Photochemical Runaway in Exoplanet Atmospheres: Implications for Biosignatures

The detection of biologically produced gases indicative of life ("biosignature gases") in rocky exoplanet atmospheres is a key goal of exoplanet science. Yet simulations predict that observations of even the main atmospheric gases will be challenging, mainly due to the small sizes of rocky planets and their atmospheres. Observations of trace biosignature gases will be even more challenging (Morley et al. 2017; Batalha et al. 2018; Lustig-Yaeger et al. 2019). On modern Earth, most products of biology do not accumulate to atmospheric concentrations that can be remotely detected over interstellar distances, because either their production rates are low, or they are too photochemically reactive, or both (Kasting et al. 2014; Rugheimer & Kaltenegger 2018; Kaltenegger 2017). Photochemical reactivity is also predicted to restrict diverse biosignature gases to undetectably low concentrations for exoplanets dissimilar to modern Earth as well, including gases for which efficient abiotic "false positive" production mechanisms have not yet been identified (e.g., Domagal-Goldman et al. 2011; Sousa-Silva et al. 2020; Zhan et al. 2021).

A notable exception to the pessimism regarding biosignature gases is oxygen (O₂). On modern Earth, O₂ constitutes 21% of modern Earth's atmosphere by volume. Thanks to its high abundance, O₂ and its photochemical by-product O₃ are accessible to detection by next-generation telescopes for Earth-twin exoplanets orbiting small, nearby stars, though even these observations will be challenging (Rodler & López-Morales 2014; Reinhard et al. 2017; Kawashima & Rugheimer 2019; Fauchez et al. 2020). While not unambiguous as a biosignature, the detectability of O₂ and its by-product O₃ make oxygen a prime target for biosignature searches (Meadows et al. 2018). However, the oxygenation of Earth's atmosphere was not straightforward. Earth's atmosphere was anoxic for approximately the first half of its history, and up to hundreds of millions of years may have elapsed between the emergence of biological O₂ production and its accumulation in the atmosphere to >1 ppmv levels. O₂'s accumulation to a dominant atmospheric gas (>10% by volume) is even more recent, within the last billion years (Lyons et al. 2014). This is because O₂ is very reactive, and readily reacted with reductants in the atmosphere of early Earth. At low surface production fluxes, such reactions photochemically confine the atmospheric concentration of O₂ to undetectably low levels. However, when the net production flux of O₂ exceeded the supply of reductants to the atmosphere on a sustained basis, O₂ atmospheric concentrations rose dramatically, until they were ultimately limited by surface processes (Goldblatt et al. 2006; Zahnle et al. 2006; Daines et al. 2017).

O₂ may not be unique. At high enough production rates, diverse gases may come to saturate their photochemical sinks and increase rapidly in concentration as a function of surface flux. We term this general process "photochemical runaway," after the prototypical "CO runaway" (Zahnle 1986; Kasting 2014). The term "runaway" is often used to describe a time-dependent phenomenon, but despite its etymology, photochemical runaway refers to an essentially stationary effect. ⁹ The photochemical runaway of CO has been the most studied in the literature, but photochemical runaways of other gases (e.g., CH₄, PH₃, and isoprene) have also been briefly reported (Kasting 1990; Pavlov et al. 2003; Kharecha et al. 2005; Segura et al. 2005; Schwieterman et al. 2019; Sousa-Silva et al. 2020; Zhan et al. 2021).

The physical mechanism underlying photochemical runaway is that the photochemical sinks limiting trace gas accumulation in the atmosphere are finite, and can be overwhelmed with high gas production. More fully, photochemistry generally controls the removal of biogenic gases from habitable planet atmospheres, because thermochemistry is generally slow at habitable temperatures. Photochemical removal of atmospheric gases is mediated by UV photons, either directly, via photolysis, or indirectly, via reactions with radicals produced by photolysis (Catling & Kasting 2017; Grenfell et al. 2018). As the supply of UV photons and the supply of photolyzable substrates are both finite, the ability of the atmosphere to photochemically cleanse itself is also finite. If emitted at fluxes exceeding this finite threshold, gases can overwhelm the photochemical controls on their accumulation and rapidly increase in concentration, until they are ultimately limited by other processes, e.g., surface uptake by biogeochemical sinks.

Photochemical runaway is important because it suggests that even reactive biosignature gases can accumulate to high, detectable concentrations at biochemically plausible fluxes, particularly for planets orbiting smaller, cooler stars with lower UV emission compared to higher-mass stars. Photochemical runaways are nonlinear: past the runaway threshold, a small increase in surface emission flux may result in dramatic increases in atmospheric concentration and hence detectability. The precise threshold for runaway varies by gas and planet scenario, but is often, though not always, set by the UV output of the host star. This is because it is UV photons that ultimately mediate the photochemical removal of atmospheric gases (Segura et al. 2005; Zahnle et al. 2006). Fortuitously for observations, this suggests that planets orbiting M-dwarf stars are more prone to runaways compared to planets orbiting Sun-like stars, because of their lower emission of photolytic near-UV (NUV) radiation (Segura et al. 2005; Rugheimer et al. 2015). Older, cooler white dwarf stars should be similarly favorable for runaway due to their lower UV output (Kozakis et al. 2020; Lin et al. 2022). Due to the observational advantages derived from their small host stars, planets orbiting cool stars like M dwarfs and white dwarfs are the only plausible rocky planet targets for near-term atmospheric characterization via transmission spectroscopy. Thus, the planets most amenable to atmospheric characterization are also the most generally prone to runaways.

Photochemical runaway has been studied for individual gases as a photochemical phenomenon, but its observational implications, particularly for reactive biosignature gases, have not been made clear. Here, we study photochemical runaway as a general phenomenon, with emphasis on its observational implications. We illustrate the effect of photochemical runaway and its implications for trace gas detectability in exoplanet atmospheres by exploring the case study of NH₃ runaway in an H₂–N₂ exoplanet atmosphere. We discuss the generality of photochemical runaway, showing that with the same photochemical model and reaction network, a broad range of gases in diverse planet scenarios, including non-H₂-dominated atmospheres, can undergo runaway. We address literature concerns regarding the physicality of runaway, demonstrating that the previous blanket dismissal of runaway on thermodynamic grounds is not justified, and interpreting the rise of O₂ on Earth as an actualized example of photochemical runaway, giving empirical grounding to the theory. We close with a discussion of the observational implications and uncertainties of runaway.

