© T. Kozakis et al. 2022

1 Introduction

In the search for life in the Universe, molecular oxygen (O₂) is commonly recognized as a promising atmospheric biosignature gas. However, while O₂ is largely created by biological sources on Earth, it can also be produced abiotically in a variety of settings, and thus alone would not constitute a guarantee of life (e.g., Hu et al. 2012; Wordsworth & Pierrehumbert 2014; Domagal-Goldman et al. 2014; Tian et al. 2014; Luger & Barnes 2015; Gao et al. 2015; Harman et al. 2015). Instead of being a standalone biosignature, O₂ as a biosignature will be most powerful when detected simultaneously with a reducing gas as a “disequilibrium biosignature pair” (e.g., Lovelock 1965; Lederberg 1965; Lippincott et al. 1967), and when evidence of abiotic O₂ production scenarios can be ruled out (see Meadows 2017; Meadows et al. 2018b for a review).

In scenarios where O₂ is not directly detectable, it has been suggested that its photochemical product ozone (O₃) could be used as a proxy for O₂ (e.g., Leger et al. 1993; Des Marais et al. 2002; Segura et al. 2003; Léger et al. 2011; Meadows et al. 2018b). Using O₃ as a proxy for O₂ would be extremely useful in two particular scenarios: 1) at wavelengths where O₂ features are not present (i.e., mid-infrared wavelengths), and 2) when O₂ is present in small amounts (as it was for a significant fraction of Earth’s geological history).

The mid-infrared wavelength region (MIR; 3–20 μm) provides an excellent opportunity for the search for life, as it contains features for multiple biosignature gases, as well for gaseous species that could provide evidence for or against biological O₂ production (Des Marais et al. 2002; Schwieterman et al. 2018; Quanz et al. 2021). Furthermore, thermal emission observations are less impacted by clouds (e.g., Kitzmann et al. 2011), and could also allow measurements of a planet’s surface temperature (Des Marais et al. 2002). The collisionally-induced absorption O₂ feature at 6.4 μm is the only MIR feature that allows for the direct detection of O₂, although it would be extremely difficult to use for abundances of O₂ consistent with biological production (Fauchez et al. 2020). It will, however, be useful for identifying high-O₂ desiccated atmospheres, a possible mechanism for abiotic O₂ production (Luger & Barnes 2015; Tian 2015). Inferring the presence of biologically produced O₂ will be restricted to indirect detections via the 9.7 μm O₃ feature in the MIR.

In addition, although O₂ has existed in appreciable amounts on Earth for a significant part of its history, it has only existed in large amounts for a relatively short period of time, posing a fundamental drawback to O₂ as a biosignature (Meadows et al. 2018b). Molecular oxygen was first created produced biologically ~2.7 Ga (billion years ago) by oxygenic photosynthesis via cyanobacteria, although it did not build up to appreciable amounts in Earth’s atmosphere until the Great Oxidation Event (GOE) ~2.45 Ga (see e.g., Catling & Kasting 2017 for a review). Although the Phanerozoic era (541 Ma-present day) saw the widespread colonization of land plants and O₂ levels comparable to our present atmospheric level (PAL), during the Proterozoic era (2.5 Ga–541 Ma) it is expected O₂ levels could have been significantly lower (Catling & Kasting 2017; Lenton & Daines 2017; Dahl & Arens 2020). As a result, it is likely that O₂ only would have been detectable on Earth for the last ~0.5 Gyr. However, since O₃ is a logarithmic tracer of O₂, it is possible that O₃ could be capable of revealing small, undetectable amounts of O₂ (e.g., Kasting et al. 1985; Leger et al. 1993; Des Marais et al. 2002; Segura et al. 2003; Léger et al. 2011). Additionally, a detection of O₃ could provide information about UV shielding, and whether surface life is adequately protected from high-energy UV capable of DNA damage.

Some studies have suggested or already adopted O₃ as a substitute for O₂ (e.g., Segura et al. 2003, Kaltenegger et al. 2020, Lin et al. 2021), and others have noted a potentially powerful “triple biosignature” in planetary emission with CO2, H₂O, and O₃, where O₂ spectral features are absent (Selsis et al. 2002). O₃ is also expected to build up in the stratospheres of planets, allowing characterization via transmission spectroscopy (e.g., Bétrémieux & Kaltenegger 2013, 2014; Misra et al. 2014; Meadows et al. 2018b).

However, it is uncertain how reliably a measurement of O₃ could allow us to infer the amount of O₂. Ozone is known to have a nonlinear relationship with O₂, as well as a strong dependence on the UV spectrum of the host star (Ratner & Walker 1972; Kasting & Donahue 1980; Kasting etal. 1985; Segura etal. 2003; Rugheimer et al. 2013). Although several studies have modeled the O₂–O₃ relationship for varying O₂ abundances and different stellar hosts (e.g., Ratner & Walker 1972; Levine et al. 1979; Kasting & Donahue 1980; Kasting etal. 1985; Segura etal. 2003; Gregory et al. 2021), there has been no in-depth study evaluating the ability of O₃ to predict O₂ as a biosignature. In this series of papers, we will explore the O₂–O₃ relationship in depth for a variety of stellar hosts and atmospheric conditions. For this first paper, we focus on the O₂–O₃ relationship for “Earth-like” planets for different stellar hosts. Here, we take Earth-like to mean a planet that has the same composition and size as Earth, receives the equivalent total incident flux from the Sun as modern Earth, and has a similar atmospheric composition. This study currently contains the largest number of models run with a fully coupled climate and photochemistry code dedicated to understanding the O₂–O₃ relationship, along with exploring the widest range of stellar hosts as well as the largest number of different O₂ atmospheric abundances.

Fig. 1 Absorption cross sections of O2 (left) and O3 (right), both plotted on the same y-axis scale to enable easier comparison. The y-axis is the same for both to enable easier comparison. Relevant O2 bands are the Schumann-Runge continuum (137–175 nm), the Schuman-Runge bands (175–200nm), and the Herzberg continuum (195–242nm). For less than 175nm an excited O atom, the O(1D) radical, is formed along with a ground state O atom during photolysis. O3 bands are the Hartley bands (200–300 nm), the Huggins bands (310–350 nm), and the Chappuis bands (410–750 nm). Photolysis within the Hartley bands will produce the O(1D) radical while other O3 bands create a ground state O atom. Absorption cross section data is from Brasseur & Solomon (2005).

2 Chemistry of O₃ production and destruction

In this section, we give a brief overview of the most important reactions for the production and destruction of O₃. The wavelength-dependent absorption cross sections for O₂ and O₃ are shown in Fig. 1 as a reference for the reader, as they determine photolysis rates in different wavelength regions. Incident stellar UV flux as well as the amount of nitrogen- and hydrogen-bearing species primarily control the concentration of O₃ in the atmosphere.

2.1 The Chapman mechanism

Ozone is primarily created in the stratosphere by a set of reactions called the Chapman mechanism (Chapman 1930). These reactions begin with the photolysis of O₂, $${\text{O}}_2+\text{h}v\to \text{O}+\text{O}\left(175<\lambda <242\text{\hspace{0.17em}nm}\right),$$(1)

which creates ground state O atoms (also written as O(³P)), which are highly reactive due to two unpaired electrons. These O atoms then combine with O₂ molecules to form O₃, $$\text{O}+{\text{O}}_2+M\to {\text{O}}_3+M,$$(2)

where M is a background molecule that carries away excess energy. Reaction (2) is a 3-body reaction, meaning it is more efficient at lower temperatures and higher atmospheric densities. It is faster in denser atmospheric regions with a larger availability of O atoms, causing bulk of O₃ on Earth to exist in the stratosphere rather than at higher altitudes.

Photolysis of O₂ can also occur higher in the atmosphere with higher energy photons, $${\text{O}}_2+\text{h}v\to \text{O}+\text{O}\left({}^1\text{D}\right)\left(\lambda <175\text{\hspace{0.17em}nm}\right),$$(3)

where the O(¹D) radical is created along with a ground state O atom. Free radicals are by nature extremely reactive as they have at least one unpaired valence electron. Thus, they tend to have extremely brief lifetimes. The O(¹D) radical can return to the ground state by being “quenched” via a collision with a background molecule, $$\text{O}\left({}^1\text{D}\right)+M\to \text{O}+M,$$(4)

or it can react with another molecule. Reactions with other molecules will be further explored in Sects. 2.2 and 4.1.

Although O₂ absorption cross sections are significantly larger at wavelengths that produce O(¹D) radicals (<175nm; see Fig. 1), these photons are absorbed high in the atmosphere and therefore do not contribute to the creation of stratospheric O₃ on modern Earth. Absorption caused by Lyman-α photons (121.6 nm) is generally absorbed in the mesosphere, and photons in the Schumann-Runge continuum (130–175 nm) are absorbed in the thermosphere. Also note that some wavelengths shorter than Lyman-α can ionize O₂, although that wavelength region is not included in our photochemistry model due to the low amount of photons in that region emitted by GKM stars (see Sect. 3.1).

Although O₂ photolysis from these higher energy photons (<175 nm) occurs above the stratosphere on modern Earth, planets with different amounts of atmospheric O₂ would experience absorption of these photons at varying atmospheric altitudes. Less O₂ would allow high energy photons to travel deeper into the atmosphere before absorption via O₂ photolysis. Although this will not cause the bulk of O₃ formation, it will impact the upper atmospheric chemistry by creating more O(¹D) at lower altitudes. The effects of this will discussed at length in Sect. 4.1.

Once O₃ is created by Reaction (2), it is often quickly photolyzed. O₃ photolysis from a photon in the Hartley band (200–300 nm) will create an O(¹D) radical, while photons from the lower energy Huggins bands (310–350 nm), Chappuis bands (410–750 nm), and longer wavelengths will create a ground state O atom, $${\text{O}}_3+\text{h}v\to {\text{O}}_2+\text{O}\left({}^1\text{D}\right)\left(\lambda <310\text{\hspace{0.17em}nm}\right),$$(5) $${\text{O}}_3+\text{h}v\to {\text{O}}_2+\text{O}\left(310\text{\hspace{0.17em}<\hspace{0.17em}}\lambda <1140\text{\hspace{0.17em}nm}\right).$$(6)

Photons with wavelengths shorter than 200 nm are often absorbed high in the atmosphere by O₂ and other molecules. As with O₂ photolysis, O(¹ D) radicals created by Reaction (5) will either be quenched by a background molecule and returned to the ground state (Reaction (4)), or they will react with other molecules.

Photolysis of O₃ is not seen as a loss of O₃, as the resulting O atom and O₂ molecule often quickly recombine into O₃ via Reaction (2). Due to the rapid cycling between O₃ and O, it is instead the conversion of O₃ + O (called “odd oxygen”) into O₂ that actually results in a loss of O₃, as occurs in the final reaction of the Chapman mechanism, $${\text{O}}_3+\text{O}\to 2{\text{O}}_2.$$(7)

Odd oxygen (O₃ + O) being converted into O₂ is considered a loss of O₃ because the photolysis of O₂ (Reactions (1), (3)) is the slowest of the Chapman mechanism reactions, and the limiting factor in O₃ production. Therefore the loss of odd oxygen on long timescales causes a true decrease in O₃.

