# Can Carbon Fractionation Provide Evidence for Aerial Biospheres in the
Atmospheres of Temperate Sub-Neptunes?

Ana Glidden Department of Earth, Atmospheric and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Kavli
Institute for Astrophysics and Space Research, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA  Sara Seager Department of Earth,
Atmospheric and Planetary Sciences, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Department of Physics and Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Jingcheng
Huang Department of Chemistry, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Janusz J. Petkowski Department of Earth, Atmospheric
and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  Sukrit Ranjan Center for Interdisciplinary Exploration and
Research in Astrophysics, Northwestern University, Evanston, IL 60201, USA

###### Abstract

The search for signs of life on other worlds has largely focused on
terrestrial planets. Recent work, however, argues that life could exist in the
atmospheres of temperate sub-Neptunes. Here, we evaluate the usefulness of
carbon dioxide isotopologues as evidence of aerial life. Carbon isotopes are
of particular interest as metabolic processes preferentially use the lighter
12C over 13C. In principle, the upcoming James Webb Space Telescope (JWST)
will be able to spectrally resolve the 12C and 13C isotopologues of CO2, but
not CO and CH4. We simulated observations of CO2 isotopologues in the
H2-dominated atmospheres of our nearest ($<40$ pc), temperate (equilibrium
temperature of 250-350 K) sub-Neptunes with M dwarf host stars. We find 13CO2
and 12CO2 distinguishable if the atmosphere is H2-dominated with a few
percentage points of CO2 for the most idealized target with an Earth-like
composition of the two most abundant isotopologues, 12CO2 and 13CO2. With a
Neptune-like metallicity of 100$\times$ solar and a C/O of 0.55, we are unable
to distinguish between 13CO2 and 12CO2 in the atmospheres of temperate sub-
Neptunes. If atmospheric composition largely follows metallicity scaling, the
concentration of CO2 in a H2-dominated atmosphere will be too low to
distinguish CO2 isotopologues with JWST. In contrast, at higher metallicities,
there will be more CO2, but the smaller atmospheric scale height makes the
measurement impossible. Carbon dioxide isotopologues are unlikely to be useful
biosignature gases for the JWST era. Instead, isotopologue measurements should
be used to evaluate formation mechanisms of planets and exoplanetary systems.

##  1 Introduction

So far the search for signs of life on other worlds has focused on terrestrial
planets, but recent work has explored whether life could originate and survive
in the liquid water clouds of temperate sub-Neptune-sized planets (Seager et
al., 2021). Sub-Neptunes are more readily observable than terrestrial planets
due to their larger size and low mean molecular weight (MMW), H2-dominated
atmospheres (e.g., Bean et al., 2021). Passive microbial-like particles could
persist aloft in regions with liquid water clouds for long enough to
metabolize, reproduce, and spread before sinking to altitudes that may be too
hot for life of any kind to survive (Seager et al., 2021). Isotope
fractionation is thought to be among the strongest signs of life that
theoretically can be remotely detected in a planet’s atmosphere (Neveu et al.,
2018). On Earth, carbon isotope fractionation has been used as evidence of
early life as biotic deposits of carbon have a higher ratio of 12C/13C than
abiotic deposits (e.g., Rothschild & Desmarais, 1989). The key metabolic
processes that fractionate carbon are photosynthesis, chemosynthesis,
respiration, and decomposition of organic matter (e.g., Mackenzie & Lerman,
2006). Isotopic compositions, however, can also be changed by geophysical or
chemical processes (e.g., degassing of basaltic magma (Mattey, 1991) and
chemical exchange in the protoplanetary disk (Woods & Willacy, 2009)).

The upcoming James Webb Space Telescope (JWST) (Gardner et al., 2006),
launched on December 25, 2021, provides an opportunity to characterize
exoplanets using isotopologues. JWST is predicted to be able to make
measurements of the protosolar D/H ratio ($2\times 10^{-5}$) using the methane
isotopologue, CH3D, for nearby, cool brown dwarfs in just 2.5 hr of JWST
observing time (Morley et al., 2019). In addition, oxygen isotopes could be
used to look for evidence of ocean loss. Simulated observations suggest that
JWST could observe oxygen isotopologues in water and carbon dioxide molecules
in the atmospheres of terrestrial planets around the M dwarf star TRAPPIST-1.
The oxygen isotopic ratio, 18O/16O, can be used as a marker of ocean loss and
atmospheric escape as the lighter 16O is preferentially removed from
photodissociated water vapor. Simulated JWST observations show that we may be
able to distinguish Venus-like fractionation ($\delta^{18}$O 100) potentially
caused by massive ocean loss from Earth-like fractionation in as little as 4
transits for TRAPPIST-1b and 5 transits for TRAPPIST-1d (Lincowski et al.,
2019).