We studied NH₃ as a case study for photochemical runaway and its implications for the detectability of trace biosignature gases. To simulate NH₃ runaway, we choose an H₂–N₂-dominated atmospheric scenario, corresponding to the Cold Haber World scenario (Seager et al. 2013a, 2013b; Phillips et al. 2021), in which life would have a metabolic incentive for the high production of NH₃. We model the photochemical runaway of NH₃ in this planetary scenario (Section 2.1), the implications of runaway for the detectability of NH₃ (Section 2.2), and its climate feedback (Section 2.3).

2.1. Photochemical Modeling

2.2. Simulated Transmission Spectra and Observations

2.3. Climate Calculation

We hypothesize that photochemical runaway is a general phenomenon controlling the atmospheric abundance of gases in a planetary atmosphere. As a case study, we illustrate this phenomenon and its observational implications for exoplanets with an analysis of the runaway of NH₃ (ammonia) on a Cold Haber World with an H₂–N₂ atmosphere orbiting a small, cool M-dwarf star (Figure 1). Cold Haber Worlds are hypothetical planets where biological NH₃ production is intense enough to saturate the surface with NH₃ and suppress uptake by surface deposition, which would otherwise regulate it to undetectably low concentrations (Seager et al. 2013a, 2013b; Huang et al. 2022). We choose to model the runaway of NH₃ because NH₃ is photochemically reactive (main photochemical loss mechanism: direct photolysis), and we wish to demonstrate that runaway can occur for even reactive gases, whose concentrations are otherwise undetectably low. We further choose NH₃ because NH₃ is a relatively well-studied gas whose photochemistry is comparatively well understood (Kasting 1982; Hu et al. 2012; Seager et al. 2013b; Catling & Kasting 2017). We choose an H₂–N₂ atmosphere because life in such an atmosphere would have a metabolic incentive to produce excess NH₃, following the original scenario for the Cold Haber World. We choose an M-dwarf host star because these small stars are the only class of stellar host around which near-term facilities can hope to characterize the atmospheres of small, rocky exoplanets, i.e., this is the observationally relevant case (Cowan et al. 2015). However, we argue that the phenomenon of runaway generalizes to all atmosphere types and stellar hosts, including non-H₂-dominated atmospheres and Sun-like stars, as shown in Appendix C, and by the example of terrestrial O₂.

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We find NH₃ to enter runaway at biochemically plausible surface production fluxes for Cold Haber Worlds orbiting M-dwarf stars (represented by GJ 876). Specifically, our simulations indicate NH₃ to enter runaway for ${\phi }_{{\mathrm{NH}}_{3}}\,\geqslant 1\times {10}^{10}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$. For a production flux of ${\phi }_{{\mathrm{NH}}_{3}}\,=2\times {10}^{10}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, NH₃ concentrations are ∼70 ppmv. For comparison, the globally averaged modern NH₃ flux to Earth's atmosphere is estimated as ${\phi }_{{\mathrm{NH}}_{3}}=1.1\mbox{--}1.8\times {10}^{10}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ (Bouwman et al. 1997), and the preindustrial NH₃ flux is estimated as ${\phi }_{{\mathrm{NH}}_{3}}=2\mbox{--}9\times {10}^{9}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ (2–5 times lower; Zhu et al. 2015), meaning that even a modern-Earth-like biosphere emits NH₃ to the atmosphere at rates within an order of magnitude of the runaway threshold for an M dwarf–hosted Cold Haber World. If NH₃ were net emitted at rates comparable to the net emission of O₂ on Earth (${\phi }_{{{\rm{O}}}_{2}}=4\times {10}^{10}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ net; Zahnle et al. 2006), e.g., as a waste product of primary energy metabolism as in the Cold Haber World scenario, then NH₃ would be in the runaway regime for M-dwarf worlds. This statement is robust to sensitivity tests regarding climate and wet/dry deposition of non-NH₃ species. High surface deposition of non-NH₃ species increases the threshold for runaway by a factor of 2, but does not prevent the phenomenon (Appendix B). However, high surface deposition of NH₃ inhibits runaway: NH₃ runaway is critically dependent on the assumption that the surface is saturated in NH₃, as modern Earth's surface is saturated in O₂ (Section 4; Huang et al. 2022). Irradiation by a Sun-like UV field also suppresses runaway at the fluxes studied here, due to higher photolytic NUV irradiation. M-dwarf planets are more amenable to runaway compared to G-dwarf planets, due to their lower NUV output, as shown previously for other gases like CH₄ (Segura et al. 2005). We find metabolic ammonia production to be thermodynamically profitable over the parameter space we model here (Appendix D). Overall, the example of our biosphere suggests that NH₃ production fluxes compatible with photochemical runaway on M-dwarf worlds are plausible, provided the critical assumption of surface saturation is met.

The implications of photochemical runaway for NH₃ detectability are remarkable. In photochemical runaway (i.e., past a critical flux value), a mere order-of-magnitude increase in NH₃ production flux translates to the difference between NH₃ being essentially invisible and being highly detectable. We consider the detection of NH₃ on a Cold Haber World via transmission spectroscopy with the upcoming JWST, anticipated to be the premier near-term exoplanet characterization opportunity (Cowan et al. 2015). We do not expect NH₃ to be detectable at all on a 1.5 R_Earth exoplanet with an H₂-dominated atmosphere orbiting a GJ 876–like star for a surface emission flux of 3 × 10⁹ cm⁻² s⁻¹, below the runaway threshold. At this surface emission flux, NH₃ is confined to near the surface and rapidly decays as a function of altitude, and the marginal absorption produced by NH₃ is not greater than the JWST noise floor. By comparison, two transits of JWST would suffice to detect the 1.45–1.55 μm feature of NH₃ with an average significance of 5.0σ for a surface emission flux of 2 × 10¹⁰ cm⁻² s⁻¹, above the runaway threshold (Figures 2 and 3; Appendix B). At this surface emission flux, NH₃ is in runaway. In runaway, NH₃ concentrations are high and NH₃ populates the upper atmosphere, leading to significantly enhanced spectral features over the non-runaway cases.

