# Large Interferometer For Exoplanets (_LIFE_): XII. The Detectability of
Capstone Biosignatures in the Mid-Infrared - Sniffing Exoplanetary Laughing
Gas and Methylated Halogens

Daniel Angerhausen ETH Zurich, Institute for Particle Physics & Astrophysics,
Wolfgang-Pauli-Str. 27, 8093 Zurich, Switzerland  National Center of
Competence in Research PlanetS, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
Daria Pidhorodetska Department of Earth and Planetary Sciences, University of
California, Riverside, CA, USA  Michaela Leung Department of Earth and
Planetary Sciences, University of California, Riverside, CA, USA  Janina
Hansen ETH Zurich, Institute for Particle Physics & Astrophysics, Wolfgang-
Pauli-Str. 27, 8093 Zurich, Switzerland  National Center of Competence in
Research PlanetS, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  Eleonora
Alei ETH Zurich, Institute for Particle Physics & Astrophysics, Wolfgang-
Pauli-Str. 27, 8093 Zurich, Switzerland  National Center of Competence in
Research PlanetS, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  NPP Fellow,
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Felix Dannert ETH
Zurich, Institute for Particle Physics & Astrophysics, Wolfgang-Pauli-Str. 27,
8093 Zurich, Switzerland  National Center of Competence in Research PlanetS,
Gesellschaftsstrasse 6, 3012 Bern, Switzerland  Jens Kammerer European
Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  Sascha P. Quanz ETH Zurich, Institute for Particle Physics &
Astrophysics, Wolfgang-Pauli-Str. 27, 8093 Zurich, Switzerland  National
Center of Competence in Research PlanetS, Gesellschaftsstrasse 6, 3012 Bern,
Switzerland  ETH Zurich, Department of Earth Sciences, Sonneggstrasse 5, 8092
Zurich, Switzerland  Edward W. Schwieterman Department of Earth and Planetary
Sciences, University of California, Riverside, CA, USA  Blue Marble Space
Institute of Science, Seattle, WA, 98154, USA  https://life-space-mission.com/

###### Abstract

This study aims to identify exemplary science cases for observing N2O, CH3Cl,
and CH3Br in exoplanet atmospheres at abundances consistent with biogenic
production using a space-based mid-infrared nulling interferometric
observatory, such as the _LIFE_ (Large Interferometer For Exoplanets) mission
concept. We use a set of scenarios derived from chemical kinetics models that
simulate the atmospheric response of varied levels of biogenic production of
N2O, CH3Cl and CH3Br in O2-rich terrestrial planet atmospheres to produce
forward models for our LIFEsim observation simulator software. In addition we
demonstrate the connection to retrievals for selected cases. We use the
results to derive observation times needed for the detection of these
scenarios and apply them to define science requirements for the mission. Our
analysis shows that in order to detect relevant abundances with a mission like
_LIFE_ in it’s current baseline setup, we require: (i) only a few days of
observation time for certain very near-by “Golden Target” scenarios, which
also motivate future studies of “spectral-temporal” observations (ii) $\sim$10
days in certain standard scenarios such as temperate, terrestrial planets
around M star hosts at 5 pc, (iii) $\sim$50 - 100 days in the most challenging
but still feasible cases, such as an Earth twin at 5 pc. A few cases for very
low fluxes around specific host stars are not detectable. In summary,
abundances of these capstone biosignatures are detectable at plausible
biological production fluxes for most cases examined and for a significant
number of potential targets.

Astrobiology (74); Exoplanet atmospheres (487); Exoplanets (498); Habitable
planets (695); Nitrous oxide (1114); Biosignatures (2018), Direct-detection
interferometry (386)

††software: LIFEsim (Dannert et al., 2022), petitRT (Mollière et al., 2019),
Atmos (https://github.com/ VirtualPlanetaryLaboratory/atmos; Arney et al.
2016), SMART (Meadows & Crisp 1996), Planetary Spectrum Generator
(https://psg.gsfc.nasa. gov/; Villanueva et al. 2018)

##  1 Introduction

Nitrous oxide (N2O) and methylated halogens (e.g., CH3Cl, CH3Br) are part of
the group of molecules that have been proposed as potential
biosignatures111For a more general and detailed introduction about
biosignatures we refer to Des Marais et al. (2002); Seager et al. (2016);
Schwieterman et al. (2018); Krissansen-Totton et al. (2018) and references
therein. for detecting life in exoplanetary contexts (see e.g., Schwieterman
et al., 2022; Leung et al., 2022). A large inferred flux of these biogenic
gases is most consistent with a productive global photosynthetic biosphere,
which could be revealed in tandem with O3. None of these three gases are
produced in chemical equilibrium, which reduces the false positives potential
when compared to other potential biosignatures that do have equilibrium
sources (e.g., CH4, PH3, NH3). N2O is produced by certain microbes during
nitrification and denitrification processes, which are common in many
environments on Earth. Similarly, CH3X gases are produced by marine microbes
and terrestrial plants. The short photochemical lifetimes of these gases
require large production rates to sustain significant (or detectable)
abundances. The detection of nitrous oxide or methylated halogens in the
atmosphere of a terrestrial, temperate exoplanet could therefore indicate the
presence of fluxes that can only be explained by a global biosphere of
(microbial) life producing it. In the next decades our community will start to
to investigate the atmospheric properties for a statistically significant,
comprehensive and consistent, large observational set of rocky, warm
exoplanets (see e.g., Fujii et al., 2018). First steps, albeit with a focus on
larger planets, in this direction will be made with selected or proposed
ground-based projects (see e.g., Snellen et al., 2013; Lovis et al., 2017;
Ben-Ami et al., 2018) and space-based missions such as the JWST (Greene et
al., 2016; Morley et al., 2017), Roman (Kasdin et al., 2020) or the
Atmospheric Remote-sensing Infrared Exoplanet Large-survey (Ariel, Tinetti et
al., 2018). The NASA Habitable Worlds Observatory (HWO) is a proposed
flagship-class mission that aims to study planets beyond our solar system and
search for signs of habitability and life probing the exoplanets in reflected
stellar light. The HWO will utilize a combination of spectroscopic and imaging
techniques to explore the atmospheres and surfaces of temperate and rocky
exoplanets (National Academies of Sciences & Medicine, 2021) 222HWO is based
on the studies for the Large UV/Optical/IR Surveyor (LUVOIR, The LUVOIR Team,
2019) , and the Habitable Exoplanet Observatory (HabEx, Gaudi et al., 2020).

An alternative approach to the coronagrapy-based HWO concept is to cancel out
the stellar contribution and separate the thermal emission of the planet using
a nulling interferometer. The Large Interferometer for Exoplanets (_LIFE_) is
a European-lead international project with the goal to consolidate various
efforts and define a road map that leads to the launch of such a space-based
mid-infrared nulling interferometer (Quanz et al., 2018, 2019, 2022). This
mission will be designed with the capability to investigate the atmospheric
properties of a large sample of (primarily) terrestrial exoplanets. LIFE
directly addresses the scientific theme of detecting and characterizing
temperate exoplanets in the MIR, which was recommended with ’highest
scientific priority’ by ESA’s Voyage 2050 Senior Committee report
333https://www.cosmos.esa.int/web/voyage-2050 as a candidate topic for a
future L-class mission in the ESA Science Programme. Quanz et al. (2022);
Dannert et al. (2022) and Kammerer et al. (2022) discussed the detection yield
of a mission like LIFE. Konrad et al. (2022) and Alei et al. (2022b)
critically checked the ability of the proposed mission to characterize an
Earth-twin at 10 pc and Earth analogs over its geologic history. Hansen et al.
(2022, 2023) compared various technical implementations of the interferometric
setup, while Matsuo et al. (2023) explored phase-space synthesis decomposition
(PSSD) to potentially improve the sensitivity of a mission like LIFE. Konrad
et al. (2023) analysed the detectability of a Venus twin exoplanet and in
particular how clouds impact the spectral retrieval process. The observability
of exocomets with LIFE was discussed in Janson et al. (2023). Carrión-González
et al. (2023) studied how LIFE can detect of currently already known
exoplanets and how it can leverage synergies HWO. Lastly Angerhausen et al.
(2023) reported on the detectability of phosphine (PH3) in different
exoplanetary scenarios with LIFE. Here we explore the detectability of nitrous
oxide and methylated halogens with a mid-infrared space nulling interferometer
observatory like LIFE. In section 2 we introduce the exoplanetary atmospheric
chemistry models and software used to simulate the LIFE observations. Section
3 summarizes the results of our feasibility study of various observational
scenarios. In section 4 we discuss these results and their implications and
conclude with our main findings.

##  2 Models and Simulations

###  2.1 Photochemical Modelling

In this study, we focus on warm, terrestrial, “Earth-like” planets. To
maintain consistency, simplify reproducibility and to focus solely on
examining the impact of changing surface molecular fluxes for the respective
gases, we assume an Earth-like bulk atmosphere (78$\%$ N2, 21$\%$ O2 by
volume) along with the Earth’s temperature-pressure profile, which has a
globally averaged surface temperature of 288 K. We also assume a planetary
radius and surface gravity identical to that of Earth (R=6371 km; g=9.8 m
s-1). We provide further details in the subsections below and the original
sources for these atmospheric simulations (Schwieterman et al., 2022; Leung et
al., 2022).

####  2.1.1 Nitrous Oxide Atmospheres

N2O is produced by life as an intermediate product of biological
denitrification, the transformation of NO${}_{3}^{-}$ to N2 gas through
multiple steps, which is an essential component of the biological nitrogen
cycle on Earth. N2O is also produced by other microbial metabolisms including
the direct oxidation of ammonia by certain bacteria and archaea (Prosser &
Nicol, 2012). The modern biological production rate of N2O is $\approx$0.4
teramole per year ($10^{12}$ moles per year; Tmol/yr), which includes both
marine and terrestrial sources (Tian et al., 2020) and results in a modern
atmospheric N2O concentration of $\approx$330 ppb (parts-per-billion).
However, the biological N2O flux may have varied greatly through geological
time. For example, the H2S-rich Proterozoic (2.5 to 0.541 Ga) oceans would
have sharply limited the availability of copper, an essential component of the
nitrous oxide reductase enzyme that facilitates the last step in the
denitrification cycle from N2O to N2 (Buick, 2007). In the case of severe
limitation of this enzyme (or its failure to evolve on an inhabited
exoplanet), the N2O flux to the atmosphere would be limited instead by the
denitrification flux of the biosphere, which is substantially greater than the
modern N2O flux. Photolysis and reactions with radical species transforms
atmospheric N2O into N2 and O2 abiotically with an average lifetime of
$\approx$120 years on Earth (Prather et al., 2015), though this would vary for
other host stars and atmospheric compositions (e.g., O2 concentrations). There
are no substantial surface sinks for N2O once it is released into the
atmosphere.