From the ground, high-resolution data can be used to detect isotopologues via
direct imaging and spectroscopy. Recently, 13CO became the first carbon
isotopologue to be measured in an exoplanet’s atmosphere (Zhang et al., 2021).
Using the SINFONI instrument on the Very Large Telescope (VLT), Zhang et al.
(2021) observed the atmosphere of super-Jupiter TYC 8998-760-1 b and found a
12CO/13CO ratio of $31^{+17}_{-10}$ (90% confidence) in contrast to our solar
system average ratio of approximately 89 (Woods & Willacy, 2009) and local
interstellar medium value of about 68 (Milam et al., 2005). Zhang et al.
(2021) attribute the significant 13C enrichment to the formation location of
the planet past the CO snowline where isotopic ion-exchange reactions and
isotope-selective photodissociation can lead to an enhancement in 13C in CO
ice compared to CO gas.

Additionally, simulations of high-resolution observations of 13C16O, HDO, and
CH3D have been created based on models of the CRyogenic InfraRed Echelle
Spectrograph Upgrade (CRIRES+) instrument on the Very Large Telescope (VLT)
and the Mid-infrared ELT Imager and Spectrograph (METIS) instrument on the
upcoming Extremely Large Telescope (ELT) (Molliere & Snellen, 2019). 13C16O
was detectable in the dayside emission of hot Jupiters using the simulated VLT
observation (Molliere & Snellen, 2019). 40 m-class telescopes, like the ELT,
might make detection of CH3D possible for cool planets (Molliere & Snellen,
2019). CH3D might also be detectable in nearby super-Earths if they are
irradiated or transiting (Molliere & Snellen, 2019). However, HDO observations
may be hampered by methane absorption, which occurs at similar wavelengths.
The ELT will likely be necessary for observations of HDO unless the methane is
quenched (Molliere & Snellen, 2019).

We extend past work to focus on assessing the usefulness of isotopologues as
biosignature gases. Here, we quantify the detectability of 12C/13C via CO2 in
the atmospheres of nearby sub-Neptunes. We choose sub-Neptunes as they are
more readily observable than super-Earths due to their larger size and low
MMW, H2-dominated atmospheres. We choose carbon dioxide isotopologues as
carbon is fractionated by life, and the spectral separation of 12CO2 from
13CO2 is theoretically large enough to be resolved with JWST. In Section 2, we
explain how we modeled the detection of isotopologues using spectra generated
with petitRADTRANS (Mollière et al., 2019) and a simulated JWST noise model
using PandExo (Batalha et al., 2017). In Section 3, we show our results and
explain how we assessed detectability. In Section 4, we expound on the
significance of our findings and evaluate the usefulness of isotopologues as
biosignature gases in exoplanetary atmospheres. Our framework is designed to
assess if carbon fractionation is a detectable biosignature gas or if the
technology needed will be out of reach for decades to come. Knowing what kinds
of measurements we can and cannot make will help guide future mission
development.

##  2 Methods

We used petitRADTRANS to generate simulated spectra. petitRADTRANS (Mollière
et al., 2019) is a well validated Python package to generate transmission
spectra that has been broadly accepted by the community. As input to
petitRADTRANS, we calculated 13CO2 isotopologues cross sections using ExoCross
(Yurchenko et al., 2018) from input line list that are available publicly on
the High-Resolution Transmission Molecular Absorption (HITRAN) database
(Gordon et al., 2017). We use the temperature-pressure profile of temperate
sub-Neptune K2-18b by Blain et al. (2021). We calculate chemical abundances
using the chemical equilibrium implementation from petitRADTRANS. The chemical
abundances of the dominant volatiles at 1 bar are used as input boundary
conditions to our photochemical model of the atmosphere.

Our photochemistry model (Hu et al., 2012) is a simplified one-dimensional
chemical transport model. By calculating the atmosphere’s steady-state
chemical compositions, our model can simulate a variety of atmospheres, such
as H2-dominated reducing atmospheres and CO2-dominated highly oxidizing
atmospheres. The photochemistry model has been validated by simulating modern
Earth’s and Mars’ atmospheres (Hu et al., 2012). For more detailed information
and applications of our model see Hu et al. (2012, 2013); Seager et al.
(2013); Sousa-Silva et al. (2020); Zhan et al. (2021); Huang et al. (2022).