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The planet scenario we have considered corresponds to a rocky, habitable planet with an H₂-dominated atmosphere, for which life would have a strong metabolic incentive to produce NH₃. Such planets have no analog in the solar system, and it is not known whether they exist. Terrestrial-mass planets overlaid by H₂-dominated atmospheres are predicted for second-generation planets orbiting white dwarf stars (Lin et al. 2022), and are allowed by theory for main-sequence stars depending on the extreme-UV irradiation level (Owen et al. 2020). Habitable (but not rocky) planets overlaid by H₂-dominated atmospheres have been proposed based on exoplanet mass/radius measurements (Madhusudhan et al. 2021), and H₂-dominated atmospheres have been experimentally demonstrated to be compatible with life (Seager et al. 2020). However, the main motivation for considering planets with H₂-dominated atmospheres is observational: such planets are the only habitable worlds whose atmospheres will be generally accessible to spectral characterization over the next one to two decades, due to their light (therefore extended) atmospheres. Even if rocky planets with H₂-dominated atmospheres do not exist, planets with H₂-rich atmospheres are thermodynamically capable of supporting Cold Haber Worlds. For Cold Haber Worlds that do not feature H₂-dominated atmospheres, runaway would still occur, but NH₃ detection would require next-generation telescopes with a noise floor lower than JWST, a host star smaller and closer than GJ 876, like TRAPPIST-1, or both (Huang et al. 2022).

We reiterate that our intent is not to singularly emphasize NH₃ as a biosignature gas, but rather to use it as a case study for illustrating photochemical runaway and its implications for the detectability of trace atmospheric gases. Indeed, NH₃ is just one of a steadily growing list of biogenic gases that can undergo runaway (Schwieterman et al. 2019; Sousa-Silva et al. 2020; Zhan et al. 2021). Because the phenomenon of runaway rests on the general observation that a gas's atmospheric sinks are finite, we expect a broad range of gases in diverse habitable planetary scenarios to undergo runaway if emitted at sufficiently high fluxes, as shown in Appendix C. Specific pathological cases in which runaway fails can be identified with detailed photochemical measurements and modeling (Appendix E). Abiotic production can also drive runaways (e.g., impacts may lead to CO runaway; Kasting 1990); therefore, abiotic false-positive analyses remain essential for biosignature gases, in or out of runaway.

Photochemical runaway lifts the photochemical control on biosignature gas accumulation. Photochemical processes like photolysis are predicted to limit the concentrations of most gaseous products of biology to undetectable levels on habitable planets (Domagal-Goldman et al. 2011; Kasting et al. 2014; Sousa-Silva et al. 2020; Zhan et al. 2021). However, in the runaway phase, this control is lifted, making possible much higher, potentially detectable concentrations of biosignature gases. For example, the biosignature gases PH₃ and isoprene are challenging to impossible to detect on habitable planets with JWST unless they enter a runaway phase (Sousa-Silva et al. 2020; Zhan et al. 2021).

Researchers disagree on whether photochemical runaways are physically realistic. While photochemical runaways arise in a range of models, some researchers postulate runaways to be unphysical, and set model boundary conditions that prevent them from occurring. For example, Segura et al. (2005) argue that CH₄ runaway on a modern-Earth-like planet is implausible because the high pCH₄ and temperature associated with CH₄ runaway should thermodynamically inhibit methanogenesis, which other workers extend into a general dismissal of runaway (Rugheimer et al. 2015; Rugheimer & Kaltenegger 2018). However, this objection is specific to planets similar to the modern Earth. On planets analogous to early Earth (i.e., with high pCO₂ and pH₂), methanogenesis is thermodynamically compatible with runaway (Appendix D). Furthermore, biology may produce a gas even if it is not metabolically profitable to do so, if that production meets other biological needs. For example, terrestrial biology produces abundant isoprene at considerable energetic cost, because isoprene accomplishes important secondary functions (e.g., stress mitigation; Zhan et al. 2021). Finally, modeling of the rise of O₂ on Earth suggests that O₂, too, underwent runaway, i.e., rapidly and nonlinearly increasing in concentration as a function of surface flux (Gregory et al. 2021; Appendix C). We therefore argue that the rise of O₂ on Earth represents an actualized example of photochemical runaway, affirming its physicality.

Efficient surface deposition (e.g., via biogeochemistry) may prevent biogenic gases from becoming detectable even if they are otherwise able to enter photochemical runaway, but the example of terrestrial O₂ suggests that even this barrier can be overcome. Uptake by the surface can limit the concentrations of atmospheric gases. For example, if its surface deposition is efficient, NH₃ is restricted to undetectably low concentrations (Huang et al. 2022). Surface deposition can be inefficient; for example, the surface deposition of CO is inefficient due to its insolubility, and CO may enter runaway on M-dwarf ocean worlds even if it is deposited at the maximum possible velocity (Kharecha et al. 2005; Schwieterman et al. 2019). However, more importantly and more generally, high biogenic gas production can make surface deposition inefficient by saturating the surface. This extreme scenario occurred with O₂ on Earth. O₂ dry deposition into the ocean can theoretically be as high as 10⁻⁴ cm s⁻¹ (Kharecha et al. 2005), which on its own would limit O₂ to 20 ppmv, assuming a modern-Earth atmospheric pressure and net O₂ production flux. Such oxygen concentrations are extremely low compared to modern oxygen levels of 21%, and indeed it has been suggested that O₂ levels were low for some time after the advent of oxygenic photosynthesis. However, over time, O₂ saturated its surface sinks, rendering deposition inefficient and permitting further O₂ accumulation (Lyons et al. 2014; Daines et al.2017). We can gain a sense of just how inefficient O₂ surface deposition has become by calculating the effective "deposition velocity" equired to balance the modern net O₂ surface flux in modern Earth's 21% O₂ atmosphere: ${v}_{\mathrm{dep},\mathrm{eff}}={\phi }_{{{\rm{O}}}_{2}}/{n}_{02}$ =(4 × 10¹⁰ cm⁻² s⁻¹)/(0.21 × 2.5 × 10¹⁹ cm⁻³) = 10⁻⁸cm s⁻¹, 4 orders of magnitude below the theoretical upper limit. Sustained high production of O₂ has saturated O₂'s surface biogeochemical sink, rendering it inefficient and permitting O₂ accumulation. This is the scenario invoked for NH₃ in the Cold Haber World simulated here. We cannot expect this to happen with every biogenic gas: O₂'s modest solubility facilitates saturation, and even so its complete domination of the surface-atmosphere system is limited to the last 0.5–1 Ga (Lyons et al. 2014). However, the possibility that other gases can also saturate their surface sinks and hence suppress their surface deposition rates is not implausible.