Schwieterman et al. (2022) used a biogeochemical model and a photochemical
model to circumscribe the plausible envelope of N2O concentrations on Earth-
like exoplanets with microbial biospheres. We refer to that work for a more
expansive discussion of the biological and abiotic sources and sinks of N2O.
For the purposes of this work, we are interested what range of N2O production
fluxes can result in detectable N2O signatures in the directly imaged thermal
infrared spectra of terrestrial exoplanets with the understanding that
detectability at lower production rates enhances the probability such a
signature may be found.

For the cases presented here, we chose those results with Earth’s modern O2
concentration (21%) and N2O fluxes corresponding to biological production
levels of (i) 1 teramole per year (equivalently, 3.7$\times$109 molecules cm-2
s-1), (ii) 10 Tmol/yr (3.7$\times$1010 molecules cm-2 s-1), and (iii) 100
Tmol/yr (3.7$\times$1011 molecules cm-2 s-1). These values correspond to
scenarios where (i) 5-10% of Earth’s denitrification flux is released as N2O,
(ii) 50%-100% of Earth’s total denitrification flux is released as N2O, and
(iii) 50-100% of the denitrification flux of an Earth-like planet with twice
the nutrient availability of Earth’s oceans is released as N2O. These flux
levels were obtained via biogeochemical modeling as described in Section 2 of
Schwieterman et al. (2022). As points of comparison, the 100 Tmol/yr case
corresponds to an N2O flux about three times the modern CH4 flux and is
similar to the PH3 flux required to generate a detectable PH3 signature on a
CO2-rich planet orbiting an M dwarf star (Sousa-Silva et al., 2020, see their
Table 3).

The chemical profiles for our N2O detectability analyses were sourced from
Schwieterman et al. (2022), which describes their generation in detail.
Briefly, these abundance profiles were calculated with the photochemical model
component of the Atmos code (Arney et al.,
2016)444https://github.com/VirtualPlanetaryLaboratory/atmos. The photochemical
model is based originally on the work of Kasting et al. (1979) but has
undergone numerous subsequent modifications and upgrades (Pavlov et al., 2001;
Zahnle et al., 2006; Arney et al., 2017; Lincowski et al., 2018). The model
template used here includes 50 species and 238 photochemical reactions,
including all major species in Earth’s modern atmosphere and the dominant
photochemical destruction channels for N2O. This version is appropriate for
modeling atmospheres with substantial free oxygen concentrations (pO2 $\geq$
1% present atmospheric level; PAL) and was previously used to model possible
Earth-like atmospheric scenarios for Proxima Centauri b (Meadows et al.,
2018a). The simulated atmosphere is divided into 200 layers of 0.5 km
thickness with a maximum altitude of 100 km. The model incorporated
recommended H2O cross-sections and reaction rate corrections from Ranjan et
al. (2020). We assumed the modern Earth’s temperature-pressure profile for all
simulations, to isolate the unique impact of different N2O fluxes
(abundances). The chemical mixing ratio profiles were otherwise calculated
self-consistently with respect to varied stellar spectra and N2O flux levels.
These chemical profiles were generated assuming host star spectra identical to
those of the Sun (Thuillier et al., 2004), the K6V star HD 85512 (France et
al., 2016; Loyd et al., 2016), the M5.5 Ve star Proxima Centauri (Loyd et al.,
2018; Peacock et al., 2020; Shkolnik & Barman, 2014), and the ultracool dwarf
(M8V) star TRAPPIST-1 (Peacock et al., 2019). See Appendix C and Table 13 for
the ground-level N2O mixing ratios that correspond to each flux and host star
combination.

We briefly note here that all photochemical simulations were done with 1D
models using key assumptions (such as average solar zenith angle) most
appropriate for rapidly rotating planets, and thus do not take into account
circulation impacts from synchronous rotation, which would be likely for
habitable zone planets orbiting M dwarf stars. However, Chen et al. (2018)
showed that the differences between full 3D and 1D predictions for abundant
biosignature gases like N2O and CH4 differ by only $\sim$20$\%$, which is
relatively small given the uncertainty from other intrinsic and extrinsic
factors such as bulk atmospheric composition, biosignature gas production
rate, and distance from the host star. Schwieterman et al. (2022)
quantitatively examine the sensitivity of N2O flux-abundance relationships to
other 1D model assumptions (such as vertical mixing parameterizations and
background N2 pressure) in their Section 5.5, finding small or modest effects,
and we direct the reader there for more details. We emphasize the universe of
potential atmospheric compositions and planetary parameters for habitable
worlds is much greater than assessed here.

####  2.1.2 Methylated Halogen Atmospheres

The chemical profiles of Earth-twin planets with various levels of biological
CH3Cl and CH3Br production were sourced from Leung et al. (2022) who
determined the abundance using the photochemical model part of the Atmos code
(Arney et al., 2016). In contrast to the version used for the N2O calculations
described above, this version of the photochemical model incorporated
additional reactions to account for the inclusion of Cl and Br chemistry.
There are a total of 89 unique kinetically active chemical species and 413
reactions in this version. To compute CH3X flux-abundance calculations, we
adopted the same stellar spectra as described above for HD 85512 (K6V),
Proxima Centauri (M5.5 Ve), and TRAPPIST-1 (M8V). We additionally use the M3.5
Ve star AD Leo with stellar spectra from the Atmos library, which was
ultimately sourced from (Segura et al., 2005). We do not consider G dwarf
(Sun-like) or F dwarf host stars because the atmospheric accumulation of CH3
gases is spectrally insignificant for these scenarios even at the largest
plausible fluxes (Leung et al., 2022).

CH3Cl and CH3Br fluxes were independently and jointly co-varied according to
factors of 1, 10, 100, and 1000 times the modern flux of each species. In
other words, we varied: CH3Cl while other gas fluxes are held constant (cases
labeled “CH3Cl”), CH3Br while other gas fluxes are held constant (cases
labeled “CH3Br”), and both CH3Cl+CH3Br together, by the same factor based on
their original Earth-like fluxes (cases labeled “CH3X”). For more details see
Appendix C, Table 14. Importantly, even the highest flux scenarios are equal
to or less than flux of these species present in productive local environments
(Leung et al., 2022). Since the methylation process is often an adaptation
used for environmental detoxification (Jia et al., 2013), the gas fluxes
produced can be directly related to the abundance of metals and metalloids in
the local environment. A higher supply of substrates (Br, Cl, etc.) could
generate higher fluxes. Since the highest fluxes are produced at wetlands,
salt marshes, and other marine/terrestrial cross over ecosystems (Tait &
Moore, 1995; Yang et al., 2022), a planet with greater productivity may simply
require a greater percentage of these environments or accelerated weathering
processes that concentrate halogens and other heavy ions (Fuge, 1988). Highly
productive salt marsh environments cover only .00017 % of the Earth’s surface,
so our most productive case would only require 1.7% total surface coverage,
equivalent to 5% of vegetation present today (Murray et al., 2022; Zhu et al.,
2016). The actual coverage necessary may be higher or lower depending on the
uniformity of production across salt marsh environments. Alternative
evolutionary paths such as widespread radiation of the methylation adaptation
could yield higher global productivity. Furthermore, the greatest atmospheric
loss process is through reaction with OH, which sizably decreases in abundance
for later star types (Segura et al., 2005). For targets such as TRAPPIST-1,
this bestows a considerable advantage in sustaining atmospheric buildup and
generating potentially detectable atmospheric features. For further discussion
of methylated biosignature candidate production and accumulation, see Leung et
al. (2022).

###  2.2 Spectral Simulations

####  2.2.1 PSG

Schwieterman et al. (2022) used the Planetary Spectrum Generator (PSG) to
calculate the radiance (thermal emission) spectra for the Earth spectra with
varying N2O fluxes. PSG is a highly flexible and publicly available radiative
tool used to simulate the remote spectral observables of planetary objects
across a full range of viewing geometries and distances (Villanueva et al.,
2018, 2022). PSG uses the HITRAN 2020 database for its input infrared
opacities (Gordon et al., 2022). Planetary spectra were produced from 5-20
$\mu$m and are averaged 50% clear sky and 50% cloud scenarios. The clouds
consisted of equal fractions liquid water cloud and cirrus cloud particles.

####  2.2.2 SMART

Leung et al. (2022) used the Spectral Mapping and Radiative Transfer code
(SMART; Meadows & Crisp, 1996) to simulate emission spectra. This model has an
extensive history of use for both solar system and exoplanet objects and has
previously been used to simulate biosignatures such as O2 and organic sulfur
compounds (Robinson et al., 2011; Arney et al., 2014; Meadows et al., 2018b;
Domagal-Goldman et al., 2011). As input, SMART uses the Line-by-Line
Absorption Coefficients code (LBLABC) which are calculated based on the HITRAN
2020 linelists (Gordon et al., 2022). For this application, 50% cloudy spectra
with 25% cirrus and 25% stratocumulus clouds were modeled.

###  2.3 LIFEsim observation and population simulations

LIFEsim is a state of the art simulator software specifically designed for the
Large Interferometer For Exoplanets. As a tool it provides accurate and
reliable simulations of the interferometric measurement processes involved in
the operation of LIFE. With LIFEsim, users can explore the capabilities of
LIFE and gain insights into the parameter space accessible to LIFE for the
detection and characterization of exoplanets.

In this work we used two features of LIFEsim:

  * •

a module based on the population synthesis tool P-Pop (Kammerer & Quanz, 2018)
that simulates random exoplanetary systems around an input catalog of target
stars based on current exoplanet statistics, e.g., from transit or radial
velocity surveys. LIFEsim can then compute the detectability of each
individual simulated planet and derive an optimized observing sequence for the
stellar sample. This can be used to compute detection yields in the blind
(target) search detection phase of LIFE (see Quanz et al., 2022; Dannert et
al., 2022; Kammerer et al., 2022). In section 3.1 we used this to calculate
the number of potential targets available for the analysis discussed here. The
assumed mission time available for the blind search phase (2.5 yrs, 20%
overheads) is optimally distributed among the synthetic planetary systems to
optimize the number of planets detected in the HZ.

  * •

a simulator for individual spectroscopic observations in LIFE’s
characterization phase which is used for the feasibility study in the
following sections following the same approach as Angerhausen et al. (2023).

LIFEsim incorporates astrophysical noise sources such as stellar leakage and
thermal emission from local zodiacal and exo-zodiacal dust. While only
fundamental photon noise is considered in this study, the software is also
flexible to accommodate instrumental noise terms in the future. LIFEsim offers
an accessible way to predict the expected SNR of future observations based on
various instrument and target parameters (see Dannert et al., 2022, for more
details) .