Our fiducial sub-Neptune atmosphere for the photochemical model is an
H2-dominated, Neptune-like atmosphere ([M/H]=100, C/O=0.55) orbiting an M
dwarf star. We adopt the mass and radius of K2-18 b to describe the planet and
the M dwarf stellar radiation model of GJ 876 (France et al., 2016; Loyd et
al., 2016). Our simulated atmosphere consists of two segments: a lower
convective layer ($10^{5}$ Pa to $10^{-1}$ Pa) and an upper radiative layer
($<10^{-1}$ Pa). (The two segments are unrelated to our 100-layer atmosphere
model used to simulate the transmission spectrum.) The temperature-pressure
profile of the convective layer comes from Figure 4 of Blain et al. (2021).
Since we do not consider heating in the upper atmosphere, we assume the
temperature to be constant (isothermal) in the upper radiative layer. In our
photochemistry model, the vertical mixing processes are parameterized by the
atmosphere’s eddy diffusion coefficient ($K_{zz}$). We use the free-convection
and mixing-length theories (Stone, 1976; Flasar & Gierasch, 1977; Gierasch &
Conrath, 1985; Visscher & Moses, 2011) to help us constrain the value of
$K_{zz}$. However, the constraints are loose, and hence we tested the impact
of using a range of values of Kzz, $1\times 10^{8}$ to $1\times 10^{10}$
(Gierasch & Conrath, 1985; Visscher & Moses, 2011; Hu & Seager, 2014). We
found that the Kzz did not change our column averaged mixing ratios. In our
fiducial simulation run, we adopt a uniform Kzz of $1\times 10^{9}$ cm2s-1, a
value also adopted by Moses et al. (2013); Miguel & Kaltenegger (2013), and Hu
& Seager (2014). In our simulation, we include all the reactions mentioned in
Hu et al. (2012), except for HSO2 thermal decay, high-temperature reactions,
and reactions that involve more than two carbon atoms (Hu et al., 2012). Given
our choice of the temperature-pressure profile, we omit NH4SH and NH3 aerosols
since the atmosphere is too hot for them to condense (Hu, 2021). Furthermore,
we do not consider rainout in our simulation as there is no ocean and the
temperature at the bottom of our simulated atmosphere is such that any rain
will inevitably evaporate.

Using the results of our photochemistry model, we simulate observations of the
Near Infrared Spectrograph (NIRSpec) Instrument on JWST. NIRSpec covers 0.6 to
5.3 $\mu$m (STScI, 2020). Using the PRISM disperser, the entire bandpass can
be measured at a resolution of R$\approx$100\. For high-resolution
observations at an R$\approx$2700, we simulate the G395H disperser over the
range of 2.87 $\mu$m to 5.27 $\mu$m (STScI, 2020).

We calculate the anticipated on-orbit noise for JWST using the Space Telescope
Science Institute Exposure Time Calculator for Exoplanets, PandExo (Batalha &
Line, 2017). PandExo performs throughput calculations using the Space
Telescope Science Institute’s (STScI) Pandeia. Schlawin et al. (2021)
estimated the magnitude of the noise for NIRCam, which has similar systematic
error to NIRSpec. They found that the pointing uncertainty and jitter will be
less than 6 ppm; thermal instabilities in the optics will be less than 2 ppm;
persistence will be less than 3 ppm; and detector temperature fluctuations
will be about 3 ppm. Given the sources of uncertainties, we adopt a noise
floor of 10 ppm for our model. To further configure our noise model, we set an
80% saturation level for each pixel. We also set the in-transit time equal to
the out-of-transit time. We use input stellar spectrum from PHOENIX (Husser et
al., 2013) based on the magnitude, temperature, metallicity, and surface
gravity of the host star. In addition, we define the properties of the planet
and host star.

##  3 Results

We present exoplanet transmission spectra with and without 13CO2 in order to
quantify the detectability of carbon isotopic composition in the atmosphere of
a sub-Neptune-sized exoplanet with JWST. When 13C is included, we assume
Earth-like fractionation.

