A BIOMASS-BASED MODEL TO ESTIMATE THE PLAUSIBILITY OF EXOPLANET BIOSIGNATURE GASES

The canonical concept for the search for atmospheric biosignature gases is to find a terrestrial exoplanet atmosphere severely out of thermochemical redox equilibrium (Lovelock 1965). Redox chemistry⁴ is used by all life on Earth and is thought to enable more flexibility for biochemistry than nonredox chemistry (Bains & Seager 2012). Redox chemistry is also used to capture environmental energy for biological use. The idea is that gas by-products from metabolic redox reactions can accumulate in the atmosphere and would be recognized as biosignature gases because abiotic processes are unlikely to create a redox disequilibrium. Indeed, Earth's atmosphere has oxygen (a highly oxidized species) and methane (a very reduced species), a combination several orders of magnitude out of thermodynamic equilibrium.

In practice, it could be difficult to detect molecular features of two different gases that are out of redox disequilibrium. The Earth as an exoplanet, for example (see Figure 8 in Meadows & Seager 2010), has a relatively prominent oxygen absorption feature at 0.76 μm, whereas methane at present-day levels of 1.6 ppm has only extremely weak spectral features. During early Earth, CH₄ may have been present at much higher levels (1000 ppm or even 1%), as it was possibly produced by widespread methanogenic bacteria (Haqq-Misra et al. 2008, and references therein). Such high CH₄ concentrations would be easier to detect, but because the Earth was not oxygenated during early times, O₂ and CH₄ would not have been detectable concurrently (see Des Marais et al. 2002). There may have been a short period of time in Earth's history when CH₄ levels were high and before the rise of oxygen when both could have been detected (Kaltenegger et al. 2007).

The more realistically identifiable atmospheric biosignature gas from future remote sensing observations is a single gas completely out of chemical equilibrium with the other known or expected atmospheric constituents. Earth's example again is oxygen or ozone, with the oxygen level being about 10 orders of magnitude higher than expected from equilibrium chemistry (Kasting & Walker 1981; Segura et al. 2007; Hu et al. 2012) and having no known abiotic production at such high levels. Although a single biosignature gas may be all that is detectable by future exoplanet atmosphere observations, reliance on a single biosignature gas is more prone to false positives than the detection of two (or more) gases that are out of equilibrium. In the paradigm of detecting signs of life by a single biosignature gas, we still retain the assumption that life uses chemical reactions to extract, store, and release energy, such that biosignature gases are generated as by-products somewhere in life's metabolic process.

How can we decide upon the exoplanet atmosphere gases that are identifiable as biosignature gases? Regardless of the strategy used, only the spectroscopically active, globally mixed gases would be visible in an exoplanet spectrum. Most work to date has focused on conservative extensions of the dominant biosignature gases found on Earth, O₂ (and its photochemical product O₃), and N₂O, as well as the possibility of CH₄ on early Earth. Research forays into biosignature gases that are negligible on present-day Earth but may play a significant role on other planets has started. Pilcher (2003) suggested that organosulfur compounds, particularly methanethiol (CH₃SH, the sulfur analog of methanol) could be produced in high enough abundance by bacteria, possibly creating a biosignature on other planets. CH₃Cl was first considered by Segura et al. (2005) and sulfur biogenic gases on anoxic planets were comprehensively investigated by Domagal-Goldman et al. (2011).

A slight deviation from terracentricity is to consider Earth-like atmospheres and Earth-like biosignature gases on planets orbiting M stars. Segura et al. (2005) found that CH₄, N₂O, and even CH₃Cl have higher concentrations and, therefore, stronger spectral features on planets orbiting quiet M stars compared to Earth. The Segura et al. (2005) work strictly focuses on Earth's production rates for the biosignature gases.⁵ The reduced ultraviolet (UV) radiation on quiet M stars enables longer biosignature gas lifetimes and, therefore, higher concentrations to accumulate. Specifically, lower UV flux sets up a lower atmospheric concentration of the OH radical than in Earth's solar UV environment. OH is the major destructive radical in Earth's atmosphere and with less OH, most biosignature gases have longer lifetimes. Seager et al. (2012) have reviewed the range of gases and solids produced by life on Earth.