Table 1: Overview of simulation parameters used in LIFEsim. These are the same standard values as e.g. used in Quanz et al. (2022) or Angerhausen et al. (2023) Parameter | Value
---|---
Quantum efficiency | 0.7
Throughput | 0.05
Minimum Wavelength | 4 $\mu$m
Maximum Wavelength | 18.5 $\mu$m
Spectral Resolution | 50
Interferometric Baseline | 10-100 m
Apertures Diameter | 2m
Exozodi | 3x local zodi

Following the same approach as in Angerhausen et al. (2023) we used LIFEsim to
produce synthetic observations of the outlined exoplanet cases with different
flux levels of the discussed species and also without them being present in
their atmospheres. For the presented output spectra, LIFEsim is configured
with the current LIFE “baseline” setup with four apertures of 2 m diameter
each, a broadband wavelength range of 4-18.5 $\mu$m, a throughput of 5
percent, and a spectral resolution of $R=50$. While the detection phase
simulation sampled over a distribution of exozodi levels, we assume an exo-
zodi level of 3 times the local zodi density for the characterization
observations (following the results from the HOSTS survey for the expected
median level of emission in Ertel et al., 2020) and a nulling baseline setup
between 10 and 100 m 555Here we assume that the planets are known from other
surveys or detected in the LIFE detection phase, so that we can optimize the
baselines for each case. (see Table 1). In section 4.3 we present a short
analysis of the impact that changes in this setup have for the dectectability
of selected cases.

##  3 Results

###  3.1 Predicted Distance Distribution of HZ Planets around M and FGK-type
stars detectable with LIFE

Figure 1: Distance distribution of HZ planet populations around M and FGK-type
stars detectable with LIFE in the current baseline setup (see Table 1). Left:
Detection yield predictions for planets around M-type stars with an underlying
AFGKM exoplanet population following occurrence rate estimates from NASA’s
ExoPaG SAG13 (Kopparapu et al., 2018) and Dressing & Charbonneau (2015).
Right: Detection yield predictions around FGK-type stars with an underlying
FGK exoplanet population based on occurence rates from Bryson et al. (2021).
We differentiate between three HZ definitions: optimistic (opt) HZ,
conservative (con) HZ and exo-Earth candidates (EECs). The bars show the
predicted median planet yields and 1-$\mathrm{\sigma}$ uncertainties derived
from the Monte Carlo simulations.

As a first step in our study we identify how many planets we would encounter
in our survey for this analysis and at what typical distances from the solar
system their host stars appear. Therefore we used the LIFEsim population part
to estimate the distance distribution of habitable zone (HZ) planets with
radii between 0.5 and 1.5 $R_{\earth}$ around M and FGK-type stars within 20
pc of the Sun that are detectable with LIFE. For the sake of comparability to
previous studies, our yield predictions were based on planet populations
generated for Quanz et al. (2022) and Kammerer et al. (2022) respectively.

Hence, we note that the number of planets around M and FGK-type stars were
calculated in two separate simulations, (1) optimizing on maximum yield of HZ
planets in general using a synthetic planet populations around a sample of
AFGKM-type and (2) optimizing on number of HZ planets around FGK stars only
using a subsample of FGK-type host stars within our target database (Quanz et
al., 2022).

These populations were derived from two sets of rocky planet occurrence rate
estimates: (1) Similar to Quanz et al. (2022), occurrence rates from NASA’s
ExoPaG SAG13 (Kopparapu et al., 2018) were used for AFGK-type stars with
effective temperatures between 3940-9700 K and results from Dressing &
Charbonneau (2015) were applied to M-type stars with effective temperatures
between 2440-3800 K. (2) As in Kammerer et al. (2022), exoplanet occurrence
rate estimates from Bryson et al. (2021), based on Kepler DR25 planet catalog
data (Thompson et al., 2018) and Gaia-based stellar properties (Gaia
Collaboration et al., 2018), were used to compute separate planet yield
predictions around a subsample of FGK-type stars with effective temperatures
between 3940-7220 K. In comparison to estimates from NASA’s ExoPaG SAG13
(Kopparapu et al., 2018), planet occurrence rates in Bryson et al. (2021)
cover the entire parameter range of the optimistic HZ around early-type stars.
Here, we used the model 1 hab2 stars high bound scenario from Bryson et al.
(2021). We focused on model 1 because it considers more parameters to model
the underlying planet population, including the stellar effective temperature.
Moreover, the hab2 stars sample is based on a larger number of planet
candidates and a wider range of stellar effective temperatures. Finally, high
bound is considering a more optimistic extrapolation of the Kepler occurrence
rates beyond orbital periods of 500 days for which completeness
characterization is not available in Kepler DR25 (Thompson et al., 2018), in
which the completeness beyond 500 days is assumed to be zero. For further
details about the planet occurrence rate model, we refer the reader to Bryson
et al. (2021). Based on these occurrence rates, (1) 500 and (2) 1000 synthetic
planet populations were generated around each star in our target sample (Quanz
et al., 2022) with the population synthesis tool P-Pop (Kammerer & Quanz,
2018). We associated all planetary systems with circular orbits which were
uniformly distributed on the sphere. A multi-planet stability criterion was
assumed to have a negligible impact on the derived yield estimates. For
further details see Kammerer et al. (2022). By averaging over a multitude of
Monte Carlo realizations, we marginalized over different population properties
such as number of planets per simulated universe, exozodiacal dust levels as
well as orbital parameters and with this are able account for uncertainties in
the underlying occurrence rate model.

For retrieving the integration time required to detect each planet in the
synthetic planet populations, we simulated photon noise from all major
astrophysical noise sources with the observation simulation tool LIFEsim
(Dannert et al., 2022). The observation time was distributed such that the
number of planets in the HZ around their respective host stars was optimized.
Since instrumental noise is not considered in the current implementation of
LIFEsim (Dannert et al., in prep), we assumed a conservatively high signal-to-
noise ratio (SNR) of 7 integrated over the full wavelength range, partly to
also leave some margin for currently unaccounted instrumental errors. We
assigned each planetary system an exozodiacal dust level randomly drawn from
the nominal exozodi level distribution with a median of $\sim$ 3 zodi
according to results from the HOSTS survey (Ertel et al., 2018, 2020). Since
Kammerer et al. (2022) previously showed the planet yield to be largely
independent of the interferometric baseline length optimization scheme, we
chose a baseline length optimization for the center of the optimistic HZ. We
assumed a reference implementation of LIFE mission parameters corresponding to
an aperture size of $D$ = 2 m, throughput of 5% and a wavelength coverage of
$\lambda$ = 4-18.5 $\mathrm{\mu m}$. Other adopted mission specifications
correspond to the descriptions in Quanz et al. (2022). We compared predicted
planet yields for three different HZ definitions: planets located within the
optimistic HZ, within the conservative HZ and exo-Earth candidates (EEC). For
incident stellar flux and planetary radii limits of the respective HZ models
see Kopparapu et al. (2014) and Stark et al. (2019). The derived distance
distributions of detectable HZ planets around M and FGK-type stars are shown
in Figure 1.

In summary we find that we will have a typical sample of 15-20 HZ planets at
distances less than 6 pc. This motivates and justifies the choice of our
examples at 5 pc. These would be the typical distance for HZ planets around
late type stars and the case for a few best targets around earlier types.

###  3.2 Detectability of N2O

We modelled the detectability of N2O for a set of observation times of 10
days, 50 days and 100 days using the LIFE baseline setup shown in Table 1.
Based on our experience from previous LIFE studies (e.g. Konrad et al., 2022;
Alei et al., 2022b; Angerhausen et al., 2023) the 10 days case represents a
relatively short (potentially preliminary) characterization observation that
can be conducted for a larger sample of targets, 50 days represent a more
thorough observation and 100 days will be the deepest characterization
observation for only the most interesting/promising targets for LIFE. In
section 4.3 we also vary the integration times and explore setups beyond the
LIFE baseline. It is worthwhile to mention that these numbers may correspond
to a significant fraction of the orbital periods of the considered planets,
and in some cases they even clearly exceed them. Here we assume that the
planet signal is stationary in LIFEsim and that we can add the signal of
multiple visits without significantly increasing the noise contributions.

For all simulated observations we calculated two metrics for the detectability
of the discussed cases: the maximum difference in a single spectral line
(usually in the absorption band of the feature in question) in units of the
respective sensitivity in that channel and a bandpass-integrated SNR defined
as

$SNR=\sqrt{\Sigma_{i=1}^{n}(\frac{\Delta y_{i}}{\sigma(y_{i})})^{2}}$

where $\Delta y_{i}$ is the difference between the two spectra (one spectrum
containing the species and the other that does not) in each of the n spectral
bins and $\sigma(y_{i})$ is the LIFE sensitivity the respective bin. This
assumes independence between the bins and was used in a similar manner in e.g.
Lustig-Yaeger et al. (2019) or Bixel & Apai (2021). As a rule of thumb we
assume a case is observable (i.e. the feature distiguishable) if the band-
integrated SNR is above $5-10$ and the single line sigma above 3 (more on the
justification of these number in section 3.4, where we compare those to some
exemplary full retrievals).

Figure 2: Detectability of various fluxes of N2O in the emission spectrum of
an Earth-like planet around a (from top left to bottom right:) Sun-like, K6V,
Proxima Centauri type and Trappist-like star at 5pc, after 50 days of
observation with LIFE.Top: planet flux for atmospheres with and without N2O .
The grey area represents the 1-$\sigma$ sensitivity; the dark grey error bars
show an individual simulated observation. Bottom: Statistical significance of
the detected differences between an atmospheric models with and without N2O.
For the Sun-like case the main contribution to the detectability is in the
16-18 $\mu m$ band. For the later type star cases the differences especially
in the 8-9 $\mu m$ (see also discussion in Section 4.1.

####  3.2.1 Sun-like G star

The results for an Earth-like planet orbiting a Sun-like star at 5 pc distance
are listed in Table 2 and shown in Figure 2 for a 50 day observation (more
cases for 10 and 100 days are shown in Appendix B.1 Figures 14 and 15 ). In
these figures (also for the other N2O cases in sections 3.2.2 to 3.2.4) the
top panel shows the planet flux for atmospheres with and without N2O and the
grey area represents the 1-$\sigma$ sensitivity calculated with LIFEsim while
the dark grey error bars show an individual simulated observation. The bottom
panel analyses the statistical significance of the detected differences
between an atmospheric models with and without N2O. Our analysis shows that
the 100 Tmol/yr case is likely observable already after 10 days (with SNR of
6.6/3.3 in our two metrics), while the 10 Tmol/yr model seems to become
observable around or slightly after day 50. The 1 Tmol/yr is beyond our
sensitivity , only reaching SNRs of 2.1/1.3 even for integration times of 100
days. Noteworthy here is that this detection is driven by the longer (16-18
$\mu$m) wavelength bands of N2O.