###  3.1 Detection of Carbon Isotopes in an Ideal Target

We find 13CO2 to be detectable with JWST for the most idealized, simulated
target. To best distinguish 13CO2 from 12CO2 the atmospheric composition needs
to be predominately hydrogen gas with trace amounts of carbon dioxide. Benneke
et al. (2019) found that K2-18 b has a H2-dominated, a low MMW (2.42)
atmosphere that contains water. While Benneke et al. (2019) did not
conclusively detect other gases, they were able to place upper limits on CO,
CO2, NH3, and CH4 gas. We simulated an observation using a similar atmospheric
composition based on the low MMW and upper limits. We found 13CO2 was
distinguishable from 12CO2 at an SNR of 9.1 after a 10 transit observation as
seen in Figure 1. However, this result holds only for the most ideal
artificial target of the sub-Neptune TOI-1231 b placed around our nearest M
dwarf host star, LTT 1445 A. We are unable to distinguish 13CO2 from 12CO2 for
any of the real temperate sub-Neptune targets.

Figure 1: Simulated observation of the sub-Neptune TOI-1231 b artificially
placed around our nearest M dwarf host star, LTT 1445 A, observed in the PRISM
mode for 10 transits. The simulated atmosphere has an MMW of 2.42 and contains
similar molecular abundances to those found in K2-18 b (Benneke et al., 2019).
The upper panel shows the relative transit depth in parts per million (ppm)
for the wavelengths associated with JWST’s PRISM mode. The blue spectrum does
not include 13CO2 while the orange one does. The lower panel shows the signal
to noise ratio (SNR) of the deviation between the models with and without
13CO2. As seen in lower panel, for a 10 transit observation, the SNR value is
9.1.

###  3.2 Non-Detection of Carbon Isotopes in Simulated Sub-Neptune Atmospheres

Our results show that we we will not be able to distinguish between carbon
dioxide isotopologues for known temperate sub-Neptunes regardless of the
atmospheric composition. We construct an atmosphere with a Neptune-like
metallicity of 100x solar and a C/O ratio of 0.55 using our photochemistry
model. We simulate a 10 transit observation for our most readily observable,
temperate sub-Neptune, TOI-1231 b, with JWST’s PRISM mode as shown in Figure
2. The upper panel shows the relative transit depth in parts per million (ppm)
over the wavelength coverage of the PRISM mode (R $\sim$ 100). The blue
spectrum includes only CO2 with 12C while the orange spectrum also includes
13CO2. The lower panel shows the signal-to-noise ratio of the deviation
between the models or how well we would be able to distinguish observing CO2
with and without 13C. The SNR for a 10 transit observation is very low at 0.2.

We also simulated observations of LHS 1440 b, K2-18 b, and an artificial sub-
Neptune around our closest M dwarf host star, LTT 1445 A. In all cases, we
found we were unable to distinguish between our models with and without 13CO2.
The SNR of the deviation between the model with and without 13CO2 for the four
different planets is shown in Figure 3. The planets are listed in the rows,
and the number of transits observed changes with the columns. The first planet
listed is an artificial planet, a sub-Neptune around the closest known M dwarf
host star LTT 1445 A. (In reality, LTT 1445 A b is a 1.38 REarth super-Earth,
not a sub-Neptune.)

We also tested the impact of varying the metallicity of the atmosphere and
found that there is no “sweet spot” between a low MMW atmosphere and a CO2
abundance that allowed for a positive detection of 13CO2 if the atmosphere
followed metallicity scaling. The range of possible sub-Neptune atmospheric
compositions remains largely unknown (Bean et al., 2021, and references
therein). The compositions are believed to be H2 dominated, though the
metallicity range remains uncertain. While a lower metallicity atmosphere has
a larger scale height, making it more readily observable, it comes at the cost
of decreased CO2 gas. A more metal-rich atmosphere would increase the amount
of CO2, but would also increase the MMW of the atmosphere, thus shrinking the
scale height of the atmosphere and making it harder to detect overall, mostly
due to large amounts of the heavy molecules, water and methane. Fortunately,
CO2 has a relatively large cross section, making it detectable at relatively
low concentrations. In addition, carbon fractionation between the most
abundant isotopologue and second must abundant isotopologue is relatively
large at Earth-like fractionation. The carbon isotopologues of CO2 are well
separated compared with those of methane and carbon monoxide, allowing them to
be potentially distinguishable even at low (R$\sim 100$) spectral resolution
such as with JWST.