A necessary new area of biosignature gas research will be predicting or identifying molecules that are potential biosignature gases on super-Earth planets different from Earth. The reasons are twofold. First, the microbial world on Earth is incredibly diverse, and microorganisms yield a broad range of metabolic by-products far beyond the gases called out in exoplanet biosignature research so far. In an environment different from Earth's, these metabolic by-products may accumulate to produce detectable biosignature gases different from those on past and present Earth. Second, while we anticipate the discovery of transiting super-Earths in the habitable zones of the brightest low-mass stars (Nutzman & Charbonneau 2008) and in the future Earths from direct imaging (e.g., Cash 2006; Trauger & Traub 2007; Lawson 2009), the prize targets around bright stars will be rare. It follows that the chance of finding an Earth twin might be tiny and so we must be prepared to identify a wide range of biosignature gases.

In this paper, we take a step forward to expand the possibilities for biosignature gas detection in the future. We provide a quantitative framework to consider biosignature gas source fluxes of any type and any value in any exoplanet environment, via a new biomass model estimate that provides a physical reality plausibility check on the amount of biomass required. This new method liberates modelers from assuming that exoplanet biosignature gas source fluxes are identical to those on Earth.

We summarize terrestrial biosignature gas fluxes for later reference as to what is a physically reasonable local (F_field, in units of mole m⁻² s⁻¹) and global annual total biosignature gas flux ($\mathcal {F}_{\rm global},$ in units of Tg yr⁻¹). Biological production of gases on Earth are limited by the availability of energy and nutrients. We emphasize that these terrestrial biosignature gas fluxes—which we call field fluxes—are strictly used in this work for consistency checks by comparison with our calculated biosignature gas fluxes.

For Earth as a whole, the dominant energy-capture chemistry is photosynthesis. Photosynthesis generates around 2.0 × 10⁵ Tg (of oxygen) yr⁻¹ (e.g., Friend et al. 2009). The primary carbon production rate from photosynthesis is about 1 × 10⁵ Tg yr⁻¹ (Field et al. 1998).

Earth has many biosignature gases beyond photosynthesis-produced O₂. Some of the other biosignature gases can be produced at relatively high flux rates, as listed in Table 1. In Table 1, we list the geometric mean of the maximum field flux from one or more environmental campaigns. The main point is that very high fluxes of biosignature gases can be generated where the surface environment is appropriate (suitable levels of relevant nutrients and energy sources).

We now turn to some specific examples of high terrestrial biosignature gas fluxes. As listed in Table 1, fluxes of some biosignature gases (e.g., isoprene and N₂O) can be very large when extrapolated from their local maximum values to a global total. In addition to the values in Table 1, biogenic NO_x fluxes from natural (unfertilized) environments can be 10–30 ng (N) m⁻² s⁻¹ (Williams et al. 1992; Davidson & Kingerlee 1997), which translates to a global flux across Earth's land surface of ∼150 to 300 Tg yr⁻¹. For environments where organic matter, water, and other nutrients are abundant (such as swamps), flux rates of methane can reach 10⁴ ng (C) m⁻² s⁻¹ (Prieme 1994; Dalal et al. 2008), which if scaled to a global flux would be 10–20 Pg yr⁻¹. We note, however, that scaling the flux from a swamp, which is rapidly degrading biomass imported from other environments, to a global flux is not realistic, so we do not include these methane rates in Table 1.