Table 2: Modelled SNR ratios for various intergration times and different fluxes of N2O at 5 pc Sun like star Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1 $\frac{Tmol}{yr}$ N2O | 0.7 | 0.4
10 | 10 $\frac{Tmol}{yr}$ N2O | 2.3 | 1.2
10 | 100 $\frac{Tmol}{yr}$ N2O | 6.6 | 3.3
50 | 1 $\frac{Tmol}{yr}$ N2O | 1.5 | 0.9
50 | 10 $\frac{Tmol}{yr}$ N2O | 5.1 | 2.7
50 | 100 $\frac{Tmol}{yr}$ N2O | 14.7 | 7.5
100 | 1 $\frac{Tmol}{yr}$ N2O | 2.1 | 1.3
100 | 10 $\frac{Tmol}{yr}$ N2O | 7.2 | 3.8
100 | 100 $\frac{Tmol}{yr}$ N2O | 20.7 | 10.6

This prototypical science case of an Earth twin scenario with these additional
fluxes will be discussed in more detail in sections 3.4 and 4.3 where we use
these for exemplary retrievals and derive consequences for the current mission
design in the context of science and technology requirements.

####  3.2.2 Proxima Centauri type star

The results for an Earth-like planet orbiting a M5.5 Ve Proxima Centauri type
star at 5 pc distance are listed in Table 3 and shown in Figure 2 for a 50 day
observation (more cases simulating 10 and 100 days of integration time shown
in Appendix B.1, Figures 14 and 15). In section 4.2 we discuss the case for a
planet orbiting Proxima Centauri at its actual distance of 1.3 pc as an
example for a “golden target” that allows very detailed, potentially even time
resolved LIFE observations. For this scenario the 100 as well as the 10
Tmol/yr case are detectable in the 10 day simulations with SNRs consistently
above 5, while the 1 Tmol/yr seems to only barely touch the detection
threshold after 100 days (with SNRs of 4.3/3.0). This case is one of the best
observable ones in this study. In comparison to the previous case, here the
shorter (8-10 $\mu$m) wavelength bands of N2O contribute the most to the
bandintegrated SNR (see Section 4.1).

Table 3: Modelled SNR ratios for various integration times and different fluxes of N2O at 5 pc Proxima Centauri like star Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1 $\frac{Tmol}{yr}$ N2O | 1.3 | 1.0
10 | 10 $\frac{Tmol}{yr}$ N2O | 7.4 | 5.2
10 | 100 $\frac{Tmol}{yr}$ N2O | 18.3 | 11.1
50 | 1 $\frac{Tmol}{yr}$ N2O | 3.0 | 2.2
50 | 10 $\frac{Tmol}{yr}$ N2O | 16.5 | 11.6
50 | 100 $\frac{Tmol}{yr}$ N2O | 40.9 | 24.8
100 | 1 $\frac{Tmol}{yr}$ N2O | 4.3 | 3.0
100 | 10 $\frac{Tmol}{yr}$ N2O | 23.4 | 16.4
100 | 100 $\frac{Tmol}{yr}$ N2O | 57.9 | 35.0

####  3.2.3 K6V

The results for an Earth-like planet orbiting a K6V star at 5 pc distance are
listed in Table 4 and shown in Figure 2 for a 50 day observation (more cases
simulating 10 and 100 days of integration time are shown in Appendix B.1,
Figures 14 and 15). The results are very similar to and even slightly more
significant than the Proxima Centauri type case. Once again the 100 and 10
Tmol/yr cases are detectable in the 10 day simulations reaching SNR of over
10/5 in our two metrics. The 1 Tmol/yr case crosses the detection threshold
with an SNR of 8.1/3.7 at around 50 days.

Table 4: Modelled SNR ratios for various integration times and different fluxes of N2O at 5 pc K6V star Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1 $\frac{Tmol}{yr}$ N2O | 3.6 | 1.7
10 | 10 $\frac{Tmol}{yr}$ N2O | 10.8 | 5.1
10 | 100 $\frac{Tmol}{yr}$ N2O | 15.0 | 6.4
50 | 1 $\frac{Tmol}{yr}$ N2O | 8.1 | 3.7
50 | 10 $\frac{Tmol}{yr}$ N2O | 24.1 | 11.4
50 | 100 $\frac{Tmol}{yr}$ N2O | 33.6 | 14.3
100 | 1 $\frac{Tmol}{yr}$ N2O | 11.5 | 5.3
100 | 10 $\frac{Tmol}{yr}$ N2O | 34.1 | 16.1
100 | 100 $\frac{Tmol}{yr}$ N2O | 47.5 | 20.3

####  3.2.4 TRAPPIST-1 like star

The results for an Earth-like planet orbiting a TRAPPIST-1 like star at 5 pc
distance are listed in Table 5 and shown in Figure 2 for a 50 day observation
(more cases simulating 10 and 100 days of integration time are shown in
Appendix B.1, Figures 14 and 15). Similar to the above cases for the K6V and
Proxima Centauri type host stars, the 100 and 10 Tmol/yr case cross the
detection threshold in the 10 day simulations with the SNR metrics at 4.8/9.7
and 3.4/6.1 respectively. The 1 Tmol/yr case only seems on the edge of
detectability even after 100 days reaching bandintegrated SNR of 3.0.

Table 5: Modelled SNR ratios for various integration times and different fluxes of N2O at 5 pc TRAPPIST-1 like star Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1 $\frac{Tmol}{yr}$ N2O | 0.9 | 0.7
10 | 10 $\frac{Tmol}{yr}$ N2O | 4.8 | 3.4
10 | 100 $\frac{Tmol}{yr}$ N2O | 9.7 | 6.1
50 | 1 $\frac{Tmol}{yr}$ N2O | 2.1 | 1.6
50 | 10 $\frac{Tmol}{yr}$ N2O | 10.8 | 7.6
50 | 100 $\frac{Tmol}{yr}$ N2O | 21.8 | 13.7
100 | 1 $\frac{Tmol}{yr}$ N2O | 3.0 | 2.2
100 | 10 $\frac{Tmol}{yr}$ N2O | 15.2 | 10.7
100 | 100 $\frac{Tmol}{yr}$ N2O | 30.8 | 19.3

###  3.3 Detectability of CH3X

Similarly to the N2O cases discussed in the last section, we modelled the
detectability of CH3X for a set of observation times of 10 days, 50 days and
100 days. Again, we used the two metrics for the detectability introduced
above: a maximum difference in single line in units of the respective
sensitivity in that channel and a bandpass-integrated SNR.

####  3.3.1 Proxima Centauri type star

The results for an Earth-like planet orbiting a Proxima Centauri (M5.5 Ve)
type star at 5 pc distance from the Sun are listed in Table 6 and shown in
Figure 3 for a 50 day observation (modelled observations of 10 and 100 days
are shown in Appendix B.2, Figures 20 \- 21). After ten days the 100x and 10x
CH3X and 100x CH3Cl cases are detectable with SNRs above 10/5 in the two
metric used here. After 50 days the 100x CH3Br case becomes detectable,
reaching SNRs of 14.4/7.1. After 100 days all the 1x cases are still below our
detectability limit, while all the 10x and 100x cases seem detectable.

Figure 3: Detectability of various levels of CH3Cl and CH3Br fluxes in the emission spectrum of an Earth-like planet around an Proxima Centauri type star, after 50 days of observation with LIFE. Top: planet flux for atmospheres with and without CH3Cl and CH3Br. The grey area represents the 1-$\sigma$ sensitivity; the grey error bars show an individual simulated observation. Bottom: Statistical significance of the detected differences between an atmospheric model with and without CH3Cl and CH3Br. Table 6: Modelled SNR ratios for various integration times and different fluxes of CH3X around Proxima Centauri type host at 5 pc Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1x CH3X | 0.8 | 0.5
10 | 10x CH3X | 6.9 | 3.1
10 | 100x CH3X | 21.0 | 8.7
10 | 1x CH3Cl | 1.6 | 1.2
10 | 10x CH3Cl | 3.4 | 2.0
10 | 100x CH3Cl | 11.5 | 5.1
10 | 1x CH3Br | 0.5 | 0.2
10 | 10x CH3Br | 2.4 | 1.2
10 | 100x CH3Br | 6.4 | 3.2
50 | 1x CH3X | 1.9 | 1.1
50 | 10x CH3X | 15.4 | 7.0
50 | 100x CH3X | 46.9 | 19.5
50 | 1x CH3Cl | 3.6 | 2.6
50 | 10x CH3Cl | 7.6 | 4.6
50 | 100x CH3Cl | 25.8 | 11.5
50 | 1x CH3Br | 1.1 | 0.5
50 | 10x CH3Br | 5.3 | 2.7
50 | 100x CH3Br | 14.4 | 7.1
100 | 1x CH3X | 2.7 | 1.6
100 | 10x CH3X | 21.8 | 9.9
100 | 100x CH3X | 66.3 | 27.6
100 | 1x CH3Cl | 5.1 | 3.7
100 | 10x CH3Cl | 10.8 | 6.4
100 | 100x CH3Cl | 36.5 | 16.2
100 | 1x CH3Br | 1.6 | 0.7
100 | 10x CH3Br | 7.5 | 3.8
100 | 100x CH3Br | 20.3 | 10.1

####  3.3.2 AD Leonis type star

The results for an Earth-like planet orbiting a AD Leonis type M3.5V star at 5
pc distance from the Sun are listed in Table 7 and shown in Figure 4 for a 50
day observation (more cases for 10 and 100 day observations are shown in
Appendix B.2, Figures 16 \- 17). In this scenario only the 100x and (since
this case is dominated by CH3Cl) 100x cases are detectable after 10 days with
SNRs of 9.8/4.6 and 8.7/4.6. It would, however take more than 50 and up to 100
days in the LIFE baseline setup to make the various 10x cases observable. All
of the cases with 1x and the 10x CH3Br case do not cross the threshold if
detectability even after 100 days.