Currently, there are only four known nearby, temperate sub-Neptunes. LHS 1140
b is the closest at 12.47 $\pm$ 0.42 pc, but it is small for a sub-Neptune,
right at the accepted cutoff between super-Earth and sub-Neptune at 1.727
$\pm$ 0.032 RE (Dittmann et al., 2017; Ment et al., 2019). It has an estimated
equilibrium temperature of 235.0 $\pm$ 5 K (Ment et al., 2019). TOI-270 d is
the next closest at 22.453 $\pm$ 0.021 pc and it has an estimated equilibrium
temperature of 340 $\pm$ 14 K (Günther et al., 2019). Farther away, TOI-1231 b
is located at 27.4932 $\pm$ 0.0123 pc and has an equilibrium temperature of
330.0 $\pm$ 3.8 K (Burt et al., 2021). Lastly, K2-18 bis located at 38.07
$\pm$ 0.08 pc and has an estimated equilibrium temperature of 284 $\pm$ 15 K
(Sarkis et al., 2018).

As more TESS Targets of Interest (TOIs) become validated planets, it is likely
that additional temperature sub-Neptunes around nearby, bright M dwarfs,
emerge as better targets. However, additional temperate sub-Neptunes will not
prove amenable to isotopologue detection with JWST if the atmospheres follow
solar metallicity scaling.

Figure 2: Simulated 10 transit, PRISM mode observation of TOI-1231 b with a
Neptune-like metallicity of 100$\times$ solar and a C/O ratio of 0.55. The
upper panel shows the relative transit depth in parts per million (ppm) for
the wavelengths associated with JWST’s PRISM mode. The blue spectrum does not
include 13CO2 while the orange one does. The lower panel shows the signal to
noise ratio (SNR) of the deviation between the models with and without 13CO2.
As seen in lower panel, for a 10 transit observation, the SNR value is low at
0.2. Figure 3: Summary plot of the SNR of the deviation between models that
include 13C via CO2 vs those that do not for an atmosphere with a Neptune-like
metallicity of 100x solar and C/O of 0.55. The row labels show the names of
the simulated target planets. The first planet is our artificial sub-Neptune
(TOI-1231 b) around our closest known M dwarf host star LTT 1445 A, which in
reality is host to a super-Earth, not a sub-Neptune. The column labels show
the numbers of transits observed, from 1 to 50. A 10 transit observation is
roughly the longest reasonable observation with JWST. The colors of the boxes
correspond to the SNR value shown in each box where low values are cool colors
with purple representing the lowest values. The SNR values range from 0.0 to
2.0, indicating that 13CO2 is not detectable for a Neptune-like 100x solar
metallicity atmosphere for even the most ideal, artificial sub-Neptune.

###  3.3 Non-Detectability at Higher Spectral Resolution

We also simulated observations using JWST’s high-resolution G395H disperser.
The simulations revealed that our inability to distinguish 13CO2 from 12CO2 is
not limited by the PRISM modes’ lower resolution, but by the number of photons
received during the observation. In the high-resolution mode, the number of
photons per bin decreased, leading to increased noise that obscured the
spectral differences between 13CO2 and 12CO2.

###  3.4 Evaluation of Ground-based Observations

We also considered high-resolution ground-based observations of our targets.
The velocity of our proposed targets is not a limiting issue. However, the
cross-correlation technique will not be possible for temperate sub-Neptunes as
the contrast between planet and star is too small for current giant
telescopes. The SNR in the photon limited regime can be calculated as

$\text{SNR}_{\text{planet}}=\frac{\text{S}_{\text{p}}}{\text{S}_{*}}\text{SNR}_{\text{star}}\sqrt{\text{N}_{\text{lines}}}$

(Birkby, 2018). A coronagraph on a large ground-based telescope may allow for
low-contrast observations in the future. Currently though, JWST is the best
near-future instrument for measuring carbon dioxide isotopologues in the
atmospheres of temperate planets.

##  4 Discussion

Even if someday we can detect carbon fractionation via 13CO2, it will be
nearly impossible to prove that it is caused by life and not by another
process. Today, we do not even have a clear understanding of the composition
of sub-Neptune atmospheres. Much of the early observations with JWST will
simply focus on first assessing if small planets have atmospheres or not and
then on measuring their atmospheric composition.