2.2 Catalytic cycles of HO_x and NO_x

The Chapman mechanism on its own overestimates the amount of atmospheric O₃ because it does not take into account catalytic cycles that destroy O₃. These destruction cycles follow the format, $$\begin{array}{c}\text{X}+{\text{O}}_3\to \text{XO}+{\text{O}}_2\\ \text{XO}+\text{O}\to \text{X}+{\text{O}}_2\\ {\text{Net: O}}_3+\text{O}\to 2{\text{O}}_2\end{array}$$

where X is a free radical. During this process X and XO will cycle between each other while converting odd oxygen (O₃ + O) into O₂, similarly to the last step of the Chapman mechanism (Reaction (7)). As stated above, this results in the overall loss of O₃ because O₂ photolysis is the limiting reaction of O₃ formation. X and XO can cycle between each other and continuously destroy O₃ until reactions that convert either X or XO into non-reactive “reservoir” species occur. The primary catalytic cycles of O₃ destruction in modern Earth’s atmosphere are the HO_x (hydrogen oxide) and NO_x (nitrogen oxide) catalytic cycles. We note that on modern Earth there are also O₃ destroying catalytic cycles that are powered by molecular compounds primarily created anthropogenically (e.g., chlorine and bromine cycles; Crutzen & Lelieveld 2001), but they will not be included in this study.

The HO_x catalytic cycle is powered by the OH (hydroxyl) and HO₂ (hydroperoxyl) radicals. When an O(¹D) radical is created either by photolysis of O₂ (Reaction (3)) or O₃ (Reaction (5)) it can react with H₂O to form OH, $${\text{H}}_2\text{O}+\text{O}\left({}^1\text{D}\right)\to \text{OH\hspace{0.17em}+\hspace{0.17em}OH.}$$(8)

The OH radical is a major sink for multiple atmospheric gases (e.g., CH₄, CO) and is often called the ‘detergent of the atmosphere’ for this reason. It destroys O₃ during the HO_x catalytic cycle as follows, $$\text{OH}+{\text{O}}_3\to {\text{HO}}_2+{\text{O}}_2,$$(9) $${\text{HO}}_2+\text{O}\to \text{OH}+{\text{O}}_2.$$(10)

In addition to this primary destruction cycle, other HO_x cycles can contribute significantly to O₃ destruction via, $$\text{OH}+{\text{O}}_3\to {\text{HO}}_2+{\text{O}}_2,$$(9) $${\text{HO}}_2+{\text{O}}_3\to \text{OH}+2{\text{O}}_2,$$(11)

resulting in two O₃ molecules converted to three O₂ molecules, or, $$\text{OH}+\text{O}\to \text{H}+{\text{O}}_2,$$(12) $$\text{H}+{\text{O}}_2+M\to {\text{HO}}_2+M,$$(13) $${\text{HO}}_2+\text{O}\to \text{OH}+{\text{O}}_2,$$(10)

with a net result of two O atoms converted into an O₂ molecule. Because OH production via O(¹D) is a byproduct of the Chapman mechanism, HO_x catalytic cycle efficiency can be increased with higher rates of O₃ formation. This process can be slowed through reactions that convert OH/HO₂ into a reservoir species such as H₂O, HNO₂, or H₂O₂, which are significantly less reactive.

The NO_x catalytic cycle destroys O₃ with the NO (nitric oxide) and NO₂ (nitrogen dioxide) radicals. The primary source of these radicals in the stratosphere is from N₂O (nitrous oxide) which is biologically produced by nitrification and denitrification processes within soil. N₂O can additionally be produced anthropogenically, primarily through agriculture. It is converted into NO by interactions with the O(¹D) radical, $${\text{N}}_2\text{O}+\text{O}\left({}^1\text{D}\right)\to \text{NO}+\text{NO.}$$(14)

A secondary source of NO is production via lightning in the upper troposphere, which can then be transported into the lower stratosphere. The NO_x catalytic cycle destroys O₃ as follows: $$\text{NO}+{\text{O}}_3\to {\text{NO}}_2+{\text{O}}_2\text{,}$$(15) $${\text{NO}}_2+\text{O}\to \text{NO}+{\text{O}}_2.$$(16)

NO_x can destroy O₃ with the following cycle as well, $$\text{NO}+{\text{O}}_3\to {\text{NO}}_2+{\text{O}}_2,$$(15) $${\text{NO}}_2+{\text{O}}_3\to {\text{NO}}_3+{\text{O}}_2.$$(17) $${\text{NO}}_3+\text{h}v\to \text{NO}+{\text{O}}_2.$$(18)

with a net conversion of two O₃ molecules into three O₂ molecules. NO_x reactions are highly temperature dependent and are faster at hotter temperatures. The main reservoir species associated with NO_x are HNO₃ and N₂O₅, which have slow photolysis rates.

We note that although in the stratosphere NO_x destroys O₃ through this catalytic cycle, that lower in the atmosphere it can help create O₃ through the “smog mechanism” (see Sect. 5.2). This low altitude O₃ is a pollutant that can cause biological damage. In this study we will focus on the majority of O₃ in the stratosphere created by the Chapman mechanism. In this study we will focus on the efficiency of the Chapman mechanism, along with the ability of the HO_x and NO_x catalytic cycles to destroy O₃ for varying O₂ levels around different host stars.

3 Methods

3.1 Atmospheric models

We modeled planetary atmospheres with Atmos¹, a 1D coupled climate and photochemistry code to explore O₃ formation for varying levels of O₂ on Earth-like planets around a variety of host stars. Numerous studies have used either of these climate or photochemistry modules, as well as both coupled (e.g., Arney et al. 2017; Meadows et al. 2018a; Lincowski et al. 2018; Madden & Kaltenegger 2020; Gregory et al. 2021; Teal et al. 2022). We give a brief overview of Atmos and refer readers to Arney et al. (2016) and Meadows et al. (2018a) for extensive details.

The photochemistry model originates from Kasting (1979) and was expanded upon and updated by Zahnle et al. (2006). It has been used extensively by many studies (e.g., Kasting & Donahue 1980; Segura et al. 2003, 2005, 2010; Domagal-Goldman et al. 2014; Gregory et al. 2021). The atmosphere is broken up in 200 plane parallel layers from 0 to 100 km. The abundance of each gaseous species is calculated simultaneously with the flux and continuity equations using a reverse-Euler method for individual atmospheric layers. Vertical transport between different layers include molecular and eddy diffusion. Radiative transfer is computed with a δ-2-stream method as described in Toon et al. (1989). For modern Earth Atmos uses 50 gaseous species, with nine of them being short lived and thus not included in transport calculations. The photochemistry model is considered converged when its adaptive time step length reaches 10¹⁷ s within 100 time steps.

The climate model was originally developed by Kasting & Ackerman (1986), but has been significantly updated as described in Kopparapu et al. (2013) and Arney et al. (2016). Multiple studies have used this code to calculate habitable zones around a variety of stellar hosts used to study habitable zones and atmospheres of Earth-like planets around different stars (e.g., Kopparapu et al. 2013; Segura et al. 2003, 2005, 2010). The atmosphere is broken up into 100 plane parallel layers from the surface to an atmospheric pressure of 1 mbar. A correlated-k method computes the absorption of O₃, H₂O, CH₄, CO₂, and C₂H₆ throughout the atmosphere. Total absorption of incident stellar flux is calculated for each atmospheric layer with a δ-2-stream scattering algorithm (Toon et al. 1989), and outgoing IR radiation is calculated with correlated-k coefficients for each species individually. Updated H₂O cross sections from Ranjan et al. (2020) have been incorporated into the code. Convergence criteria are reached when both changes in temperature and the flux out of the top of the atmosphere are sufficiently small (<10⁻⁵).

We run the climate and photochemistry models coupled with inputs including host stellar spectrum (121.6–45 450 nm), initial mixing ratios of atmospheric species, upper and lower boundary conditions for individual species, and initial temperature/pressure profiles. Using initial conditions the photochemistry code runs first and then transfer computed H₂O, CH₄, CO₂, and C₂H₆ mixing ratio profiles to the climate code. The climate code then updates the temperature and H₂O vapor profiles to feed back into the photochemistry. These processes iterate with profiles from the photochemistry allowing for more accurate climate code calculations and vice-versa, until a converged solution is reached.

The climate code has not been successfully run to convergence for the same atmospheric height as the photochemistry code (Arney et al. 2016), so temperature and H₂O profiles of the upper, thin part of the atmosphere (typically <60–70 km) are held constant at the highest computed value from the climate code. Sensitivity tests from Arney et al. (2016) suggest that the impact on the radiative transfer and climate of these models is not significant.

This study also implements the “short-stepping” method of convergence, as described in Teal et al. (2022). When iterating back and forth between the photochemistry and climate code, occasionally the code will oscillate between two different solutions. For example, if the photochemistry code computes a large quantity of O₃, the climate code will respond with a large amount of atmospheric heating. However, due to the temperature sensitivity of O₃ production (Reaction (2)), this hotter atmosphere will cause lower amounts of O₃ on the subsequent photochemistry iteration. Using the “short-stepping” method we do not allow the climate code to fully adjust to the updated atmospheric profiles from the photochemistry on a single iteration, and instead reach convergence slowly by iterating back and forth between the climate and photochemistry codes until a stable solution is reached.

We modeled planetary atmospheres orbiting a variety of stellar hosts (see Sect. 3.2) at the Earth-equivalent distance with varying levels of O₂. Here, we take Earth-equivalent distance to mean that the planet receives the same total amount of incident flux from their parent stars as modern Earth receives from the Sun. We set O₂ as a constant mixing ratio for all cases, with values varying from 0.01-150% PAL O₂ (mixing ratios of 2.1 × 10⁻³–0.315). Higher O₂ levels are not explored because large O₂ levels would unstable with biological compounds (Kump 2008). Lower O₂ are not modeled because it is thought that O₂ abundances from ~10⁻³% to ~1% PAL are not expected to be stable in an Earth-like atmosphere as calculated by Gregory et al. (2021) (details on these limits in Sect. 5.4).

Other initial conditions for the models were chosen to resemble modern Earth including atmospheric mixing ratios, planetary composition, and size. Atmos haze production was not used. All models were run at a zenith of 60° degrees (Lambertian average) and with cloudless skies. Fixed mixing ratios were used for CH₄ (1.8×10⁻⁶), N₂O (3.0×10⁻⁷), and CO₂ (3.6×10⁻⁴). All other species used initial atmospheric profiles and boundary conditions as defined in Atmos’s modern Earth template, and surface pressure remained constant at 1 bar. We note that defining CH₄ at a constant mixing ratio resembling modern Earth differs from several studies modeling “Earth-like” planets, which have adjusted CH₄ mixing ratios to reflect the CH₄ ground flux of modern Earth, resulting in much higher atmospheric CH₄ mixing ratios (e.g., Rugheimer et al. 2015a; Wunderlich et al. 2019; Teal et al. 2022). We chose to maintain CH₄ mixing ratio of modern Earth to better isolate the effects of different stellar hosts on the O₂–O₃ relationship. The impact of changing CH₄ levels on O₃ abundance is discussed further in Sect. 5.2.

Fig. 2 Stellar spectra of the planet host stars. G0V-K5V hosts are comprised of IUE UV data from Rugheimer et al. (2013), and the M5V host comes from UV observations of GJ 876 from the MUSCLES survey (France et al. 2016). Visible and IR wavelengths use ATLAS models of the same stellar temperature (Kurucz 1979). The right-hand figure zooms in on the UV region relevant for photolysis with important biological UV regimes (see Sect. 4.4).