Figure 4: Detectability of various levels of CH3Cl and CH3Br fluxes in the emission spectrum of an Earth-like planet around an AD Leonis type star, after 50 days of observation withLIFE.Top: planet flux for atmospheres with and without CH3Cl and CH3Br. The grey area represents the 1-$\sigma$ sensitivity; the grey error bars show an individual simulated observation. Bottom: Statistical significance of the detected differences between an atmospheric model with and without CH3Cl and CH3Br. Table 7: Modelled SNR ratios for various integration times and different fluxes of CH3X around AD Leonis type host at 5 pc Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1x CH3X | 0.8 | 0.4
10 | 10x CH3X | 3.1 | 2.3
10 | 100x CH3X | 9.8 | 4.6
10 | 1x CH3Cl | 0.8 | 0.4
10 | 10x CH3Cl | 3.1 | 2.3
10 | 100x CH3Cl | 8.7 | 4.6
10 | 1x CH3Br | 0.7 | 0.4
10 | 10x CH3Br | 0.7 | 0.4
10 | 100x CH3Br | 2.0 | 1.0
50 | 1x CH3X | 1.8 | 1.0
50 | 10x CH3X | 7.0 | 5.1
50 | 100x CH3X | 21.8 | 10.2
50 | 1x CH3Cl | 1.8 | 1.0
50 | 10x CH3Cl | 6.9 | 5.1
50 | 100x CH3Cl | 19.4 | 10.2
50 | 1x CH3Br | 1.5 | 0.8
50 | 10x CH3Br | 1.6 | 0.8
50 | 100x CH3Br | 4.5 | 2.3
100 | 1x CH3X | 2.5 | 1.4
100 | 10x CH3X | 9.9 | 7.2
100 | 100x CH3X | 30.9 | 14.4
100 | 1x CH3Cl | 2.5 | 1.4
100 | 10x CH3Cl | 9.7 | 7.2
100 | 100x CH3Cl | 27.4 | 14.4
100 | 1x CH3Br | 2.1 | 1.2
100 | 10x CH3Br | 2.2 | 1.2
100 | 100x CH3Br | 6.4 | 3.2

####  3.3.3 K6V type star

The results for an Earth-like planet orbiting a K6V type star at 5 pc distance
from the Sun are listed in Table 8 and shown in Figure 5 for a 50 day
observation (more cases shown in Appendix B.2, Figures 22 \- 23). This is the
least favorable case discussed in this paper and almost none of the cases seem
to be observable. Only for 100x CH3X and 100x CH3Cl after 100 days of
observation do we barely cross the detection threshold with our SNR metrics at
7.8 and 4.9 repspectively.

Figure 5: Detectability of various levels of CH3Cl and CH3Br fluxes in the emission spectrum of an Earth-like planet around a K6V type star, after 50 days of observation withLIFE.Top: planet flux for atmospheres with and without CH3Cl and CH3Br. The grey area represents the 1-$\sigma$ sensitivity; the grey error bars show an individual simulated observation. Bottom: Statistical significance of the detected differences between an atmospheric model with and without CH3Cl and CH3Br. None of these cases seem to be detectable. Table 8: Modelled SNR ratios for various integration times and different fluxes of CH3X around K6V star at 5 pc Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1x CH3X | 0.2 | 0.1
10 | 10x CH3X | 0.4 | 0.3
10 | 100x CH3X | 2.5 | 1.6
10 | 1x CH3Cl | 2.1 | 1.1
10 | 10x CH3Cl | 0.4 | 0.3
10 | 100x CH3Cl | 2.4 | 1.5
10 | 1x CH3Br | 0.2 | 0.1
10 | 10x CH3Br | 0.3 | 0.2
10 | 100x CH3Br | 1.4 | 1.0
50 | 1x CH3X | 0.5 | 0.3
50 | 10x CH3X | 0.8 | 0.6
50 | 100x CH3X | 5.5 | 3.5
50 | 1x CH3Cl | 4.6 | 2.5
50 | 10x CH3Cl | 0.9 | 0.6
50 | 100x CH3Cl | 5.4 | 3.4
50 | 1x CH3Br | 0.5 | 0.3
50 | 10x CH3Br | 0.8 | 0.5
50 | 100x CH3Br | 3.1 | 2.1
100 | 1x CH3X | 0.7 | 0.4
100 | 10x CH3X | 1.1 | 0.9
100 | 100x CH3X | 7.8 | 4.9
100 | 1x CH3Cl | 6.5 | 3.5
100 | 10x CH3Cl | 1.2 | 0.9
100 | 100x CH3Cl | 7.7 | 4.8
100 | 1x CH3Br | 0.7 | 0.4
100 | 10x CH3Br | 1.1 | 0.8
100 | 100x CH3Br | 4.4 | 3.0

####  3.3.4 TRAPPIST-1 type star

The results for an Earth-like planet orbiting a TRAPPIST-1 type star at 5 pc
distance from the Sun are listed in Table 9 and shown in Figure 6 for a 50 day
observation (more cases for 10 and 100 days of observation are shown in
Appendix B.2, Figures 18 \- 19). For this case the 100x CH3X case is
detectable wit SNRs of 9.3/4.0 already after 10 days. The 10x CH3X (10.3/4.7)
as well as the 100x CH3Cl (11.8/5.2) become detectable after 50 days. Even
after 100 days of simulated observation do all 1x cases and the 10x CH3Cl and
CH3Br stay undetectable.

Figure 6: Detectability of various levels of CH3Cl and CH3Br fluxes in the emission spectrum of an Earth-like planet around a TRAPPIST-1 type star, after 50 days of observation withLIFE.Top: planet flux for atmospheres with and without CH3Cl and CH3Br. The grey area represents the 1-$\sigma$ sensitivity; the grey error bars show an individual simulated observation. Bottom: Statistical significance of the detected differences between an atmospheric model with and without CH3Cl and CH3Br. Table 9: Modelled SNR ratios for various integration times and different fluxes of CH3X around TRAPPIST-like star at 5 pc Tint [d] | Feature | Band-int. SNR | Max. line sigma
---|---|---|---
10 | 1x CH3X | 0.7 | 0.4
10 | 10x CH3X | 4.6 | 2.1
10 | 100x CH3X | 9.3 | 4.0
10 | 1x CH3Cl | 0.6 | 0.4
10 | 10x CH3Cl | 1.7 | 0.9
10 | 100x CH3Cl | 5.3 | 2.3
10 | 1x CH3Br | 0.5 | 0.2
10 | 10x CH3Br | 1.1 | 0.5
10 | 100x CH3Br | 2.2 | 1.1
50 | 1x CH3X | 1.5 | 0.8
50 | 10x CH3X | 10.3 | 4.7
50 | 100x CH3X | 20.8 | 8.9
50 | 1x CH3Cl | 1.5 | 0.8
50 | 10x CH3Cl | 3.9 | 2.1
50 | 100x CH3Cl | 11.8 | 5.2
50 | 1x CH3Br | 1.2 | 0.5
50 | 10x CH3Br | 2.4 | 1.2
50 | 100x CH3Br | 5.0 | 2.5
100 | 1x CH3X | 2.2 | 1.2
100 | 10x CH3X | 14.6 | 6.7
100 | 100x CH3X | 29.5 | 12.5
100 | 1x CH3Cl | 2.1 | 1.2
100 | 10x CH3Cl | 5.5 | 2.9
100 | 100x CH3Cl | 16.7 | 7.3
100 | 1x CH3Br | 1.7 | 0.7
100 | 10x CH3Br | 3.4 | 1.6
100 | 100x CH3Br | 7.0 | 3.5

###  3.4 Comparison to full spectral retrievals

In order to benchmark the results of the previously presented exercise of
comparing spectra with and without the species present in the atmosphere, we
performed a few exemplary retrievals. This was done in the following manner:
the input spectra were produced as described in the sections above while our
retrievals were performed with the retrieval suite described in Konrad et al.
(2022) and Alei et al. (2022b). The retrieval routine couples the forward
model petitRADTRANS (Mollière et al., 2019) with the parameter estimation
module pyMultiNest (Buchner et al., 2014). The retrieval routine - in
constrast to the forward models used for the input spetra - neglected clouds
and assumed pressure-constant abundance profiles for every species included in
the calculation. The spectral calculation within the retrieval was performed
considering HITRAN 2020 opacities, assuming air broadening and a line wing
cutoff at 25 cm-1 from the line core.

As shown in Alei et al. (2022b), neglecting clouds in retrievals when
considering spectra of partly cloudy planets is overall not impacting a
correct retrieval of the chemical composition of the atmosphere. However, the
opacity linelists used in the retrievals are generally not consistent with the
linelists used by PSG and SMART that produced the input spectra. As discussed
in Alei et al. (2022a), differences in opacities might cause considerable
differences in retrievals. Other differences in the implementation of
scattering and raytracing methods might also generate biases. For this reason,
an intercomparison among these three forward models (as well as other ones)
has been ongoing within the community (Villanueva et al., in prep.) within the
Climates Using Interactive Suites of Intercomparisons Nested for Exoplanet
Studies (CUISINES) sponsored by the Nexus for Exoplanet System Science
(NExSS).

Besides relaying the most basic system parameters (such as the distance of the
system and stellar type of the host) this was done without any other prior
knowledge of the atmosphere or about the process of generating the model
spectra. This experimental setup reproduces the circumstances of an actual
observation very well, in which case we also would not know any of the true
values a priori.

The main question we asked was for which cases (i.e. which levels of band-
integrated/max line SNR) we would get a detection and/or upper limits for the
presence of the species of interest.

Figure 7: Comparison - Retrieval. Histograms of the posterior distributions
for N2O abundances in the 3 retrieval cases compared to the “ground truth”
model values. While the 100 and 10 Tmol/yr case are retrieved within $\sim$
1.5 sigma, the 1 Tmol/yr case only produces an upper limit. Biases seen here
can be largely attributed to a degeneracy between abundances (in particular
H2O and N2O) as shown in the cornerplots in Appendix Section A.

As example we chose the N2O Earth at 5 pc around Sun-like star 50d cases and
ran retrievals on the the spectra for 1, 10 and 100 Tmol/y fluxes of N2O. In
the direct comparison analysis above these slightly more challenging cases
cases were distiguishable from a no N2O case at a band integrated SNR of about
1.5,5.1 and 14.7 (max. channel SNR of 0.9, 2.7, 7.5). This gives us the
opportunity to compare our ability to retrieve the N2O abundances to one order
of magnitude in our SNR metric, giving as a first order estimate of the
detection threshold in that metric. Furthermore it connects this study with
Konrad et al. (2022) and Alei et al. (2022b) who also focused on Sun-like
hosts in their studies of Earth-twins.

The results are shown in Figure 7, where we show the histograms of the
posteriors for the N2O abundances for the different cases, in comparison to
the “ground truth” of the input spectra. All our retrievals derive N2O
abundances within 1.5 sigma of the input value of the original models run
through the LIFE observation simulator. For the 1 Tmol/yr case we can only
retrieve an upper limit. More details for the retrievals, such as corner plots
and values for all retrieved parameters are presented in Appendix A.

This analysis confirms our first order estimate that a band-integrated SNR of
about 5-10 should be sufficient to detect the feature in question and
justifies our choice of this line as a rational, rather pessimistic detection
limit in our reasoning.