###  4.1 The Challenge of Disentangling Abiotic and Biotic Isotope
Fractionation

A major complication of using isotopologues as biosignature gases is
disentangling abiotic and biotic isotope fractionation. While isotope
fractionation could be a strong indicator of life that is able to be detected
remotely with the right instrument, we need to understand the context to rule
out false positive detections (Neveu et al., 2018). The context includes both
a habitability assessment of a planet and our understanding of abiotic
fractionation processes. The magnitude of the fractionation alone will not be
enough to unambiguously disentangle different biotic and abiotic fractionation
processes.

On Earth, isotopic fractionation is measured by comparing the isotopic
composition of a biotic carbon reservoir against an inorganic carbon
reservoir. The composition of one isotope compared to another is not a
biosignature on its own–it must be compared to a baseline inorganic value.

####  4.1.1 Abiotic Carbon Fractionation

Carbon fractionation occurs abiotically through processes such as chemical
exchange reactions, photodissociation, gas release, and the kinetic isotope
effect (Quay et al., 1991; Woods & Willacy, 2009). One known planetary process
that fractionates carbon is volcanism (Mattey, 1991). The degassing of
basaltic magma enriches the melt in 12CO2, while enhancing the gas in 13CO2
(Mattey, 1991). The magnitude of this effect is only $\sim 2$‰(Mattey, 1991).
Our only example of a habitable planet (Earth) is subject to volcanic
activity. Thus, carbon fractionation through magma outgassing will likely
prove an important false positive that will need to be disentangled from
biotic fractionation.

Another possible cause of fractionation could be differences in bulk isotopic
composition between the remote exosystem and our own. If for instance, the
solar system formed in an area near intermediate-mass AGB stars, it would be
enriched in 13C (Kobayashi et al., 2011). Understanding the composition of the
baseline abiotic carbon reservoir is the key to being able to interpret
atmospheric measurements of 13CO2.

####  4.1.2 Using Carbon Fractionation via Methane to Rule Out False Positives

Detection of carbon fractionation in an exoplanetary atmosphere can only be
considered a sign of life if we have a full understanding of its context.
While biologically mediated fractionation of carbon dioxide through
photosynthesis is too subtle to be detectable, other carbon-bearing species
like CH4 or CO may prove more amenable for fractionation studies.

In contrast to our work assessing biologically fractionated carbon via CO2,
Molliere & Snellen (2019) suggested that metabolic carbon fractionation could
be measured by comparing the composition of 13C vs 12C in CO2 vs CH4. Isotopic
composition via CO2 would serve as the baseline inorganic carbon reservoir
while isotopic composition via CH4 would be considered the organic carbon
reservoir. Thus, an important application of our framework could be to assess
the detectability of carbon fractionation via methane. However, as the
spectral resolution required is too high for JWST and the contrast between
host star and temperate planet is too low for ground-based high-resolution
observations, the path forward to measure biologically driven isotope
fractionation seems bleak.

###  4.2 Metabolic Carbon Fractionation Pathways

Several metabolic processes are known to fractionate carbon, releasing waste
gases like CO2 and CH4 that can accumulate in the atmosphere. In the context
of a H2-dominated sub-Neptune, there are three potentially key metabolic
strategies that are capable of altering the atmospheric carbon isotopic ratio:
(1) hydrogenic photosynthesis, (2) methanogenesis, and (3) anaerobic oxidation
of methane or organic matter.

####  4.2.1 Hydrogenic Photosynthesis

Photosynthesis, or the conversion of light energy to chemical energy, is one
of the oldest and most fundamental energy-harnessing biochemical processes on
Earth. Photosynthesis is broadly accepted as likely to occur on other planets
with life (e.g., Seager et al., 2005; Kiang et al., 2007). Earlier work has
evaluated the detectability of the vegetation “red edge” and the byproducts of
photosynthesis, such as O2, along with its secondary products (Seager et al.,
2005; Kiang et al., 2007). Even if photosynthesis itself might be a cosmically
common phenomenon, life on other worlds might use different kinds of
photosynthesis than life on Earth. On Earth, oxygenic photosynthesis
fractionates CO2, but in a H${}_{2}-$dominated sub-Neptune atmosphere,
hydrogenic photosynthesis is the more likely form (Bains et al., 2014).