3.2 Input stellar spectra

All host star spectra inputted into Atmos comprise of actual UV observations supplemented with synthetic ATLAS model spectra (Kurucz 1979) for the visible and IR. Table 1 contains information about the host stars and their spectra are shown in Fig. 2. The G0V-K5V stellar spectra were created in Rugheimer et al. (2013) and are a combination of UV data from the International Ultraviolet Explorer (IUE) data archives² and model ATLAS spectra for the same stellar temperature (Kurucz 1979). UV data for the M5V host is from GJ 876 observations obtained by the Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) survey (France et al. 2016).

The UV spectrum of a planet’s host star is extremely important in the photochemical modeling of O₃ production. Not only does the total amount of UV dictate photolysis rates, but the UV spectral slope determines the creation and destruction rates of O₃. The far-UV (FUV; λ < 200 nm) is primarily responsible for photolysis of O₂ (and the creation of O₃), while the mid- and near-UV (abbreviated NUV, for brevity; 200 nm < λ < 400 nm) is responsible for the photolysis of O₃. The NUV additionally can photolyze H₂O, which creates the HO_x species responsible for destroying O₃, causing NUV flux to destroy O₃ both directly and indirectly. Hence, a higher FUV/NUV flux ratio will create O₃ more efficiently. Low-mass, active stars tend to have lower FUV/NUV flux ratios as activity will cause excess FUV chromospheric radiation, while NUV wavelengths are often absorbed for cool stars by TiO (Harman et al. 2015).

3.3 Radiative transfer model

After Atmos computes the compositions of our model atmospheres, the Planetary Intensity Code for Atmospheric Scattering Observations (PICASO) computes planetary emission spectra (Batalha et al. 2019, 2021). PICASO is a publicly available³ radiative transfer code capable of producing transmission, reflected light, and emission spectra for a diverse range of planets. Our emission spectra were calculated at a phase angle of 0° (full phase) with altitude dependent pressure, temperature and mixing ratio profiles computed by Atmos. Output spectra cover a wavelength range of 0.3–14 μm, although particular focus is put on the O₃ 9.7 μm feature in this study.

Fig. 3 O2–O3 relationship for Earth-like planets orbiting different host stars (indicated in legend) with varying amounts of O2 mixing ratios. Molecular oxygen levels compared to Earth’s present atmospheric level (PAL) are shown as dashed vertical lines for reference. The left-hand figure shows the relationship in terms of total integrated O3 column density, and the right-hand figure in terms of total O3 normalized at the amount produced in the 100% PAL O2 case for each stellar host. The nonlinearity in these relationships is primarily due to the pressure dependence of Reaction (2) which forms O3. The main takeaway is that the O2–O3 relationship is significantly different for hotter host stars (GOV, Sun, K2V) versus cooler host stars (K5V, M5V), with hotter hosts experiencing peak O3 formation occurring at O2 levels under 100% PAL. See Sect. 4.1 for a detailed explanation.

4 Results

4.1 O₂–O₃ relationship

Figure 3 shows the O₂–O₃ relationship for all of our model planetary atmospheres. The O₂–O₃ relationship is highly dependent on the stellar host, with different trends for model atmospheres having hotter host stars (GOV, Sun, K2V) versus cooler host stars (K5V, M5V). Since O₃ is produced via the Chapman mechanism by converting O₂ into O₃, one would naively expect the O₃ concentration to increase as the O₂ mixing ratio increases, which the case for the cooler host stars. However, the O₂–O₃ relationship for hotter stellar hosts behaves unexpectedly such that O₃ abundance peaks and then decreases as the abundance of O₂ decreases from modern Earth levels. Maximum O₃ abundance occurs in the 25% PAL O₂ models for the GOV and Sun hosts, and the 55% PAL O₂ model for the K2V host. This effect does not occur for cooler host stars, with O₃ abundance dropping consistently for models with less O₂, though not in a linear fashion. As a result, the K5V and M5V models with maximum O₂ considered (150% PAL) created the maximum amount of O₃. These results are summarized in Table 2. To allow for a simple parameterization of the O₂–O₃ relationships shown in Fig. 3 that can be used as an approximation in, for instance, GCM and retrieval modeling, we fit a fifth degree polynomial of the form, $$y=a{x}^5+b{x}^4+c{x}^3+d{x}^2+ex+f,$$(19)

where y is the integrated O₃ column density (cm⁻²), x is the base 10 logarithm of the O₂ mixing ratio, and α, b, c, d, e, and f are the best fit polynomial coefficients listed in Table 3. This fit is valid over the range of O₂ abundances modeled in this study (0.01%–150% PAL).

The seemingly counterintuitive phenomenon of hotter hosts having O₃ levels increase as O₂ levels decrease can be explained by two factors: UV shielding abilities of O₂, and the pressure dependency of O₃ formation. First, we will address the UV shielding ability of O₂. Despite the fact that O₂ UV absorption cross sections are either significantly smaller than those of O₃ or require far higher energy photons (see Fig. 1), O₂ remains an important UV shield on modern Earth, primarily due to its large abundance. Although O₂ is less efficient at absorbing UV photons than O₃, O₂ makes up ~21% of the atmosphere, whereas O₃ is a trace gas with a maximum value of ~10 ppm on modern Earth. This allows the far larger number of O₂ molecules to compensate for its smaller absorption crosssections and absorb many photons with wavelengths shorter than 240 nm (the required wavelength for O₂ photolysis, see Reaction (1)). As a result, as O₂ decreases, UV shielding in that wavelength range decreases, allowing photolysis to occur deeper in the atmosphere. This is illustrated in Fig. 4, where mixing ratio profiles of O₃, H₂O, CH₄, and N₂O are shown for all host stars at O₂ abundances of 100%, 10%, 1%, and 0.1% PAL O₂. Photolysis occurs at lower atmospheric altitudes as O₂ decreases, leading the O₃ layer to shift downward in the atmosphere. This effect is more pronounced for hotter host stars with high UV fluxes (particularly high FUV fluxes capable of O₂ photolysis), and therefore higher photolysis rates.

Secondly, the depth in which O₂ photolysis occurs is of particular importance to the altitudes at which the O₃ forming Chapman mechanism takes place, because as O₂ decreases, photolysis reaches not only deeper but also denser regions of the atmosphere. This is of significant relevance to O₃ formation due to the pressure dependency of the Chapman mechanism: Reaction (2), in which an O atom and O₂ molecule combine (with the help of a background molecule) to form O₃, is a 3-body reaction, and therefore is faster at higher atmospheric densities. Denser regions allow O, O₂, and background molecules to come together and react more rapidly than in a thinner region of the atmosphere. For hotter host stars in our sample (GOV, Sun, K2V), the UV fluxes are strong enough to allow O₂ photolysis to reach much denser atmospheric layers as O₂ decreases, allowing the benefit of faster O₃ production via Reaction (2) to outweigh the smaller source of O₂, resulting in peak O₃ abundance at lower O₂ levels.

Our cooler host stars (K5V, M5V), however, have weaker UV fluxes, meaning photons capable of O₂ photolysis cannot travel as deep in the atmosphere as for hotter hosts when O₂ decreases. The additional speed of the Chapman mechanism for lower O₂ does not make up for the smaller amount of O₂, causing O₃ abundance to decrease for decreasing O₂ abundance with these cooler host stars.

This result of an increase in O₃ production as O₂ levels decrease has been noted for the Earth-Sun system by several studies (e.g., Ratner & Walker 1972; Levine et al. 1979; Kasting & Donahue 1980; Kasting et al. 1985; Leger et al. 1993), although this is the first time it has been explored for Earth-like planets around different stellar hosts. Whether or not this would occur for an Earth-like planet will depend on if the UV flux (particularly the FUV flux) from its host star will be strong enough to incite O₂ photolysis at dense enough atmospheric levels that the increased rate of O₃ production will be enough to counter the decreased amounts of O₂ from which O₃ can form. This effect contributes to the strong dependency of the O₂–O₃ relationship on the spectral type of the host star. For example the G0V host star models have more O₃ at 10% PAL O₂ than at 100% PAL O₂, whereas for the M5V host star O₃ abundance in the 10% PAL O₂ model is nearly 60% less than it is for the 100% PAL O₂ model.

When looking at specific O₃ mixing ratios, Fig. 3 also indicates an increase in O₃ above the stratosphere for all models. This upper atmosphere O₃ (the “secondary O₃ layer”) is produced primarily by O₂ photolysis from higher energy photons (>175nm; Reaction (3)) which produces the radical O(¹D). Photons of these wavelengths are absorbed high in the atmosphere but do not contribute significantly to stratospheric O₃, even when a decrease in O₂ allows photolysis to reach deeper layers of the atmosphere. Instead, these photons create O₃ above the primary O₃ layer, generally in the mesosphere and thermosphere (see Sect. 2 for more details). Although O₃ mixing ratios are high at these altitudes, due to the thin atmosphere, O₃ creation at these elevations does not add considerably to the total amount of O₃.

Also note that although the K2V host star produces enough UV photons capable of O₂ photolysis to have peak O₃ production in its 55% PAL O₂ model, both the K5V and M5V host models show a larger amount of O₃ than the K2V host for O₂ levels near 100% PAL (Fig. 3). This is because although the K2V host has more FUV than the K5V and M5V hosts (Fig. 2), the cooler hosts have higher FUV/NUV ratios (Table 1), allowing more efficient O₃ production without as much NUV O₃ destruction.

In summary, the O₂–O₃ relationship is highly dependent on the UV flux of the host star, with different trends for hotter and cooler host stars. Hotter host stars with high FUV fluxes experience peak O₃ abundance at lower O₂ levels due to O₃ formation occurring in deeper, denser parts of the atmosphere where the Chapman mechanism is more efficient. Cooler host stars do not emit enough FUV flux for this effect to occur, and experience consistently decreasing O₃ as O₂ decreases.

Fig. 4 Mixing ratio profiles of O3, H2O, CH4, and N2O; all potential biosignature species. Each row represents results for model atmospheres orbiting different stellar hosts as indicated on the right-hand vertical axis. Each plot shows the mixing ratio profiles for O2 abundances of 100%, 10%, 1% and 0.1% PAL. O2 on modern Earth is a significant UV shield, allowing model atmospheres with decreasing O2 values to have photolysis occur at consistently lower altitudes. This is demonstrated well with the bulk of O3 forming at lower altitudes with less O2, as well as increased upper atmospheric depletion for H2O, CH4, and N2O via photolysis. The downward shift of O3 and upper atmospheric depletion of other species is shown to decrease for model atmospheres around cooler stars with lower incident UV flux, and hence lower photolysis rates. Full details of this atmospheric chemistry is shown in Sects. 4.1 and 4.3.

