11institutetext: Space Research Institute, Austrian Academy of Sciences,
Schmiedlstrasse 6, Graz, A-8042, Austria 22institutetext: Centre for Exoplanet
Science, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK
33institutetext: School of Earth & Environmental Sciences, University of St
Andrews, Bute Building, Queen’s Terrace, St Andrews, KY16 9TS, UK
44institutetext: SUPA, School of Physics & Astronomy, University of St
Andrews, North Haugh, St Andrews, KY16 9SS, UK 55institutetext: Stuttgart
Center for Simulation Science, University of Stuttgart, Pfaffenwaldring 5a,
70569 Stuttgart, Germany
55email<EMAIL_ADDRESS>66institutetext: Fakultät für
Mathematik, Physik und Geodäsie, TU Graz, Petersgasse 16, Graz, A-8010,
Austria 77institutetext: Department of Earth and Planetary Sciences,
University of California, Riverside, CA, USA 88institutetext: Blue Marble
Space Institute of Science, Seattle, WA, USA 99institutetext: School of
Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne,
NE1 7RU, UK

# The effect of lightning on the atmospheric chemistry of exoplanets and
potential biosignatures

Patrick Barth 1122334455 Eva E. Stüeken 2233 Christiane Helling 1166 Edward W.
Schwieterman 7788 Jon Telling 99

(Received 26.06.23; accepted 19.02.2024)

###### Abstract

Context. Lightning has been suggested to play a role in triggering the
occurrence of bio-ready chemical species. Future missions like PLATO, ARIEL,
HWO, and LIFE but also the ground-based ELTs will investigate the atmospheres
of potentially habitable exoplanets.

Aims. We therefore aim to study the effect of lightning on the atmospheric
chemistry, how it affects false-positive and false-negative biosignatures, and
if its effect would be observable on an exo-Earth and on TRAPPIST-1 planets.

Methods. A combination of laboratory experiments, photochemical and radiative
transfer modelling is utilised. Spark discharge experiments are conducted in
N2-CO2-H2 gas mixtures, representing a range of possible rocky-planet
atmospheres. The production of potential lightning signatures (CO, NO),
possible biosignature gases (N2O, NH3, CH4), and important prebiotic
precursors (HCN, Urea) is investigated. Using the measured CO and NO
production rates, photochemical simulations are conducted for oxygen-rich and
anoxic atmospheres for rocky planets orbiting in the habitable zones of the
Sun and TRAPPIST-1 fosr a range of lightning flash rates. Synthetic spectra
are calculated using SMART to study the atmosphere’s reflectance, emission and
transmission spectra.

Results. Lightning enhances, through direct production, the spectral features
of NO, NO2, and, in some cases, CO; CH4 and C2H6 may be enhanced indirectly.
Lightning at a flash rate slightly higher than on modern Earth is able to mask
the ozone features of an oxygen-rich, biotic atmosphere, making it harder to
detect the biosphere of such a planet. Similarly, lightning at a flash rate at
least ten times higher than on modern Earth is also able to mask the presence
of ozone in the anoxic, abiotic atmosphere of a planet orbiting a late M
dwarf, reducing the potential for a false-positive life-detection.

Conclusions. The threshold lightning flash rates to eliminate oxygen
($>0.1\%$) and ozone false positive biosignatures on planets orbiting ultra-
cool dwarfs is up to ten times higher than the modern flash rate, suggesting
that lightning cannot always prevent these false-positive scenarios.

###### Key Words.:

Astrobiology – Astrochemistry – Methods: laboratory: molecular – Techniques:
spectroscopic – Planets and satellites: atmospheres – Planet-star interactions

##  1 Introduction

In the past decades, more than 5500 extrasolar planets have been confirmed,
the majority of which are located in the solar neighbourhood. Of these, 69
planets are potentially habitable111https://phl.upr.edu/hwc, accessed
23.01.2024. These rocky planets orbit their host star at a distance where
water may exist in liquid form, the circumstellar habitable zone. Including
the stellar and galactic environments, the number of potentially habitable
known extrasolar planets decreases to just five (Spinelli et al., 2023). The
limiting factor is the high-energy radiation which enables or disables the
necessary chemical pathways to form complex molecules. JWST, launched in
December 2021, is the first telescope that enables detailed observations of
exoplanet atmosphere composition through its infrared (IR) instruments. The
first step towards detecting habitable planets, however, is the verification
that a rocky planet has an atmosphere (e.g., Turbet et al., 2022; Ih et al.,
2023). Assuming an atmosphere is indeed present, extensive studies have been
conducted to assess the detectability of the biosignature pairs CO2-CH4 or
CH4-O3 (Lin & Kaltenegger, 2022; Rotman et al., 2023) with JWST and the future
Extremely Large Telescopes (ELTs) in the atmosphere of, for example, the
TRAPPIST-1 planets.

To interpret observations from present (JWST) and future missions and
telescopes (PLAnetary Transits and Oscillations of stars, PLATO, Atmospheric
Remote-sensing Infrared Exoplanet Large-survey, ARIEL, ELTs), so-called
‘biosignatures’ have been postulated. Biosignatures are gases or other
planetary features that — singly or in combination — are potentially
indicative of life (e.g., Seager et al., 2012; Grenfell, 2017; Schwieterman et
al., 2018). To avoid misinterpreting such signatures, other processes that can
lead to an observable abundance of these gases need to be quantified. One such
group of processes is electrostatic discharges in atmospheres, the largest of
which is lightning. Lightning is expected to be present in various kinds of
environments, including planetary atmospheres and planet-forming disks (e.g.,
Helling et al., 2016). Lightning in the cloudy atmosphere of a potentially
habitable exoplanet is presenting a strong energy source for disequilibrium
chemistry to take place. Lightning is a significant though small source of
fixed nitrogen on modern Earth (Schumann & Huntrieser, 2007, and references
therin). Previous studies have shown that lightning can also produce fixed
nitrogen in an N2-CO2 atmosphere, similar to the early Archean (Nna Mvondo et
al., 2001; Navarro-González et al., 2001; Summers & Khare, 2007; Barth et al.,
2023), albeit Hu & Diaz (2019) suggest that lightning-fixed nitrogen will be
quickly returned into to the atmosphere as N2. Further, lightning has also
been postulated to have played an important role in the origin of life itself
(Miller, 1953).

The most abundant biological-produced gas on modern Earth and therefore prime
candidate for a biosignature is O2 and its byproduct ozone O3 that is more
easily detectable with a prominent absorption feature at
$9.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (O2 only has weak absorption
features in the mid-infrared within the
$6.3\text{\,}\mathrm{\SIUnitSymbolMicro m}$ water band) (Segura et al., 2003;
Meadows et al., 2018). On modern Earth, O2 is produced by photosynthesis, but
in other circumstances, large amounts of O2 can be produced abiotically. For
example when a rocky planet around an M dwarf loses a large part of its water
inventory during the early, active phase of its host star. Selective escape of
lighter H and retention of heavier O could overwhelm reductant sinks and cause
O2 accumulation in the atmosphere (Ramirez & Kaltenegger, 2014; Wordsworth &
Pierrehumbert, 2014; Luger et al., 2015; Meadows, 2017; Wordsworth et al.,
2018; Johnstone, 2020; Barth et al., 2021a). Particularly on planets orbiting
M dwarfs with a large atmospheric CO2 concentration, the increased intensity
of the X-ray & UV (XUV) radiation can robustly dissociate the CO2 to produce
CO and O, as we will discuss below. The recombination of CO and O is
restricted by deficient near UV (NUV) radiation from the M dwarf host star,
which is key to generating photochemical catalysts that facilitate this
reaction (the direct CO + O reaction is spin-forbidden), potentially producing
a false positive O2 biosignature (Segura et al., 2007; Harman et al., 2015).
Harman et al. (2018) suggest that lightning-produced NO might act as a
catalyst to prevent the buildup of O2 in such an atmosphere. We will discuss
this possibility later.

Nitrous oxide (N2O) has been stipulated as another potential biosignature
(Rauer et al., 2011; Grenfell, 2017; Schwieterman et al., 2022). In the
Earth’s spectral energy distribution, N2O produces detectable peaks in the
near- and mid-IR (Sagan et al., 1993; Gordon et al., 2022). Further, N2O in
the Earth’s atmosphere is mainly from biological origin and there are only a
few abiotic sources. Mainly, stellar radiation or lightning can
photochemically produce NO, which in an anoxic and weakly reducing atmosphere
can undergo further reactions to produce N2O. To distinguish biotically from
abiotically produced N2O, spectral discriminants can be used, such as HCN and
NO2, which are abiotically produced together with the N2O (Airapetian et al.,
2016, 2020; Schwieterman et al., 2022).

In many circumstances, the detection of a single biosignature gas such as O2
would be insufficient evidence to claim the detection of life. Extensive
planetary context to rule out false positives — see Sousa-Silva et al. (2019)
for PH3 or Thompson et al. (2022) for CH4 — and/or additional biosignature
gases would be required for a confident biosignature claim, for example O2 in
combination with CH4 (Lovelock et al., 1975; Sagan et al., 1993), which in
equilibrium would react to CO2 and H2O (Segura et al., 2005). Or the
combination of N2 and O2, i.e. modern Earth’s atmosphere, as this gas mixture
would likely not be stable over geological timescales without the constant
production of both O2 and N2 by life (Stüeken et al., 2016; Krissansen-Totton
et al., 2018b; Lammer et al., 2019; Sproß et al., 2021). However, it still
needs to be assessed whether photolysis of aqueous nitrite and nitrate could
provide enough N2 to the atmosphere to stabilise the N2 concentration
abiotically (Zafiriou & True, 1979a, b; Carpenter & Nightingale, 2015; Ranjan
et al., 2019). Wogan & Catling (2020) discuss the potential of chemical
disequilibria as biosignatures: only an ‘inedible’ disequilibrium, where a
high activation energy is needed to move the system to equilibrium, can be
considered a biosignature. Krissansen-Totton et al. (2018b; 2019) suggest the
combination of CO2 and CH4, which was present in the Archean atmosphere, as
such a disequilibrium biosignature. This biosignature would be strengthened by
the absence of CO which has been suggested as an antibiosignature for
exoplanets (Wang et al., 2016).

In contrast to a false-positive biosignature, where life can still be present
on a planet, an antibiosignature suggests that the planet is not inhabited and
is usually defined as the evidence for free energy not being exploited by life
(Schwieterman et al., 2019). CO provides a source of chemical free energy and
reduced carbon to life in metabolisms such as the Wood-Ljungdahl pathway
(Ragsdale, 2004). Previous simulations of the atmospheric chemistry during the
early Archean represented several metabolisms that govern the concentration of
CO in early Earth’s atmosphere (Kharecha et al., 2005): Methanogens provide a
source of CO, as the CH4 they produce will be photochemically oxidised to CO
if irradiated by far UV (FUV) radiation. Acetogens, on the other hand, provide
a biological sink of CO that is limited by the rate at which CO is deposited
in the ocean (assuming immediate consumption of CO by acetogens). A major
abiotic CO source is the photolysis of atmospheric CO2, and an abiotic sink is
the oxidation of CO by hydroxyl radicals (OH) which are mainly produced by
photochemical reactions (Schwieterman et al., 2019).

Past studies demonstrated that many exoplanets will be covered in clouds for
an extended period during their evolution such that it is reasonable to expect
lightning to occur also in extrasolar planets (Woitke & Helling, 2003; Helling
et al., 2008, 2013a, 2013b; Hodosán et al., 2021). Moreover, lightning will
contribute to the formation of a global electric circuit (Helling, 2019) and
produce chemical tracers of a convectively active atmosphere of any planet
(Hodosán et al., 2016b). However, the only planets where in-situ measurements
can be conducted are those within the Solar System, and the only planet for
which lightning can be studied to a reasonable degree of completeness
concerning flash density and energy range is modern Earth (Hodosán et al.,
2016a). The global lightning flash rate on modern Earth is estimated to be
$44\pm$5\text{\,}{\mathrm{s}}^{-1}$$ (Christian et al., 2003) with an energy
of $6.7\text{\,}\mathrm{GJ}$ per flash (Price et al., 1997), but much
uncertainty remains for the lightning flash rate on the early Earth,
terrestrial planets, and exoplanets in general (Hodosán et al., 2021).

Wong et al. (2017) used climate simulations and the convective available
potential energy to estimate the lightning flash rate in potential Archean
atmospheres with varying CO2 partial pressure. They found the lightning flash
rate to peak at 3.4 times the modern Earth’s flash rate at
$1\text{\,}\mathrm{bar}$ of CO2, with values lower than on modern Earth for
CO2 partial pressures of 0.1 and $10\text{\,}\mathrm{bar}$ (with
$1-$2\text{\,}\mathrm{bar}$$ of N2). Braam et al. (2022) suggest that the
lightning flash rate on tidally locked exoplanets such as Proxima Centauri b
is less than 10% of modern Earth’s. An additional factor that can influence
the occurrence of lightning is cosmic rays. Planets orbiting M dwarfs will
experience more frequent and intense stellar flares that are associated with
flares of charged particles, known to enhance the ionisation in the planet’s
atmosphere (Stozhkov, 2003; Rimmer & Helling, 2013; Grießmeier et al., 2015;
Fraschetti et al., 2019; Scheucher et al., 2020; Barth et al., 2021b).
Comparison between lightning flash rates and cosmic ray ionisation rates in
Earth’s atmosphere has shown a strong correlation between these two quantities
(Stozhkov, 2003). However, the increased influx of charged particles into the
atmospheres of planets orbiting M dwarfs is likely only more efficiently
enabling lightning discharges in already existing electric fields in the
clouds of these atmospheres. We might therefore only find a slightly enhanced
lightning activity on these planets, but more detailed studies on the
connection between cosmic ray ionisation and lightning are necessary to fully
understand these processes.

This paper adopts an approach of combining laboratory experiments and
modelling to investigate the impact of lightning on the atmospheric chemistry
of exoplanets. We present results from spark-discharge experiments with
different gas mixtures initially containing N2, CO2, and H2. The setup of the
experiments and the photochemical model are described in Section 2. In Section
3, we present the results of our experiments and their implications. We apply
our experimental results to two different hypothetical exoplanets and use
photochemical simulations and calculated spectra to determine potentially
observable signatures from lightning and the prospect for false-positive or
false-negative biosignatures (Section 4). Due to the wide range of work
presented in this paper and the large amount of results, we decided to discuss
the implications of individual results in the same sections. We discuss our
assumptions on lightning flash rates and atmospheric composition in Section 5
and present our conclusions in Section 6.

##  2 Methods

###  2.1 Spark Experiments

Figure 1: Schematic of the experimental setup of the discharge experiment.
First published in Barth et al. (2023) by Springer Nature.