Measured field fluxes, F_field, as presented in the literature vary over many orders of magnitude for the same gas species either within a given study or among different studies. We must therefore take an average of the literature reported F_field values and we choose to take the geometric mean of the maximum F_field values reported in each study. We choose to use the maximum of the field fluxes for a given study because the maximum represents the ecology with the maximum number of gas-producing organisms in an environment where they are producing gas with maximal efficiency, and a minimum density of non-producing organisms and gas-consuming organisms. The huge variation in measured F_field is due to different growth conditions, different nutrient and energy supply, and different diffusion rates. It is important to note that the biomass of bioflux-producing organisms in the field is rarely measured. Because the field fluxes are measured from an ecosystem with a range of organisms other than the bioflux-producing organisms, in some cases the biosignature gas of interest is consumed before it reaches the atmosphere. To take an average of all of the maximum field fluxes from different studies for a given organism, we use the geometric mean (of the maximum).

The geometric mean is the appropriate average of concentrations of processes limited by energy. There is a log relationship between concentration and the energy needed to drive a reaction:

$$\begin{equation} \Delta G = {-}RT \ln (K), \end{equation} \tag{ 1 }$$

where G is the Gibbs free energy, R is the universal gas constant, T is temperature, and K is the equilibrium constant. To properly compare a set of concentrations produced by metabolism requiring energy, the logs of the concentrations are appropriate. For R_lab just as for F_field, we take the geometric mean of the maxima of each study. We choose the maximum observed rate because it represents the closest approximation to the case where the organisms are dependent on the gas-generating reaction for the majority of their energy.

The bioflux produced by laboratory cultures is also relevant for exoplanet biomass calculations, in addition to the above described field fluxes. We call the lab-measured metabolic by-product production rate per unit mass R_lab, in units of mole g⁻¹ s⁻¹. The R_lab values of a variety of biosignature gases are listed in Table 2. R_lab is used for validation of the biomass models and as input into one of the biomass models (see Section 3.3). The R_lab measurements are an important complement to field measurements as they are made on pure cultures of known mass, unlike the mixed culture of unknown mass in the field. A summary of different flux definitions is provided in Table 3.

Table 3. Definition of Fluxes

Flux	Definition	Units
${\mathcal {F}}_{\rm global}$	Global	Tg yr−1
	flux
Fsource	Field or	mole m−2 s−1
	biosignature flux
Rlab	Lab culture	mole g−1 s−1
	flux
$P_{m_e}$	Minimal maintenance	kJ g−1 s−1
	energy rate

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The lab production rates R_lab vary by several orders of magnitude. The variation in lab production rates is in part due to differences in the organisms studied in the lab, but mainly due to different laboratory conditions, especially growth conditions (nutrient concentration, temperature, and other environmental factors such as whether the organisms are stressed by stirring or shaking, non-natural light levels or spectra, or the presence or absence of trace chemicals such as metal ions). For R_lab for biological reactions based on energy extraction from the environment (defined as Type I biosignature gases; see Section 2.1), we again use the geometric mean as an average quantity of R_lab, because the energy released is related to the log of the concentration of the reactants and products (see above). For biological reactions that do not extract energy from the environment (defined as Type III biosignature gases; see Section 2.3), we use the maximum value of R_lab. Their production rate is determined by the ecology of the organism. Ecological factors include the chemical environment of the species and the presence of other species, which are rarely mimicked accurately in the laboratory. As a result laboratory production is likely to be very substantially lower than that in the wild. We therefore take the maximum flux found in the laboratory measurement of Type III biosignature gas production as being the nearest approximation to the natural flux capacity.

We summarize terrestrial biomass surface densities for later reference as to what is a reasonable biomass surface density. For our exoplanet biomass model use and validation, we require an understanding of the range of biomass surface densities on Earth. Based on life on Earth, a summary overview is that a biomass surface density of 10 g m⁻² is sensible, 100 g m⁻² is plausible, and 5000 g m⁻² is possible. Real-world situations are nearly always limited by energy, bulk nutrients (carbon, nitrogen), trace nutrients (iron, etc.), or all three.