4.2 impact of varying O₂ on H₂O, CH₄, and N₂O

Figure 4 shows the impact of varying O₂ levels on the biologically relevant atmospheres species H₂O, CH₄, and N₂O. As O₂ decreases, photons usually absorbed by O₂ (λ < 240 nm) travel deeper into the atmosphere and drive the majority of atmospheric changes. This allows photolysis in general to reach lower altitudes, as well as photolysis caused by high energy photons that create the O(¹D) radical, which reacts quickly with many species. O(¹D) is produced via photolysis of O₂, O₃, N₂O, and

CO₂ as follows: $${\text{O}}_2+\text{h}v\to \text{O}+\text{O}\left({}^1\text{D}\right)\left(\lambda <175\text{\hspace{0.17em}nm}\right),$$(3) $${\text{O}}_3+\text{h}v\to {\text{O}}_2+\text{O}\left({}^1\text{D}\right)\left(\lambda <310\text{\hspace{0.17em}nm}\right),$$(5) $${\text{N}}_2\text{O}+\text{h}v\to {\text{N}}_2+\text{O}\left({}^1\text{D}\right)\left(\lambda <200\text{\hspace{0.17em}\hspace{0.17em}nm}\right),$$(20) $${\text{CO}}_2+\text{h}v\to \text{CO}+\text{O}\left({}^1\text{D}\right)\left(\lambda <167\text{\hspace{0.17em}\hspace{0.17em}nm}\right).$$(21)

As O₂ decreases, O(¹ D) creation moves deeper into the atmosphere for all these species. For our models, O₃ photolysis consistently creates the most O(¹D), particularly at lower atmospheric heights. O₂ photolysis is also a significant producer of O(¹ D), although it is limited to the stratosphere and above, even for the lowest O₂ levels modeled in this study. CO₂ and N₂O photolysis contribute to O(¹D) production as well, although CO₂ photolysis is constrained to the upper atmosphere similarly to O₂ photolysis, while N₂O photolysis can occur much closer to the planetary surface for low O₂ levels. Increased rates of photolysis as O₂ shielding decreases as well as increased O(¹D) production reaching lower atmospheric levels causes the depletion of many species.

H₂O is increasingly depleted for decreasing levels of O₂ due to both photolysis in the atmosphere and O(¹D) reactions lower in the atmosphere. Both of these reactions create the OH radical while removing H₂O, $${\text{H}}_2\text{O}+\text{h}v\to \text{H}+\text{OH,}$$(22) $${\text{H}}_2\text{O}+\text{O}\left({}^1\text{D}\right)\to \text{OH}+\text{OH.}$$(8)

On modern Earth, Reaction (8) is the primary source of OH in the stratosphere, which is a major sink for several species. As H₂O levels in the upper atmosphere drop with decreasing O₂, this causes OH production to move to lower levels of the atmospheres as seen in Fig. 5. Upper atmospheric depletion of H₂O and OH production at lower altitudes is seen more strongly for hotter host stars, as they have higher incident UV for photolysis and O(¹D) creation.

CH₄, an important biosignature gas, is also depleted in the upper atmosphere for models around all host stars, primarily though oxidation via OH (created via reactions with H₂O), along with photolysis and reactions with O(¹D), $${\text{CH}}_4+\text{OH}\to {\text{CH}}_3+{\text{H}}_2\text{O,}$$(23) $${\text{CH}}_4+\text{O}\left({}^1\text{D}\right)\to {\text{CH}}_3+\text{OH.}$$(24)

In the upper atmosphere, depletion is dominated by photolysis. Reaction (23) is both the main sink of stratospheric CH₄ and OH depletion on modern Earth, with CH₄ and OH acting as a major sinks for each other. Reactions with O(¹D) and OH occur deeper in the atmosphere for decreasing O₂ levels as both these radicals are produced at lower altitudes. Reaction (24) is an additional source of OH in the lower stratosphere/troposphere. CH₄ depletion is limited to the upper stratosphere for model atmospheres around cooler hosts, although can reach the lower stratosphere for model atmospheres with hotter hosts.

N₂O, another potential biosignature gas, experiences extreme depletion for hotter hosts down to the troposphere for lower levels of O₂, and significantly less depletion constrained to the upper atmosphere around cooler stars. This is due primarily to photolysis (Reaction (20)) in the upper atmosphere, although there are contributions from interactions with O(¹D) as well, $${\text{N}}_2\text{O}+\text{O}\left({}^1\text{D}\right)\to \text{NO}+\text{NO.}$$(14)

Depletion rates of N₂O vary significantly between different stellar hosts due to the strong dependence of incident UV flux on N₂O destruction.

In summary, the majority of changes to an atmosphere as O₂ decreases are caused by increased photolysis rates as O₂ UV shielding decreases as well as O(¹D) production from either O₂, O₃, N₂O, or CO₂ photolysis occurring at lower levels of the atmosphere. These effects cause upper atmospheric depletion of H₂O, CH₄, and N₂O, with more depletion for hotter stellar hosts with stronger UV fluxes.

Fig. 5 Mixing ratio profiles of HOx (OH + HO2) and NOx (NO + NO2) species that power the catalytic cycles which destroy O3 for models with 100%, 10%, 1%, and 0.1% PAL O2. Here, we show models for the hottest (GOV) and coolest (M5V) stellar hosts. For decreasing O2 levels photolysis reaches lower levels of the atmosphere, causing OH and HO2 formation to occur at lower levels. The HOx is not significantly impacted by these changes since O3 formation is pushed deeper into the atmosphere as well. NOx species experience depletion via N2O and NO photolysis, although are less affected for models around cooler stars with lower photolysis rates. The efficiency of the NOx catalytic cycle decreases consistently for all host stars with decreasing O2 levels. See Sect. 4.3 for full details.

4.3 Impact of varying O₂ on catalytic cycles

Varying O₂ levels impacts HO_x (OH + HO₂) and NO_x (NO + NO₂) species, which are the main contributors of catalytic cycles that destroy O₃ (see Sect. 2.2 for details). Mixing ratio profiles of these species are shown in Fig. 5 for our hottest and coolest host stars. Once again, the impact on these species as O₂ levels are decreased is controlled by photolysis reaching deeper levels of the atmosphere along with O(¹D) production moving to lower levels as well.

As O₂ decreases, HO_x species (OH and HO₂) in all models decrease in the upper atmosphere, but increase in the lower atmosphere. OH production via reactions with H₂O (Reactions (8), (22)) and CH₄ (Reaction (24)) occur at lower altitudes for lower O₂ levels, especially since both H₂O and CH₄ are depleted in the upper atmosphere from photolysis. This “pushing down” of HO_x species is more noticeable for hotter host stars with higher photolysis rates. Also note that stars with lower FUV/NUV ratios can better remove O₃ via the HO_x catalytic cycle, as FUV wavelengths create O₃, while NUV wavelengths photolyze H₂O to form OH. However, for all host stars the efficiency of the HO_x catalytic cycle of O₃ destruction is not largely impacted for different O₂ and O₃ abundances since OH and HO₂ move down in the atmosphere along with O₃ concentrations. Decreased O₂ UV shielding and increased photolysis does not destroy HO_x species, but rather converts them into other HO_x species. When HO₂ is photolyzed, $${\text{HO}}_2+\text{h}v\to \text{OH}+\text{O},$$(25)

it creates OH. The OH radical itself is extremely reactive with a short lifetime, and typically will react quickly with other species or react with O₃ to create HO₂ (Reaction (9)).

Although with decreasing O₂ abundance HO_x species are formed lower in the atmosphere rather than destroyed by photolysis, NO_x species (NO + NO₂) can be depleted via photolysis. The main source of NO_x in the stratosphere is via N₂Õ reactions with O(¹D). However, as shown in Fig. 4, N₂O is significantly depleted in the atmosphere via photolysis, especially for hotter host stars. While H₂O, the primary source of HO_x species in the stratosphere creates HO_x during photolysis, N₂O, the primary source of NO_x species, does not. Instead it creates N₂ and O(¹D) (Reaction (20)), cutting off the main source of NO production from N₂O. As for NO_x species themselves, NO₂ photolysis creates more NO, while NO photolysis simply breaks the molecule apart, $${\text{NO}}_2+\text{h}v\to \text{NO}+\text{O},$$(26) $$\text{NO}+\text{h}v\to \text{N}+\text{O},$$(27)

causing NO photolysis to be a sink of NO_x. NO can be formed once again via reactions between N atoms and O₂ molecules, $$\text{N}+{\text{O}}_2\to \text{NO}+\text{O},$$(28)

although the rate of NO photolysis is faster than Reaction (28), causing it to be a gradual sink of NO_x. Often the N atom created by Reaction (27) will remove NO_x via, $$\text{NO}+\text{N}\to {\text{N}}_2+\text{O},$$(29)

or the N atoms will recombine with other N atoms, $$\text{N}+\text{N}\to {\text{N}}_2,$$(30)

with this reaction becoming more efficient as O₂ levels drop. This sink via NO photolysis has less of an impact on cooler host stars with lower photolysis rates, hence less NO_x depletion.

As seen in Fig. 5, NO_x species are depleted throughout the atmosphere for the G0V host star, while the M5V host star experiences less NO_x depletion, and actually an increase in NO in the lower stratosphere. This is due to primarily to lower photolysis rates for the cooler M5V star which depletes less N₂O and NO (Reaction (14)). However, for model atmospheres around all host stars the ability of the NO_x catalytic cycle to deplete O₃ diminishes consistently with decreasing O₂ levels, even for cooler stellar host models with less NO_x depletion.

In summary, the HO_x catalytic cycles are not hugely impacted by decreasing O₂ because increased photolysis rates tend to push HO_x species to lower altitudes rather than destroy them. However, NO_x catalytic cycles decrease in efficiency with lower O₂ levels since photolysis of N₂O and NO remove NO_x from the atmosphere.

4.4 Surface UV flux for different O₂ and O₃ levels

Atmos was used to calculate the amount of UV flux reaching the planetary surface in each model atmosphere. Surface UV flux is strongly dependent on incident stellar Uv flux and the amount of UV shielding from both O₂ and O₃. High UV fluxes can cause substantial damage to biological organisms, hence UV surface environments will be critical for determining surface habitability. These results are summarized in Table 4 and shown in Fig. 6. Surface UV fluxes calculated here using a zenith angle of 60° (see Sect. 3.1).

Integrated surface UV fluxes are broken up into three biologically relevant wavelength regimes: UVA, UVB, and UVC. UVA flux (315–400 nm) is the lowest energy type of UV and is only partially shielded by O₃, so a large percentage of incident UVA on modern Earth reaches the planetary surface. UVB (280-315 nm) is more harmful for life, contributing to sun burn and skin cancer in humans and damage to other organisms (e.g., Kiesecker et al. 2001). UVB is shielded much more efficiently by O₃ than UVA, with a smaller fraction of incident UVB reaching the surface of modern Earth. UVC (121.6–280 nm) is capable of causing DNA damage, but is fortunately shielded almost entirely by O₃ on modern Earth. Ozone is most efficient at shielding UV in this wavelength region, as evidenced by the O₃ absorption cross sections shown in Fig. 1. We note that O₂ photolysis, the first step in O₃ formation (Reactions (1), (3)), requires a UVC photon (λ < 240 nm), allowing O₂ to contribute partially to UVC shielding. However, since O₃ is the primary shielder of UVC, the requirement of a UVC photon to produce O₃ creates interesting correlations between incident and surface UVC flux.

Because UVA is not strongly shielded by O₃, UVA surface fluxes for all models are closely correlated with the amount of incident UVA flux (see Table 4 and Fig. 6). For all host stars at O₂ levels of 100%, 10%, 1%, and 0.1% PAL the amount of incident UVA that reaches the surface of these model planets is roughly ~80% for all cases. Because O₃ plays only a small role in UVA shielding, all model results are quite similar.