All experiments were carried out at the University of St Andrews in the St
Andrews Isotope Geochemistry lab (StAIG). We used the experimental setup
described in Barth et al. (2023), similar to the one described by Parker et
al. (2014) (Fig. 1). The spark discharge (generated by a BD-50E heavy-duty
spark generator with a maximum voltage of $49\text{\,}\mathrm{kV}$) was
contained in the 1-litre reaction flask (Pyrex glass), which contained
$50\text{\,}\mathrm{ml}$ of water at the bottom and the spark electrodes
(tungsten metal) secured in the headspace. The water was agitated with a
magnetic stir bar. The system was evacuated and purged with N2 three times
before adding the desired gas mixture and starting the experiment. To
investigate the effect of water vapour in the gas phase on the final results,
a set of dry experiments was run. For these, we added the water with a syringe
through the septum port on the flask only after the spark had been turned off.
The water was previously flushed with pure N2 (10 min at
$\sim$50\text{\,}\mathrm{ml}\text{\,}{\mathrm{min}}^{-1}$$) to remove
dissolved oxygen. We then let the experiment with the water sit for 3 hours
(with the spark still switched off) to allow for the gaseous and liquid phases
to equilibrate. The water was continuously stirred with the magnetic stir bar
to facilitate gas exchange between the headspace and the liquid phase.

Before and after each experiment, gas from the flask was analysed by a
quadrupole mass spectrometer gas analyser. After the experiment, a gas sample
was extracted from the flask with a gas-tight, lockable syringe to determine
the concentration of CH4 and N2O with a gas chromatograph. From a limited
sample of experiments, multiple gas samples were extracted for analyses of CO.
The fluid phase was transferred into a 50ml Falcon centrifuge tube for
subsequent analyses of dissolved nitrite, nitrate, ammonium, urea, and cyanide
(see below). The analytical methods used to determine the concentrations of
these species are detailed in Appendix A. From these concentrations, the
energy yield
($\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$)
can be calculated, using the energy of the spark $E=1/2UIt$ with the applied
voltage $U=$49\text{\,}\mathrm{kV}$$, the current $I=$1\text{\,}\mathrm{mA}$$,
and the duration $t$ of the spark. To extrapolate this yield to the annual,
global production, we used an estimate for the global lightning flash rate on
modern Earth of $44\pm$5\text{\,}{\mathrm{s}}^{-1}$$ (Christian et al., 2003)
with an energy of $6.7\text{\,}\mathrm{GJ}$ per flash (Price et al., 1997).

###  2.2 Photochemical Simulations

Figure 2: Spectral Energy Distributions at the top of the planets’ atmospheres
of the Sun (red) and TRAPPIST-1 (black) as used in the photochemical model and
for the planetary spectra.

We conducted photochemical simulations to calculate the mixing ratios of CO,
NO, and NO2 in the atmosphere of different test planets for a range of NO and
CO production rates, corresponding to a range of lightning flash rates. To
conduct these tests, we used the photochemical model component of the Atmos
coupled climate-photochemistry code (Arney et al., 2016; Lincowski et al.,
2018)222https://github.com/VirtualPlanetaryLaboratory/atmos. We conducted all
simulations in uncoupled mode (no climate adjustment) to isolate the specific
chemical impact of varying CO and NO fluxes from lightning. When simulating
anoxic atmospheres, we adopt an Archean-Earth planet template with 74 chemical
species and 392 photochemical reactions. For O2-rich atmospheres, we adopt a
modern Earth-like template with 50 species and 239 reactions. We have
incorporated the latest H2O cross-sections and corrected sulfur reaction rate
as recommended by Ranjan et al. 2020. The model normally includes the impact
of Earth-like lightning by injecting NO into the troposphere (Harman et al.,
2018); however, we have removed this feature and replaced it with a variable
NO injection rate to assess the impact of varying NO production from
lightning. The model includes diffusion-limited hydrogen escape (Harman et
al., 2015).

We ran the simulations for an Earth-sized planet, orbiting the Sun at
$1\text{\,}\mathrm{a}\mathrm{u}$ and the M dwarf TRAPPIST-1 at an instellation
identical to that of TRAPPIST-1 e (Agol et al., 2021). The initial atmospheric
composition was set to be similar to our high-CO2 experiments (4.6% CO2 with
N2 as filler gas). We also calculated the CO and NO2 mixing ratios in a
corresponding oxic atmosphere (21% O2, 4.6% CO2 with N2 as filler gas). In
both cases, the CO2 concentration is fixed to the initial value of 4.6%. The
tropospheric water vapour concentration is governed by the surface temperature
of the planet: 0.5% H2O for $T=$275\text{\,}\mathrm{K}$$, 1.2% H2O for
$T=$288\text{\,}\mathrm{K}$$, and 2.5% H2O for $T=$300\text{\,}\mathrm{K}$$.
The pressure-temperature profiles for the anoxic simulations assume surface
temperatures of $T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$ and
$T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$, adiabatic cooling throughout the
troposphere, and then an isothermal temperature of
$T_{\mathrm{gas}}=$180\text{\,}\mathrm{K}$$. For the oxic simulations, the
pressure-temperature profile of modern Earth is used, with a surface
temperature of $T_{\mathrm{surf}}=$288\text{\,}\mathrm{K}$$. The spectra of
the Sun and TRAPPIST-1 (Fig. 2) are used for the photochemistry simulations
and to simulate the planetary spectra. The spectrum of the Sun was sourced
from Thuillier et al. (2004) while the TRAPPIST-1 spectrum represents an
average of the three activity models presented in Peacock et al. (2019). Each
spectrum is re-interpolated onto the standard Atmos base grid (Lgrid=0
setting).

We ran the model for different scenarios: Abiotic scenario: Volcanic fluxes of
CH4
($10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$),
H2
($10^{10}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
deposition velocity into the ocean: $v_{\mathrm{dep}}=2.4\times
10^{-4}\,$\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$), H2S ($3.5\times
10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
$v_{\mathrm{dep}}=2\times 10^{-2}\,$\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$),
and SO2 ($3.5\times
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
$v_{\mathrm{dep}}=1$\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$) are included and
distributed over the bottom $10\text{\,}\mathrm{km}$ of the atmosphere profile
(as is the variable CO flux). The CO deposition velocity is
$v_{\mathrm{dep}}=10^{-8}\,$\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$ which is
the limit for the abiotic formation of formate (Kharecha et al., 2005). Biotic
scenario: In addition to the volcanic sources of the abiotic scenario, a
biological methane production of
$10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
is included, which corresponds to the Earth’s current biogenic methane flux
(Jackson et al., 2020). The CO deposition velocity in the biotic case is
$v_{\mathrm{dep}}=1.2\times 10^{-4}\,$\mathrm{cm}\text{\,}{\mathrm{s}}^{-1}$$
which is the maximum deposition velocity for an ocean with a CO concentration
of 0, i.e. where all CO is immediately consumed by acetogens (Kharecha et al.,
2005). A detailed table containing the parameters for all the different
scenarios can be found in the Appendix.

###  2.3 Spectral Simulations

To simulate reflectance, emission, and transmission spectra we used the
Spectral Mapping Atmospheric Radiative Transfer code (SMART, Meadows & Crisp,
1996; Crisp, 1997) with transit updates as described in Robinson (2017). SMART
is a versatile and well-validated line-by-line, multi-stream, multiple
scattering, and absorption model that can produce planetary spectra from the
far-UV to far-IR. SMART relies on the DISORT Fortran code (Stamnes et al.,
1988) to solve the radiative transfer equation via the discrete ordinate
method. SMART includes opacity data from HITRAN (Gordon et al., 2017) that are
preprocessed by their Line-By-Line Absorption Coefficients (LBLABC) companion
model. SMART has been used to simulate spectra of planets inside and outside
of the Solar System including the TRAPPIST-1 planets (Tinetti et al., 2005;
Robinson et al., 2011; Arney et al., 2014; Lustig-Yaeger et al., 2019). For
the spectra presented in Section 4.4, we show reflectance spectra degraded to
a spectral resolving power of R=400, transmission spectra degraded to R=200,
and emission spectra with a spectra resolution of 1 cm-1.

##  3 Results and Implications of Experimental Measurements

Table 1: Initial gas compositions in our experiments in bara.

Species | Gas mixture
---|---
pure N2 |  N2-H2 |  \+ low CO2 |  \+ high CO2
$120\text{\,}\mathrm{min}$ experiments (wet)
N2 |  $0.99\pm 0.00$ |  $0.98\pm 0.00$ |  $0.98\pm 0.00$ |  $0.93\pm 0.01$
H2 |  $0.00\pm 0.00$ |  $(9.98\pm 0.01)\times 10^{-3}$ |  $(9.98\pm 0.01)\times 10^{-3}$ |  $(9.3\pm 0.1)\times 10^{-3}$
CO2 |  $(2.6\pm 0.9)\times 10^{-5}$ |  $(1.1\pm 0.1)\times 10^{-4}$ |  $(2.5\pm 0.1)\times 10^{-3}$ |  $(4.6\pm 0.6)\times 10^{-2}$
O2 |  $(1.3\pm 0.4)\times 10^{-4}$ |  $(8\pm 1)\times 10^{-5}$ |  $(1.2\pm 0.2)\times 10^{-4}$ |  $(1.3\pm 0.3)\times 10^{-4}$
H2O |  $(1.1\pm 0.1)\times 10^{-2}$ |  $(1.4\pm 0.1)\times 10^{-2}$ |  $(1.0\pm 0.1)\times 10^{-2}$ |  $(1.21\pm 0.03)\times 10^{-2}$
$120\text{\,}\mathrm{min}$ experiments (dry)
N2 |  $0.99\pm 0.00$ |  $0.99\pm 0.00$ |  $0.98\pm 0.01$ |  $0.94\pm 0.01$
H2 |  $0.00\pm 0.00$ |  $(9.85\pm 0.02)\times 10^{-3}$ |  $(9.77\pm 0.03)\times 10^{-3}$ |  $(9.37\pm 0.04)\times 10^{-3}$
CO2 |  $(2\pm 1)\times 10^{-6}$ |  $(2\pm 2)\times 10^{-5}$ |  $(6\pm 2)\times 10^{-3}$ |  $(4.7\pm 0.5)\times 10^{-2}$
O2 |  $(6\pm 2)\times 10^{-5}$ |  $(1.4\pm 0.3)\times 10^{-4}$ |  $(5\pm 3)\times 10^{-4}$ |  $(2.6\pm 0.1)\times 10^{-4}$
H2O |  $(6\pm 3)\times 10^{-3}$ |  $(4\pm 2)\times 10^{-3}$ |  $(6\pm 2)\times 10^{-3}$ |  $(6\pm 2)\times 10^{-3}$
Overnight experiments (wet)
N2 |  $0.99\pm 0.00$ |  $0.97\pm 0.00$ |  $0.97\pm 0.00$ |  $0.94\pm 0.01$
H2 |  $0.00\pm 0.00$ |  $(9.74\pm 0.01)\times 10^{-3}$ |  $(9.71\pm 0.02)\times 10^{-3}$ |  $(9.4\pm 0.1)\times 10^{-3}$
CO2 |  $(1.1\pm 0.1)\times 10^{-5}$ |  $(4\pm 3)\times 10^{-5}$ |  $(4\pm 1)\times 10^{-3}$ |  $(3.8\pm 0.5)\times 10^{-2}$
O2 |  $(9\pm 3)\times 10^{-5}$ |  $(5\pm 1)\times 10^{-5}$ |  $(2.5\pm 1.2)\times 10^{-4}$ |  $(1.4\pm 0.4)\times 10^{-4}$
H2O |  $(1.0\pm 0.5)\times 10^{-2}$ |  $(1.6\pm 0.1)\times 10^{-2}$ |  $(1.5\pm 0.2)\times 10^{-2}$ |  $(1.8\pm 0.1)\times 10^{-2}$

a values are averaged from multiple sets of experiments, errors are standard
errors of the mean ($\sigma/\sqrt{N}$)

We performed spark discharge experiments in gas mixtures with different
combinations of N2, CO2, and H2 to investigate the effect of lightning on the
chemistry of lightly reducing gas mixtures with varying fractions of CO2. Our
goal is to give a complete picture of the most abundant gaseous and aqueous
compounds produced in spark discharge experiments in such gas mixtures. These
compounds can be grouped into three categories: (1) CO and NO are, as we will
see later, the most abundant products and are directly produced in the spark
channel. Because of that, they might present signatures for lightning activity
in exoplanetary atmospheres as we will discuss in Section 4. (2) N2O, NH3, and
CH4 are potential biosignatures (e.g., Seager et al., 2013b; Phillips et al.,
2021; Huang et al., 2022; Schwieterman et al., 2022; Thompson et al., 2022)
and we want to investigate whether lightning might present a significant
source of these gases. (3) NH4^+, NO2^-, NO3^-, HCN, and Urea are important
prebiotic compounds, either as precursors for the formation of biological
macromolecules or as nutrients for early life forms (e.g., Miller, 1957;
Miller & Urey, 1959; Abelson, 1966; Sanchez et al., 1967; Miller &
Schlesinger, 1983; Schopf et al., 2007; Ducluzeau et al., 2009; Wong et al.,
2017; Das et al., 2019). We investigated how the gas composition changes the
yields of these products and what effect the presence of water vapor in the
gas mixture has. We conducted a range of short, 120-minute experiments as well
as longer, overnight experiments to study the production of molecules with low
yields that could not be detected in our short experiments. First, we present
the results from our short experiments in individual sections for each
compound and discuss their implications on the importance of lightning as a
source of the specific molecule in the same section (Sections 3.1–3.8). We
then present and discuss the results from our overnight experiments (Section
3.9). The different gas compositions for all experiments are compiled in Table
1.

Figure 3: Final abundance of ammonium (NH4^+), ammonia (NH3), methane (CH4),
nitrate (NO3^-) and nitrite (NO2^-), nitrous oxide (N2O), and nitric oxide
(NO) in $120\text{\,}\mathrm{min}$ spark experiments with different gas
compositions (see Tab. 1 for individual gas compositions). Results from
experiments with (blue) and without (orange) water are shown separately. If no
concentrations were measurable, the detection limit is indicated with an
arrow. The data presented here are based on averages of multiple measurements
with the error bars representing the individual standard error of the mean
($\sigma/\sqrt{N}$). Data for NH3 is calculated from aqueous NH4^+ and not
measured directly. Measurements of methane abundance are within $1\sigma$ of 0
(red line) and are therefore shown without error bars and semi-transparent.

For our short, 120-minute experiments, we performed experiments both with
(wet) and without water (dry) in the flask during the spark to investigate the
effect of water vapor on the yields of our products. As described in Section
2, we added $50\text{\,}\mathrm{ml}$ of water to the dry experiments after
turning off the spark. We then analysed the gas and water for the
concentrations of NO, CO, N2O, CH4, NH4^+, NO2^-, and NO3^-. Figure 3 shows
the combined results from our short experiments. The individual measurements
of each gas composition are averaged over 3 to 7 replicates (a detailed table
with individual results is available
online333https://doi.org/10.17630/8b72510f-62a8-43dc-94f1-af9b7766f817), the
results for wet and dry experiments are shown in different colors next to each
other. As expected, one of the main results is that reduced nitrogen and
carbon species (ammonium, ammonia, and methane) are more abundant in the pure
N2-H2 and low-CO2 experiments. Oxidised forms of nitrogen (nitrate, nitrite,
nitric oxide, and nitrous oxide) are more abundant in the high CO2 experiments
where the dissociation of CO2 provides the necessary oxygen source for NO and
subsequent nitrogen oxides.