##  4 Discussion and conclusions

###  4.1 Wavelength dependent sensitivity between different cases

In our simulations, the sensitivity of the interferometric measurement is
fundamentally limited by astrophysical noise sources. In the longer wavelength
regime of the simulated measurement, this astrophysical noise is dominated by
the thermal emission of the local-zodical dust in the solar system. The
diffuse nature of the emission makes the amount of local-zodi induced noise
that is present after the nulling independent from the length of the chosen
interferometric baseline. Therefore, towards longer wavelengths the instrument
sensitivity is independent from the observed target. 666The local-zodi noise
does strongly depend on the position of the target in relation to the ecliptic
plane Dannert et al. (2022), which is kept equal ($lat_{s}=0.78$) for all
cases simulated in the ‘characterization phase’ in this study. At short
wavelengths, the noise is dominated by the host star. As the flux ratio
between the exoplanet and its host star becomes more favourable towards later
stellar types, the sensitivity of the observations increase for such star
types. Coupled with more prominent spectra features, this results in the
demonstrated higher significance detection in the shorter wavelength bands for
the M-star targets compared to the G- and K-star targets.

###  4.2 Golden Targets and dynamic atmospheric signatures

One of the most interesting outcomes of this analysis is the expected quality
of data obtainable for the closest target planets. For example for the Proxima
Centauri case at original distance (see Fig. 8) or similar cases within $<$
3pc distance from the Sun , “spectral temporal resolution” of a few days is
possible, meaning that changes caused by fluxes of the same magnitude assumed
in our models could be detected on timescales of days or weeks. This could be
used to characterize exoplanetary variability and dynamic processes in the
atmospheres.

Figure 8: Detectability of various fluxes of N2O in the emission spectrum of
an Earth-like planet around Proxima Centauri at its original distance, after
only 1 day of observation with LIFE. Top: planet flux for atmospheres with and
without N2O . The grey area represents the 1-$\sigma$ sensitivity; the dark
grey error bars show an individual simulated observation. Bottom: Statistical
significance of the detected differences between an atmospheric model with and
without N2O.

###  4.3 Consequences for Science and Technology Requirements

Fig. 9 shows the dependence of the observation time needed to constrain N2O
for the 10 Tmol/y Earth twin case with various design parameters of the LIFE
mission. The bottom plot of Figure 9 shows a relatively weak dependence on the
shorter wavelength cut off but a very strong dependence on the longer
wavelength which is explained by the location of the N2O features in the MIR
for the G star case.777It is important to note that in full retrievals, the
contextual information provided by other wavelength bands is very important to
constrain the abundances. This fact is not included in this analysis and
should hence be taken with a grain of salt. The Figure 9 center panel shows
how for the 2 m mirror size at 5% throughput (or an equivalent size/throughput
combination) it would take about 15 days to reach the 10 sigma band integrated
threshold while it would only take about 5 days in the 3.5m configuration. For
a descoped 1m setup we would not reach that in a reasonable time ($>$ 100
days). Fig. 9 top panel shows almost no dependence on spectral resolution, due
to the relatively wide bands of N2O.

Figure 9: Dependence of observation time needed to detect 10 Tmol/y N2O in the
Earth twin around Sun like star at 5 pc example case on various mission
parameters.

###  4.4 Synergies and comparison with other observational platforms

Schwieterman et al. (2022) and Leung et al. (2022) showed that some of the
scenarios discussed here may be observable with JWST in transiting systems
such as TRAPPIST-1. However these observations would need to add the signal
from 10-100s of individual transits and will therefore only be feasible for
very few, selected, transiting planets around very late type stars. On the
other hand, it was shown that the long baselines of LIFE, which result in
extremely high spatial resolution will be particularly well suited for systems
around late type stars with very close in habitable zones, that are also
inaccessible to direct imaging techniques at shorter wavelengths (Dannert et
al., 2022; Carrión-González et al., 2023, see also Fig.1). Furthermore N2O
shows orders of magnitude difference in the line intensities between the
strongest MIR regions and the strongest NIR regions (see Fig.10). The ability
to characterize terrestrial temperate exoplanets around late type stars and
the access to molecules that only show strong features in the MIR are two of
the main synergies of LIFE with HWO, which will mostly focus on FGK systems
and observe in the UV to NIR range.

If there are late type star exoplanetary systems in the solar neighborhood
with planets that exhibit global biospheres producing N2O and CH3X signals,
LIFE will be the best suited future mission to systematically search for and
eventually detect them.

Figure 10: HITRAN line intensities for N2O showing orders of magnitude
stronger features in the MIR vs. the NIR. This comparison is not possible for
CH3Br/CH3Cl, because their absolute cross-sections have not been
systematically measured in the 0.2-2 micron region relevant to reflected light
observations of terrestrial planets (e.g., HWO).

###  4.5 Summary of results

  1. 1.

Our first order analysis of the detectability of exoplanetary spectra with the
modelled fluxes of potentially biogenic gases shows that most of the discussed
cases are indeed observable with a space telescope like LIFE with observation
times between 10 and 100 days for habitable planetary systems within 5 pc.

  2. 2.

We compare some of these results to selected retrievals, confirm the
detectability and generally show consistency with the direct comparison of
forward models in the detectability metric used here.

  3. 3.

Using simulations of potential yields of the LIFE mission we can show that
dozens of terrestrial temperate exoplanets can be tested for these molecules
in the way discussed here. In terms of distance the cases at 5 pc are typical
for M star host and likely the best cases for FGK hosts.

  4. 4.

For some “golden targets” (e.g. a very nearby system like Proxima Centauri)
LIFE could detect levels of the discussed species on very short timescales,
delivering high “spectral-temporal” resolution of days to week to observe 10s
of Tmol/yr fluxes, potentially opening up future avenues for variability
studies.

  5. 5.

Comparison of the LIFE baseline with other potential setups of the space
telescope confirm observability also for different instrumental configuration
and informs the mission design about trade offs driven by the detectability of
these features.

## Acknowledgements

We thank the anonymous reviewer for their careful reading of our manuscript
and their many insightful comments and suggestions. This work has been carried
out within the framework of the National Centre of Competence in Research
PlanetS supported by the Swiss National Science Foundation under grants
51NF40_182901 and 51NF40_205606. EA acknowledges the financial support of the
SNSF. DP, ML, and ES gratefully acknowledge support from the NASA Exobiology
program through grant No. 80NSSC20K1437, the NASA Interdisciplinary Consortia
for Astrobiology Research (ICAR) Program via grant Nos. 80NSSC21K0905 and
80NSSC21K0905, and the Virtual Planetary Laboratory funded by NASA
Astrobiology Program grant No. 80NSSC18K0829. DP acknowledges additional
support from the NASA FINESST program via grant 80NSSC22K1319. We thank
Philipp Huber, Adrian Glauser and the ETH LIFE team for very informative and
instructive discussions about LIFEsim and flux units.

##  Appendix A Retrieval Details

In this appendix section we show the cornerplots with all posteriors, the
derived pressure-temperature profiles and the fitted spectra for the three
cases discussed in Section 3.4.

\begin{overpic}[width=416.27809pt]{Figures/retrievals/plot_corner_1tmol_truths.pdf}
\put(50.0,60.0){\includegraphics[scale={0.6}]{Figures/retrievals/plot_pt_structure_1tmol_truths.pdf}}
\end{overpic}

Figure 11: Retrieval results for 1 Tmol/y N2O case.

Table 10: 1 Tmol/yr retrieval results. Here, $L(\cdot)$ stands for $log_{10}(\cdot)$.  Value | Retrieved result
---|---
$L\left(\mathrm{P_{0}}\left[\mathrm{bar}\right]\right)$ | 0.03 ${}_{\,-0.24}^{\,+0.41}$
$\mathrm{R_{pl}}\left[\mathrm{R_{Earth}}\right]$ | 0.98 ${}_{\,-0.05}^{\,+0.05}$
$L\left(\mathrm{M_{pl}}\left[\mathrm{M_{Earth}}\right]\right)$ | 0.03 ${}_{\,-0.31}^{\,+0.30}$
$L\left(\mathrm{N_{2}}\right)$ | –
$L\left(\mathrm{O_{2}}\right)$ | –
$L\left(\mathrm{CO_{2}}\right)$ | -3.58 ${}_{\,-0.61}^{\,+0.60}$
$L\left(\mathrm{CH_{4}}\right)$ | -7.49 ${}_{\,-4.12}^{\,+1.75}$
$L\left(\mathrm{H_{2}O}\right)$ | -3.69 ${}_{\,-0.68}^{\,+0.65}$
$L\left(\mathrm{O_{3}}\right)$ | -6.90 ${}_{\,-0.47}^{\,+0.48}$
$L\left(\mathrm{CO}\right)$ | –
$L\left(\mathrm{N_{2}O}\right)$ | -9.42 ${}_{\,-3.47}^{\,+2.53}$

\begin{overpic}[width=416.27809pt]{Figures/retrievals/plot_corner_10tmol_truths.pdf}
\put(50.0,60.0){\includegraphics[scale={0.6}]{Figures/retrievals/plot_pt_structure_10tmol_truths.pdf}}
\end{overpic}

Figure 12: Retrieval results for 10 Tmol/y N2O case.

Table 11: 10 Tmol/yr retrieval results. Here, $L(\cdot)$ stands for $log_{10}(\cdot)$.  Value | Retrieved result
---|---
$L\left(\mathrm{P_{0}}\left[\mathrm{bar}\right]\right)$ | 0.17 ${}_{\,-0.25}^{\,+0.30}$
$\mathrm{R_{pl}}\left[\mathrm{R_{Earth}}\right]$ | 0.98 ${}_{\,-0.04}^{\,+0.05}$
$L\left(\mathrm{M_{pl}}\left[\mathrm{M_{Earth}}\right]\right)$ | 0.03 ${}_{\,-0.30}^{\,+0.29}$
$L\left(\mathrm{N_{2}}\right)$ | –
$L\left(\mathrm{O_{2}}\right)$ | –
$L\left(\mathrm{CO_{2}}\right)$ | -3.76 ${}_{\,-0.54}^{\,+0.52}$
$L\left(\mathrm{CH_{4}}\right)$ | -10 ${}_{\,-3}^{\,+3}$
$L\left(\mathrm{H_{2}O}\right)$ | -3.90 ${}_{\,-0.59}^{\,+0.59}$
$L\left(\mathrm{O_{3}}\right)$ | -7.20 ${}_{\,-0.46}^{\,+0.44}$
$L\left(\mathrm{CO}\right)$ | –
$L\left(\mathrm{N_{2}O}\right)$ | -5.83${}_{\,-0.52}^{\,+0.49}$

\begin{overpic}[width=416.27809pt]{Figures/retrievals/plot_corner_100tmol_truths.pdf}
\put(50.0,60.0){\includegraphics[scale={0.6}]{Figures/retrievals/plot_pt_structure_100tmol_truths.pdf}}
\end{overpic}

Figure 13: Retrieval results for 100 Tmol/y N2O case.