UVB surface fluxes are significantly more variable because O₃ shielding is much more important for these wavelengths. Although the G0V host star provides a higher incident UVB flux than the Sun, G0V-hosted models still maintain slightly less surface UVB flux until O₂ decreases to 0.1% PAL, at which point the G0V and Sun model surface fluxes become roughly equal. This is due to the larger amount of O₃ created by the G0V host star compared to the Sun, which allows for stronger UVB shielding (see Fig. 3 for O₂–O₃ relationship). The percentage of incident UVB flux that reaches the planetary surface varies significantly between different host stars. For our hottest host star (GOV) the amount of incident UVB flux reaching the planetary surface increases from 6.7% to 26.3% as O₂ levels drop from 100% to 0.1% PAL. As a result of less O₃ shielding, these percentages are higher for our coolest host star (M5V), which experiences an increase of 18.4% to 56.3% of incident UVB reaching the surface as O₂ decreases from 100% to 0.1% PAL. Even though the cooler stellar hosts allow a higher percentage of UVB flux to travel through the atmosphere, they still maintain lower surface UVB values than hotter hosts due to their weaker incident UVB flux.

The strong reliance of UVC absorption on O₃ abundance, along with the fact that O₃ creation requires UVC photons, leads to some unexpected UVC surface flux results. A striking consequence of this is that while the GOV host star provides the highest incident UVC flux of all our host stars, it maintains the lowest surface UVC flux for the 100% PAL O₂ model by several orders of magnitude, while the much cooler K2V stellar host model experiences the highest surface UVC flux. The much higher incident UVC flux of the GOV host causes much faster O₃ production than other host stars, allowing for UVC shielding strong enough to counteract the high incident UVC flux. Another interesting result for the 100% PAL O₂ case is that the M5V model has a slightly higher UVC surface flux than the K5V model, despite the fact that the M5V model has the lowest incident UVC flux. Again, this effect is due to the higher O₃ abundance of the K5V-hosted planet, created by the stronger incident UVC flux. For all host stars, the atmospheric models with 100% PAL O₂ allowed only extremely tiny fractions of incident UVC flux reach the surface (<10⁻¹⁷% in all cases).

UVC surface fluxes for models with 10% and 1% PAL O₂ have similar trends when comparing stellar hosts. Sun-hosted models had the largest surface UVC fluxes in both scenarios. Notice that although the model atmospheres hosted by the G0V star and the Sun have higher O₃ levels for the 10% PAL O₂ cases compared to their 100% PAL O₂ cases, overall UVC shielding is significantly less for the 10% PAL O₂ cases due to the lesser contribution of O₂ absorbing photons with wavelengths less than 240 nm. Even though the G0V host and the Sun produce much larger amounts of O₃ than cooler stars, for low O₂ levels the combined decrease in O₂ and O₃ UV shielding causes them to have higher surface UVC fluxes than cooler stars that produce significantly less O₃. For model atmospheres with O₂ levels of only 0.1% PAL, surface UVC levels begin to converge to the incident UVC flux as O₂ and O₃ levels have dropped enough that they shield UVC far less effectively. It has previously been suggested that the usefulness in the ability of O₃ to shield UV drops off drastically at these O₂ values (e.g., Segura et al. 2003). However, due to CO₂ shielding, all models in this study had virtually no photons with wavelengths less than 200 nm reach the planetary surface, even with the lowest O₂ abundance modeled (0.01% PAL).

Although the model atmospheres hosted by the hottest stars create the highest levels of O₃, they constantly experience the highest UVA and UVB surface fluxes due to the limited shielding abilities of O₃ in these wavelength ranges. However, for the far more damaging UVC wavelengths at 100% PAL O₂ it is the G0V host star that provides the lowest UVC surface flux by orders of magnitude, with the Sun-hosted models having comparable UVC surface flux to cooler host star models. Somewhat ironically, for lower O₂ levels of 1-10% PAL, it is the Sun that is the host star with the least “hospitable” conditions for surface life with the highest UVC surface fluxes. As O₂ drops to 0.1% PAL UVC surface flux will begin to converge to the incident UVC flux as O₂ and O₃ shielding drops dramatically. However, though life on modern Earth requires a substantial O₃ layer for UV protection, it is important to remember that evidence for life on Earth dates back to 3.7 Gyr ago (Rosing 1999), long before the O₂ levels rose during the Great Oxidation Event 2.5 Gyr ago. The lack of significant atmospheric UV shielding may prevent life as we know it, but it does not rule out its existence. Life could exist, for instance, underwater, at a depth in which significant damaging UV has been absorbed by water (e.g., Cockell & Raven 2007).

Fig. 6 Top-of-the atmosphere (TOA) and surface fluxes for UVA (top), UVB (middle), and UVC (bottom) wavelengths for 100%, 10%, 1%, and 0.1% PAL O2 model atmospheres for all stellar hosts. We note the differences in y-axis scale for different subplots. UVA flux is only slightly shielded by O3 so surface fluxes scale roughly with TOA fluxes. UVB flux is partially shielded by O3 and therefore allows the GOV-hosted models to receive less surface UVB than Sun-hosted models despite higher TOA UVB due to more efficient O3 production. UVC surface fluxes for high O2 levels are strongly influenced by O3 abundance due to strong UV shielding from O3 in this wavelength range. For models with only 0.1% PAL O2 levels all surface UV fluxes begin to converge to TOA values as the shielding of O3 is significantly decreased. See Sect. 4.4 for full details.

4.5 O₃ spectral features for different O₂ levels

Emission spectra from our model atmospheres are shown in Fig. 7, zoomed in on the primary MIR O₃ feature at 9.7 μm, along with the corresponding O₃ mixing ratio and temperature profiles, which are necessary for interpreting the features. The temperature difference between the absorbing and emitting layers of the planet’s atmosphere, rather than the overall abundance of that gaseous species, determines the depth of planetary emission spectrum features. Because O₃ is a main contributor of stratospheric heating, the strength of O₃ features has a highly nonlinear relationship to O₃ abundance. Once again, we see counterintuitive trends for hotter host stars (G0V, Sun, K2V), and different, more straightforward trends, for cooler host stars (K5V, M5V).

For all host stars, the 0.1% PAL O₂ case has the shallowest O₃ feature in emission spectra, but the O₂ level for the deepest feature depends on the host star. For the G0V-hosted models the O₃ feature for the 100% PAL O₂ case has a similar depth to the 0.1% PAL O₂ case, despite the fact that they have significantly different integrated O₃ column densities (7.06 × 10¹⁸ cm⁻² for 100% PAL O₂; 1.23 × 10¹⁸ cm⁻² for 0.1% PAL O₂). For the two hottest host stars (G0V, Sun), the 10% and 1% PAL O₂ cases are the deepest features. The strong features of the 10% PAL O₂ models are not surprising since both the G0V and Sun models have higher O₃ abundances at 10% PAL than at 100% PAL O₂, but the 1% PAL O₂ models have significantly less O₃ than both the 10% and 100% PAL O₂ cases (see Fig. 3 for reference). Conversely, O₃ features for the coolest host star models correspond more intuitively to O₂ and O₃ levels, with the highest O₂ and O₃ abundances having the deepest features, and the lowest O₂ and O₃ abundances having the shallowest features.

The relationship between the depth of O₃ spectral features and actual O₃ abundance is dictated by atmospheric temperature profiles. The temperature difference between the emitting and absorbing layers of a gaseous species determines feature depth, therefore O₃ feature depth is determined by the temperature difference between the altitude of peak O₃ concentration in the stratosphere and the planet’s surface temperature. Because O₃ NUV absorption is a dominant source of stratospheric heating, a higher O₃ concentration with significant incident NUV flux for O₃ to absorb results in higher stratospheric temperatures and thus a shallower spectral feature. This explains why an atmosphere with a large amount of O₃ and high incident NUV flux (and more stratospheric heating) has a weaker O₃ feature than an atmosphere with less O₃ and weaker incident NUV, but a larger temperature difference between the stratospheric and surface temperatures. Cooler host star models with less O₃ formation and lower incident NUV flux have significantly less stratospheric heating (Fig. 7), and therefore O₃ spectral feature depths which correspond more strongly with the actual abundance of O₃ in their atmospheres.

In summary, in order to interpret O₃ features in planetary emission spectra and retrieve the O₃ (and O₂) abundances it will require modeling of the atmospheric temperature profiles. Both photochemistry and climate modeling will be essential in this process.

5 Discussion

5.1 Comparison to other studies

Multiple studies have explored O₃ formation in Earth-like atmospheres using a variety of models, each providing valuable insight on the O₂–O₃ relationship. Here, we briefly describe relevant past studies on this topic. With 1D modeling of Earth’s atmosphere, early O₃ studies revealed the nonlinear link between O₃ and O₂. Both Ratner & Walker (1972) and Levine et al. (1979) discuss the phenomenon of the O₃ layer moving down in the atmosphere as O₂ levels decreased (see Sect. 4.1 for details on this process) and agreed on peak O₃ abundance occurring at ~10% PAL O₂. Total O₃ abundances calculated for these studies differed because they each included different chemical reactions. The model in Ratner & Walker (1972) contained only the Chapman mechanism, while Levine et al. (1979) additionally HO_x and NO_x catalytic cycle destruction of O₃ in their model. Later Kasting et al. (1985) replicated the O₃ peak in abundance at lower O₂ levels using a more sophisticated model including chemistry beyond the Chapman mechanism and catalytic cycles, incorporating 20 gaseous species overall. They predicted maximum O₃ production to occur at 50% PAL O₂, a higher O₂ estimate than previously. It is important to note that none of these studies included a climate model to calculate self-consistent atmospheric temperatures. Because the Chapman mechanism is temperature dependent, this helps account for discrepancies with later O₃ calculations.

Studies in later years began to model O₃ production in planetary atmospheres with different types of host stars. Segura et al. (2003) used what they described as a “loosely coupled” ID climate and photochemistry code (partially based off the Kasting et al. 1985 model) for different O₂ levels around F2V, G2V, and K2V type stars. We note that this model is a predecessor of the model used in this study: Atmos. No host star displayed a peak O₃ abundance at an O₂ level less than 100% PAL, but this is likely because the modeled O₂ levels were evenly spaced on a logarithmic scale from 0.001-100% PAL O₂, whereas more finely spaced O₂ levels are required to capture this effect. Atmospheric chemistry and temperature profiles computed in Segura et al. (2003) are similar to our Sun and K2V host star models. There are slight differences in total O₃ abundance in these models compared to those in this study (our models tend to have lower O₃), although this is likely due to differences in input UV spectra, boundary conditions, and model updates. Overall this is the most similar study to ours in terms of variety of O₂ levels and host stars.

Other studies have also modeled O₃ formation in Earth-like planetary atmospheres around different stellar hosts. The effect of varying orbital separations inside the habitable zone on O₃ formation was explored for F2V, G2V, and K2V hosts (same as Segura et al. 2003) in Grenfell et al. (2007), and for a variety of M dwarfs in Grenfell et al. (2014). Both these studies used the ID “loosely coupled” climate and photochemistry model developed in Segura et al. (2003). An increase in star-planet separation for FGK stars caused cooler atmospheric temperatures, which correlated to an increase in O₃. This is because the 3-body reaction that creates O₃ (Reaction (2)) is faster at cooler temperatures. However, this O₃ increase was not large because larger orbital distances also caused higher levels of HO_x and NO_x species which destroy O₃ (Grenfell et al. 2007). When repeating this study for M dwarfs they found what they described as a “Goldilocks” effect in which there was a range of UV that was best for creating the most detectable O₃. If incident UV flux is too low it will create small amounts of O₃ making it harder to detect, but if the UV flux is too high it will create enough O₃ to cause significant stratospheric heating, making it more difficult to detect in planetary emission spectra (see Sect. 4.5 details on this phenomenon). M7V spectral types were found to produce the amount of UV that was “just right” in creating detectable amounts of O₃ (Grenfell et al. 2014). Although these models were run only at 100% PAL O₂, their results are consistent with this study.