We distinguish active biomass from inactive biomass. Active biomass is the mass of organisms metabolizing at a sufficiently high rate to grow (see ahead to the discussion on the microbial minimal maintenance energy consumption rate in Section 3.1.2). Most terrestrial environments contain an excess of material that is biologically derived but is not actively metabolizing. For example, the mass of organic material in soil is 10–100 times greater than the mass of actively metabolizing microorganisms (e.g., Anderson & Domsch 1989; Insam & Domsch 1988). Some of this organic material is dormant organisms but most is the remains of dead organisms (bacteria, fungi, and plants). In the following paragraphs, we are concerned solely with the surface density of active biomass—the biomass actively generating by-product gases.

We now turn to some specific examples of biomass surface densities on Earth.

Photosynthesizing marine microorganisms are the dominant life over the majority of the surface area of Earth. Their biomass is limited by phosphate, nitrogen, iron, and other micronutrients (because there is no "soil" in the surface of the deep ocean from which to extract micronutrients), and reaches 5–10 g m⁻² on the ocean surface (Ishizaka et al. 1994; Karl et al. 1991; Mitchell et al. 1991). Adding nutrients can boost the photosynthesizing marine microorganism surface density to 50 g m⁻² or more (Bishop et al. 2002; Buesseler et al. 2004; Boyd et al. 2000).

The biomass surface densities for ocean life described above are all in about the top 10 m of water, i.e., the well-mixed surface zone. Nearly all of the active ocean biomass is in the top layers of the ocean, both photosynthetic organisms and their predators. The above ocean biomass estimates do not include the biomass in the deep ocean, where light does not penetrate. Deep-living organisms must gain their energy either from the small amount of biological material that falls from the photosynthetic layer above, or from rare geochemical energy sources, such as ocean ridge or mantle hot-spot volcanic sites. While deep heterotrophs and hot-spot geotrophs are of great conceptual importance in our understanding of the range of environments in which life can exist, their contribution to the total active biomass of the Earth is not dominant.

Microbial biofilms are limited by nutrients, energy, and space. Films on seashores, in rivers, in acid mine drainage have a huge range of organism surface densities ranging from 0.1 g m⁻² to 10 g m⁻² (MacLulich 1987; Lawrence et al. 1991; Neu & Lawrence 1997; Gitelson et al. 2000). Densities of 1000 g m⁻² or more can be achieved if very high density of nutrients are provided, as, for example, in agricultural waste water (Gitelson et al. 2000).

The mass of actively metabolizing microorganisms in soil is approximately⁶ 100–200 g m⁻² (Olsen & Bakken 1987; Anderson & Domsch 1989). Energy-generating nutrients are probably limiting in this case: if unlimited energy-generating substrates are provided to fungi, as occurs, for example, in commercial mushroom farming, densities of >20,000 g m⁻² can be reached routinely (Shen et al. 2002).

Actively metabolizing land plant tissue has surface densities varying from 0 to over 5000 g m⁻², depending on the availability of energy and nutrients. Densities of 5000–10,000 g m⁻² of active biomass are achieved in environments where sunlight provides unlimited energy and nutrients are provided in excess, for example, in modern agriculture settings (Brereton 1971; Hamilton & Bernier 1975). Densities of 100 g m⁻² are more typical of productive grasslands.

We do not include trees or forests in our biomass density comparisons. While forests are visually very obvious, high-density accumulations of organic carbon, nearly all of that carbon is relatively metabolic inactive. Wood (formally, secondary xylem) acts as a passive mechanical support for trees and a conduit for transport of water and nutrients between the metabolically active leaves and root surfaces. Wood produces negligible amounts of metabolic product on its own. As most of a tree is wood, it is an inappropriate comparison for active microbial or algal biomass. Nevertheless, for comparison, tree biomass densities of ∼6.0 × 10⁴ g m⁻², of which 1%–5% represents actively metabolizing green matter, are common in mature temperate forests (Whittaker 1966).