This follows the results from different studies in the past: Experiments with
electric discharges in reducing CH4-NH3 and CH4-N2 gas mixtures produced a
variety of reduced nitrogen and carbon products, including H2, NH3,
hydrocarbons, and nitriles such as HCN (Toupance et al., 1975). Similar
experiments simulating corona discharges in Titan’s reducing atmosphere (10%
CH4 and 2% Ar in N2) have shown show the production of reduced nitrogen and
carbon in the form of various hydrocarbons and nitriles (Reid Thompson et al.,
1991; Navarro-González & Ramírez, 1997; Navarro-González et al., 2001b). Spark
experiments with different N2-CO2 gas mixtures have shown that predominantly
oxidised forms of nitrogen and carbon are produced, such as NO, N2O, NO2,
HNO3, or CO (e.g., Levine et al., 1982; Nna Mvondo et al., 2005; Heays et al.,
2022). Navarro-González et al. (2001) and Nna Mvondo et al. (2001) studied the
production of NO by lightning in gas mixtures with varying CO2 concentration
and found a clear trend of decreasing nitrogen fixation efficiency with
decreasing availability of oxygen from CO2.

We found increased efficiency of nitrogen oxides production in the experiments
that contained water in the flask during the spark. The presence of liquid
water resulted in approximately 1% of water vapour in the gas phase at room
temperature (Table 1), which was also dissociated in the spark, providing
additional oxygen for the NO production. The individual products shown in Fig.
3 as well as CO are discussed in the following sections.

###  3.1 Ammonium (NH4^+)

Ammonium is an important nutrient for microbial life on Earth and was the
product of the first developed pathways of biological nitrogen fixation
(Schopf et al., 2007; Dodd et al., 2017). Lightning-produced ammonium would
therefore present a potential nutrient source for life before the onset of
biological nitrogen fixation. We found that maximum ammonium production
happens in experiments with no or $<1\%$ of CO2. A higher CO2 concentration
limits the efficiency of ammonium production. However, except for a few
individual experiments, we found the final ammonium concentration to be lower
than the concentration of nitrite and nitrate, in particular for the wet
experiments. Our highest ammonium production rate (the wet, CO2-free case) is
$(3.8\pm 1.7)\times
10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
which, using the modern Earth flash rate, corresponds to a yearly production
of $(1.1\pm 0.5)\times 10^{-3}\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$.
With a higher CO2 concentration, more likely resembling early Earth’s
atmosphere, this reduces to $(1.8\pm 1.2)\times
10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
and $(0.5\pm 0.3)\times 10^{-3}\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$.
This is much lower than the production of nitrite and nitrate (see below),
though nitrite can subsequently be reduced to ammonium by Fe^+2 and FeS in the
ocean, while FeS can also reduce nitrate to ammonium albeit with a lower yield
(Summers & Chang, 1993; Summers, 2005). Direct production of ammonium by
lightning is therefore not significant on planets with a substantial
concentration of CO2 and/or water vapour in the atmosphere.

###  3.2 Ammonia (NH3)

Ammonium is not directly produced by the spark. Instead, ammonia is the
gaseous product of the spark discharge that then equilibrates with the water
where it reacts to ammonium. Ammonia can be produced biologically and has been
previously suggested as a biosignature for planets with a significant H2
fraction in the atmosphere (Seager et al., 2013a, b; Huang et al., 2022).
Ranjan et al. (2022) describe a scenario where NH3 is produced in such high
quantities that it saturates its photochemical sinks, such as O2 in modern
Earth’s atmosphere, and goes into a runaway mode. The surface flux above which
the NH3 concentration enters into this runaway state, depends on the level of
UV-radiation. In their simulations of atmospheres with 10% H2 and 90% N2 (with
1% water vapour) on an Earth-sized planet orbiting an M dwarf, Ranjan et al.
find this flux to be approximately
$10^{11}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$, and as low as
$10^{8}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$ for an elevated
stratospheric temperature (from $T_{\mathrm{strat}}=$170\text{\,}\mathrm{K}$$
to $210\text{\,}\mathrm{K}$). The modern Earth NH3 flux is $(1.1-1.8)\times
10^{10}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$ (Bouwman et al.,
1997) and the pre-industrial flux $(2-9)\times
10^{9}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$ (Zhu et al., 2015).
The maximum lightning-induced NH3 flux we can extrapolate from our experiments
with an atmosphere of 1% H2 and 1% H2O (in N2), including the aqueous NH4^+,
is approximately $(2.2\pm 1.0)\times
10^{5}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$ (wet, pure N2-H2).
This is many orders of magnitude below the flux necessary to enter into a
runaway state, suggesting that lightning cannot be responsible for a false-
positive biosignature detection with NH3.

###  3.3 Methane (CH4)

Methane is frequently discussed as a potential biosignature, in particular for
Archean Earth-like worlds (e.g., Thompson et al., 2022). If lightning could
produce significant amounts of methane in an early Earth-like atmosphere, this
would present an important restriction on methane’s role as a biosignature.
However, in our experiments, only small amounts of methane are produced. Most
of the measurements are below the error of an individual measurement
($0.6\text{\,}\mathrm{p}\mathrm{p}\mathrm{m}$) which means that they are
within $1\sigma$ of 0. We therefore assume
$0.6\text{\,}\mathrm{p}\mathrm{p}\mathrm{m}$ (or a total production of
$0.024\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}\mathrm{o}\mathrm{l}$) to
be the upper limit for methane production in our experiments, as indicated by
the red line in Fig. 3. This limit corresponds to an annual methane production
with a modern lightning flash rate of less than $2\times
10^{-5}\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$ or $1.3\times
10^{-6}\,$\mathrm{T}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{yr}$$. The
annual methane production on modern Earth is
$$37\text{\,}\mathrm{T}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{yr}$=$596\text{\,}\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$,
of which $\sim 40\%$ is natural (not anthropogenic) (Jackson et al., 2020)
while the possible Archean biological methane production was between 9 and
$20\text{\,}\mathrm{T}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{yr}$
(Sauterey et al., 2020). The upper limit for abiotic methane production by
serpentinising systems (hydrothermal alteration of crustal mafic rocks) is
between 0.02 and
$10\text{\,}\mathrm{T}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{/}\mathrm{yr}$
(Krissansen-Totton et al., 2018b). This suggests that in the atmospheric
conditions explored in this study, methane production by lightning is
negligible compared to other abiotic and biotic sources. The lightning flash
rate in such an atmosphere would have to be 5 – 6 orders of magnitude higher
than on modern Earth to produce a comparable amount of methane.

###  3.4 Carbon Monoxide (CO)

Figure 4: CO concentration in 4 different spark experiments (high and low-CO2,
wet and dry), measured at 3 different points in time during the experiment.
Fitted lines give the CO concentration assuming CO is the product of an
equilibrium reaction, following
$c_{\ce{CO2}}=(1-(k_{1}+k_{2}\cdot\exp{(-(k_{1}+k_{2})t)})/(k_{1}+k_{2}))\cdot
c_{1}$. Shaded areas represent errors in CO measurements.  Figure 5: CO and NO
concentrations in chemical equilibrium as a function of gas temperature (with
GGChem, Woitke et al., 2018) for high-CO2 gas mixtures. The different cases
considered are: 0% (solid lines), 0.9% (dashed), 5% (dash dotted), and 10%
(dotted) of H2. As H2 is binding free oxygen into H2O, increasing the H2
concentration prevents the recombination of CO to CO2 as well as the
production of NO. CO (red) and NO (blue shaded area) measurements with
uncertainties from wet $120\text{\,}\mathrm{min}$ experiments. Minimum freeze-
out temperature estimates for CO (orange) and NO (green) with uncertainties.

In contrast to methane, carbon monoxide has been discussed as a potential
antibiosignature (Wang et al., 2016; Schwieterman et al., 2019). If on an
inhabited planet, lightning were to produce detectable amounts of CO by
overwhelming biological sinks, this would provide a limitation on the use of
CO as an antibiosignature. We analysed the CO concentrations of four
experiments, each at three different points in time during the experiment
(after 30, 60, and $120\text{\,}\mathrm{min}$). These results are shown in
Fig. 4. The CO production rate decreased with time, likely because CO
concentration reaches equilibrium. We extrapolated the CO concentration to
estimate the equilibrium concentration (Fig. 4). Following the equilibrium
reaction A1 ¡=¿ A2 (A2 is CO in this case) with the reaction coefficients
$k_{1}$ and $k_{2}$, the change in $c_{2}$ (the concentration of A2) is given
by

$\frac{dc_{2}}{dt}=-k_{2}c_{2}+k_{1}c_{1}$ (1)

Starting with all molecules in A1 ($c_{1,0}=c_{\mathrm{tot}},c_{2,0}=0$),
$c_{2}$ increases with time:

$c_{2}=\left(1-\frac{k_{2}+k_{1}\cdot\exp{(-(k_{1}+k_{2})t)}}{k_{1}+k_{2}}\right)\cdot
c_{\mathrm{tot}}.$ (2)

The resulting equilibrium concentration of $c_{2}$ (for $t\rightarrow\infty$)
is then given by

$c_{2,\mathrm{eq}}=\left(\frac{k_{1}}{k_{1}+k_{2}}\right)\cdot
c_{\mathrm{tot}}.$ (3)

For our experiments, the estimates for CO equilibrium concentrations are 1.5%
for the high-CO2 experiments (4.5-4.6% CO2) and 0.85% for the low-CO2
experiments (0.6-0.7% CO2).

###  3.5 Extrapolating CO-Production to Different Atmospheres

In past studies, the lightning production rates of different gases like NO
have been determined by assuming the equilibrium concentration of said gases
at the so-called ‘freeze-out temperature’ (e.g., Chameides et al., 1977; Hill
et al., 1980; Borucki & Chameides, 1984). The freeze-out temperature is the
temperature at which the equilibrium timescale is larger than the cooling
timescale of the gas mixture, freezing in the gas composition at that
temperature. Every time a gas parcel has been heated up by a lightning strike
and is cooling down again, the concentration of NO, CO, and other lightning
products in the air parcel is increased to its equilibrium concentration at
the respective freeze-out temperature. Comparison to experimental results of
NO production rates by lightning show that this method is a valid approach to
determine the production of NO etc. by lightning (see reviews by Schumann &
Huntrieser, 2007; Heays et al., 2022).

In this study, we used our experimental results and chemical equilibrium
calculations to determine the freeze-out temperatures of NO and CO, allowing
us in the next step to extrapolate our results to different gas compositions.
To evaluate the effect of H2 on the CO and NO production, we carried out
equilibrium calculations with GGChem (Fig. 5; Woitke et al., 2018). We used a
subset of the species within GGChem with 87 charged and neutral species
containing the elements H, C, N, and O, as well as electrons. We calculated
the thermochemical equilibrium composition of gas mixtures with varying H2
fractions resembling our wet, high-CO2 experiments (4.6% CO2, 1% H2O, $0-10\%$
H2, with the rest to 100% N2) for temperatures between 300 and
$4000\text{\,}\mathrm{K}$. By comparing our CO and NO measurements from the
experiments with 0.9% H2 (red and blue shaded areas, respectively) to the
corresponding calculations (dashed lines), we can estimate a minimum freeze-
out temperature for the respective gas. Here, the CO measurement is from only
one experiment, the NO concentration is the average of multiple experiments.

While the CO measurements with time allow us to estimate the equilibrium
composition of CO in the flask (see Fig. 4), we only have one measurement of
NO after the full $120\text{\,}\mathrm{min}$ run time of the experiment, which
might increase slightly further. We therefore can only give a minimum estimate
on the freeze-out temperature for NO. Our estimates are
$T_{\mathrm{f}}(\mathrm{CO})=(2430\pm 65)\,$\mathrm{K}$$ and
$T_{\mathrm{f}}(\mathrm{NO})\geq(3000\pm 160)\,$\mathrm{K}$$. The latter is
similar to previous estimates by of
$T_{\mathrm{f}}(\mathrm{NO})=$2300\text{\,}\mathrm{K}$$ (Gilmore, 1975;
Chameides et al., 1977), $2660\text{\,}\mathrm{K}$ (Picone et al., 1981;
Borucki & Chameides, 1984), and $3500\text{\,}\mathrm{K}$ (Kasting & Walker,
1981). These estimates are based on different methods and assumptions on the
cooling timescale of the gas heated in the lightning channel, showing that
extrapolating from lab experiments and theoretical calculations to real-world
lightning strikes comes with large uncertainties. The errors we report with
our freeze-out temperatures represent the range of temperatures necessary to
explain the range of CO and NO concentrations in our experiments but do not
include further uncertainties that arise when extrapolating our experimental
conditions to real-world lightning strikes. Our estimate of the NO freeze-out
temperature also allows us to determine a lower limit of the maximum
temperature reached within the spark channel of approximately
$3000\text{\,}\mathrm{K}$.

There are much fewer estimates for the CO freeze-out temperature (compared to
NO), with $3500\text{\,}\mathrm{K}$ when the CO is produced in the expanding
shock front around the lightning channel (Levine et al., 1979; Chameides,
1979) and $2000\text{\,}\mathrm{K}$ if the CO is produced in the inner core of
the cooling channel (Chameides, 1979). Hill et al. (1980) point out that the
cooling channel is more important for the production of NO, CO, and other
gases because of its larger volume compared to the expanding shock front.
According to Stark et al. (1996), this is particularly true for spark
experiments. Our estimate for the freeze-out temperature is thus slightly
higher than the estimate of $2000\text{\,}\mathrm{K}$ for the cooling channel,
potentially explained by an additional contribution of the higher freeze-out
temperature of the shock front.

The estimates for the freeze-out temperatures allow us to extrapolate the CO
and NO production to atmospheres with different H2 fractions. As the freeze-
out temperature depends on the cooling timescale of the spark and the
equilibrium timescale of the gas mixture, changing the gas composition can
lead to a change in the freeze-out temperature. In our case, we only slightly
vary the atmospheric composition, which allows us to assume a constant freeze-
out temperature. Figure 5 shows additional equilibrium calculations for gas
mixtures without H2 (solid lines), with 5% (dash-dotted) and with 10% H2
(dotted). The addition of H2 is increasing the abundance of CO in the lower
temperature regime where (in the absence of H2) CO2 would be more stable. The
H2 reacts with the atomic oxygen produced by the dissociation of the CO2 to
form H2O, preventing the CO from recombining with the O to CO2. Eventually,
the abundance of CO is limited by the availability of C from the initial CO2.
At the freeze-out temperature of $\sim$2400\text{\,}\mathrm{K}$$ this means an
increase of the CO abundance by a factor of 2.5 when increasing the H2
fraction from 0.9% to 10% (in a background of 4.6% CO2 and in the context of
the limited chemistry applied in these calculations). At the same time, the
presence of H2 (and subsequent production of H2O) reduces the availability of
oxygen for the production of NO. At $3000\text{\,}\mathrm{K}$, we find that
the NO concentration for 10% H2 is only $1/3$ of the concentration expected in
the 0.9%-H2 case.