The impact of stellar host UV on O₃ formation has also been modeled using Exo-Prime, a 1D coupled climate and photochemistry originally based off the same codes as Atmos, for Earth-like planets orbiting FGKM stars (Rugheimer et al. 2013), M dwarfs (Rugheimer et al. 2015a), cool white dwarfs (Kozakis et al. 2018), and red giants (Kozakis & Kaltenegger 2019). However, all these studies were constrained to O₂ abundances of 100% PAL, although our corresponding models results are consistent. Another Exo-Prime study (Rugheimer et al. 2015b) modeled Earth at different points throughout geological history for FGKM stars, including four different O₂ abundances, although the large variations in abundances of many gaseous species (i.e., CH₄, CO₂) does not allow for a straightforward comparisons of results with our study.

Of the 1D models discussed in this study, only Atmos models photochemistry in the mesosphere and lower thermosphere (up to an altitude of 100 km), whereas other photochemistry models are limited to atmospheric heights below ~65 km (Kasting & Donahue 1980; Kasting et al. 1985; Segura et al. 2003; Grenfell et al. 2007, 2014; Rugheimer et al. 2013, 2015a,b; Kozakis et al. 2018; Kozakis & Kaltenegger 2019). This is relevant for O₃ formation because of the “secondary O₃ layer” on Earth above the stratosphere (see details in Sects. 2 and 4.1). High energy photons (λ < 175 nm) are normally absorbed above the stratosphere by O₂ photolysis, creating the O(¹D) radical in the process (Reaction (3)). This could yield different findings for a photochemistry model that does not include higher altitudes since the high-energy photons will then be absorbed at far lower altitudes than in reality. This would change both the O(¹ D) and O₃ atmospheric profiles, and account for the differences in O₃ production the we see from different models. However, overall results from the Segura et al. (2003) model, Exo-Prime, and Atmos remain fairly consistent.

Along with 1D models, O₃ formation has been modeled in 3D. In reality, O₃ formation and abundance is dependent on both the atmospheric latitude and time of day. On the night side of a planet, O₃ cannot be generated by the Chapman method nor destroyed by photolysis. During the day O₃ is created most efficiently at the equator where incident UV flux is highest, and then is transported toward the poles by Dobson-Brewer circulation, causing peak O₃ abundance to vary in altitude depending on the latitude. On modern Earth, there is only a ~2% difference in O₃ between the day and night sides, while planets with differing rotation periods may have more unevenly distributed O₃. Despite the fact that 1D models (like ours) can use a zenith angle to represent the “average” of incoming radiation, they cannot accurately predict O₃ formation and transport for slowly rotating planets, especially ones that are tidally-locked. Several studies have used 3D modeling to explore O₃ formation and distribution on tidally locked planets. Proedrou & Hocke (2016) used a 3D climate and photochemistry model to compare O₃ distribution on modern Earth and a tidally-locked version of Earth. They found that O₃ could be distributed to the night-side of the planet and accumulate there in the absence of photolysis. Hemispheric maps of O₃ distribution at different phases demonstrated that the amount of detectable O₃ will be phase-dependent during observations.

Tidally-locked Earth-like planets are most likely found around lower mass stars, where the tidal-locking radius is within the habitable zone, and rotation periods are substantially shorter than the “tidally-locked Earth around the Sun” scenario investigated in Proedrou & Hocke (2016). Carone et al. (2018) used a 3D GCM to model how the rapid rotation of a tidally-locked planet would affect O₃ transport on a planet with a 25-day period. This faster rotation created an “anti-Dobson-Brewer circulation” effect, with O₃ accumulating at the equator rather than being transported toward the poles as on modern Earth. However, this study did not employ a photochemistry model, only circulation effects.

Chen et al. (2018) and Yates et al. (2020) also performed 3D modeling of tidally-locked habitable zone planets orbiting M dwarfs, although they incorporated both climate and photochemistry models as well. Chen et al. (2018) used CAM-Chem, a 3D model including 97 species in chemistry computations, while Yates et al. (2020) used the Met Office Unified Model including only Chapman mechanism and HO_x catalytic cycle chemistry. Both studies found that O₃ would be transferred to the night-side after being created on the day-side, where it could accumulate to a higher quantity than on the day-side. HO_x species that were also transported to the night-side would be the primary sink of night-side O₃. However, Yates et al. (2020) computed a thinner O₃ layer than Chen et al. (2018), with the latter’s model also computing that O₃ would exist at higher altitudes. These differences are likely due to differing chemical networks, land mass fraction (only Chen et al. 2018 had continents), and input stellar spectra. Overall these results agreed well with O₃ abundances calculated by Rugheimer et al. (2015a) for a similar host star, although H₂O mixing ratios (important for creating HO_x species) were shown to vary significantly more, showing that 1D models do not include important feedback loops contained within 3D models.

The closest similar 3D modeling work to ours is Cooke et al. (2022), which uses a 3D climate-chemistry code to model the Earth-Sun system across geological history at various O₂ levels from 0.1% to 150% PAL. Comparing their results to our Sun-hosted models there is agreement between trends in the time-averaged mixing ratios for different gaseous species. However, a main finding of Cooke et al. (2022) is that their 3D model predicts lower O₃ abundances for O₂ levels 0.5% to 50% PAL when compared to 1D models, including those calculated here as well as in Segura et al. (2003) and Rugheimer et al. (2015b). The cause for these lower estimates from this 3D model is uncertain, although is possibly related to how 1D codes simulate diurnal averages, or different CO₂ abundances/boundary conditions. Further inter-model comparison will be needed in order to clarify these discrepancies (Cooke et al. 2022).

Overall our results for O₃ formation are consistent with previous 1D studies and roughly similar to time-averaged results from 3D models. Despite this, it is important to remember that the night-sides of slowly rotating and tidally locked planets may have significantly more O₃ than the day-side, introducing phase-angle dependency on the amount of detectable O₃ for observations.

Fig. 7 Emission spectra, O3 mixing ratio profiles, and temperature profiles for model atmospheres with 100%, 10%, 1%, and 0.1% PAL O2 for all host stars. The depth of spectral features in emission spectra is dependent on the temperature difference between the absorbing and emitting layers of the atmosphere, causing the O3 feature depth to strongly correlate with the temperature difference between the stratosphere and planetary surface. However, since O3 is responsible for the majority of stratospheric heating, this results in higher O3 abundances (with more stratospheric heating) having shallower spectral features than atmospheres with less O3 and cooler stratospheres. For full details see Sect. 4.5. We note that temperatures for parts of the atmosphere above 1 mbar are held constant as that is the maximum height computed by the climate code (see Sect. 3.1 for more details).

5.2 Factors that impact the O₂–O₃ relationship

The O₂–O₃ relationship is strongly dependent on the host star as well as the planetary atmospheric composition. Here we will briefly describe several ways the O₂–O₃ relationship can diverge from the results in this study.

We have shown that the O₂–O₃ relationship is highly influenced by the UV spectrum of the host star, both in terms of the total amount of UV flux and the FUV/NUV flux ratio, with FUV primarily responsible for creating O₃, and NUV destroying it. In this study we selected stellar hosts from a range of spectral types, but have not yet explored the variation of UV activity and fUv/NUV ratios within specific spectral types. This is of particular importance for K and M dwarfs, as they are subject to larger amounts of UV variability, and thus greater variations in the O₂–O₃ relationship for the planets such stars host (e.g., France et al. 2013, 2016; Youngblood et al. 2016; Loyd et al. 2018). For instance, the UV spectrum for our M5V host star comes from GJ 876 which displays low amounts of chromospheric activity (France et al. 2016). If the stellar host in question was a more active star of a similar type, such as Proxima Centauri (classified as an M5.5V star; Boyajian et al. 2012; Anglada-Escudé et al. 2016), an orbiting Earth-like planet would be subject to a different O₂–O₃ relationship due to the significant change UV spectral slope of the star. A more in-depth study of the impact of varying UV activity levels for K and M dwarf planetary hosts will be necessary to fully understand how O₃ production would vary for different O₂ atmospheric abundances.

Another important aspect of this study to note is that the initial conditions of atmospheric species are kept constant across all models to better understand how the O₂–O₃ relationship differs for different host star spectra. However, the O₂–O₃ relationship could be altered by a variety of scenarios due to the potentially huge diversity of terrestrial planet atmospheric compositions.

The HO_x and NO_x catalytic cycles are the most prominent sinks for O₃ on modern Earth, and could significantly impact O₃ formation if there was an increase or decrease of the species powering these cycles. Therefore, changes in the amount of stratospheric H₂O or N₂O would alter the efficiency of O₃ destruction, as they are the primary sources of stratospheric HO_x and NO_x. On modern Earth H₂O is generally prevented from traveling into the stratosphere by the cold trap, although it can be created in the stratosphere via CH₄ reactions with OH (Reaction (23)), implying a change in CH₄ will additionally impact O₃ destruction. The impacts on the O₂–O₃ relationship as these abundances change will be explored at length in the next paper of this series. Reducing gases in general (e.g., CH₄, H₂) can impact O₂ and O₃ levels, whether produced biologically or through volcanic outgassing (e.g., Hu et al. 2012; Black et al. 2014; Gregory et al. 2021; Cooke et al. 2022). O₃ can also be depleted by cometary impacts (e.g., Marchi et al. 2021) and through solar flares (e.g., Pettit et al. 2018). In addition, O₃ can vary throughout different seasons on modern Earth (Olson et al. 2018).

Oxygen-bearing species in general can also influence the O₂–O₃ relationship, especially in situations where O₂ is produced abiotically via photolysis-driven production (see Meadows 2017 for full review). In particular, CO₂-rich atmospheres may create significant amounts of O₃ through CO₂ photolysis (Hu et al. 2012; Domagal-Goldman et al. 2014; Tian et al. 2014; Harman et al. 2015; Gao et al. 2015) around host stars with high FUV/NUV flux ratios. FUV photons (λ < 200 nm) photolyze $${\text{CO}}_2+\text{h}v\to \text{CO}+\text{O},$$(31)

to produce an O atom (or the O(¹D) radical if λ < 167 nm; Reaction (21)). Oxygen atoms can combine to create O₂, $$\text{O}+\text{O}+M\to {\text{O}}_2+M,$$(32)

which can then combine with O atoms to create O₃ (Reaction (2)). Because O₂ is photolyzed at shorter wavelengths than O₃ (λ < 240 nm, see Fig. 1), stellar hosts with high incident FUV/NUV flux ratios can allow abiotic O₃ accumulation without significant corresponding O₂ buildup (Hu et al. 2012; Domagal-Goldman et al. 2014; Tian et al. 2014; Harman et al. 2015). In such scenarios the O₃/O₂ ratio would be higher than what would be predicted if O₃ were formed directly from O₂, implying that a high O₃/O₂ ratio could indicate non-biological O₃ (and O₂) creation (Domagal-Goldman et al. 2014). However, it remains uncertain which types of stellar hosts would be favorable for this scenario. Some studies find Sun-like stars can accumulate significant O₃ through CO₂ photolysis if outgassing rates of reduced species are low (Hu et al. 2012), while others restrict this scenario to K and M dwarfs with high FUV/NUV flux ratios (Tian et al. 2014; Harman et al. 2015). This scenario might likewise be produced by F star hosts with their strong FUV fluxes, although with enough NUV flux, O₃ destruction rates could prevent O₃ buildup (Domagal-Goldman et al. 2014). Differences in model lower boundary conditions, which control the impact of different O₂ ground sinks, are likely to blame for the disparity in the capacity of O₃ to accumulate between different studies (Domagal-Goldman et al. 2014; Tian et al. 2014; Harman et al. 2015; Meadows 2017). Despite uncertainties in O₂ surface sinks, it is clear K/M dwarfs with high FUV/NUV ratios are susceptible, and potentially hotter stars with low abundances of reduced gaseous species. The effect of a CO₂-rich atmosphere on the O₂–O₃ relationship will be highly influenced by the host star and atmospheric abundances of reduced gaseous species.