Hydrogenic photosynthesis uses CH4 instead of CO2 as a carbon source. Thus,
hydrogenic photosynthesis does not directly contribute to the atmospheric CO2
isotopic fractionation. However, it can lead to fractionation of CH4 and the
carbon isotopic fractionation of the produced organic matter (CH2O) through
the following reaction: CH4 \+ H2O $\rightarrow$ CH2O + 2H2. The substrates of
hydrogenic photosynthesis, CH4 and H2O, are readily available in the
atmospheres of sub-Neptunes as CH4 is expected to be the dominant form of
carbon and H2O the dominant form of oxygen. CO2, on the other hand, is likely
rare and as a result an unlikely substrate for photosynthesis. The product of
the hydrogenic photosynthesis, just like in oxygenic photosynthesis, is
organic matter (CH2O). Life preferentially uses the lighter 12C in reactions,
leading to a preferential accumulation of 12CH2O. Hydrogenic photosynthesis
could therefore indirectly lead to CO2 fractionation in sub-Neptune
atmospheres as the anaerobic oxidation of the produced 12CH2O organic matter
could in principle result in the release of more 12CO2.

####  4.2.2 Methanogenesis

Methanogenesis is another process known to cause carbon fractionation. When
organisms perform methanogenesis, they catalyze the reduction of CO2 to CH4
and release energy through the following reaction: CO2 \+
4H${}_{2}\rightarrow$ CH4 \+ 2H2O. The reduction of CO2 by H2 could be a
ubiquitous source of energy for life in a H2-rich atmosphere (Seager et al.,
2021). Methanogenesis can proceed even under conditions where only trace
amounts of CO2 are available, such as in the H2-dominated atmospheres of sub-
Neptunes (Bains et al., 2014). Therefore, life can yield enough energy
released by the reduction of CO2 to CH4 with small amounts of CO2 being
regenerated by photochemistry. If life preferentially acquires 12CO2 from the
atmosphere as a substrate for methanogenesis, then a potential for
biologically-driven CO2 isotopic fractionation exists as more 13CO2 will be
left in the atmosphere as more 12CH4 is produced.

####  4.2.3 Anaerobic Oxidation of Methane

The third possible metabolic strategy for life in a sub-Neptune aerial
biosphere is anaerobic oxidation of methane (AOM) or anaerobic oxidation of
organic matter (Timmers et al., 2017). The AOM process is a type of
respiration that oxidizes CH4 with sulfate, nitrate, nitrite, or metal oxides
for example:

$CH_{4}+4NO_{3}^{-}\rightarrow CO_{2}+4NO_{2}^{-}+2H_{2}O$

(Haroon et al., 2013). Methane and organic matter oxidation reactions are
possible in sub-Neptune atmosphere conditions where there is an abundance of
CH4. The potential challenges for AOM reactions in sub-Neptunes involve
insufficient abundance of non-volatile oxidants like sulfates, nitrates,
nitrites, or metals (Seager et al., 2021). AOM might be the source of
biologically fractionated CO2 where the preferentially released CO2 is the
lighter 12CO2 variant, if life efficiently acquires the light 12CH4 substrate
for AOM.

###  4.3 Carbon Isotopic Composition Measurements with Future Mission Concepts

We have also considered the feasibility of detecting CO2 isotopologues with
future space-based mission concepts. In order to distinguish CO2 isotopologues
in the atmospheres of sub-Neptunes, we need telescopes with apertures larger
than JWST. We estimate the required size of the telescopes using a simple
scaling relationship. The SNR is equal to the number of photons received on
the detector divided by the noise. In the best case scenario, the noise is
limited by the shot noise from the target star and is equal to the square root
of the number of photons. As the number of photons scales proportionally to
the square of a telescope’s diameter, the SNR scales linearly with telescope
aperture (SNR $\propto$ D). With our fiducial atmospheric composition of
100$\times$ solar and C/O=0.55, it will take a 20 m-class telescope to
distinguish carbon dioxide isotopologues in 25 transits even for a sub-Neptune
artificially placed around our closest M dwarf host star. If we instead
consider a low MMW atmosphere with similar molecular abundances to the upper
limits measured in K2-18 b (Benneke et al., 2019), it would take only a 10
m-class telescope to distinguish the two most abundant carbon dioxide
isotopologues in the atmosphere of TOI-1231 b. As of yet, there is no upcoming
space-based telescope of this size. However, the next generation giant ground-
based telescopes will be in the 30 to 40 m range.