From the initial slope of our fit to the CO concentration with time (Fig. 4) a
global, annual production of
$(6-18)\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$ and a surface flux of
$(7.6-24)\times 10^{8}\,${\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$$ can be
estimated for the different H2 concentrations (assuming modern Earth’s
lightning flash rate). Using those estimates for surface fluxes, a grid of
photochemical simulations were performed, similar to those presented by
Schwieterman et al. (2019). This allowed us to test under which conditions a
lightning contribution to CO production could be observable (Section 4).

Previous experimental results and calculations for the CO production by
lightning in modern Earth’s atmosphere are
$0.01\text{\,}\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$ (Green et al., 1973),
$0.04\text{\,}\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$ (Levine et al., 1979),
and $(0.004-0.2)\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$ (Chameides, 1979).
If we use the approach outlined above, using the equilibrium concentration of
CO at $2430\text{\,}\mathrm{K}$ in a gas mixture resembling modern Earth’s
atmosphere, our estimate for the global CO production by lightning is
$(0.01\pm 0.003)\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$ which is in
agreement with the values presented in the literature.

###  3.6 Nitrogen Oxide (NO) Production and Extrapolation to Different
Atmospheres

Barth et al. (2023) have shown that lightning can produce large amounts of
nitrogen oxide in both N2-O2 and N2-CO2 atmospheres. This NO provides the
precursor of other nitrogen oxides in the gas phase as well as nitrite and
nitrate in the aqueous phase (see below). From our equilibrium calculations,
we find that the maximum possible NO concentration (at
$\sim$3300\text{\,}\mathrm{K}$$) is only slightly higher than our measurement
for the wet, high-CO2 experiments (Fig. 5). This suggests, that at the time we
took the NO measurement, the NO concentration in the flask had (nearly)
reached equilibrium. We cannot fit the production law we used for CO (Reaction
2) to this single data point, but, assuming our data point represents the
equilibrium NO concentration, we can find the slowest production that will
reach equilibrium after $120\text{\,}\mathrm{min}$ (within 1%). The slope of
this production curve at the origin provides a lower limit for the NO
production rate. For the wet experiments with a high CO2 concentration, this
returns a lower limit of $(5.6\pm 1.0)\times
10^{15}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
or a yearly production of $(2.6\pm
0.4)\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$ with modern Earth’s lightning
flash rate.

For the other three sets of wet experiments (with N2, N2-H2, and low CO2 gas
mixtures), the minimum NO production is independent from the CO2 and H2
fraction in the gas $(3\pm 1)\times
10^{15}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
or $(1.2\pm 0.3)\times 10^{-2}\,$\mathrm{Tg}\text{\,}{\mathrm{yr}}^{-1}$$. In
these experiments, water vapour in the gas mixture ($1-1.4\%$) provides the
necessary oxygen to oxidise nitrogen to NO. In the corresponding dry
experiments, the NO production is lower than in the wet experiments, but not 0
due to traces of CO2 (in particular in the low-CO2 experiments), water vapour,
and O2 being present in the gas mixture. Barth et al. (2023) found in their
wet experiments with only trace amounts of O2 (0.06%) that $\sim 3\times
10^{15}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
of NO are produced. This production rate is similar to our wet experiments
without any or with only small amounts of CO2, suggesting that dissociation of
water vapour is the main production pathway for NO in all of these experiments
where the concentration of CO2 and O2 is low.

From the high-CO2 experiments and subsequent equilibrium calculations (Fig. 5)
we find that the presence of H2 in the gas mixture decreases the NO
production. Instead, more H2O is produced. We used these results for the NO
production rate as input for photochemical simulations of the NO2
concentration in the atmospheres of different potential exoplanets (Section
4). NO and NO2 are spectrally active at
$5.3\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$6\text{\,}\mathrm{\SIUnitSymbolMicro m}$, respectively, and therefore
potential signatures for lightning activity in exoplanet atmospheres (Gordon
et al., 2022).

###  3.7 Nitrous Oxide (N2O)

N2O is another potential biosignature, making an investigation of the
possibility of a false-positive signature from lightning important. The
maximum N2O production found in our experiments is
$2.5\text{\,}\mathrm{\SIUnitSymbolMicro mol}$ which corresponds to an energy
yield of $8.5\times
10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
or $1.3\times 10^{-4}\,$\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$$ with modern
Earth’s lightning flash rate (see Section 2). This value is similar to
experimental results for Earth’s atmosphere (Levine et al., 1979; Hill et al.,
1984; Chameides, 1986). The total biological N2O emission on Earth is much
larger with $0.45\text{\,}\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$ (Bouwman
et al., 2002; Tian et al., 2020). This N2O is produced by incomplete
denitrification of Nitrate to N2 (Schwieterman et al., 2022). In the
Proterozoic, the N2O flux might have been significantly higher due to the
limited availability of copper catalysts, preventing the last step of
denitrification from N2O to N2 (Buick, 2007).

In addition to the N2O directly produced by lightning, other forms of fixed
nitrogen (e.g. NO, NO2, or HNO3) can be deposited into the ocean, converted to
N2O by Fe^2+ (Ranjan et al., 2019), and again outgassed into the atmosphere.
If all lightning-produced NO (based on our experimental results) were to be
converted to N2O eventually, that would correspond to an annual production of
$0.09\text{\,}\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$. This would only be a
factor of 5 lower than the modern Earth N2O flux and potentially detectable in
the emission spectrum of an Earth-like planet orbiting a K dwarf (Schwieterman
et al., 2022). This would be particularly true if the lightning flash rate in
the atmosphere of such a planet is larger than that on modern Earth.

However, in the anoxic atmosphere of an Archean Earth-like planet, the N2O
abundance will be reduced by the missing O2-shielding, decreasing the
probability of a detectable signal and strengthening the case for the O2/O3 +
N2O biosignature. Moreover, an O2-rich planet probably does not have
Fe^2+-rich oceans. In addition, UV photolysis of nitrate and nitrite,
releasing nitrogen back into the atmosphere as N2 (Zafiriou & True, 1979a, b;
Carpenter & Nightingale, 2015; Ranjan et al., 2019) would reduce the feed-
stock to produce abiotic N2O. A detectable NO2 signature from lightning (see
Section 4.4) might help to distinguish a lightning-produced N2O signature from
a biogenic source (Schwieterman et al., 2022). We use our results from the
photochemical simulations to estimate the maximum potential N2O production and
compare it to the NO2 concentration (Section 4.3).

###  3.8 Nitrate (NO3^-) & Nitrite (NO2^-)

Lightning-produced nitrite and nitrate have been hypothesised as potential
nutrients for life on early Earth before the onset of biological nitrogen
fixation (e.g., Ducluzeau et al., 2009; Canfield et al., 2010; Nitschke &
Russell, 2013; Shibuya et al., 2016; Wong et al., 2017; Ranjan et al., 2019).
Even though Barth et al. (2023) have shown that life likely became independent
from lightning as a nutrient source very early, it might have still
contributed to support Earth’s earliest biosphere. Further, this nitrate and
nitrite could present a nutrient source for life on exoplanets.

We combined the concentrations of nitrate and nitrite (Fig. 3) because part of
the nitrite will oxidise to nitrate in the solution during the experiment. The
extent of this oxidation varies depending on the individual experiment setup.
As was the case for NO, we find that in wet experiments, the production of
nitrite and nitrate increases compared to the dry experiments. Also the
experiments without CO2 show some nitrite and nitrate production: in the wet
experiments, this is due to the presence of water, but also in the dry
experiments, some nitrite and nitrate are present. This small residue may
reflect the presence of trace amounts of gaseous H2O, CO2, or O2 in the
initial gas mixture due to the limits of our vacuum. Overall, in the high-CO2
experiments the nitrite and nitrate yield is very similar to the NO yield,
with a maximum production of $\sim$400\text{\,}\mathrm{\SIUnitSymbolMicro
mol}$$. With modern Earth’s lightning flash rate, that corresponds to
$\sim$0.02\text{\,}\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$$ or
$\sim$0.3\text{\,}\mathrm{T}\mathrm{g}\mathrm{N}\mathrm{/}\mathrm{yr}$$ of
fixed nitrogen. This yield is very similar to the value presented by Barth et
al. (2023) for a potential Archean atmosphere (0.16% CO2 in N2).

Our dry experiments suggest that the oxidation from lightning produced NO to
NO_x^- takes place very fast, while the NO- and HNO-rich air (HNO is also a
lightning product) and the droplets of the cloud deck are still in contact to
each other, even at some time after the flash. This is in contradiction to Hu
& Diaz (2019) who argue that the separation of HNO and NO before the
equilibration with the ocean and the subsequent aqueous chemistry quickly
return lightning-fixed nitrogen into to the atmosphere as N2.

###  3.9 Overnight Experiments

Figure 6: Final abundances of gaseous ([g]; nitrous oxide (N2O), methane
(CH4), hydrogen cyanide (HCN), nitric oxide (NO), and ammonia (NH3)) and
aqueous ([aq]) products (CN^-, nitrite + nitrate, NH4^+, and urea) in
overnight experiments. Data points represent individual experiments with
varying CO2 fractions. Experiments without any H2 and CO2 are indicated by
squares and not included in fits. Lines are best linear fits for dependency
between CO2 concentration and the final abundance of products. Measurements
below the detection limit (arrows) are included as (Detection Limit
$/\sqrt{2}$) in the fitting process. Shaded areas give $1\sigma$-range. No fit
is shown for methane since all measured values are within $1\sigma$ of 0 (red
line), for nitrous oxide since there is no trend visible in the data, and for
urea as most measurements for CO2 $>1\%$ below the detection limit. Abundances
of HCN and NH3 are calculated from measured aqueous abundances of CN^- and
NH4^+, respectively.

In addition to the short 120-min experiments, we also conducted overnight
experiments with an average total spark time of $(925\pm 35)\,$\mathrm{min}$$
to investigate the production of compounds that were not detectable in the
short experiments or had only very small yields. Figure 6 shows the abundances
of gaseous and aqueous products after the overnight experiments and linear
fits to show the relation between CO2 concentration and the final abundance of
the product. Again, the abundances of HCN and NH3 are calculated from the
measured aqueous abundances of CN^- and NH4^+, respectively, with their
respective Henry’s law constants as described in Appendix A. Similar to the
short experiments, we see an increasing production of oxidised nitrogen (NO,
nitrate and nitrite) and a decreasing production of reduced nitrogen
(ammonium) with increasing CO2 concentration. The maximum ammonium
concentration (at 0% CO2) is only about $2-4$ times the corresponding ammonium
concentration in the short experiments, even though the spark was running for
$\sim 8$ times as long, suggesting that the ammonium concentration reached
equilibrium during the experiment. For a CO2 concentration of $\gtrsim 5\%$
basically no ammonium was produced. Instead, the dissociated nitrogen was
likely oxidised to NO and eventually nitrite and nitrate. A higher H2
concentration might allow the production of ammonium at higher CO2
concentrations, but eventually, if there is significantly more CO2 (or a
different oxygen source) than H2 in the gas mixture, the ammonium production
would probably still be suppressed. As discussed above, significant amounts of
ammonium can still be produced by subsequent reduction of nitrite by Fe^+2 and
FeS in the ocean, and to a lesser extent by reduction of nitrate by FeS
(Summers & Chang, 1993; Summers, 2005).

The concentration of nitrite and nitrate as well as NO in our discharge
experiments shows a very clear trend with CO2 concentration in the initial gas
mixture. For CO2 concentrations around 0, water vapour in the gas mixture is a
significant source of oxygen for the production of nitrogen oxides. The
slightly increased scatter of measurements at that point can be explained by
the additional uncertainty of the concentration of water vapour and other
trace gases like O2. We also find the nitrite and nitrate concentration in the
overnight experiments to be $5-10$ times the concentration in the
corresponding short experiments, suggesting that even though NO equilibrium in
the gas phase is reached rather quickly (the final NO concentration in the
overnight experiments is similar to the short experiments), the subsequent
oxidation to NO2 and equilibration with the aqueous phase takes more time, in
particular in the experiments where relatively small amounts of nitrite and
nitrate are produced. All of these experiments were run with
$50\text{\,}\mathrm{ml}$ of water in the flask, so even when the CO2 content
is 0, there was sufficient oxygen available from the water to provide oxygen
for the production of some NO and subsequently nitrite and nitrate. The
presence of water as an oxygen source is likely also the reason that we again
see only very small concentrations of methane, below the measurement error.
Unlike the other forms of oxidised nitrogen, we do not see a clear trend in
the production of N2O with CO2 concentration. This follows the trend in our
short, wet experiments where also no clear trend was visible, suggesting that
if enough oxygen is available, nitrogen oxides with a higher oxidation state
are preferred. N2O has an oxidation state of $+1$ while NO, NO2, nitrite and
nitrate have oxidation states of $\geq 2$.

Urea (CO(NH2)2) is an important precursor for cyanamide (CH2N2) which itself
is a precursor for RNA (Das et al., 2019). In our experiments, urea follows a
similar trend as ammonium, with abundances of roughly one order of magnitude
lower. However, because most measurements for CO2 concentrations above 1% were
below the detection limit, we did not try to fit a line to the urea data. It
thus seems that the production of (detectable levels of) urea is only possible
under reducing conditions.