Another method of creating O₃ without using the Chapman mechanism is via the “smog mechanism”, which can produce O₃ photochemically using a volatile organic compound (i.e., CH₄) and NO_x. This process is responsible for smog pollution often occurring in large cities on modern Earth, but could also have occurred during the Proterozoic (2.5 Ga – 541 Ma) with high levels of CH₄ and NO_x (Grenfell et al. 2006). Under some circumstances Grenfell et al. (2006) computed that nearly double the amount of O₃ on modern Earth could have been produced with just 1% PAL O₂ via the smog mechanism. Additionally, Grenfell et al. (2013) found that the O₃ smog mechanism may become more efficient than the Chapman mechanism for habitable zone planets around late M dwarf with low UV that is less efficient at O₂ photolysis. Not only would O₃ created primarily by the smog mechanism rather than the Chapman mechanism change the O₂–O₃ relationship, but “smog” O₃ can be harmful for life. Smog mechanism O₃ is created in the troposphere rather than the stratosphere, and could result in significant ground-level O₃. Although on Earth our stratospheric O₃ protects life by shielding harmful UV, ground level O₃ on a smog-dominated planet can become fatal to Earth organisms at ~1 ppm.

Overall the O₂–O₃ relationship could be subject to large variations based both on the UV spectral slope of the host star, as well as atmospheric composition. Ozone formation via either CO₂ photolysis or hydrocarbon reactions would not be expected to resemble the O₂–O₃ relationship that “Earth-like” atmospheres would demonstrate. However, the FUV/NUV flux ratio of the host star may allow us to rule out certain certain scenarios without observations of the planetary atmosphere.

5.3 Can we infer O₂ abundance from an O₃ measurement?

Returning to the question that prompted this study: is O₃ a reliable proxy for O₂? Variations in the O₂–O₃ relationship (Sect. 5.2) would increase the difficulty in using O₃ to infer O₂ abundance, and would require additional atmospheric information to provide the proper context. For the sake of simplicity, we will discuss the possibility of inferring O₂ from an O₃ measurement from our “Earth-like” models in this paper. But even in this simplified case where we keep initial conditions of all atmospheric species constant (apart from O₂ and O₃ and let them adapt to different stellar hosts) precisely determining O₂ from O₃ is not straightforward due to the nonlinear O₂–O₃ relationship.

Figure 3 clearly demonstrates that not only does the amount of O₃ created for different O₂ levels change significantly for different spectral types, but also the trend that the O₂–O₃ relationship will follow as O₂ is changed will depend on the stellar host. Section 4.1 details how planets around hotter stars with higher UV flux (G0V, Sun, K2V) all experience their maximum O₃ formation efficiency at O₂ levels lower that 100% PAL, while there is a continuous (albeit nonlinear) decrease of O₃ production for cooler hosts with lower UV flux (K5V, M5V). Whether a model atmosphere experiences an increase in O₃ production as O₂ decreases (as seen for hotter stars) is dependent primarily on whether O₂ photolysis (λ < 240 nm) can reach deep into the atmosphere. The total amount of O₃ depends on the FUV/NUV flux ratio of the host star as well, with FUV flux creating O₃ while NUV wavelengths will cause its destruction (see Sects. 3.2 and 4.1). Although the K2V-hosted models demonstrate this effect with the maximum amount of O₃ production occurring at 55% PAL O₂, for models at O₂ levels near 100% PAL O₂ the K5V and M5V hosts have higher O₃ abundances due to their larger FUV/NUV ratios. Therefore, to predict the O₂–O₃ relationship for a given star even with knowledge of “Earth-like” conditions knowing both the total UV emitted and UV spectral slope of the host star will be essential.

Idealized planetary emission spectra of the 9.7 μm O₃ features in Fig. 7 show a non-trivial relationship between both O₂ and O₃ abundance and spectral feature depth for hotter stellar hosts, with more “straightforward” correlation of O₂ and O₃ abundances and feature depth for cooler hosts (K5V, M5V). This is due to the dependence of feature strength in emission spectra on the atmospheric temperature profile, with O₃ measurements being particularly complicated by the fact that O₃ highly influences stratospheric heating. Measuring O₃ abundance from an emission spectra will require modeling of atmospheric temperature and pressure profiles for an accurate estimate, especially for stars emitting enough UV capable of creating and absorbing O₃ for significant stratospheric heating. Smaller amounts of O₃ as created by cooler stars have less of an impact on stratospheric heating, and therefore will maintain a more consistent temperature profile even for large variation in O₂ abundance.

Even operating under the unlikely assumption that an accurate measurement of atmospheric O₃ could be done, inferring O₂ abundance will still not be straightforward, especially for hotter host stars (G0V, Sun, K2V) where O₃ does not always decrease as O₂ levels decrease. For example, in our Sun-hosted models the total integrated O₃ column density at 150% PAL O₂ is roughly the same as the amount at 5% PAL O₂ (4.92 × 10¹⁸ cm⁻² and 4.80 × 10¹⁸ cm^-2, respectively). This implies that for hotter stellar hosts, it is unlikely O₂ could be well constrained from an O₃ measurement for relatively high levels of O₂. It could, however, be possible to use an O₃ measurement to differentiate between pre- and post-GOE O₂ levels, as well as infer the existence of a substantial O₃ layer providing surface UV shielding. Due to the consistent decrease in O₃ abundance with decreasing O₂ for cooler hosts, it appears that inferring O₂ from O₃ may be much simpler for planets orbiting cooler stars that those around hotter stars. It is important to note that specific knowledge of the UV spectral slope for cool K and M dwarfs will be extremely important to model O₃ levels, especially due to the increased likelihood of O₃ buildup via abiotic means and the diversity of activity levels (hence FUV/NUV flux ratios) around such stars.

5.4 is it necessary to constrain O₂ abundance for O₃ to be a useful biosignature?

Although inferring O₂ levels precisely from O₃ measurements will not be possible for hot stellar hosts and will still require additional atmospheric context and knowledge of the UV spectral slope for cooler hosts, what does this mean for O₃ as a biosignature? Would it be necessary to infer O₂ for O₃ to be a useful indicator of life, or could it serve as a promising biosignature without precise O₂ information? Two of the strongest arguments against O₂ as a biosignature are 1) it can be produced abiotically, and 2) it has been at relatively high abundances for only a small fraction of Earth’s geological history (see review in Meadows 2017; Meadows et al. 2018b). We examine these arguments as they pertain to O₃ as a biosignature.

The multiple proposed pathways for abiotic O₂ production will prevent O₃ from being a “standalone” biosignature as well. These mechanisms include production via CO₂ photolysis as discussed in Sect. 5.3, as well as via H₂O photolysis either from an extremely active pre-main sequence star (Luger & Barnes 2015; Tian 2015) or an atmosphere that has allowed H₂O to enter the stratosphere due to a lack of cold trap from low abundances of non-condensable gases (Wordsworth & Pierrehumbert 2014). Ruling out these scenarios could be possible by detections or non-detections of gaseous species that would be produced or destroyed during these processes. For example, O₂ and O₃ abiotic buildup from CO₂ photolysis could be revealed via a detection of CO, sometimes called an “antibiosignature” (for detailed descriptions of these mechanisms and their spectral discriminants see Meadows 2017; Meadows et al. 2018b).

Potential abiotic production will require contextual knowledge of an atmosphere to use either O₂ or O₃ as a biosignature. Abiotic buildup from CO₂ photolysis with high FUV/NUV flux ratio stellar hosts could potentially impact O₃ more than O₂, as it is possible to accumulate O₃ more easily than O₂ in this scenario, and could potentially allow simultaneous detection of abiotic O₃ and CH₄ under certain conditions (Domagal-Goldman et al. 2014). However, predictions of abiotic O₂ and O₃ buildup are dependent on the lower boundary conditions of the model in question, so these estimates vary (Hu et al. 2012; Domagal-Goldman et al. 2014; Tian et al. 2014; Harman et al. 2015; Gao et al. 2015). Detections or non-detections of CO and CO₂ will be important especially in assessing the origin of an O₃ detection.

The second main argument against O₂ as a reliable biosignature (even when accounting for abiotic sources) is that O₂ levels have only been relatively high for a short period of Earth’s geological history. Oxygenic photosynthesis is thought to have been first used by cyanobacteria -2.7 Ga, although O₂ buildup during the GOE was not thought to have occurred until ~2.5 Ga (e.g., Poulton et al. 2020). O₂ levels comparable to modern Earth were not reached until the Phanerozoic (541 Ma – present day) sparked by the Cambrian explosion when land began to be colonized by plants (Lenton & Daines 2017; Dahl & Arens 2020). Before the GOE O₂ levels were expected to be well below 10^-3% PAL, and potentially remained relatively low during the majority of the Proterozoic (2.5 Ga–541 Ma) with estimates ranging from ~0.3–10% PAL O₂ (e.g., Catling et al. 2018). Even if the lowest O₂ estimates for the Proterozoic were reality (~0.01% PAL O₂), there is evidence of an O₃ layer after 2.4 Ga (Crockford et al. 2018). Although an O₂ detection would be extremely difficult at this abundance, it has been suggested that O₃ could reveal this undetectable O₂ (e.g., Leger et al. 1993; Des Marais et al. 2002; Segura et al. 2003; Léger et al. 2011; Harman et al. 2015). Results of this paper only further prove this point, especially around hotter stars (see Fig. 3). For the G0V and Sun-hosted planets even at a level of 0.01% PAL O₂, they still produce -15% the amount of O₃ they do at 100% PAL O₂. This number falls to -2% for the M5V-hosted planet, although it still demonstrates a less drastic decrease in O₃ as O₂ decreases. This implies that especially for planets orbiting hotter stars that O₃ is a much longer lived detectable biosignature than O₂ for an Earth-like planet, as detections may be sensitive to Proterozoic O₃ levels.

Although gaining precise information about O₂ abundance from an O₃ measurement will be extremely difficult or not possible (see discussion in Sect. 5.3), knowing O₃ abundance alone would still provide valuable information about the atmosphere. There appears to be a “bistability limit” for atmospheric O₂, implying that certain O₂ levels would not be stable in the atmosphere due to O₂ sinks and geochemical cycles, as atmosphere switches from reduced to oxidizing (e.g., Segura et al. 2003; Goldblatt et al. 2006). Gregory et al. (2021) calculated that there are only a few stable solutions with O₂ abundances between 3×10^-6 and 1% PAL for an Earth-like planet orbiting the Sun. The existence of this “bistability limit” could explain the -300 Myr delay between the advent of oxygenic photosynthesis and appreciable O₂ accumulation in the atmosphere (Goldblatt et al. 2006). O₃ abundance drastically falls off for all our host stars under 0.01% PAL O₂, implying that an O₃ detection would allow us to distinguish between pre- and post-GOE O₂ levels with relative ease. In the search for Earth-like planets, O₃ appears to be a viable biosignature for a much longer portion of Earth’s history, potentially allowing us to infer the existence of oxygenic photosynthesis for much longer than an O₂ detection.