Table 12: 100 Tmol/yr retrieval results. Here, $L(\cdot)$ stands for $log_{10}(\cdot)$.  Value | Retrieved result
---|---
$L\left(\mathrm{P_{0}}\left[\mathrm{bar}\right]\right)$ | -0.26 ${}_{\,-0.20}^{\,+0.25}$
$\mathrm{R_{pl}}\left[\mathrm{R_{Earth}}\right]$ | 1.00${}_{\,-0.04}^{\,+0.05}$
$L\left(\mathrm{M_{pl}}\left[\mathrm{M_{Earth}}\right]\right)$ | 0.01 ${}_{\,-0.29}^{\,+0.31}$
$L\left(\mathrm{N_{2}}\right)$ | –
$L\left(\mathrm{O_{2}}\right)$ | –
$L\left(\mathrm{CO_{2}}\right)$ | -3.01 ${}_{\,-0.52}^{\,+0.50}$
$L\left(\mathrm{CH_{4}}\right)$ | -9 ${}_{\,-3}^{\,+3}$
$L\left(\mathrm{H_{2}O}\right)$ | -3.29 ${}_{\,-0.57}^{\,+0.53}$
$L\left(\mathrm{O_{3}}\right)$ | -7.36 ${}_{\,-3.81}^{\,+0.70}$
$L\left(\mathrm{CO}\right)$ | –
$L\left(\mathrm{N_{2}O}\right)$ | -3.97 ${}_{\,-0.51}^{\,+0.51}$

##  Appendix B Modelled Observations for different observation times

In the following two appendix sections we show the simulated observations for
10 and 100 days of observation in addition to the 50 day observations already
shown in the main text.

###  B.1 Supplementary Results N2O

Figure 14: Same as Figure 2 for 10 days of observation time.

Figure 15: Same as Figure 2 for 100 days of observation time.

###  B.2 Supplementary Results CH3x

####  B.2.1 AD Leonis type host

Figure 16: Results for AD Leonis Type star in 10 days.

Figure 17: Results for AD Leonis Type star in 100 days.

####  B.2.2 TRAPPIST-1 type host

Figure 18: Results for TRAPPIST-1 Type star in 10 days.

Figure 19: Results for TRAPPIST-1 Type star in 100 days.

####  B.2.3 Proxima type host

Figure 20: Results for Proxima Type star in 10 days.

Figure 21: Results for Proxima Type star in 100 days.

####  B.2.4 K6V type host

Figure 22: Results for K6V Type star in 10 days.

Figure 23: Results for K6V Type star in 100 days.

##  Appendix C N2O and CH3X Flux-Abundance Details

The predicted abundance of a trace gas, while highly dependent on its
production flux, can also vary as a function of the background atmosphere and
other assumptions embedded in the photochemical model used to calculate it
including fundamental inputs such as stellar spectra, reaction rates, and
molecular cross-sections (e.g., Ranjan et al., 2020). To facilitate future
reproduction of our results, in Tables 13 and 14 we provide a cross-
referencing of the N2O and CH3X fluxes and their respective predicted ground-
level mixing ratios used in this study. As stated above, these calculations
are sourced from Schwieterman et al. (2022) for N2O and Leung et al. (2022)
for CH3Cl, CH3Br, and CH3X.

Table 13: Flux vs. Ground-level Abundance for N2O Scenario | Earth-like flux | 1 $\frac{Tmol}{yr}$ | 10 $\frac{Tmol}{yr}$ | 100 $\frac{Tmol}{yr}$
---|---|---|---|---
Sun | 3.39$\times$10-7 | 7.34$\times$10-7 | 5.44$\times$10-6 | 4.54$\times$10-5
K6V | 2.96$\times$10-6 | 7.20$\times$10-6 | 9.14$\times$10-5 | 1.63$\times$10-3
Proxima Centauri | 1.14$\times$10-6 | 2.75$\times$10-6 | 2.82$\times$10-5 | 6.54$\times$10-4
TRAPPIST-1 | 1.27$\times$10-6 | 3.08$\times$10-6 | 3.09$\times$10-5 | 3.26$\times$10-4
Table 14: Flux vs. Ground-level Abundance for CH3Cl, CH3Br, and CH3X Scenario | Earth-like flux | 10x Earth-like flux | 100x Earth-like flux | 1000x Earth-like flux
---|---|---|---|---
K6V–CH3Cl | 4.82$\times$10-9 | 4.82$\times$10-8 | 3.64$\times$10-7 | 2.09$\times$10-6
K6V–CH3Br | 1.28$\times$10-10 | 1.23$\times$10-9 | 1.05$\times$10-8 | 1.34$\times$10-7
K6V–CH3X | 4.94$\times$10-9 | 4.94$\times$10-8 | 3.73$\times$10-7 | 2.11$\times$10-6
AD Leo–CH3Cl | 5.92$\times$10-8 | 5.02$\times$10-7 | 3.43$\times$10-6 | 3.69$\times$10-5
AD Leo–CH3Br | 3.47$\times$10-9 | 3.42$\times$10-8 | 4.61$\times$10-7 | 1.49$\times$10-6
AD Leo–CH3X | 6.27$\times$10-8 | 5.39$\times$10-7 | 3.57$\times$10-6 | 4.77$\times$10-5
Proxima Centauri–CH3Cl | 5.38$\times$10-7 | 1.64$\times$10-6 | 1.34$\times$10-5 | 1.40$\times$10-4
Proxima Centauri–CH3Br | 1.15$\times$10-7 | 7.77$\times$10-7 | 2.86$\times$10-6 | 9.39$\times$10-6
Proxima Centauri–CH3X | 2.87$\times$10-7 | 3.80$\times$10-6 | 3.21$\times$10-5 | 3.94$\times$10-4
TRAPPIST-1-CH3Cl | 1.26$\times$10-7 | 1.18$\times$10-6 | 9.65$\times$10-6 | 7.45$\times$10-5
TRAPPIST-1–CH3Br | 9.81$\times$10-8 | 4.47$\times$10-7 | 1.24$\times$10-6 | 4.60$\times$10-6
TRAPPIST-1–CH3X | 2.24$\times$10-7 | 4.30$\times$10-6 | 2.14$\times$10-5 | 6.16$\times$10-4