Photochemical runaway requires high but biochemically plausible production fluxes, comparable to net O₂ production on Earth (${\phi }_{{{\rm{O}}}_{2}}=4\times {10}^{10}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ net; Zahnle et al. 2006). The magnitude of O₂ production is much higher (Gebauer et al. 2017), but most of this O₂ is consumed either directly or indirectly by biology; the value we utilize corresponds to production net of these biogenic sinks, as measured by reductant burial and oxidative weathering (Jacob 1999; Catling & Kasting 2017). It is challenging to predict from first principles which gases are likely to be produced at such high fluxes in exo-biospheres. Even on modern Earth, biogenic gas production is contingent on evolutionary history, and hard to predict from first principles. For example, isoprene is a major product of terrestrial biology, with production rates rivaling those of simple gases associated with primary metabolism (e.g., CH₄), despite the fact that isoprene synthesis expends energy and fixed carbon. Rather, isoprene appears to fulfill secondary roles in terrestrial biology, such as stress mitigation. Despite isoprene's high energetic cost of synthesis, terrestrial production of isoprene is nevertheless high enough to be near the photochemical runaway threshold on planets orbiting M-dwarf stars (Zhan et al. 2021). The example of isoprene illustrates the challenge of trying to predict a gas's production from first principles; we argue it is more observationally relevant to be aware of the possibility of diverse biogenic absorbers in exo-atmospheres.

In summary, biogenic gases produced at high but not unrealistic production fluxes can experience nonlinear increases in concentration via the phenomenon of photochemical runaway. Through this phenomenon, even photochemically reactive biosignature gases may accumulate to detectable concentrations, dramatically expanding the palette of potential molecular indicators of life's presence. Photochemical runaway occurred for O₂ on Earth; it may occur for other gases on other worlds. Runaways are especially likely on planets orbiting cool stars with low UV output like M dwarfs or white dwarfs. Excitingly, photochemical runaway implies that a world need not develop oxygenic photosynthesis or even terrestrial-type biology in order to have a biosphere that can be remotely detected. Exoplanets to date have proved to be physically more diverse than the worlds of our own solar system; their biologies and their concomitant biosignatures may prove to be similarly diverse (Seager & Bains 2015).

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This work was supported in part by a grant from the Simons Foundation (SCOL grant 495062 to S.R.). S.R. gratefully acknowledges the support of Northwestern University's Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) via the CIERA Fellowship. D.K. was supported by grant 80NSSC20K0269XX from NASA's XRP program. S.S., Z.Z., W.B., and J.P. received support from the Heising-Simons Foundation (2018-1104). S.S., Z.Z., J.P., and J.H. received support from NASA (80NSSC19K0471). Z.L. received support from an MIT Presidential Fellowship. This research has made use of NASA's Astrophysics Data System. We thank B. Gregory and R. Hu for sharing preprints, and we thank B. Gregory, R. Hu, B. Hayworth, C. Harman, S. Rugheimer, R. O. Parke Loyd, and C. Sousa-Silva for discussions. We thank an anonymous referee for detailed feedback that materially improved this paper.

The photochemical model outputs that underlie Figures 1 and 4 are available on GitHub at https://github.com/sukritranjan/ranjan_runaway/. The line-by-line climate model used to compute the impact of NH₃ and CH₄ is available on GitHub: https://github.com/ddbkoll/PyRADS-shortwave. The radiative transfer model used to simulate transmission spectra is available on GitHub: https://github.com/zhuchangzhan/SEAS. The scripts used to implement the thermodynamic calculations reported in Appendix D are available on GitHub at https://github.com/sukritranjan/ranjan_runaway/. The photochemical code used in this paper (Hu et al. 2012, 2013) is not publicly available, but its input files are available by request.

In this section, we present more details regarding the model inputs used in our study.

A.1. Stellar Spectra

Figure 5 shows the stellar spectra used as inputs in our photochemical model. They are formulated as described in Section 2.1.2, and shown scaled to the modern solar constant (1 AU equivalent).

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A.2. GJ 876 Stellar Parameters

We draw stellar parameters for GJ 876 (Table 2) from the TESS Input Catalog (TIC; Stassun et al. 2019) and from Correia et al. (2010). These parameters are used in the simulated JWST observations of the Cold Haber World orbiting GJ 876 (Section 2.2). To match our assumptions of a planetary instellation equivalent to that received at 1.6 au orbiting the Sun, we assign a planetary semimajor axis of $a=\sqrt{\tfrac{{L}_{\star }}{{L}_{\odot }}}\times 1.6\,\mathrm{au}=0.18\,\mathrm{au}$, in turn implying a period of $P=2\pi \sqrt{\tfrac{{a}^{3}}{{{GM}}_{\star }}}=48$ days, an orbital velocity of $v=\sqrt{\tfrac{{{GM}}_{\star }}{a}}=4.1\times {10}^{4}$ m s⁻¹, and a transit duration of ${T}_{\mathrm{transit}}=\tfrac{2{R}_{\star }-2{R}_{\mathrm{planet}}}{v}=3.2$ hr. Here, we have assumed a circular orbit with an impact parameter of zero (negligible orbital inclination). Assuming an impact parameter of zero maximizes the time in transit, meaning that our calculations represent a best-case scenario for the number of transits required to detect the trace gas species.