Although O₃ is not created by life, its UV shielding capabilities could allow estimates of whether the surface environment is safe for life. As seen in Fig. 6 and Table 4, the amount of UV flux reaching the planetary surface begins to converge quickly to the UV incident upon the planet when O₂ abundance drops below 1% PAL, and it has been predicted that O₂ levels less than this will not be efficient at preventing DNA damage (e.g., Segura et al. 2003). If an upper O₂ “bistability limit” indeed exists at 1% PAL (Gregory et al. 2021), a detection of O₃ in a planetary atmosphere could imply a certain amount of UV shielding, and potential surface life.

However, it is important to remember that the first evidence of life dates back 3.7 Ga, long before the GOE, or even oxygenic photosynthesis (Rosing 1999). Although O₃ may be a longer lived biosignature than O₂ and can indicate substantial UV surface shielding, a non-detection of O₃ (or O₂) could not rule out the existence of life. Although the surface UV environment would have been harsh before the GOE, it is possible that without a UV screen that life could thrive in the photic zone of the ocean, and perhaps colonize land (Cockell & Raven 2007). It has even been suggested that a significant amount of UV may have been necessary to synthesize prebiotic molecules (e.g., Patel et al. 2015; Ranjan & Sasselov 2016; Rimmer et al. 2018). Even substituting O₃ for O₂ in biosignature searches, life on pre-GOE Earth would be undetectable.

6 Conclusions

In this first part of our paper series we show that the nonlinear O₂–O₃ relationship varies significantly for model atmospheres of planets orbiting different types of host stars, with different trends for planets with hotter host stars versus those with cooler host stars. As seen in Fig. 3, planets orbiting hotter host stars display peak O₃ abundance at lower O₂ levels than modern Earth, while planets with cooler hosts have O₃ decrease along with O₂. The increase in O₃ at lower O₂ levels for hotter host stars is due to the O₃ layer shifting downward in the atmosphere as O₂ levels (and its ability to absorb UV) decrease. At these deeper and denser levels of the atmosphere the 3-body reaction that creates O₃ (Reaction (2)) allows more efficient O₃ production than at high O₂ abundances. Cooler stars do not experience this effect since it requires a stronger incident FUV flux to push O₃ formation deep enough in the atmosphere to allow for much faster production.

As O₂ decreases in the atmosphere, photolysis of many gaseous species as well as O(¹D) production will occur at lower atmospheric levels. The biologically relevant molecules H₂O, CH₄, and N₂O all experience upper atmospheric depletion to different degrees, with these effects significantly more prominent around host stars with higher UV fluxes (Fig. 4). As O₂ decreases and photolysis rates increase, HO_x species are primarily pushed to lower altitudes rather than destroyed, while NO_x species are destroyed by photolysis as well as produced at lower atmospheric levels (Fig. 5).

UVA and UVB wavelengths are only partially shielded by O₃, so the amount of photons in this wavelength range that reach the planetary surface scales with the amount of incident UVA and UVB flux. However, for biologically damaging UVC photons, there is a much stronger dependence on both O₂ and O₃ abundance. For high O₂ levels, our hottest host star (G0V) had the lowest surface UVC flux, despite also having the highest incident UVC flux (Fig. 6). As O₂ and O₃ abundances decreases these UVC surface levels begin to converge to incident UVC flux as UV shielding becomes inefficient.

Ozone features in planetary emission spectra were found to require knowledge of the atmospheric temperature profiles, as the depth of features is dictated by the temperature difference between the emitting and absorbing layers of the gaseous species. Since O₃ NUV absorption is a significant source of stratospheric heating, a large amount of O₃ along with significant incident NUV flux will cause a smaller temperature difference between the stratosphere and planetary surface, resulting in a shallower spectral feature (Fig. 7). For cooler stars with slower O₃ production, and therefore less stratospheric temperature inversion, O₂ spectral features are more intuitive to interpret. Overall it is clear that interpreting any observation of O₃ will require the UV spectrum of the host star as well as photochemical and climate modeling of the planetary atmosphere.

Now that we have explored the O₂–O₃ relationship and its impact on planetary emission spectra, let us now return again to our original question: is O₃ a reliable proxy for O₂? In short, the complicated nature of the O₂–O₃ relationship tells us that O₃ is not a reliable tracer of O₂. Our results show us that for hotter stars, using O₃ as a precise tracer for O₂ will not be possible due to the degeneracies in the O₂–O₃ relationship, and for cooler stars it will be very difficult without knowledge of the UV spectrum of the host star as well as planetary atmospheric composition. However, an O₃ measurement on its own is still an insightful measurement, even if it does not provide precise information on O₂ abundance. Not only is O₃ detectable in trace amounts (unlike O₂), it additionally allows for an assessment of the UV surface environment of the planet.

There is likely no “standalone” atmospheric biosignature, but either O₂ or O₃ along with atmospheric context could provide evidence of oxygenic photosynthesis. Both will require detections of other gaseous species to rule out various mechanisms for abiotic O₂ or O₃ production. Although it is important to note that a CO₂ rich planet may be more likely to have an abiotic buildup of O₃ without O₂ - a strike against O₃ as a biosignature gas (see Sect. 5.2 for detailed discussion). However, there is a strike against O₂ in comparison to O₃:O₂ has only existed on Earth in relatively high amounts for a short fraction of Earth’s geological history. Ozone, on the other hand, is detectable in trace amounts, potentially making it a longer lived detectable biosignature for Earth-like planets. It seems that neither O₂ or O₃ is inherently a “better” biosignature than the other; simply that they give different information and can be more or less useful depending on the scenario. With knowledge of the UV spectrum of the host star along with careful climate and photochemistry modeling we can begin to understand the O₂–O₃ relationship and use O₃ as a reliable indicator for oxygenic photosynthesis.

Acknowledgements

We thank both the anonymous referee and journal editor for their comments which helped improve the clarity of this manuscript. All computing was performed on the HPC cluster at the Technical University of Denmark (DTU Computing Center 2021). This project is funded by VILLUM FONDEN.

References

All Tables

All Figures

Fig. 1 Absorption cross sections of O2 (left) and O3 (right), both plotted on the same y-axis scale to enable easier comparison. The y-axis is the same for both to enable easier comparison. Relevant O2 bands are the Schumann-Runge continuum (137–175 nm), the Schuman-Runge bands (175–200nm), and the Herzberg continuum (195–242nm). For less than 175nm an excited O atom, the O(1D) radical, is formed along with a ground state O atom during photolysis. O3 bands are the Hartley bands (200–300 nm), the Huggins bands (310–350 nm), and the Chappuis bands (410–750 nm). Photolysis within the Hartley bands will produce the O(1D) radical while other O3 bands create a ground state O atom. Absorption cross section data is from Brasseur & Solomon (2005).

In the text

Fig. 2 Stellar spectra of the planet host stars. G0V-K5V hosts are comprised of IUE UV data from Rugheimer et al. (2013), and the M5V host comes from UV observations of GJ 876 from the MUSCLES survey (France et al. 2016). Visible and IR wavelengths use ATLAS models of the same stellar temperature (Kurucz 1979). The right-hand figure zooms in on the UV region relevant for photolysis with important biological UV regimes (see Sect. 4.4).

In the text

Fig. 3 O2–O3 relationship for Earth-like planets orbiting different host stars (indicated in legend) with varying amounts of O2 mixing ratios. Molecular oxygen levels compared to Earth’s present atmospheric level (PAL) are shown as dashed vertical lines for reference. The left-hand figure shows the relationship in terms of total integrated O3 column density, and the right-hand figure in terms of total O3 normalized at the amount produced in the 100% PAL O2 case for each stellar host. The nonlinearity in these relationships is primarily due to the pressure dependence of Reaction (2) which forms O3. The main takeaway is that the O2–O3 relationship is significantly different for hotter host stars (GOV, Sun, K2V) versus cooler host stars (K5V, M5V), with hotter hosts experiencing peak O3 formation occurring at O2 levels under 100% PAL. See Sect. 4.1 for a detailed explanation.

In the text

Fig. 4 Mixing ratio profiles of O3, H2O, CH4, and N2O; all potential biosignature species. Each row represents results for model atmospheres orbiting different stellar hosts as indicated on the right-hand vertical axis. Each plot shows the mixing ratio profiles for O2 abundances of 100%, 10%, 1% and 0.1% PAL. O2 on modern Earth is a significant UV shield, allowing model atmospheres with decreasing O2 values to have photolysis occur at consistently lower altitudes. This is demonstrated well with the bulk of O3 forming at lower altitudes with less O2, as well as increased upper atmospheric depletion for H2O, CH4, and N2O via photolysis. The downward shift of O3 and upper atmospheric depletion of other species is shown to decrease for model atmospheres around cooler stars with lower incident UV flux, and hence lower photolysis rates. Full details of this atmospheric chemistry is shown in Sects. 4.1 and 4.3.

In the text

Fig. 5 Mixing ratio profiles of HOx (OH + HO2) and NOx (NO + NO2) species that power the catalytic cycles which destroy O3 for models with 100%, 10%, 1%, and 0.1% PAL O2. Here, we show models for the hottest (GOV) and coolest (M5V) stellar hosts. For decreasing O2 levels photolysis reaches lower levels of the atmosphere, causing OH and HO2 formation to occur at lower levels. The HOx is not significantly impacted by these changes since O3 formation is pushed deeper into the atmosphere as well. NOx species experience depletion via N2O and NO photolysis, although are less affected for models around cooler stars with lower photolysis rates. The efficiency of the NOx catalytic cycle decreases consistently for all host stars with decreasing O2 levels. See Sect. 4.3 for full details.

In the text

Fig. 6 Top-of-the atmosphere (TOA) and surface fluxes for UVA (top), UVB (middle), and UVC (bottom) wavelengths for 100%, 10%, 1%, and 0.1% PAL O2 model atmospheres for all stellar hosts. We note the differences in y-axis scale for different subplots. UVA flux is only slightly shielded by O3 so surface fluxes scale roughly with TOA fluxes. UVB flux is partially shielded by O3 and therefore allows the GOV-hosted models to receive less surface UVB than Sun-hosted models despite higher TOA UVB due to more efficient O3 production. UVC surface fluxes for high O2 levels are strongly influenced by O3 abundance due to strong UV shielding from O3 in this wavelength range. For models with only 0.1% PAL O2 levels all surface UV fluxes begin to converge to TOA values as the shielding of O3 is significantly decreased. See Sect. 4.4 for full details.

In the text

Fig. 7 Emission spectra, O3 mixing ratio profiles, and temperature profiles for model atmospheres with 100%, 10%, 1%, and 0.1% PAL O2 for all host stars. The depth of spectral features in emission spectra is dependent on the temperature difference between the absorbing and emitting layers of the atmosphere, causing the O3 feature depth to strongly correlate with the temperature difference between the stratosphere and planetary surface. However, since O3 is responsible for the majority of stratospheric heating, this results in higher O3 abundances (with more stratospheric heating) having shallower spectral features than atmospheres with less O3 and cooler stratospheres. For full details see Sect. 4.5. We note that temperatures for parts of the atmosphere above 1 mbar are held constant as that is the maximum height computed by the climate code (see Sect. 3.1 for more details).

In the text