## References

  * Alei et al. (2022a) Alei, E., Konrad, B. S., Mollière, P., et al. 2022a, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12180, Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave, ed. L. E. Coyle, S. Matsuura, & M. D. Perrin, 121803L, doi: 10.1117/12.2631692
  * Alei et al. (2022b) Alei, E., Konrad, B. S., Angerhausen, D., et al. 2022b, A&A, 665, A106, doi: 10.1051/0004-6361/202243760
  * Angerhausen et al. (2023) Angerhausen, D., Ottiger, M., Dannert, F., et al. 2023, Astrobiology, 23, 183, doi: 10.1089/ast.2022.0010
  * Arney et al. (2014) Arney, G., Meadows, V., Crisp, D., et al. 2014, Journal of Geophysical Research (Planets), 119, 1860, doi: 10.1002/2014JE004662
  * Arney et al. (2016) Arney, G., Domagal-Goldman, S. D., Meadows, V. S., et al. 2016, Astrobiology, 16, 873, doi: 10.1089/ast.2015.1422
  * Arney et al. (2017) Arney, G. N., Meadows, V. S., Domagal-Goldman, S. D., et al. 2017, ApJ, 836, 49, doi: 10.3847/1538-4357/836/1/49
  * Ben-Ami et al. (2018) Ben-Ami, S., López-Morales, M., & Szentgyorgyi, A. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10702, Ground-based and Airborne Instrumentation for Astronomy VII, ed. C. J. Evans, L. Simard, & H. Takami, 107026N, doi: 10.1117/12.2313445
  * Bixel & Apai (2021) Bixel, A., & Apai, D. 2021, The Astronomical Journal, 161, 228, doi: 10.3847/1538-3881/abe042
  * Bryson et al. (2021) Bryson, S., Kunimoto, M., Kopparapu, R. K., et al. 2021, AJ, 161, 36, doi: 10.3847/1538-3881/abc418
  * Buchner et al. (2014) Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, A&A, 564, A125, doi: 10.1051/0004-6361/201322971
  * Buick (2007) Buick, R. 2007, Geobiology, 5, 97, doi: 10.1111/j.1472-4669.2007.00110.x
  * Carrión-González et al. (2023) Carrión-González, Ó., Kammerer, J., Angerhausen, D., et al. 2023, A&A, 678, A96, doi: 10.1051/0004-6361/202347027
  * Chen et al. (2018) Chen, H., Wolf, E. T., Kopparapu, R., Domagal-Goldman, S., & Horton, D. E. 2018, ApJ, 868, L6, doi: 10.3847/2041-8213/aaedb2
  * Dannert et al. (2022) Dannert, F. A., Ottiger, M., Quanz, S. P., et al. 2022, A&A, 664, A22, doi: 10.1051/0004-6361/202141958
  * Des Marais et al. (2002) Des Marais, D. J., Harwit, M. O., Jucks, K. W., et al. 2002, Astrobiology, 2, 153, doi: 10.1089/15311070260192246
  * Domagal-Goldman et al. (2011) Domagal-Goldman, S. D., Meadows, V. S., Claire, M. W., & Kasting, J. F. 2011, Astrobiology, 11, 419, doi: 10.1089/ast.2010.0509
  * Dressing & Charbonneau (2015) Dressing, C. D., & Charbonneau, D. 2015, ApJ, 807, 45, doi: 10.1088/0004-637X/807/1/45
  * Ertel et al. (2018) Ertel, S., Defrère, D., Hinz, P., et al. 2018, AJ, 155, 194, doi: 10.3847/1538-3881/aab717
  * Ertel et al. (2020) —. 2020, AJ, 159, 177, doi: 10.3847/1538-3881/ab7817
  * France et al. (2016) France, K., Loyd, R. O. P., Youngblood, A., et al. 2016, ApJ, 820, 89, doi: 10.3847/0004-637X/820/2/89
  * Fuge (1988) Fuge, R. 1988, Environ. Geochem. Health, 10, 51, doi: 10.1007/BF01758592
  * Fujii et al. (2018) Fujii, Y., Angerhausen, D., Deitrick, R., et al. 2018, Astrobiology, 18, 739, doi: 10.1089/ast.2017.1733
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1, doi: 10.1051/0004-6361/201833051
  * Gaudi et al. (2020) Gaudi, B. S., Seager, S., Mennesson, B., et al. 2020, arXiv e-prints, arXiv:2001.06683.  https://arxiv.org/abs/2001.06683
  * Gordon et al. (2022) Gordon, I. E., Rothman, L. S., Hargreaves, R. J., et al. 2022, J. Quant. Spec. Radiat. Transf., 277, 107949, doi: 10.1016/j.jqsrt.2021.107949
  * Greene et al. (2016) Greene, T. P., Line, M. R., Montero, C., et al. 2016, The Astrophysical Journal, 817, 17, doi: 10.3847/0004-637X/817/1/17
  * Hansen et al. (2023) Hansen, J. T., Ireland, M. J., Laugier, R., & LIFE Collaboration. 2023, A&A, 670, A57, doi: 10.1051/0004-6361/202243863
  * Hansen et al. (2022) Hansen, J. T., Ireland, M. J., & LIFE Collaboration. 2022, A&A, 664, A52, doi: 10.1051/0004-6361/202243107
  * Janson et al. (2023) Janson, M., Patel, J., Ringqvist, S. C., et al. 2023, A&A, 671, A114, doi: 10.1051/0004-6361/202245402
  * Jia et al. (2013) Jia, G., Fu, Y., & He, C. 2013, Trends Genet., 29, 108, doi: 10.1016/j.tig.2012.11.003
  * Kammerer & Quanz (2018) Kammerer, J., & Quanz, S. P. 2018, A&A, 609, A4, doi: 10.1051/0004-6361/201731254
  * Kammerer et al. (2022) Kammerer, J., Quanz, S. P., Dannert, F., & LIFE Collaboration. 2022, A&A, 668, A52, doi: 10.1051/0004-6361/202243846
  * Kasdin et al. (2020) Kasdin, N. J., Bailey, V. P., Mennesson, B., et al. 2020, in Space Telescopes and Instrumentation 2020: Optical, Infrared, and Millimeter Wave, Vol. 11443, SPIE, 300–313
  * Kasting et al. (1979) Kasting, J. F., Liu, S. C., & Donahue, T. M. 1979, J. Geophys. Res., 84, 3097, doi: 10.1029/JC084iC06p03097
  * Konrad et al. (2022) Konrad, B. S., Alei, E., Quanz, S. P., et al. 2022, A&A, 664, A23, doi: 10.1051/0004-6361/202141964
  * Konrad et al. (2023) —. 2023, arXiv e-prints, arXiv:2303.04727, doi: 10.48550/arXiv.2303.04727
  * Kopparapu et al. (2014) Kopparapu, R. K., Ramirez, R. M., SchottelKotte, J., et al. 2014, ApJ, 787, L29, doi: 10.1088/2041-8205/787/2/L29
  * Kopparapu et al. (2018) Kopparapu, R. K., Hébrard, E., Belikov, R., et al. 2018, ApJ, 856, 122, doi: 10.3847/1538-4357/aab205
  * Krissansen-Totton et al. (2018) Krissansen-Totton, J., Olson, S., & Catling, D. C. 2018, Science Advances, 4, eaao5747, doi: 10.1126/sciadv.aao5747
  * Leung et al. (2022) Leung, M., Schwieterman, E. W., Parenteau, M. N., & Fauchez, T. J. 2022, ApJ, 938, 6, doi: 10.3847/1538-4357/ac8799
  * Lincowski et al. (2018) Lincowski, A. P., Meadows, V. S., Crisp, D., et al. 2018, ApJ, 867, 76, doi: 10.3847/1538-4357/aae36a
  * Lovis et al. (2017) Lovis, C., Snellen, I., Mouillet, D., et al. 2017, A&A, 599, A16, doi: 10.1051/0004-6361/201629682
  * Loyd et al. (2016) Loyd, R. O. P., France, K., Youngblood, A., et al. 2016, ApJ, 824, 102, doi: 10.3847/0004-637X/824/2/102
  * Loyd et al. (2018) —. 2018, ApJ, 867, 71, doi: 10.3847/1538-4357/aae2bd
  * Lustig-Yaeger et al. (2019) Lustig-Yaeger, J., Meadows, V. S., & Lincowski, A. P. 2019, AJ, 158, 27, doi: 10.3847/1538-3881/ab21e0
  * Matsuo et al. (2023) Matsuo, T., Dannert, F., Laugier, R., et al. 2023, A&A, 678, A97, doi: 10.1051/0004-6361/202345927
  * Meadows & Crisp (1996) Meadows, V. S., & Crisp, D. 1996, J. Geophys. Res., 101, 4595, doi: 10.1029/95JE03567
  * Meadows et al. (2018a) Meadows, V. S., Arney, G. N., Schwieterman, E. W., et al. 2018a, Astrobiology, 18, 133, doi: 10.1089/ast.2016.1589
  * Meadows et al. (2018b) Meadows, V. S., Reinhard, C. T., Arney, G. N., et al. 2018b, Astrobiology, 18, 630, doi: 10.1089/ast.2017.1727
  * Mollière et al. (2019) Mollière, P., Wardenier, J. P., van Boekel, R., et al. 2019, A&A, 627, A67, doi: 10.1051/0004-6361/201935470
  * Morley et al. (2017) Morley, C. V., Kreidberg, L., Rustamkulov, Z., Robinson, T., & Fortney, J. J. 2017, The Astrophysical Journal, 850, 121
  * Murray et al. (2022) Murray, N. J., Worthington, T. A., Bunting, P., et al. 2022, Science, 376, 744, doi: 10.1126/science.abm9583
  * National Academies of Sciences & Medicine (2021) National Academies of Sciences, E., & Medicine. 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s, doi: 10.17226/26141
  * Pavlov et al. (2001) Pavlov, A. A., Brown, L. L., & Kasting, J. F. 2001, J. Geophys. Res., 106, 23267, doi: 10.1029/2000JE001448
  * Peacock et al. (2019) Peacock, S., Barman, T., Shkolnik, E. L., Hauschildt, P. H., & Baron, E. 2019, ApJ, 871, 235, doi: 10.3847/1538-4357/aaf891
  * Peacock et al. (2020) Peacock, S., Barman, T., Shkolnik, E. L., et al. 2020, ApJ, 895, 5, doi: 10.3847/1538-4357/ab893a
  * Prather et al. (2015) Prather, M. J., Hsu, J., DeLuca, N. M., et al. 2015, Journal of Geophysical Research: Atmospheres, 120, 5693, doi: 10.1002/2015JD023267
  * Prosser & Nicol (2012) Prosser, J. I., & Nicol, G. W. 2012, Trends in Microbiology, 20, 523, doi: 10.1016/j.tim.2012.08.001
  * Quanz et al. (2018) Quanz, S. P., Kammerer, J., Defrère, D., et al. 2018, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 10701, Optical and Infrared Interferometry and Imaging VI, ed. M. J. Creech-Eakman, P. G. Tuthill, & A. Mérand, 107011I, doi: 10.1117/12.2312051
  * Quanz et al. (2019) Quanz, S. P., Absil, O., Angerhausen, D., et al. 2019, arXiv e-prints, arXiv:1908.01316.  https://arxiv.org/abs/1908.01316
  * Quanz et al. (2022) Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2022, A&A, 664, A21, doi: 10.1051/0004-6361/202140366
  * Ranjan et al. (2020) Ranjan, S., Schwieterman, E. W., Harman, C., et al. 2020, ApJ, 896, 148, doi: 10.3847/1538-4357/ab9363
  * Robinson et al. (2011) Robinson, T. D., Meadows, V. S., Crisp, D., et al. 2011, Astrobiology, 11, 393, doi: 10.1089/ast.2011.0642
  * Schwieterman et al. (2018) Schwieterman, E. W., Kiang, N. Y., Parenteau, M. N., et al. 2018, Astrobiology, 18, 663, doi: 10.1089/ast.2017.1729
  * Schwieterman et al. (2022) Schwieterman, E. W., Olson, S. L., Pidhorodetska, D., et al. 2022, ApJ, 937, 109, doi: 10.3847/1538-4357/ac8cfb
  * Seager et al. (2016) Seager, S., Bains, W., & Petkowski, J. J. 2016, Astrobiology, 16, 465, doi: 10.1089/ast.2015.1404
  * Segura et al. (2005) Segura, A. A., Kasting, J. F., Meadows, V., et al. 2005, Astrobiology, 5, 706, doi: 10.1089/ast.2005.5.706
  * Shkolnik & Barman (2014) Shkolnik, E. L., & Barman, T. S. 2014, AJ, 148, 64, doi: 10.1088/0004-6256/148/4/64
  * Snellen et al. (2013) Snellen, I. A. G., de Kok, R. J., le Poole, R., Brogi, M., & Birkby, J. 2013, ApJ, 764, 182, doi: 10.1088/0004-637X/764/2/182
  * Sousa-Silva et al. (2020) Sousa-Silva, C., Seager, S., Ranjan, S., et al. 2020, Astrobiology, 20, 235, doi: 10.1089/ast.2018.1954
  * Stark et al. (2019) Stark, C. C., Belikov, R., Bolcar, M. R., et al. 2019, Journal of Astronomical Telescopes, Instruments, and Systems, 5, 024009, doi: 10.1117/1.JATIS.5.2.024009
  * Tait & Moore (1995) Tait, V. K., & Moore, R. M. 1995, Limnol. Oceanogr., 40, 189, doi: 10.4319/lo.1995.40.1.0189
  * The LUVOIR Team (2019) The LUVOIR Team. 2019, arXiv e-prints, arXiv:1912.06219.  https://arxiv.org/abs/1912.06219
  * Thompson et al. (2018) Thompson, S. E., Coughlin, J. L., Hoffman, K., et al. 2018, The Astrophysical Journal Supplement Series, 235, 38, doi: 10.3847/1538-4365/aab4f9
  * Thuillier et al. (2004) Thuillier, G., Floyd, L., Woods, T. N., et al. 2004, Advances in Space Research, 34, 256, doi: 10.1016/j.asr.2002.12.004
  * Tian et al. (2020) Tian, H., Xu, R., Canadell, J. G., et al. 2020, Nature, 586, 248, doi: 10.1038/s41586-020-2780-0
  * Tinetti et al. (2018) Tinetti, G., Drossart, P., Eccleston, P., et al. 2018, Experimental Astronomy, 46, 135, doi: 10.1007/s10686-018-9598-x
  * Villanueva et al. (2022) Villanueva, G. L., Liuzzi, G., Faggi, S., et al. 2022, Fundamentals of the Planetary Spectrum Generator
  * Villanueva et al. (2018) Villanueva, G. L., Smith, M. D., Protopapa, S., Faggi, S., & Mandell, A. M. 2018, J. Quant. Spec. Radiat. Transf., 217, 86, doi: 10.1016/j.jqsrt.2018.05.023
  * Yang et al. (2022) Yang, L., Zhang, S., Yin, L., & Zhang, B. 2022, Ecol. Indic., 142, 109307, doi: 10.1016/j.ecolind.2022.109307
  * Zahnle et al. (2006) Zahnle, K., Claire, M., & Catling, D. 2006, Geobiology, 4, 271, doi: 10.1111/j.1472-4669.2006.00085.x
  * Zhu et al. (2016) Zhu, Z., Piao, S., Myneni, R. B., et al. 2016, Nat. Clim. Chang., 6, 791, doi: 10.1038/nclimate3004