Table 2. Stellar Parameters Used in the Simulated Observations

Parameter	Value
M⋆, Mass (MSun)	0.34
R⋆, Radius (RSun)	0.35
L⋆, Luminosity (LSun)	0.0128
Effective Temperature (K)	3271
Surface Gravity (${\mathrm{log}}_{10}(g)$, cgs)	4.87
J-band Magnitude	5.934
Metallicity (dex)	0.05

Note. The stellar parameters correspond to GJ8 76 and, except for metallicity, are drawn from the TIC (version 8.1, accessed 08/11/2021, https://exofop.ipac.caltech.edu/tess/target.php?id=188580272; Stassun et al. 2019). Metallicity is drawn from Correia et al. (2010).

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A.3. Chemical Boundary Conditions

We discuss here the runaway of NH₃ in the Cold Haber World scenario in more detail, including sensitivity tests. NH₃ runaway has not been previously reported in the literature. The solubility of NH₃ means that in most terrestrial planet contexts, wet deposition (rainout) will regulate pNH₃ and photochemistry is largely irrelevant (Huang et al. 2022). However, if the surface can be saturated in NH₃, e.g., due to a biosphere that is a net source of NH₃, as invoked in the Cold Haber World scenario we simulate, then photochemistry controls pNH₃ (Kasting 1982; Seager et al. 2013a, 2013b). In this case, we find the main NH₃ loss mechanism to be direct photolysis, as found by Kuhn & Atreya (1979) and Kasting (1982) for N₂-dominated atmospheres (early Earth). We found photolysis to dominate other photochemical loss processes by orders of magnitude. Due to the generally lower UV output of M dwarfs at NH₃-photolyzing ≤ 230 nm wavelengths, NH₃ enters runaway and becomes detectable for M dwarfs at fluxes for which it is still firmly photochemically limited to undetectable concentrations for solar-type stars.

We considered the impact of NH₃ greenhouse warming on NH₃ runaway. For the H₂-dominated Cold Haber World planetary scenario we study here, we found the greenhouse warming due to NH₃ to be relatively modest, because NH₃ absorption near the peak of the planet's outgoing longwave radiation occurs at similar wavelengths as the strong H₂–H₂ collision-induced absorption in our H₂-dominated scenario. Specifically, we found that adding 55 ppmv NH₃ (corresponding approximately to the 70 ppmv predicted in our base case calculations for ${\phi }_{{\mathrm{NH}}_{3}}=2\times {10}^{10}$ cm⁻² s⁻¹) increased the surface temperature T_surf by only 11K, from 288K to 299K. At this abundance, NH₃ is already detectable with an average significance of 5σ in two transits from JWST. We constructed a new temperature–pressure profile evolving as a wet adiabat from T_surf = 299 K to an isothermal stratosphere of T_strat = 170 K (Figure 6), and reran our simulations, adjusting our surface H₂O molar mixing ratio boundary condition from 0.01 to 0.02 to account for higher H₂O saturation pressure. We found a negligible impact of higher surface temperature on NH₃ accumulation. Note that the main effect of higher T_surf is to increase the water vapor content, and hence H and OH production rates, in the lower atmosphere. As the main photochemical sink of NH₃ is direct photolysis at higher altitudes, NH₃ accumulation is not strongly affected by changes in lower-atmosphere H₂O abundance.

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We considered the possibility of higher stratospheric temperatures, and their potential effect on NH₃ accumulation. NH₃ and its photochemical product N₂H₄ are strong UV absorbers, and we considered the possibility that their absorption of UV might warm the stratosphere, as does O₃ on Earth. To conduct a sensitivity test for this possibility, we constructed a temperature–pressure profile, evolving as a wet adiabat from T_surf = 299 K to an isothermal stratosphere of T_strat = 210 K (Figure 6), and reran our simulations, adjusting our surface H₂O mixing ratio boundary condition from 0.01 to 0.02 to account for higher H₂O saturation pressure. We chose T_strat = 210 K based on modern Earth's empirical tropopause temperature, which is significantly warmer than the T_strat implied by our climate calculations and thus should provide a conservative upper bound. We found that warmer stratospheres lead to much higher NH₃ abundances for the same ${\phi }_{{\mathrm{NH}}_{3}}$, i.e., warmer stratospheres promoted the accumulation of NH₃. We attribute this to the stabilization of NH₃ due to the higher production of H driven by higher stratospheric H₂O abundances. In more detail: Hu et al. (2012) report the main source of H in the atmospheres of habitable worlds with H₂–N₂ atmospheres to be H₂O photolysis, via

$$\begin{eqnarray}&&{{\rm{H}}}_{2}{\rm{O}}+h\nu \to {\rm{H}}+\mathrm{OH};\end{eqnarray} \tag{ B1 }$$

$$\begin{eqnarray}&&\mathrm{OH}+{{\rm{H}}}_{2}\to {{\rm{H}}}_{2}{\rm{O}}+{\rm{H}}.\end{eqnarray} \tag{ B2 }$$

Therefore, increasing stratospheric H₂O increases H production. Kasting (1982) reports that increased H stabilizes NH₃ by aiding the recombination NH₂ + H + M → NH₃; we observe the same. Kasting (1982) also indicated that the removal of N₂H₃ stabilizes NH₃, since N₂H₃ is the key intermediary en route from NH₃ to N₂. Higher H suppresses N₂H₃ via N₂H₃ + H → 2NH₂, stabilizing NH₃. H also suppresses N₂H₂ and N₂H₄, which are other intermediaries in the oxidation of NH₃ to N₂. Therefore, our finding that hotter stratospheres stabilize NH₃ is consistent with past work. Indeed, we observed higher NH₃ and lower NH₂, N₂H₂, NH₂H₃, and N₂H₄ in our "hot stratosphere" simulations compared to our standard simulations, as expected by this theory.