HCN is an important precursor molecule for the formation of RNA and has been
hypothesised to be produced by lightning in reduced atmospheres (Miller, 1957;
Miller & Schlesinger, 1983; Pearce et al., 2017, 2022). In our experiments, we
can monitor the HCN production by its dissolved form, cyanide CN^-. The
cyanide abundance increases with increasing CO2 abundance, though much more
slowly than the abundance of nitrite and nitrate. This follows the
calculations performed by Chameides & Walker (1981), who predicted an increase
in HCN production when decreasing the C/O-ratio (at constant H2
concentration), which is happening when increasing the CO2 concentration
(without adding other forms of carbon this limits the C/O ratio to $1/2$).
Chameides & Walker (1981) predict an HCN production rate of $\sim 3\times
10^{9}$ to $4\times
10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{J}$$
for the range of C/O-ratios equivalent to our experiments (for a gas mixture
with $0.9\text{\,}\mathrm{bar}$ N2 and $0.05\text{\,}\mathrm{bar}$ H2, C + O =
$0.1\text{\,}\mathrm{bar}$). We find our results for HCN production to be
$\sim 2$ to 3 orders of magnitude larger than the values calculated by
Chameides & Walker (1981). The reason for this might be that the water in our
experiments acts as a buffer: produced HCN dissolves in the water, lowering
the concentration in the gas phase and allowing for more HCN to be produced.
This suggests that we over-predict the production of HCN even though lightning
occurs in the water-saturated atmosphere (clouds). In real lightning
conditions, HCN is produced with the chemical equilibrium composition at the
specific freeze-out temperature. After the HCN is produced, equilibration with
water droplets happens. The next lightning flash produces new HCN in a
different air parcel. In contrast, in our experiments, we keep adding HCN to
the same gas mixture which is constantly equilibrating with the water phase.
For other gases, this is less of a problem as we are measuring most of them in
the gas phase and their Henry’s law constants are orders of magnitude lower,
meaning less of the gas is absorbed into the water. In conclusion, these
experimental limitations suggest that our results do not apply to the real
atmosphere for HCN. Chemical equilibrium calculations (Fig. 7) show that the
concentration of HCN increases with CO2 concentration for gas temperatures
above $\sim$3000\text{\,}\mathrm{K}$$, while temperatures below
$\sim$2700\text{\,}\mathrm{K}$$ the HCN concentration decreases. This suggests
that the freeze-out temperature for HCN in our experiment is
$\gtrsim$3000\text{\,}\mathrm{K}$$. Other experiments studied the effect of
CH4 concentration on HCN production: an increase in CH4 increases the
C/O-ratio, leading to a strong increase in HCN production (Chameides & Walker,
1981; Tian et al., 2011; Pearce et al., 2022).

Figure 7: HCN concentration in chemical equilibrium (with GGChem, Woitke &
Helling, 2003) as function of gas temperature for different CO2 fractions in
the gas mixture (other gases: 1% H2, 1% H2O, rest N2). For
$T\gtrsim$3000\text{\,}\mathrm{K}$$ (right dashed grey line), HCN
concentration increases with increasing CO2 concentration (until $\sim 3-5\%$
CO2). For $T\lesssim$2700\text{\,}\mathrm{K}$$ HCN concentrations decreases
with increasing CO2 concentration (except for 0.1% CO2).

##  4 Results and Implications of Photochemical Simulations

Now that we know the production rates for CO and NO, by far the most important
direct products of lightning in N2-CO2 gas mixtures, we want to know how this
influx of CO and NO changes the composition of different planetary
atmospheres. We are particularly interested in whether lightning can produce
observable signatures in transmission, emission, and reflected light
spectroscopy. To answer these questions, we used the photochemical model of
the Atmos coupled climate-photochemistry code (Arney et al., 2016; Lincowski
et al., 2018) (see Section 2) to calculate the atmospheric mixing ratio of CO,
NO, NO2, and other gases for a large range of lightning flash rates. We
modelled both oxygen-poor (anoxic) and oxygen-rich (oxic) atmospheres on
Earth-sized planets orbiting the Sun (G-type star) and TRAPPIST-1 (M-type
star) at the inner edge of their respective habitable zones.

Figure 8: Photochemically simulated CO (a & b), NO (c & d), and NO2 (e & f)
mixing ratios in the anoxic atmosphere (4.6% CO2) of an Earth-sized planet
orbiting the Sun (a, c, e) and TRAPPIST-1 (b, d, f) for varying CO and NO
production rates and different scenarios: abiotic (solid), biotic with CO
deposition (dashed), and biotic without CO deposition (dotted). The surface
temperature (blue: $T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$, orange:
$T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$) controls the water vapour
concentration. The second $x$-axis gives the corresponding lightning flash
rate (in units of modern Earth’s flash rate), as estimated for the respective
atmospheric composition. Figure 9: Mixing ratios for biotic scenario (Sun)
without CO deposition (CO flux $\sim
10^{7}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$)
for two different surface temperatures (solid lines:
$T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$, dotted lines:
$T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$) as result of a kinetic gas-phase
calculation with photochemistry. Figure 10: Photochemically simulated CO (a &
b), NO and NO2 (c & d) mixing ratios in the oxic atmosphere (4.6% CO2, 21% O2)
of an Earth-sized planet orbiting the Sun (a & c) and TRAPPIST-1 (b & d) for
varying CO and NO production rates and the biotic scenario with CO deposition
($T_{\mathrm{surf}}=$288\text{\,}\mathrm{K}$$). The second $x$-axis gives the
corresponding lightning flash rate (in units of modern Earth’s flash rate), as
estimated for the respective atmospheric composition.

###  4.1 Photochemistry in Anoxic Atmospheres

Figure 8 (a, b) shows the resulting CO mixing ratios for the anoxic atmosphere
(4.6% CO2 in N2 filler gas), equivalent to our experiments and necessary to
keep the surface of the investigated planets clement (Meadows et al., 2018a),
for abiotic and biotic scenarios with different CH4 fluxes and CO deposition
rates and a range of lightning flash rates (Table B1). Using equilibrium
chemistry calculations as described in Section 3.5, we can estimate the
production of CO and NO with modern Earth’s lightning flash rate to be
$7.0\times 10^{8}$ and $3.8\times
10^{8}$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
respectively, in this anoxic gas mixture. The results look very differently
for the two different host stars with different spectra: On the planet
orbiting the Sun, the CO mixing ratio in the biotic scenario is up to three
orders of magnitude larger than in the abiotic scenario. On the planet
orbiting TRAPPIST-1, this trend is reversed. The CO ratio in the biotic
scenario is 100 times smaller than in the abiotic scenario for most of the CO
flux range. the high CO concentrations in the TRAPPIST-1 simulations are due
to efficient CO2 photolysis: The XUV flux is concentrated near the Ly-$\alpha$
line and the FUV continuum and therefore absorbed by the abundant CO2
molecules that are dissociated into CO and O. Thus, the CO2 is shielding water
molecules from the XUV radiation and the photolysis of water in the atmosphere
of a planet orbiting an M dwarf is less efficient and the concentration of the
OH radical is lower (Segura et al., 2005; Schwieterman et al., 2019). Since
the deposition velocity with which CO is deposited in the ocean is lower in
the abiotic than in the biotic scenario where acetogens in the ocean consume
the CO, the abiotic CO concentration remains higher than in the biotic case.

In the simulations for the planet irradiated by the Sun, the OH concentration
in the atmosphere is higher and the CO lifetime is shorter. In the biotic
scenario, the increased, biogenic flux of CH4 which is photo-oxidised to CO
leads to a higher CO concentration than in the abiotic scenario. In a test
case for the biotic scenario, where we assume no CO to be deposited into the
ocean (dotted lines in Fig. 8), the final CO concentration is increased to
well above 1% in all but one case despite OH being present. An increase in
surface temperature increases the concentration of water vapour in the
atmosphere and subsequently the concentration of OH, decreasing the lifetime
of CO and its final concentration. This is especially apparent for the biotic
planet around the Sun where we assume no CO deposition: while for a surface
temperature of $T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$ (blue) the CO
concentration is enhanced to above 1%, for a slightly higher surface
temperature of $T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$ the subsequently
higher water and OH concentrations allow for more efficient removal of CO from
the atmosphere (see Fig. 9 for comparison of mixing ratios). This suggests
that for the biotic scenario for the Sun-orbiting planet with
$T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$, recombination of CO with OH is
the major CO sink. Overall, the major sink for CO in both biotic scenarios for
TRAPPIST-1 and the biotic scenario with
$T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$ for the Sun is deposition in the
ocean.

In nearly all anoxic simulations, the CO concentration is relatively high due
to CO2 dissociation and CH4 photo-oxidation and additional contributions of CO
by lightning are not able to further increase the CO concentration. Only for
lightning flash rates around 1000 times the modern Earth lightning flash rate
we can see the CO concentration increase slightly beyond the background level.
The only scenario, where the background CO level is low enough to see an
increase in CO concentration at lower flash rates, is the abiotic scenario for
the planet orbiting the Sun. For CO production rates higher than $\sim
10^{11}$ or $\sim
10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
for $T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$ and
$T_{\mathrm{surf}}=$300\text{\,}\mathrm{K}$$ respectively, the atmosphere
enters into a CO runaway: the CO flux overwhelms the CO deposition and the CO
concentration jumps up to several per cent. Kasting (1990) showed that also an
increased NO concentration (in our simulations, the NO flux and thus
concentration increases with increasing flash rate) can lead to a longer
lifetime of CO in the atmosphere and thus to a higher CO concentration. The CO
flux where the atmosphere enters into a CO runaway is similar to the total CO
emission on the modern Earth of $\sim 2\times
10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
which is mainly from anthropogenic sources (68%) and wildfire and
deforestation (32%; Zhong et al., 2017). However, on the uninhabited Archean
Earth, the volcanic CO flux is estimated to be much lower at $\sim(1-2)\times
10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(Kasting & Walker, 1981). We also should note that for CO concentrations
larger than the CO2 concentration (4.6%) which occur in our simulations only
for extremely high lightning flash rates, our assumption of constant CO2
concentration might not be applicable anymore, as it would require very high
volcanic fluxes of CO2 to replenish the CO2 dissociated by lightning and would
greatly enhance the carbon budget in the atmosphere.

For the planet orbiting the Sun, we find a very similar trend for the NO2
concentration for all scenarios (Fig. 8, e & f): Very low abundances
($<10^{-8}$ for nearly all simulations), but a steady increase with increasing
NO flux. For the planet orbiting TRAPPIST-1, this looks a bit different: in
the biotic scenario with CO deposition, the NO2 concentration follows a very
similar trend to the same case for the Sun-planet, but with slightly higher
mixing ratios of up to 1 ppm for the highest NO fluxes. In the abiotic case,
though, the NO2 abundance is more than six orders of magnitude higher for low
NO fluxes compared to the biotic case, before it rapidly decreases, parallel
to the CO abundance, at an NO input flux of $\sim 3\times
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$.
At higher fluxes, the NO2 abundance increases again, very similar to the
biotic scenario.

We can also observe this behaviour in the CO concentration for the abiotic
scenario on the TRAPPIST-1 planet (Fig. 8b, solid lines): here the background
CO concentration (for low CO lightning fluxes) is very high at approximately
1%. Once the CO and the corresponding NO flux cross a certain threshold ($\sim
10^{10}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$),
the CO concentration drops by more than two orders of magnitude before rapidly
climbing again in a CO runaway. This drop in the CO and NO2 concentration is
accompanied by a drop in O2 concentration and a strongly increasing NO
concentration (Fig. 8, c & d). In the anoxic gas mixture in our experiments as
well as in lightning strikes in the anoxic Archean atmosphere, where NO and CO
are produced from dissociated CO2 and N2, free oxygen is produced if not the
same amount of NO and CO is produced to match the stoichiometric ratio of the
split CO2 (Kasting, 1990). When using the CO and NO production fluxes in our
photochemical simulations, we included an additional O flux, which is variable
alongside the NO and CO fluxes, to balance the ratio between the elements N,
C, and O. Together, these three fluxes replace the lightning module originally
included in Atmos (Harman et al., 2018) which we turned off for these
simulations. The background concentrations of O2 and ozone as byproducts from
CO2 photolysis are very high in this scenario and even slightly enhanced
further by the addition of free oxygen from lightning, up to an O2 surface
mixing ratio of $1.4\times 10^{-3}$ and a peak ozone concentration of
$\sim$5\text{\,}\mathrm{p}\mathrm{p}\mathrm{m}$$ at a height of
$32\text{\,}\mathrm{km}$. The high concentration of oxygen allows for
efficient oxidation of NO to NO2 (NO + O -¿ NO2), resulting in a higher
concentration of NO2 than NO. Other efficient destruction channels for NO and
NO2 are NO + HCO -¿ HNO + CO and NO2 + O -¿ NO + O2, respectively. At high NO
fluxes, the channels H + NO -¿ HNO, NO + OH -¿ HNO2, NO + O -¿ NO2, and NO +
HO2 -¿ NO2 + OH become the limiting factors controlling the NO concentration,
while NO2 photolysis and the reaction NO2 + H -¿ NO + OH control the
destruction of NO2. At high NO fluxes, the overall balance of the HOx
reservoir shifts by decreasing steady-state HO2 while increasing steady-state
OH. This shift allows for increased recombination of CO + OH -¿ CO2 + H,
leading to a sharp decrease in the concentration of CO and oxygen species,
entering a different photochemical regime (Ranjan et al., 2022). We note that
the HOx reservoir ultimately depends on H2O photolysis (Harman et al., 2015),
and all NO-mediated catalytic cycles that net recombine CO and O to CO2
require the presence of HOx species (see Harman et al., 2018, their Table 1).
For anoxic atmospheres with a Sun host, the dominant photochemical channels
are more consistent throughout the range of NO fluxes, which is reflected in
the lessened discontinuous behaviour in the flux-abundance relationships shown
in the left panels of Fig 8. For these atmospheres, NO is primarily destroyed
by NO + O -¿ NO2 and NO2 is primarily destroyed by NO2 photolysis.

This process was described by Harman et al. (2018) who suggested that
lightning-produced NO can provide a catalyst for the recombination of CO and O
to CO2, preventing a false-positive O2-biosignature. They assumed an NO
production of $\sim 6\times
10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(for modern Earth’s lightning flash rate) in an atmosphere with 5% CO2 and
found this to strongly reduce the CO and O2 concentrations (for an M dwarf
host star). This NO production rate is about 50% higher than what we assume
for modern Earth’s lightning flash rate, but even if we correct for this
difference, the additional production by lightning of CO and O in our model
moves this behaviour to flash rates at least three times that of modern Earth.
Using our assumption for the NO production per flash, a flash rate of more
than six times modern Earth’s is necessary to prevent the build-up of
significant amounts of oxygen in the atmosphere. This difference is likely due
to differences in the UV spectrum used for the simulations. Larger stellar
FUV/NUV flux ratios tend to drive higher abiotic O2 production rates (Harman
et al., 2015) and TRAPPIST-1 (M8V) has a larger FUV/NUV ratio than the latest
host star considered by Harman et al. (2018), an M4V dwarf. Importantly, this
suggests that lightning may not eliminate all O2-false positive scenarios for
CO2-rich terrestrial planets orbiting ultra-cool dwarf hosts, at least at the
$\sim 0.1\%$ level. Figure B6 shows the column density of the atmospheric
constituents for the range of simulated CO and NO fluxes, Fig. 1(a) the
atmospheric mixing ratio profiles for simulations before and after the drop in
CO and O2 concentration for the scenario with
$T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$. The spectra for these two cases
are discussed below (Fig. 12(a)).

