x
  * Öberg et al. (2011) Öberg, K. I., Murray-Clay, R., & Bergin, E. A. 2011, The Astrophysical Journal, 743, L16, doi: 10.1088/2041-8205/743/1/l16