We do not include the deep rock biosphere in our estimates of biomass density, as (as far as is known today) crustal subsurface life has minimal direct effect on the atmosphere. In the last decade, organisms have been found in deep crustal rocks that use geochemical sources of energy for growth. The amount of this ecology is unknown—some suggest that there is as much life in the crust as on its surface (Gold 1992). However, crustal life's direct impact on the atmosphere is not obvious. Subsurface life had remained undiscovered for so long because it does not impinge on the surface with gases, soluble molecules, or other obvious indicators that the subsurface organisms are present. The subsurface organisms can only be found by drilling into the rocks. A review of a number of studies of microbial communities found in deep drill rock samples (Pedersen 1993), shows that there are 10²–10⁴ microorganisms g⁻¹ of rock. Most studies look at bore-hole water. Typically water from deep (>1 km) bore-holes contains 10³–10⁵ organisms ml⁻¹, and the water probably makes up 2%–4% of the rock by mass (i.e., organism density in the total rock is around 10–10³ cells g⁻¹). Actual biomass surface densities will depend on how thick the inhabited rock layer is. Any extrapolation of these figures to the possible deep rock microbial community elsewhere on Earth, let alone on an exoplanet, must be speculative.

Closing with a total biomass on Earth estimate, the total amount of carbon on Earth as in cellular carbon in prokaryotes is estimated as 3.5–5.5 × 10¹⁴ kg (Whitman et al. 1998; Lipp et al. 2008).

The main goal of this paper is the presentation of a biomass model estimate that ties biomass surface density to a given biosignature gas surface source flux. The motivating rationale is that with a biomass estimate, biosignature gas source fluxes can be free parameters in model predictions, by giving a physical plausibility check in terms of reasonable biomass. The new approach enables consideration of a wide variety of both gas species and their atmospheric concentration to be considered in biosignature model predictions. In the future when biosignature gases are finally detected in exoplanet atmospheres, the biomass model estimate framework can be used for interpretation.

We argue that in order to explore the full range of potential exoplanet biosignature gases, the biosignature gas source flux should be a fundamental starting point for whether or not a biosignature gas will accumulate in an exoplanet atmosphere to levels that will be detectable remotely with future space telescopes. Instead, and until now, biosignature gas fluxes are always adopted as those found on Earth or slight deviations thereof (see Section 1.1 for references), and could not be considered as a free parameter because there is no first principles theoretical methodology for determining the biosignature gas source fluxes. In lieu of a first principles approach, we present model estimates which depend on both the amount of biomass and the rate of biosignature gas production per unit biomass. See Figure 1.

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Our proposed approach for biosignature gas studies is to

• 1.  
  calculate the amount of biosignature gas required to be present at "detectable" levels in an exoplanet atmosphere from a theoretical spectrum (we define a detection metric in Section 4.3);
• 2.  
  determine the gas source flux necessary to produce the atmospheric biosignature gas in the required atmospheric concentration; the biosignature gas atmospheric concentration is a function not only of the gas surface source flux, but also of other atmospheric and surface sources and sinks (Section 4.1);
• 3.  
  estimate the biomass that could produce the necessary biosignature gas source flux (Section 3);
• 4.  
  consider whether the estimated biomass surface density is physically plausible, by comparison to maximum terrestrial biomass surface density values (Section 1.3) and total plausible surface biofluxes (Section 1.2).

We begin in Section 2 with a categorization of biosignature gases into three classes, needed for the respective biomass model estimates presented in Section 3. In Section 4, we describe our atmosphere and photochemistry models used to determine both the required biosignature gas concentration for theoretical detection and the lifetimes of biosignature gases that are produced at the planet surface. In Section 5, we present our results followed by a discussion in Section 6 and a summary in Section 7.