###  4.2 Photochemistry in Oxygen-rich Atmospheres

Earth’s atmosphere was anoxic for the first $\sim$2\text{\,}\mathrm{Gyr}$$ of
its evolution. After that, the oxygen concentration increased drastically, but
it was only $\sim$0.5\text{\,}\mathrm{Gyr}$$ ago that the oxygen concentration
reached today’s level (e.g., Catling & Zahnle, 2020). Assuming that the
evolution of oxygenic photosynthesis takes a similar amount of time on other
worlds if it happens at all, it is therefore most likely that if we find an
inhabited planet, it will have an anoxic or low-oxygen atmosphere (Krissansen-
Totton et al., 2018b). However, as we have discussed in the introduction,
photochemistry and hydrogen escape can lead to the abiotic build-up of O2 in
an otherwise anoxic atmosphere. To fully investigate the impact of lightning
on observable oxygen and ozone features, we therefore also conducted
simulations for oxygen-rich atmospheres with a biosphere (4.6% CO2, 21% O2 in
N2 filler gas; biotic scenario with maximum CO deposition; Fig. 10). In
addition, the O2 and O3 features of an N2-O2 atmosphere are likely not
detectable with JWST (Krissansen-Totton et al., 2018a). Thus, the atmosphere
of a modern-Earth-like, inhabited planet might resemble the Archean Earth
instead, with CH4 and CO2 features. In this case, it is important to
understand the role of lightning in potentially producing a CO signature.

In such an oxic gas mixture, our estimate for the CO and NO production rates
at modern Earth’s lightning flash rate are $1.5\times 10^{8}$ and $2.5\times
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
respectively, using the method described in Section 3.5. Our simulations find,
for both host stars, a significantly lower CO mixing ratio than in the anoxic
atmospheres, independent from the CO deposition velocity. The high abundance
of O2 in these atmospheres offers an additional sink for atmospheric CO:
excited atomic oxygen from ozone photolysis increases the production of the OH
radical: O3 + $h\nu(\lambda<$320\text{\,}\mathrm{nm}$)$ -¿ O(^1D) + O2 and H2O
+ O(^1D) -¿ 2OH. Since the NUV radiation necessary for this pathway is lower
for M dwarfs, the CO mixing ratio on the planet around TRAPPIST-1 is higher
than on the planet around the Sun (Segura et al., 2005; Schwieterman et al.,
2019). However, for CO fluxes $>3\times
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
for the planet orbiting the Sun and
$>10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
for the planet orbiting TRAPPIST-1 we find an increase of the CO mixing ratio.
This corresponds to lightning flash rates of $\sim 10$ and $\sim 0.7$ times
modern Earth’s flash rate, respectively. In the Sun case, the CO mixing ratio
increases to $\sim 10^{-7}$ for a CO flux of $3\times
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
and then steadily to $\sim 10^{-4}$ for a CO flux of $5\times
10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$.
In the TRAPPIST-1 case, the CO mixing ratio increases to $\sim 10^{-6}$ for a
CO flux of
$10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
and then steadily to $\sim 10^{-4}$ for a CO flux of
$10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$.
To estimate the corresponding lightning flash rate, we used again equilibrium
calculations to determine the CO concentration at the freeze-out temperature
of $2430\text{\,}\mathrm{K}$ for the simulated, oxic gas mixture. We find that
at modern Earth’s lightning flash rate, the CO concentration is approximately
6 and 2 orders of magnitude smaller than in the corresponding anoxic
atmosphere for the Sun and TRAPPIST-1 planet, respectively (same CO2
concentration of 4.6%), as the abundant O2 increases the recombination of CO
to CO2. This means lightning flash rates of 3000 and 500 times the modern
Earth’s flash rate are needed to achieve CO concentrations similar to the
corresponding anoxic scenarios (biotic with maximum CO deposition).

The NO2 concentration follows a very similar trend to the CO concentrations in
the photochemical calculations with a sharp increase at CO fluxes of $\sim
3\times
10^{9}$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
and $\sim
10^{8}$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
and corresponding NO fluxes of $\sim 6\times
10^{10}$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
and $\sim 2\times
10^{9}$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
for the Sun and TRAPPIST-1 case, respectively. The changes in the slope of the
NO and NO2 abundances vs. NO flux are caused by shifts in their main
photochemical destruction channels as these species overwhelm the
photochemical sinks with the fastest kinetic rates. For NO, the NO + O3 -¿ NO2
+ O2 channel saturates near this threshold flux, and the slower NO + O -¿ NO2
and NO + OH -¿ HNO2 channels become comparable above it. This tracks with the
depletion in O3 we also see in our photochemical simulations at increasing NO
flux. For NO2, the NO2 + O -¿ NO + O2 channel saturates, and NO2 photolysis
becomes the dominant destruction channel. The flux-abundance relationships
vary between host stars due to the different distributions of radical species
generated by differences in stellar spectra. We also emphasise that these
shifts in photochemical channels with increasing NO flux differ in the oxic
vs. anoxic cases.

Similar to the anoxic case, in the oxic atmosphere, lightning will also
produce free oxygen which we expect to mostly recombine to O2. However, it is
hard to determine how much atomic oxygen is produced. Stoichiometrically, all
NO and CO can be produced from dissociated N2, O2, and CO2 without any
remaining O. To test whether the addition of free O might change the chemistry
significantly, we ran simulations with an O flux similar to the lightning NO
flux. We only found small enhancements in the final NO2 concentrations for the
highest NO fluxes
($>10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$).

###  4.3 Nitrogen Deposition into an Ocean

Figure 11: Deposition flux of fixed nitrogen into an ocean (red) for the
anoxic, abiotic planet around the Sun
($T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$) for a range of lightning NO
fluxes and corresponding lightning flash rates. For comparison, the total
lightning-produced NO flux is shown (orange). The corresponding deposition
rates in $\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$ are shown as black lines
(converted into
$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$).

To investigate the possibility of lightning-produced NO to be converted to N2O
in the ocean, which could in return be outgassed into the atmosphere where it
might produce a false-positive biosignature, we calculate the nitrogen
deposition flux into the surface of the planet. In addition to NO, also NO2,
HNO, and HNO3 are deposited from the atmosphere. The combined nitrogen
deposition flux is shown in Fig. 11 in comparison to the NO production from
lightning for the anoxic and abiotic scenario for the planet orbiting the Sun
($T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$). A large part of the introduced
NO is deposited into the surface, mainly in the form of HNO: up to $\sim 95\%$
at NO fluxes of $\sim
10^{10}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$,
decreasing to $\sim 60\%$ at NO fluxes of $\sim
10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$.
This behaviour is similar to the other anoxic-abiotic scenarios. Even if all
of this deposited nitrogen were to be converted to N2O and outgassed into the
atmosphere, a lightning flash rate of more than 100 times modern Earth’s would
be necessary to produce an N2O flux of
$10\text{\,}\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$ which would still likely
be not enough to be detectable with JWST (Schwieterman et al., 2022). On an
Earth-like planet orbiting a K dwarf, an N2O flux of
$1\text{\,}\mathrm{Tmol}\text{\,}{\mathrm{yr}}^{-1}$ or even less might be
detectable, though, potentially producing a false-positive biosignature. These
calculations present an upper limit, assuming the whole surface is covered by
an ocean, as is suggested for the exoplanet Kepler-138 d (Piaulet et al.,
2023), but on a planet with a lower ocean-to-land surface ratio, deposition of
nitrogen oxides into the ocean will be less efficient. This and other
uncertainties that will likely decrease the N2O flux significantly, such as
the efficiency of the conversion of deposited nitrogen into N2O, are the
reasons why we are not further investigating this potential signature.

###  4.4 Observational Signatures from Lightning in Transmission, Emission,
and Reflected Light

(a) Anoxic, abiotic scenario ($T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$):
CO flux of $10^{9}$ (black), $10^{10}$ (magenta), and
$10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(blue), corresponding to lightning flash rates of $\sim 2$, $\sim 35$ and
$\sim 1500$ times modern Earth’s, respectively.

(b) Oxic, biotic scenario ($T_{\mathrm{surf}}=$288\text{\,}\mathrm{K}$$): CO
flux of $10^{8}$ (black) and
$10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(blue), corresponding to lightning flash rates of $\sim 0.9$ and $\sim 680$
times modern Earth’s, respectively.

Figure 12: Simulated spectra for the TRAPPIST-1 planet: Emitted (top, MIR,
$R=400$), reflected (middle, NIR, $R=400$), and transmitted light (bottom,
NIR-MIR, $R=200$). Note that MIR features in emission are not just dependent
on the abundance of spectrally active gases, but also the temperature
structure of the atmosphere. Figure 13: Simulated spectra for the planet
orbiting the Sun: Anoxic, biotic scenario without CO deposition (CO flux $\sim
10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$).
Spectra with individual species removed are shown (without C2H6, red, and
without CH4, orange) in comparison to the full spectrum (black dotted).

To investigate whether lightning produces observable signatures, we calculated
emission, transmission, and reflectance spectra for a selection of
simulations. The most likely missions and observatories to directly image
temperate terrestrial planets will either do so in the Vis/Near-IR range, such
as NASA’s proposed Habitable Worlds Observatory or the Mid-IR, such as the
proposed ESA Large Interferometer for Exoplanets (LIFE) mission. We have thus
chosen the wavelength ranges and spectral resolving powers to accentuate
features that would be plausibly detectable with these platforms.

Figure 12 shows the calculated transmission spectrum for two scenarios of the
TRAPPIST-1 planets: The anoxic, abiotic scenario
($T_{\mathrm{surf}}=$275\text{\,}\mathrm{K}$$; Fig. 12(a)) and the oxic,
biotic scenario ($T_{\mathrm{surf}}=$288\text{\,}\mathrm{K}$$; Fig. 12(b)).
The different shapes of the CO2 feature around
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in the emission spectra are due to
the different atmospheric profiles we used: for the oxic atmosphere which is
very similar to modern Earth’s atmosphere, we used Earth’s atmospheric profile
with its stratospheric temperature inversion. Since the emission is probing
different heights in the atmosphere it registers different temperatures, with
the centre of the line at $15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ probing
furthest up in the atmosphere, where the temperature is higher than deeper in
the atmosphere. For the anoxic atmosphere, we assumed an isothermal atmosphere
above the convective troposphere, such that the absorption feature appears
flat. The spectra are shown for two different CO fluxes, representing
scenarios at lightning flash rates below and above where the atmospheric
composition changes drastically: For the anoxic/abiotic scenario, these are CO
fluxes of
$10^{9}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(black), $2\times
10^{10}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(magenta), and
$10^{12}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(blue), corresponding to lightning flash rates of $\sim 2$, $\sim 35$, and
$\sim 1500$ times that of modern Earth, respectively. For the oxic/biotic
scenario, CO fluxes of
$10^{8}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(black) and
$10^{11}\,$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{/}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{s}$$
(blue), corresponding to lightning flash rates of $\sim 0.9$ and $\sim 680$
times modern Earth’s, respectively, are shown. Most notable is how the
increased concentration of NO and NO2 is reducing the ozone features at
$9.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (transmission and emission) and
$<$0.65\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ (reflectance) in the scenario
with the higher CO flux. The individual mixing ratio profiles for the two
cases compared in Fig. 12 can be found in the appendix (Fig. B1).

In the case of the anoxic planet, the removal of the ozone feature would
prevent a possible false-positive detection of life. In contrast to the oxic
scenario, the CO concentration is much higher here (for the low and high
lightning flash rates), though, allowing for strong CO features in the
transmission spectrum at $2.35\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$4.65\text{\,}\mathrm{\SIUnitSymbolMicro m}$. This allows us to identify a
CO2-rich atmosphere and for a correct interpretation of the ozone feature as
potentially from an abiotic source. For the intermediate lightning flash rate
($\sim 35$ times modern Earth’s) we find both the CO and the ozone features to
be removed or very weak. However, in the absence of strong methane features,
the missing CO feature should not be interpreted as a sign of life. However,
if in this scenario, an increased CH4 feature from volcanism is observed it
could be misinterpreted as a biosignature. In the corresponding biotic
scenario (Fig. B5), where the CO concentration is similarly low, the biotic
methane flux produces strong features that should allow the detection of the
present biosphere.

In the oxic/biotic scenario, lightning is decreasing the ozone concentration
in the atmosphere, reducing the spectral ozone feature used to identify an
oxygen-rich atmosphere. In that case, other biosignatures are necessary to
identify that the planet is inhabited, for example, the combination of CO2 and
CH4 in the absence of CO, as suggested by Krissansen-Totton et al. (2018b). We
find an increased concentration of CH4 for the higher CO flux, most notably in
the reflected spectrum ($1.6-$1.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$$),
likely because the increased CO flux is taking up most of the available sinks
(e.g., OH). We also find an NO2 feature at
$\sim$6\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ and a C2H6 feature at
$\sim$11\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ (both in transmission and
emission spectra) to appear for the higher CO flux scenario, indicating the
presence of lightning activity and helping to explain the absence of an ozone
feature. This C2H6 feature is enhanced because other gases are soaking up the
radical sinks that would otherwise destroy C2H6. In the reflected light, we
find molecular oxygen features at $0.76\text{\,}\mathrm{\SIUnitSymbolMicro m}$
(O2 A-band) and $1.27\text{\,}\mathrm{\SIUnitSymbolMicro m}$ which are not
affected by the lightning activity, potentially allowing for the
identification of an oxygen-rich atmosphere if that wavelength range is
observed. In any way, to enhance the CO concentration to a detectable level in
the oxic scenario, significantly higher lightning flash rates are necessary.

Spectra for other scenarios and the corresponding atmospheric mixing ratio
profiles are shown in Appendix B. For the oxic, biotic Sun scenario (Fig. B2),
the behaviour is very similar to the TRAPPIST-1 planet: with higher CO and NO
fluxes, the ozone features are reduced but we find enhanced methane features.
The spectra for the anoxic, abiotic Sun planet (Fig. B3), however, look very
different compared to the TRAPPIST-1 planet: because of the lower XUV
radiation of the Sun, there is no abiotic ozone build-up in the atmosphere.
Also, the CO concentration is much lower and the spectra mainly show CO2
features. Only the NO feature at $5.3\text{\,}\mathrm{\SIUnitSymbolMicro m}$
is stronger when the CO flux is increased.

For the anoxic, biotic scenarios, we are comparing the spectra for simulations
with and without CO deposition (Fig. B4 & B5): as expected, the main
difference is that without CO deposition, we find a strong CO feature at
$4.65\text{\,}\mathrm{\SIUnitSymbolMicro m}$. For the anoxic, biotic planet
around the Sun without CO deposition, we calculated the spectra with
individual species removed to show their individual impacts on the planetary
spectrum (Fig. 13). In particular, we looked at the effect of removing methane
(orange lines) and C2H6 (red). The complete spectra are shown in comparison
(black dotted lines). As expected, we see many strong methane features in all
three spectra, masking for example the
$2.35\text{\,}\mathrm{\SIUnitSymbolMicro m}$ CO feature. For C2H6, we find a
strong feature between 11 and $13\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in
the emitted (top) and transmitted spectra (bottom). Removing NO2 and HNO3 from
the calculations did not change the spectra, suggesting features of these
molecules are small and masked by other, more abundant molecules such as CH4.