At high NH₃ concentrations, our model predicts elevated concentrations of N₂H₄ (hydrazine), which is condensable at habitable temperatures. This raises the possibility of hydrazine haze in high-NH₃ atmospheres. We compared the hydrazine concentrations predicted by our model to the saturation pressure of hydrazine in equilibrium with the solid phase, using the expression of Atreya et al. (1977). We found hydrazine to be condensable in the upper atmosphere if the stratosphere is cold (T_strat = 160 K), but not if the stratosphere is warm (T_strat ≥ 170 K). This is both because the condensation pressure of N₂H₄ is higher at higher temperatures, and because warmer stratospheres inhibit N₂H₄ accumulation, as above. Since the high NH₃ abundances that may produce condensable N₂H₄ should also produce warmer stratospheric temperatures (see Rugheimer & Kaltenegger 2018 for CH₄), it is unclear whether haze should in fact form in high-NH₃ atmospheres; coupled climate–photochemistry calculations are required to resolve this ambiguity. If N₂H₄ haze does form, then it might inhibit the detection of spectral features of NH₃ and other molecules in transmission spectra, as has been observed in large gaseous exoplanet atmospheres (Deming & Seager 2017). On the other hand, N₂H₄ ice has spectral features that may enable its unique identification, in which case N₂H₄ haze could be used as a probe of NH₃, comparable to the way in which organic haze has been suggested as a probe of organic gas production (Zheng et al. 2008; Arney et al. 2018).

We now turn to the effect of photochemical runaway on the detectability of NH₃. We compare simulated observations of our 1.5 R_Earth, 5 M_Earth Cold Haber World with ${\phi }_{{\mathrm{NH}}_{3}}=0$ cm⁻² s⁻¹, ${\phi }_{{\mathrm{NH}}_{3}}=3\times {10}^{9}$ cm⁻² s⁻¹ (not in NH₃ runaway), and ${\phi }_{{\mathrm{NH}}_{3}}=2\times {10}^{10}$ cm⁻² (NH₃ runaway), binned to R = 10, in Figure 3. The ${\phi }_{{\mathrm{NH}}_{3}}=3\times {10}^{9}$ cm⁻² s⁻¹ simulated observation cannot be differentiated from the ${\phi }_{{\mathrm{NH}}_{3}}=0$ cm⁻² s⁻¹ observation with JWST; the JWST noise floor exceeds the difference between the models. On the other hand, the ${\phi }_{{\mathrm{NH}}_{3}}=2\times {10}^{10}$ cm⁻² s⁻¹ simulated observation can be be differentiated from the ${\phi }_{{\mathrm{NH}}_{3}}=0$ cm⁻² s⁻¹ simulated observation with two JWST transits. Specifically, in a suite of 100 simulated observations ¹² of two transits of our planetary scenario with JWST, the 1.45–1.55μm NH₃ feature can be distinguished with an average significance of 5.0σ. The 2.85–3.15μm NH₃ feature is not robustly detected with two transits (average significance 2.24σ), and requires additional transit observations.

We illustrate the generality of the phenomenon of runaway by calculating the concentration as a function of surface production flux for three gases other than NH₃, using our photochemical model (see Tables 4 and 5). We consider the accumulation of CH₄ in a CO₂-dominated atmosphere and the accumulation of CO and O₂ in N₂-dominated atmospheres, for both solar and M-dwarf irradiation (represented by GJ 876), to complement our earlier simulation of NH₃ accumulation in an H₂-dominated atmosphere. We chose these gases because they are well studied in the literature, meaning that their reaction networks are relatively complete, and because runaway of these gases has been studied in previous works (albeit not as a unified concept; Kasting 1990; Pavlov et al. 2003; Segura et al. 2005; Zahnle et al. 2006; Schwieterman et al. 2019; Gregory et al. 2021). We made these choices to demonstrate that the phenomenon of runaway is not necessarily attributable to incomplete reaction networks, nor is it unique to our model. We similarly chose background atmospheres of varying redox state to illustrate the generality of the phenomenon. Unless otherwise stated, we used the same model choices as for NH₃ runaway, to illustrate the recovery of the runaway phenomenon for diverse gases with a uniform model calculation.

C.1. Methods

C.2. Results

In this section, we quantitatively examine the qualitative argument of Segura et al. (2005) and Rugheimer et al. (2015) that runaway is not physical due to biological feedbacks. Specifically, Segura et al. (2005) and Rugheimer et al. (2015) argue that microbial methanogenesis would become thermodynamically "unprofitable" at high pCH₄, thereby providing a feedback loop to stabilize pCH₄ by reducing CH₄ production. Segura et al. (2005) and Rugheimer et al. (2015) postulate an upper limit on pCH₄ of ∼0.001 bar. By analogy, Rugheimer et al. (2015) dismiss the possibility of runaway of other gases, such as N₂O, and Rugheimer & Kaltenegger (2018) dismiss the possibility of runaway for early Earth as well.

We examine this argument on thermodynamic grounds using the framework of Seager et al. (2013a), who in turn implement the criteria of Hoehler (2004). We affirm the argument of Segura et al. (2005) and Rugheimer et al. (2015) that thermodynamic constraints may prevent methanogenic microbes from triggering a CH₄ runaway on modern Earth–like planets. However, high CH₄ (pCH₄ = 0.01 bar) remains thermodynamically compatible with methanogenesis on early Earth–like worlds, which feature elevated concentrations of the CO₂ and H₂ that are the substrates of methanogenesis. We analyze the hypothetical "ammoniagenesis" metabolism (Seager et al. 2013a, 2013b; Bains et al. 2014), and show it to be compatible with runaway concentrations of NH₃ (pNH₃ = 0.001 bar). Our analysis is simple, and does not encode a full ecosystem model, e.g., Sauterey et al. (2020). However, this simplicity also reduces the terracentricity of our analysis (Seager & Bains 2015), and we contend that it is sufficient to argue against a blanket dismissal of photochemical runaway on purely thermodynamic grounds.

D.1. Thermodynamics of Metabolic Gas Production

We follow Seager et al. (2013a) in considering thermodynamic limits on metabolic gas production.

The free energy yielded by a metabolic reaction ΔG_reac can be calculated from thermodynamics, via

$$\begin{eqnarray*}&&{\rm{\Delta }}{G}_{\mathrm{reac}}={\rm{\Delta }}{G}_{\mathrm{reac}}^{0}+{RT}\mathrm{ln}Q,\end{eqnarray*}$$

where ${\rm{\Delta }}{G}_{\mathrm{reac}}^{0}$ is the standard free energy of the reaction, T is the temperature, R = 8.314 J mol⁻¹ K⁻¹ is the universal gas constant, and Q is the reaction quotient.