###  4.4 The Future of Carbon Fractionation as a Biosignature Gas

The future of using carbon fractionation to assess signs of life on remote
worlds is not bright. Most importantly, baseline carbon fractionation values
for other exoplanetary systems are not known. In the solar system, carbon
fractionation is largely homogenized (Woods, 2009). Notably, despite Earth
being the only planet known to harbor photosynthetic life, its bulk carbon
fractionation does not stand out from the rest of the solar system. In
addition, planed and near-future instruments will be unable to measure subtle
changes to atmospheric fractionation caused by metabolic processes.
Isotopologue measurements for the next several decades should focus on
evaluating planetary processes rather than biologically mediated
fractionation. There are other more readily detectable biosignature gases for
missions like the JWST to focus on such as O2, O3, CH4, N2O, CH3Cl, and sulfur
gases (Schwieterman et al., 2018).

The search for life in gaseous exoplanet atmospheres is particularly
compelling because it offers the possibility of empirically testing
environmental requirements for the the origin of life (abiogenesis) and, in
particular, whether rocky planetary surfaces are required for abiogenesis.
While origin-of-life theories invoking droplets have been proposed, their
experimental study is limited and debated, and they generally invoke spray
originating from terrestrial surface interfaces (Donaldson et al., 2004; Nam
et al., 2017; Jacobs et al., 2019). Instead, most current theories of the
emergence of life on Earth invoke the presence of a surface. Surfaces are
invoked in prebiotic chemistry as a source of mineral reagents, catalysts, or
scaffolds (e.g., Corliss et al., 1981; Ferris, 2005; Kim et al., 2016; Adam et
al., 2018), redox disequilibrium through connection of a reducing interior to
an oxidizing fluid environment (Barge et al., 2017), microenvironments that
produce favorable local conditions for prebiotic chemistry not accessed in
global mean conditions (e.g., Ranjan et al., 2019; Toner & Catling, 2020), and
heterogenous reservoirs whose coupling can enable chemistry not possible in a
one-reservoir scenario (multi-pot syntheses; e.g., Ritson et al. 2018).
Detection of life on a gaseous exoplanet atmosphere would require extremely
stringent evidence that could outweigh, e.g., the prior belief in their
uninhabitability on the basis of experimentally motivated theories of the
origin of life to date (Catling et al., 2018; Seager et al., 2021). If such
evidence could be found, however, it would empirically demonstrate the
existence of a pathway to abiogenesis without surfaces, opening new vistas in
the study of prebiotic chemistry, so long as panspermic transfer from a
neighboring rocky body could be ruled out (Lingam & Loeb, 2017; Chen &
Kipping, 2018; Rimmer et al., 2021). Carbon fractionation of atmospheric CO2,
while promising in principle, is unfortunately practically unlikely to provide
such evidence; the search for robust gaseous exoplanet biosignatures
continues.

##  5 Conclusion

It is essential to evaluate which biosignature gases will prove the most
fruitful for future observations of exoplanet atmospheres and which will never
be detectable. We have developed a robust framework to test which, if any,
isotopologues will be detectable biosignature gases for signs of remote life.
Here, we applied our framework to carbon dioxide isotopologues to assess if
12CO2 and 13CO2 at Earth-like abundances could be distinguishable in the
atmospheres of temperate sub-Neptunes orbiting M dwarf stars with the upcoming
JWST. We selected carbon isotopes as metabolic processes preferentially use
12C over 13C. However, biological processes like photosynthesis drive subtle
changes to the carbon fractionation ratio. As a first step, we assessed if we
could distinguish between 12CO2 and 13CO2 at Earth-like abundances.

We found that we will be able to distinguish the presence of 13C vs 12C via
CO2 at Earth-like abundances in the atmospheres of temperate sub-Neptunes with
H2-dominated atmospheres using JWST, but only for the most favorable
atmospheric compositions and idealized targets. Thus, it is unlikely that
13CO2 will be measured in the atmosphere of a temperate sub-Neptune with JWST.
Furthermore, ground-based high spectral resolution instruments will not enable
isotopic detection in temperate sub-Neptune atmospheres due to the low
contrast between the M dwarf host star and cool planet. When we are able to
measure carbon fractionation in exoplanet atmospheres, our understanding of
the system’s context will be essential to prove if the observed fractionation
is a possible sign of life. Isotopologue measurements for the next decade
should focus on disentangling the physical processes that drive carbon
fractionation rather than trying to detect them as unambiguous biosignature
gases.

We would like to acknowledge Dr. Kaitlin Rasmussen for a productive
conversation about the feasibility of ground-based spectroscopy of CO2
isotopologues in the atmospheres of temperate sub-Neptunes.

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