Whether these spectral features are eventually detectable or not depends on
many factors such as the wavelength range and resolving power of the
instrument, the duration of the observation, or the variability of the stellar
radiation. For example the ozone feature at
$9.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ might not be detectable with JWST
(Krissansen-Totton et al., 2018a). Future missions, dedicated to studying the
atmospheres of terrestrial exoplanets will be better suited to detect
atmospheric constituents of small planets, such as the Habitable Worlds
Observatory (HWO) recommended by the US 2020 Astronomy & Astrophysics Decadal
Survey (National Academies of Sciences & Medicine, 2021) with capabilities
informed by the Habitable Exoplanet Observatory (HabEx, Gaudi et al., 2020)
and Large UltraViolet Optical and Infrared (LUVOIR, The LUVOIR Team, 2019)
mission concepts. This mission would be able to detect O3 and O2 features in
the UV and visible and CH4 in the near-IR. The proposed Large Interferometer
For Exoplanets (LIFE, Alei et al., 2022; Quanz et al., 2022) would be able to
detect O3 and CH4 features in the MIR.

##  5 Discussion

When conducting our experiments and photochemical simulations, we encountered
several unknowns and had to make assumptions that allowed us to simulate the
atmospheric chemistry of terrestrial exoplanets. In this section, we want to
discuss three of these uncertainties in more detail: the lightning flash rate
on terrestrial exoplanets, the composition and stability of the atmosphere of
Archean Earth and similar exoplanets, and the CO metabolism.

###  5.1 Lightning Flash Rate

In this work, we estimated the production rates of several gaseous and aqueous
species by lightning in different atmospheric and planetary environments. To
do so, at several points in the paper, we used the global lightning flash rate
on modern Earth of $44\pm$5\text{\,}{\mathrm{s}}^{-1}$$ (Christian et al.,
2003) with an energy of $6.7\text{\,}\mathrm{GJ}$ per flash (Price et al.,
1997) to extrapolate from our laboratory experiments to an annual, global
production. Lightning rates and energies have been well studied on the modern
Earth (Schumann & Huntrieser, 2007; Hodosán et al., 2016a, and references
therein). However, as discussed in the introduction, much uncertainty remains
for the lightning flash rate on the early Earth, terrestrial planets, and
exoplanets in general (Wong et al., 2017; Hodosán et al., 2021; Braam et al.,
2022).

We therefore treat the lightning flash rate as an independent variable in our
photochemical simulations (while always using an energy of
$6.7\text{\,}\mathrm{GJ}$ per flash), simulating the atmospheric composition
for a range of flash rates from less than 10% to more than 1000 times modern
Earth’s flash rate ($44\pm$5\text{\,}{\mathrm{s}}^{-1}$$). This allowed us to
analyse more plausible scenarios of flash rates similar to modern Earth’s but
also to predict minimum flash rates for certain scenarios. In some scenarios,
small changes in the flash rate have very little effect on the composition of
the atmosphere and thus the observability of certain features, such as the
biotic scenarios for the anoxic planets around TRAPPIST-1 and the Sun.

In other scenarios, small changes in the flash rate, close to that of modern
Earth, can have a significant impact on the planetary spectrum. For example,
our simulations of the anoxic, abiotic atmosphere of a planet orbiting
TRAPPIST-1 show that lightning at modern Earth’s flash rate is not able to
remove the abiotic ozone feature caused by the dissociation of CO2 due to the
star’s strong XUV radiation. However, at a flash rate ten times higher, the
additional NO input and subsequent oxidation to NO2 enhances the recombination
of CO and oxygen to CO2, removing the abiotic ozone feature and preventing a
false-positive biosignature detection. This shows how sensitive the
atmospheric composition and planetary spectrum can be to the lightning flash
rate.

In addition, the lightning flash rate at which this threshold appears depends
on the individual XUV spectrum of the planet’s host star which is responsible
for the CO2 dissociation and O2 production: Larger stellar FUV/NUV flux ratios
tend to drive higher abiotic O2 production rates (Harman et al., 2015) and
TRAPPIST-1 (M8V) has a larger FUV/NUV ratio than the latest host star
considered by Harman et al. (2018), an M4V dwarf. Therefore, Harman et al.
(2018) find a flash rate equal to modern Earth’s sufficient to remove the
abiotic ozone feature in their simulations.

An additional factor that can influence the occurrence of lightning is cosmic
rays as planets orbiting M dwarfs will experience more frequent and intense
stellar flares that are associated with flares of charged particles. In
addition to their potential effect on the lightning flash rate, cosmic rays
are also an important source of disequilibrium chemistry in the atmospheres of
exoplanets. Studies of Earth-like planets orbiting M dwarfs have shown that
the enhanced cosmic ray flux leads to increased production of nitrogen oxides
(NO, NO2, HNO3) as well as a decreased concentration of ozone, similar to our
results for lightning (Grenfell et al., 2012; Tabataba-Vakili et al., 2016;
Scheucher et al., 2020).

Another uncertainty that is connected to the lightning flash rate is the
effect of the flash properties. The freeze-out temperature of a specific gas,
and thus its concentration in the air parcel cycled through the flash, depends
on the cooling timescale of the flash. Therefore, the estimate of the freeze-
out temperature depends on the properties of the flash considered in the
experiment or calculations. In addition, the chemical timescales and thus the
freeze-out temperature depend on the specific location in the discharge where
the trace gas is produced: Trace gases produced in the expanding shock wave of
a lightning strike where chemical timescales are shorter will freeze out at a
higher temperature (Chameides, 1979) than trace gases produced in the hot
channel of the strike which is cooling more slowly (Hill et al., 1980). It has
since been suggested that the latter process is more important (Uman & Rakov,
2003), in particular in spark experiments (Stark et al., 1996), but a smaller
contribution from the shock-wave could lead to an estimate of the freeze-out
temperature somewhere between both extremes. The combination of these
uncertainties explains the wide range of reported freeze-out temperatures for
both NO ($2300-$3500\text{\,}\mathrm{K}$$; Gilmore, 1975; Chameides et al.,
1977; Kasting & Walker, 1981; Picone et al., 1981; Borucki & Chameides, 1984)
and CO ($2000-$3500\text{\,}\mathrm{K}$$; Levine et al., 1979; Chameides,
1979), placing our estimates of
$T_{\mathrm{f}}(\mathrm{NO})\gtrsim$3000\text{\,}\mathrm{K}$$ and
$T_{\mathrm{f}}(\mathrm{CO})\simeq$2430\text{\,}\mathrm{K}$$ within the range
of these estimates.

###  5.2 Atmospheric Stability

In our photochemical simulations, we studied the kinetic chemistry and
photochemistry of terrestrial, habitable-zone planets around two different
types of stars: the Sun and the M dwarf TRAPPIST-1. While we assumed a CO2
concentration of 4.6% in the atmosphere (for both the anoxic and oxic
atmospheres), corresponding to our experiments and necessary to keep the
surface of the planets clement (Meadows et al., 2018a), the CO2 partial
pressure on the early Earth was likely higher (Lichtenegger et al., 2010;
Johnstone et al., 2021b). Further, for planets around M dwarfs such as
TRAPPIST-1, it will be much harder to hold on to their atmosphere because of
the intense stellar wind and the enhanced and prolonged XUV activity of the
host star (Lammer et al., 2011; Airapetian et al., 2017; Johnstone et al.,
2021a). Recent observations with JWST have shown that the innermost planet of
the TRAPPIST-1 system, TRAPPIST-1 b, is likely a bare rock without any
atmosphere (Greene et al., 2023). Even if TRAPPIST-1 e has retained an
atmosphere, the ongoing escape of hydrogen and nitrogen will continue to
modify the atmosphere, potentially enhancing the oxygen fraction in the
remaining atmosphere (Tian, 2009; Johnstone et al., 2019). Connecting the
upper atmosphere and the above-discussed escape processes to our photochemical
model is beyond the scope of this study but should be investigated further in
future studies.

To obtain our results, we used the TRAPPIST-1 spectrum from Peacock et al.
(2019), though recent work has shown that photochemical results can differ
when other versions of the TRAPPIST-1 spectrum are used (Cooke et al., 2023).
The here presented simulations are therefore not specific predictions for the
atmospheric composition of TRAPPIST-1 e but rather an example to investigate
the effect of lightning on different atmospheres around different types of
host stars. TRAPPIST-1 and the Sun are good end-members for several reasons,
including the fact that TRAPPIST-1 is an immediate/near-term target, and
terrestrial planets orbiting Sun-like stars are the targets for HWO. In case
TRAPPIST-1 e, or similar exoplanets in the habitable zones of M dwarfs, can
indeed retain an atmosphere that is similar to our simulations, this study
informs us about atmospheric signatures that one may expect to observe.

###  5.3 Adapting CO Metabolisms

In this study, we used biotic CO deposition and CH4 production rates that were
independent of temperature, following previous work (Kharecha et al., 2005;
Schwieterman et al., 2019). However, the metabolisms responsible for CH4
production and CO consumption might change depending on atmospheric
composition, pressure, and temperature, and will likely vary substantially
across a heterogeneous planetary surface. Taubner et al. (2023) show how the
production of lipids and amino acids by methanogens can strongly depend on the
temperature and nutrient supply. In addition, the productivity of a biosphere
might be limited by the availability of other nutrients like phosphorus or
fixed nitrogen, rather than CO or stellar irradiation, as is the case for
modern Earth (Moore et al., 2013; Bristow et al., 2017). In particular, the
availability of nickel can limit the CO consumption by acetogens (Dobbek et
al., 2001). Throughout Earth’s history, the concentration of nickel in the
oceans has varied, impacting the productivity of methanogens and acetogens
(Konhauser et al., 2009, 2015). These uncertainties suggest that in realistic
atmospheres the biotic CO deposition rate might be lower than assumed in this
study. The biotic and abiotic deposition rates used here thus provide an upper
and lower bound, respectively, on the efficiency of CO deposition.

##  6 Conclusions

We conducted spark discharge experiments to study the production of different
gaseous and aqueous products, including potential (anti-)biosignatures, by
lightning in atmospheres of N2, CO2, and H2. In contrast to previous studies
that focused on individual or small numbers of products, we studied the
production of a wide range of gaseous and aqueous compounds in a range of
different atmospheres. This allowed us to investigate trends in our
experiments concerning the oxidation state of lightning products and the
influence of water vapour. In particular, we were interested in the effect of
lightning on the production of potential (anti-)biosignatures in the context
of current and upcoming observations of exoplanetary atmospheres.

Our results confirm that in a slightly reducing or oxidising atmosphere of a
planet that has surface water and a habitable surface temperature, lightning
will produce more oxidised than reduced nitrogen products. We confirm
predictions by Harman et al. (2018) that in the absence of other forms of
oxygen, water vapour is responsible for a baseline production of NO and other
oxidised forms of nitrogen by lightning. In return, this allows us to predict
that for the kind of atmospheres studied here, lightning is not able to
produce a false-positive NH3 or CH4 biosignature. It is also unlikely that
lightning can produce a false-positive N2O biosignature.

We then used the CO and NO production rates determined in our experiments to
calculate the atmospheric composition over a range of different lightning
flash rates with a photochemical model. We applied this model to anoxic (CO2 -
N2) and oxic (O2 - CO2 - N2) atmospheres on Earth-sized planets in the
habitable zone of the Sun and TRAPPIST-1. In particular, we conducted
simulations with and without an assumed biosphere on the planet. We also
calculated simulated spectra to identify signatures for the different
scenarios.

We find that lightning is not able to produce a false-positive CO anti-
biosignature on an inhabited planet. In an oxygen-rich atmosphere, however,
lightning rates only a few times higher than modern Earth’s can mask the O3
biosignature. Enhanced NO, NO2, and C2H6 features might help to identify these
oxygen-rich atmospheres with increased lightning activity.

Similarly, in an anoxic, abiotic atmosphere of a planet orbiting a late M
dwarf, lightning at flash rates ten times or more than that of modern Earth
can remove the abiotic ozone feature produced by CO2 photolysis, preventing a
false-positive biosignature detection. However, this also suggests that
lightning might not be able to prevent all false-positive O2 scenarios for
CO2-rich terrestrial planets orbiting ultracool M dwarfs. In summary, our work
provides new constraints for the full characterisation of atmospheric and
surface processes on exoplanets.

###### Acknowledgements.

We thank Terry Smith, Nathan Rochelle-Bates, and Abu S. Bayida for support in
analysing our data, and Helmut Lammer and Manuel Scherf for comments on the
manuscript. P.B. acknowledges a St Leonard’s Interdisciplinary Doctoral
Scholarship from the University of St Andrews. E.E.S. acknowledges funding
from a Royal Society research grant (RGS\R1\211184) and from a NERC Frontiers
grant (NE/V010824/1). Ch.H. is part of the CHAMELEON MC ITN EJD which received
funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Sklodowska-Curie grant agreement number 860470.
E.W.S. acknowledges support from the NASA Interdisciplinary Consortia for
Astrobiology Research (ICAR) program via the Alternative Earths team with
funding issued under grant No. 80NSSC21K0594 and the CHAMPs (Consortium on
Habitability and Atmospheres of M-dwarf Planets) team with funding issued
under grant No. 80NSSC21K0905. E.W.S. additionally acknowledges support from
the Virtual Planetary Laboratory, which is a member of the NASA Nexus for
Exoplanet System Science and funded via NASA Astrobiology Program grant No.
80NSSC18K0829. In order to meet institutional and research funder open access
requirements, any accepted manuscript arising shall be open access under a
Creative Commons Attribution (CC BY) reuse licence with zero embargo. Machine-
readable tables of the data presented in this work are available online at
https://doi.org/10.17630/8b72510f-62a8-43dc-94f1-af9b7766f817.