${\rm{\Delta }}{G}_{\mathrm{reac}}^{0}$ can be estimated from the difference between the total standard Gibbs free energy of formation ΔG⁰ of the products and the reactants, i.e.,

$$\begin{eqnarray*}&&{\rm{\Delta }}{G}_{\mathrm{reac}}^{0}=({{\rm{\Sigma }}}_{i}{n}_{i}{\rm{\Delta }}{G}_{i}^{0})-({{\rm{\Sigma }}}_{j}{n}_{j}{\rm{\Delta }}{G}_{j}^{0}),\end{eqnarray*}$$

where ${\rm{\Delta }}{G}_{x}^{0})$ is the standard free energy of formation of species x, n_x is the stoichiometric coefficient associated with species x, and the indices i and j count over products and reactants, respectively.

Q is calculated as

$$\begin{eqnarray*}&&Q=\displaystyle \frac{{{\rm{\Pi }}}_{i}{A}_{i}^{{n}_{i}}}{{{\rm{\Pi }}}_{j}{A}_{j}^{{n}_{j}}},\end{eqnarray*}$$

where A_x is the activity of species x. We approximate our metabolic reactions as proceeding in dilute aqueous solution, permitting us to ignore salinity effects and to simplify ${A}_{{{\rm{H}}}_{2}{\rm{O}}}=1$.

For example, for methanogenesis,

$$\begin{eqnarray}&&{\mathrm{CO}}_{2}+4{{\rm{H}}}_{2}\to {{CH}}_{4}+2{{\rm{H}}}_{2}{\rm{O}};\end{eqnarray} \tag{ D3 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}{G}_{\mathrm{reac}}^{0}=({\rm{\Delta }}{G}_{{\mathrm{CH}}_{4}}^{0}+2{\rm{\Delta }}{G}_{{{\rm{H}}}_{2}{\rm{O}}}^{0})-({\rm{\Delta }}{G}_{{\mathrm{CO}}_{2}}^{0}+4{\rm{\Delta }}{G}_{{{\rm{H}}}_{2}}^{0});\end{eqnarray} \tag{ D4 }$$

$$\begin{eqnarray}&&Q=\displaystyle \frac{{A}_{{\mathrm{CH}}_{4}}{A}_{{{\rm{H}}}_{2}{\rm{O}}}^{2}}{{A}_{{\mathrm{CO}}_{2}}{A}_{{{\rm{H}}}_{2}}^{4}}=\displaystyle \frac{{A}_{{\mathrm{CH}}_{4}}}{{A}_{{\mathrm{CO}}_{2}}{A}_{{{\rm{H}}}_{2}}^{4}}.\end{eqnarray} \tag{ D5 }$$

We note that ${\rm{\Delta }}{G}_{x}^{0}$ is a relative quantity, and that the reference species can differ between thermodynamic databases. Therefore, it is important to use an internally consistent thermodynamic database when conducting thermodynamic calculations. We take our ${\rm{\Delta }}{G}_{x}^{0}(T)$ from Amend & Shock (2001). Further, care must be taken to use the ${\rm{\Delta }}{G}_{x}^{0}(T)$ corresponding to the phase being considered, i.e., when considering aqueous-phase x, a different ${\rm{\Delta }}{G}_{x}^{0}(T)$ must be used than when considering gas-phase x. We do so.

We can translate ΔG_reac into thermodynamic constraints on microbial metabolic gas production. We consider two constraints, using the terminology of Hoehler (2004):

• 1.  
  Biological Energy Quantum (BEQ): the Gibbs free energy liberated by metabolism (ΔG_reac) must exceed a minimum threshold to be usefully harnessed by the cell. The threshold Gibbs free energy of metabolism required to be usefully harnessed by the cell is empirically constrained for actively growing terrestrial life to be (Hoehler 2004):

  $$\begin{eqnarray*}&&{\rm{\Delta }}{G}_{{\rm{reac}}}\leqslant -20\,{\mathtt{kJ}}\,{{\mathtt{mol}}}^{-1}.\end{eqnarray*}$$

  Here, the mol⁻¹ refers to the mol of reaction, with the reaction written to minimize the number of molecules. We note this constraint to be conservative; one species identified in Hoehler (2004) could survive at ΔG_reac ≤ − 5 kJ mol ⁻¹, suggesting it could grow at ΔG_reac ≤ − 10 kJ mol ⁻¹.
• 2.  
  Maintenance Energy: organisms must generate energy at a minimum rate in order survive as active organisms able to grow. This minimum rate increases with temperature. For anaerobic terrestrial life, this minimum energy production rate P_me has been empirically measured to be ${P}_{\mathrm{me}}=(2.2\times {10}^{7}{\mathtt{kJ}}\,{{\mathtt{g}}}^{-1}{{\mathtt{s}}}^{-1})\exp [\tfrac{6.94\times {10}^{4}\,{{\mathtt{Jmol}}}^{-1}}{{RT}}]$, where g⁻¹ refers to grams of wet biomass (Tijhuis et al. 1993; Hoehler 2004; Seager et al. 2013a). P_me can be related to ΔG_reac via P_me = ΔG_reac M, where M is the production rate of the metabolic by-product in units of mol g⁻¹ s⁻¹. In the studies we reviewed, M ≤ 10⁻⁴ mol g⁻¹ s⁻¹ ( Patel et al. 1978; Patel & Roth 1977; Perski et al. 1981; Zinder & Koch 1984; Schönheit & Beimborn 1985; Müller et al. 1986; Pennings et al. 2000; Takai et al. 2008), and we adopt this as our upper limit, providing our second constraint:

  $$\begin{eqnarray*}&&\displaystyle \frac{{P}_{\mathrm{me}}}{{\rm{\Delta }}{G}_{\mathrm{reac}}}\lt {10}^{-4}\,{\mathtt{mol}}\,{{\mathtt{g}}}^{-1}\,{{\mathtt{s}}}^{-1}.\end{eqnarray*}$$

Next, we apply these constraints to methanogenesis, considered by Segura et al. (2005) and Rugheimer et al. (2015), and to the hypothetical "ammoniagenesis" metabolism postulated in the Cold Haber World scenario we model in this paper.