## References

  * Abelson (1966) Abelson, P. H. 1966, Proceedings of the National Academy of Sciences, 55, 1365
  * Agol et al. (2021) Agol, E., Dorn, C., Grimm, S. L., et al. 2021, The Planetary Science Journal, 2, 1
  * Airapetian et al. (2020) Airapetian, V. S., Barnes, R., Cohen, O., et al. 2020, International Journal of Astrobiology, 19, 136
  * Airapetian et al. (2016) Airapetian, V. S., Glocer, A., Gronoff, G., Hébrard, E., & Danchi, W. 2016, Nature Geoscience, 9, 452
  * Airapetian et al. (2017) Airapetian, V. S., Glocer, A., Khazanov, G. V., et al. 2017, ApJL, 836, L3
  * Alei et al. (2022) Alei, E., Konrad, B. S., Angerhausen, D., et al. 2022, A&A, 665, A106
  * Arney et al. (2016) Arney, G., Domagal-Goldman, S. D., Meadows, V. S., et al. 2016, Astrobiology, 16, 873
  * Arney et al. (2014) Arney, G., Meadows, V., Crisp, D., et al. 2014, J. Geophys. Res. Planets, 119, 1860
  * Barth et al. (2021a) Barth, P., Carone, L., Barnes, R., et al. 2021a, Astrobiology, 21, 1325
  * Barth et al. (2021b) Barth, P., Helling, C., Stüeken, E. E., et al. 2021b, MNRAS, 502, 6201
  * Barth et al. (2023) Barth, P., Stüeken, E. E., Helling, C., et al. 2023, Nature Geoscience, 16, 478
  * Borucki & Chameides (1984) Borucki, W. J. & Chameides, W. L. 1984, Reviews of Geophysics, 22, 363
  * Bouwman et al. (2002) Bouwman, A. F., Boumans, L. J. M., & Batjes, N. H. 2002, Global Biogeochemical Cycles, 16, 6
  * Bouwman et al. (1997) Bouwman, A. F., Lee, D. S., Asman, W. A. H., et al. 1997, Global Biogeochemical Cycles, 11, 561
  * Braam et al. (2022) Braam, M., Palmer, P. I., Decin, L., et al. 2022, MNRAS, 517, 2383
  * Bristow et al. (2017) Bristow, L. A., Mohr, W., Ahmerkamp, S., & Kuypers, M. M. 2017, Current Biology, 27, R474
  * Buick (2007) Buick, R. 2007, Geobiology, 5, 97
  * Burkholder et al. (2019) Burkholder, J., Sander, S., Abbatt, J., et al. 2019, in PL Publication 19-5 (Jet Propulsion Laboratory, Pasadena)
  * Cacace et al. (2007) Cacace, D., Ashbaugh, H., Kouri, N., et al. 2007, Analytica Chimica Acta, 589, 137
  * Canfield et al. (2010) Canfield, D. E., Glazer, A. N., & Falkowski, P. G. 2010, Science, 330, 192 LP
  * Carpenter & Nightingale (2015) Carpenter, L. J. & Nightingale, P. D. 2015, Chemical Reviews, 115, 4015
  * Catling & Zahnle (2020) Catling, D. C. & Zahnle, K. J. 2020, Science Advances, 6, 1420
  * Chameides (1979) Chameides, W. L. 1979, Geophysical Research Letters, 6, 287
  * Chameides (1986) Chameides, W. L. 1986, in The Earth’s Electrical Environment, ed. E. P. Krider, R. G. Roble (The National Academies Press, Washington, DC), 70
  * Chameides et al. (1977) Chameides, W. L., Stedman, D. H., Dickerson, R. R., et al. 1977, Journal of the Atmospheric Sciences, 34, 143
  * Chameides & Walker (1981) Chameides, W. L. & Walker, J. C. G. 1981, Origins of life, 11, 291
  * Christian et al. (2003) Christian, H. J., Blakeslee, R. J., Boccippio, D. J., et al. 2003, J. Geophys. Res. Atmospheres, 108, ACL 4
  * Cleaves et al. (2008) Cleaves, H. J., Chalmers, J. H., Lazcano, A., Miller, S. L., & Bada, J. L. 2008, Origins of Life and Evolution of Biospheres, 38, 105
  * Cooke et al. (2023) Cooke, G. J., Marsh, D. R., Walsh, C., & Youngblood, A. 2023, ApJ, 959, 45
  * Crisp (1997) Crisp, D. 1997, Geophysical Research Letters, 24, 571
  * Das et al. (2019) Das, T., Ghule, S., & Vanka, K. 2019, ACS Central Science, 5, 1532
  * Dobbek et al. (2001) Dobbek, H., Svetlitchnyi, V., Gremer, L., Huber, R., & Meyer, O. 2001, Science, 293, 1281
  * Dodd et al. (2017) Dodd, M. S., Papineau, D., Grenne, T., et al. 2017, Nature, 543, 60
  * Ducluzeau et al. (2009) Ducluzeau, A.-L., van Lis, R., Duval, S., et al. 2009, Trends in Biochemical Sciences, 34, 9
  * Edwards et al. (1978) Edwards, T. J., Maurer, G., Newman, J., & Prausnitz, J. M. 1978, AIChE Journal, 24, 966
  * Fraschetti et al. (2019) Fraschetti, F., Drake, J. J., Alvarado-Gómez, J. D., et al. 2019, The Astrophysical Journal, 874, 21
  * Gaudi et al. (2020) Gaudi, B. S., Seager, S., Mennesson, B., et al. 2020, ArXiv e-prints [arXiv:2001.06683]
  * Gilmore (1975) Gilmore, F. R. 1975, Journal of Geophysical Research (1896-1977), 80, 4553
  * Gordon et al. (2022) Gordon, I., Rothman, L., Hargreaves, R., et al. 2022, Journal of Quantitative Spectroscopy and Radiative Transfer, 277, 107949
  * Gordon et al. (2017) Gordon, I., Rothman, L., Hill, C., et al. 2017, HITRAN2016 Special Issue, 203, 3
  * Green et al. (1973) Green, A. E. S., Sawada, T., Edgar, B. C., & Uman, M. A. 1973, J. Geophys. Res. (1896-1977), 78, 5284
  * Greene et al. (2023) Greene, T. P., Bell, T. J., Ducrot, E., et al. 2023, Nature, 618, 39
  * Grenfell (2017) Grenfell, J. L. 2017, Physics Reports, 713, 1
  * Grenfell et al. (2012) Grenfell, J. L., Grießmeier, J.-M., von Paris, P., et al. 2012, Astrobiology, 12, 1109
  * Grießmeier et al. (2015) Grießmeier, J., Tabataba-Vakili, F., Stadelmann, A., Grenfell, J. L., & Atri, D. 2015, A&A, 581, A44
  * Harman et al. (2018) Harman, C. E., Felton, R., Hu, R., et al. 2018, ApJ, 866, 56
  * Harman et al. (2015) Harman, C. E., Schwieterman, E. W., Schottelkotte, J. C., & Kasting, J. F. 2015, ApJ, 812, 137
  * Heays et al. (2022) Heays, A. N., Kaiserová, T., Rimmer, P. B., et al. 2022, Journal of Geophysical Research: Planets, 127, e2021JE006842
  * Helling (2019) Helling, C. 2019, J. Phys.: Conf. Ser., 1322, 012028
  * Helling et al. (2016) Helling, C., Harrison, R. G., Honary, F., et al. 2016, Surveys in Geophysics, 37, 705
  * Helling et al. (2013a) Helling, C., Jardine, M., Diver, D., & Witte, S. 2013a, Planetary and Space Science, 77, 152
  * Helling et al. (2013b) Helling, C., Jardine, M., Stark, C., & Diver, D. 2013b, ApJ, 767, 136
  * Helling et al. (2008) Helling, C., Woitke, P., & Thi, W.-F. 2008, A&A, 485, 547
  * Hill et al. (1984) Hill, R. D., Rinker, R. G., & Coucouvinos, A. 1984, J. Geophys. Res. Atmospheres, 89, 1411
  * Hill et al. (1980) Hill, R. D., Rinker, R. G., & Wilson, H. D. 1980, Journal of the Atmospheric Sciences, 37, 179
  * Hodosán et al. (2016a) Hodosán, G., Helling, C., Asensio-Torres, R., Vorgul, I., & Rimmer, P. B. 2016a, MNRAS, 461, 3927
  * Hodosán et al. (2021) Hodosán, G., Helling, C., & Vorgul, I. 2021, Planetary and Space Science, 204, 105247
  * Hodosán et al. (2016b) Hodosán, G., Rimmer, P. B., & Helling, C. 2016b, MNRAS, 461, 1222
  * Hu & Diaz (2019) Hu, R. & Diaz, H. D. 2019, ApJ, 886, 126
  * Huang et al. (2022) Huang, J., Seager, S., Petkowski, J. J., Ranjan, S., & Zhan, Z. 2022, Astrobiology, 22, 171
  * Ih et al. (2023) Ih, J., Kempton, E. M. R., Whittaker, E. A., & Lessard, M. 2023, ArXiv e-prints [arXiv:2305.10414]
  * Jackson et al. (2020) Jackson, R. B., Saunois, M., Bousquet, P., et al. 2020, Environmental Research Letters, 15, 071002
  * Johnstone (2020) Johnstone, C. P. 2020, ApJ, 890, 79
  * Johnstone et al. (2021a) Johnstone, C. P., Bartel, M., & Güdel, M. 2021a, A&A, 649, A96
  * Johnstone et al. (2019) Johnstone, C. P., Khodachenko, M. L., Lüftinger, T., et al. 2019, A&A, 624, L10
  * Johnstone et al. (2021b) Johnstone, C. P., Lammer, H., Kislyakova, K. G., Scherf, M., & Güdel, M. 2021b, Earth and Planetary Science Letters, 576, 117197
  * Kasting (1990) Kasting, J. F. 1990, Origins of life and evolution of the biosphere, 20, 199
  * Kasting & Walker (1981) Kasting, J. F. & Walker, J. C. G. 1981, J. Geophys. Res., 86, 1147
  * Kharecha et al. (2005) Kharecha, P., Kasting, J., & Siefert, J. 2005, Geobiology, 3, 53
  * Konhauser et al. (2009) Konhauser, K. O., Pecoits, E., Lalonde, S. V., et al. 2009, Nature, 458, 750
  * Konhauser et al. (2015) Konhauser, K. O., Robbins, L. J., Pecoits, E., et al. 2015, Astrobiology, 15, 804
  * Krissansen-totton et al. (2019) Krissansen-Totton, J., Arney, G. N., Catling, D. C., et al. 2019, BAAS, 51, 158
  * Krissansen-Totton et al. (2018a) Krissansen-Totton, J., Garland, R., Irwin, P., & Catling, D. C. 2018a, AJ, 156, 114
  * Krissansen-Totton et al. (2018b) Krissansen-Totton, J., Olson, S., & Catling, D. C. 2018b, Science Advances, 4, 5747
  * Lammer et al. (2011) Lammer, H., Lichtenegger, H. I. M., Khodachenko, M. L., Kulikov, Y. N., & Griessmeier, J. 2011, in Astronomical Society of the Pacific Conference Series, Vol. 450, Molecules in the Atmospheres of Extrasolar Planets, ed. J. P. Beaulieu, S. Dieters, & G. Tinetti, 139
  * Lammer et al. (2019) Lammer, H., Sproß, L., Grenfell, J. L., et al. 2019, Astrobiology, 19, 927
  * Levine et al. (1982) Levine, J. S., Gregory, G. L., Harvey, G. A., et al. 1982, Geophysical Research Letters, 9, 893
  * Levine et al. (1979) Levine, J. S., Hughes, R. E., Chameides, W. L., & Howell, W. E. 1979, Geophysical Research Letters, 6, 557
  * Lichtenegger et al. (2010) Lichtenegger, H., Lammer, H., Grießmeier, J.-M., et al. 2010, Icarus, 210, 1
  * Lin & Kaltenegger (2022) Lin, Z. & Kaltenegger, L. 2022, MNRAS, 516, 3167
  * Lincowski et al. (2018) Lincowski, A. P., Meadows, V. S., Crisp, D., et al. 2018, ApJ, 867, 76
  * Lovelock et al. (1975) Lovelock, J. E., Kaplan, I. R., & Pirie, N. W. 1975, Proceedings of the Royal Society of London. Series B. Biological Sciences, 189, 167
  * Luger et al. (2015) Luger, R., Barnes, R., Lopez, E., et al. 2015, Astrobiology, 15, 57
  * Lustig-Yaeger et al. (2019) Lustig-Yaeger, J., Meadows, V. S., & Lincowski, A. P. 2019, AJ, 158, 27
  * Ma et al. (2010) Ma, J., Dasgupta, P. K., Blackledge, W., & Boss, G. R. 2010, Environmental Science & Technology, 44, 3028
  * Meadows (2017) Meadows, V. 2017, Astrobiology, 17, 1022
  * Meadows et al. (2018a) Meadows, V. S., Arney, G. N., Schwieterman, E. W., et al. 2018a, Astrobiology, 18, 133
  * Meadows & Crisp (1996) Meadows, V. S. & Crisp, D. 1996, J. Geophys. Res. Planets, 101, 4595
  * Meadows et al. (2018) Meadows, V. S., Reinhard, C. T., Arney, G. N., et al. 2018, Astrobiology, 18, 630
  * Miller (1953) Miller, S. L. 1953, Science, 117, 528
  * Miller (1957) Miller, S. L. 1957, Annals of the New York Academy of Sciences, 69, 260
  * Miller & Schlesinger (1983) Miller, S. L. & Schlesinger, G. 1983, Advances in Space Research, 3, 47
  * Miller & Urey (1959) Miller, S. L. & Urey, H. C. 1959, Science, 130, 245 LP
  * Moore et al. (2013) Moore, C. M., Mills, M. M., Arrigo, K. R., et al. 2013, Nature Geoscience, 6, 701
  * National Academies of Sciences & Medicine (2021) National Academies of Sciences, E. & Medicine. 2021, Pathways to Discovery in Astronomy and Astrophysics for the 2020s, Tech. rep., National Academies Press, Washington, D.C.
  * Navarro-González et al. (2001) Navarro-González, R., McKay, C. P., & Mvondo, D. N. 2001, Nature, 412, 61
  * Navarro-González et al. (2001b) Navarro-González, R., Ramírez, S., de la Rosa, J., Coll, P., & Raulin, F. 2001b, Advances in Space Research, 27, 271
  * Navarro-González & Ramírez (1997) Navarro-González, R. & Ramírez, S. I. 1997, Proceedings of the F3.2 Symposium of COSPAR Scientific Commission F, 19, 1121
  * Nitschke & Russell (2013) Nitschke, W. & Russell, M. J. 2013, Philosophical Transactions of the Royal Society B: Biological Sciences, 368, 20120258
  * Nna Mvondo et al. (2001) Nna Mvondo, D., Navarro-González, R., McKay, C. P., Coll, P., & Raulin, F. 2001, Advances in Space Research, 27, 217
  * Nna Mvondo et al. (2005) Nna Mvondo, D., Navarro-González, R., Raulin, F., & Coll, P. 2005, Origins of Life and Evolution of Biospheres, 35, 401
  * Parker et al. (2014) Parker, E. T., Cleaves, J. H., Burton, A. S., et al. 2014, Journal of Visualized Experiments, e51039
  * Peacock et al. (2019) Peacock, S., Barman, T., Shkolnik, E. L., Hauschildt, P. H., & Baron, E. 2019, ApJ, 871, 235
  * Pearce et al. (2022) Pearce, B. K. D., He, C., & Hörst, S. M. 2022, ACS Earth and Space Chemistry, 6, 2385
  * Pearce et al. (2017) Pearce, B. K. D., Pudritz, R. E., Semenov, D. A., & Henning, T. K. 2017, Proceedings of the National Academy of Sciences, 114, 11327 LP
  * Phillips et al. (2021) Phillips, C. L., Wang, J., Kendrew, S., et al. 2021, ApJ, 923, 144
  * Piaulet et al. (2023) Piaulet, C., Benneke, B., Almenara, J. M., et al. 2023, Nature Astronomy, 7, 206
  * Picone et al. (1981) Picone, J. M., Boris, J. P., Greig, J. R., Raleigh, M., & Fernsler, R. F. 1981, Journal of Atmospheric Sciences, 38, 2056
  * Price et al. (1997) Price, C., Penner, J., & Prather, M. 1997, J. Geophys. Res. Atmospheres, 102, 5929
  * Quanz et al. (2022) Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2022, A&A, 664