D.2. Thermodynamic Limits on Methanogenesis

We consider methanogenesis, with general reaction represented by (Bains et al. 2014):

$$\begin{eqnarray*}&&{\mathrm{CO}}_{2}+4{{\rm{H}}}_{2}\to {{CH}}_{4}+2{{\rm{H}}}_{2}{\rm{O}}.\end{eqnarray*}$$

Methanogens are strict anaerobes. Consequently, on oxic modern Earth, methanogens are confined to anaerobic environments, with [CO₂] present at mM concentrations and [H₂] present at nM concentrations (Megonigal et al. 2004). We calculate the T at which methanogenesis satisfies the criteria in Section D.1 for [CO₂] = 3 mM, [H₂] = 3 nM, and pCH₄ = 1.6 × 10⁻⁶ bar and 2 × 10⁻² bar, corresponding to modern Earth and an Earth in CH₄ runaway, respectively (Figure 7). For modern Earth in CH₄ runaway, we find that methanogenesis is only profitable for T ≤ 278 K. For comparison, we calculate T_surf = 301K for this planetary scenario, affirming the argument of Segura et al. (2005) and Rugheimer et al. (2015) that thermodynamic feedbacks may inhibit CH₄ runaway on a modern Earth–like planet. However, methanogenesis would be allowed if [CO₂] or [H₂] were three times higher (e.g., 9 mM, 9 nM), rather than the intermediate values (3 nM, 3 nM) we have chosen here; consequently, we cannot fully rule out the possibility of CH₄ runaway on modern Earth–like planets.

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On the other hand, planets more similar to early Earth, i.e., anoxic, with CO₂–N₂ atmospheres, are more thermodynamically favorable for methanogenesis. We simulate such a planet in Appendix C, which features pCO₂ = 0.9 bar, pH₂ = 1 × 10⁻³ bar, and pCH₄ = 6 × 10⁻⁵ and pCH₄ = 2 × 10⁻², corresponding to ${\phi }_{{\mathrm{CH}}_{4}}=3\times {10}^{8}$ cm⁻² s⁻¹ and ${\phi }_{{\mathrm{CH}}_{4}}=1\times {10}^{11}$ cm⁻² s⁻¹, respectively. Using the climate model described in Section 2.3, we predict surface warming of ≤ 13 K corresponding to this CH₄ inventory, relative to a base climate with T_surf = 288 K. Methanogenesis remains profitable up to very high temperatures for an early Earth–like world, including the T_surf ≤ 301 K (the vertical red dashed line in Figure 7) expected in CH₄ runaway.

Note that for the modern Earth–like case, we considered [CO₂] and [H₂], whereas for the early Earth–like case, we considered pCO₂ and pH₂. For these calculations, we have been careful to use ${\rm{\Delta }}{G}_{x}^{0}(T)$ from Amend & Shock (2001), corresponding to the aqueous phase and gas phase, respectively.

D.3. Thermodynamic Limits on Ammonia Production in the Cold Haber World Scenario

We consider the hypothetical "ammoniagenesis" metabolism proposed for Cold Haber Worlds and modeled in this paper, with the general reaction (Seager et al. 2013a, 2013b; Bains et al. 2014)

$$\begin{eqnarray*}&&{{\rm{N}}}_{2}+3{{\rm{H}}}_{2}\to 2{\mathrm{NH}}_{3}.\end{eqnarray*}$$

For the atmospheric scenario we simulate in this paper, pH₂ = 0.9 bar, pN₂ = 0.1 bar, and pNH₃ = 0.001 bar in runaway. For these parameters, the ammoniagenesis is profitable for T ≤ 360 K (Figure 8). For comparison, we predict T_surf = 299K for pNH₃ = 7.6 × 10⁻⁴ bar. We conclude that ammoniagenesis remains profitable in NH₃ runaway, based on the criteria from Hoehler (2004).

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We further considered whether an H₂-dominated atmosphere is required for the Cold Haber World. We reran the calculation above for pN₂ = 0.1 bar and pH₂ = 0.01 bar, and found that ammoniagenesis remains thermodynamically profitable across a wide range of habitable temperatures. Early Earth–like planets are predicted to host H₂ mixing ratios of up to 10%, if H₂ escape is below the diffusion limit, due to, e.g., cooling of the upper atmosphere by high CO₂ abundances (Tian et al. 2005; Liggins et al. 2020). This implies that even an early Earth–like planet with a non-H₂-dominated atmosphere would be thermodynamically compatible with ammoniagenesis, though the metabolic incentive to develop this metabolism would be proportionately reduced.

In this section, we consider pathological scenarios in which gases might fail to enter photochemical runaway, despite high production flux.

The key requirement for photochemical runaway is that the radical production in the atmosphere vary sublinearly with the runaway gas flux, so that the runaway gas can saturate its photochemical sinks. One scenario in which this condition fails corresponds to combustion–explosion conditions. In conditions of sufficiently extreme disequilibrium (e.g., the coexistence of sufficiently abundant H₂ and O₂), chain propagation reactions (radicals tend to make more radicals) can dominate over chain termination reactions (radicals tend to make nonradicals). In such conditions, energetic events can trigger runaway increase in radical concentrations until the substrates are exhausted. This condition can be checked by comparing to experimental combustion–explosion studies (Grenfell et al. 2018).

More generally, there may exist cases in which a biosignature gas self-limits its concentrations, e.g., through self-reaction or through the production of UV sensitizer. Photochemical models can check for this possibility, but careful study is required. For example, O₂ does produce a UV sensitizer in the form of O₃, but far from catalyzing its destruction, O₃ photochemically shields O₂ (Zahnle et al. 2006). Detailed photochemical networks are not available for many potential biosignature gases; the measurement of these photochemical data and their incorporation into photochemical models is required to explore the potential of novel biosignature gases for runaway.