We define Type I biosignatures as the by-product gases produced from metabolic reactions that capture energy from environmental redox chemical potential energy gradients. Terrestrial microbes can capture this potential energy also described as in the form of chemical disequilibria (we also favor the term "dark energy"). Specifically, chemotrophic organisms couple energetically favorable pairs of oxidation and reduction half-reactions. The disequilibria can involve either completely inorganic compounds or can make use of organic matter. In fact the only clear limitations upon the types of reactions used are that they have a negative Gibbs free energy, and that life can make the reactions occur faster than the rate of non-biological reactions. In other words, Earth-based metabolic pathways exploit chemical energy potential gradients in the form of chemical reactions that are thermodynamically favorable but kinetically inhibited (see, e.g., Madigan et al. 2003 for more details).

The canonical Type I biosignature gas discussed for exoplanets is CH₄ produced from methanogenesis (e.g., Des Marais et al. 2002 and references therein). Methanogens at the sea floor can use H₂ (released from rocks by hot water emitted from deep sea hydrothermal vents (serpentinization)) to reduce CO₂ (available from atmospheric CO₂ that has dissolved in the ocean and mixed to the bottom) resulting in CH₄ and H₂O,

$$\begin{equation} {\rm H_2 + CO_2 \rightarrow CH_4 + H_2O}. \end{equation} \tag{ 2 }$$

Methanogens also use molecules other than H₂ as reductants (including organic molecules). For a description of volatile Type I biosignature gases produced by Earth-based microbes (including H₂, CO₂, N₂, N₂O, NO, NO₂, H₂S, SO₂, and H₂O), see the review by Seager et al. (2012).

On Earth many microbes extract energy from chemical energy gradients using the abundant atmospheric O₂ for aerobic oxidation,

$$\begin{equation} {\rm X + O_2 \rightarrow oxidized X }. \end{equation} \tag{ 3 }$$

For example, H₂O is generated from H₂, CO₂ from organics, SO₂ or SO$_4^{2-}$ from H₂S, rust from iron sulfide (FeS), NO$_2^{-}$ and NO$_3^{-}$ from NH₃, etc.

Turning to an exoplanet with a H-rich atmosphere, the abundant reductant is now atmospheric H₂ such that

$$\begin{equation} {\rm H_2 + X \rightarrow reduced X }. \end{equation} \tag{ 4 }$$

The oxidant must come from the interior. In other words, for chemical potential energy gradients to exist on a planet with a H-rich atmosphere, the planetary crust must (in part) be oxidized in order to enable a redox couple with the reduced atmosphere. The by-product is always a reduced gas, because in a reducing environment H-rich compounds are the available reductants. Hence, H₂S is expected from SO₂, CH₄ from CO or CO₂, etc. To be more specific, oxidants would include gases, such as CO₂ and SO₂:

$$\begin{equation} {\rm H_2 + oxidant \rightarrow CH_4 or NH_3 or H_2O}. \end{equation} \tag{ 5 }$$

The by-product gases are typically those already present in thermodynamical equilibrium. Life only has the same gases to work with as atmospheric chemistry does.

False positives⁷ for redox by-product gases are almost always a problem because nature has the same source gases to work with as life does. Furthermore, while in one environment a given redox reaction will be kinetically inhibited and thus proceed only when activated by life's enzymes, in another environment with the right conditions (temperature, pressure, concentration, and acidity), the same reaction might proceed spontaneously. Methane, for example, is produced geologically and emitted from mid-ocean floor ridges. Only a reduced gas that has accumulated to significant, unexpected levels, because the gas has a very short atmospheric lifetime, would be a candidate biosignature gas in an oxidized environment. Alternatively, the presence of reduced biosignature gases (such as CH₄) in an oxidized atmosphere will stand out as candidate biosignature gases (Lederberg 1965; Lovelock 1965); but compare the comments in Section 1 about the potential simultaneous observability of reduced and oxidized gases.

We define Type II biosignatures as by-product gases produced by the metabolic reactions for biomass building. On Earth these are reactions that capture environmental carbon (and to a lesser extent other elements) in biomass. Type II biosignature reactions are energy-consuming, and on Earth the energy comes from sunlight via photosynthesis. On Earth photosynthesis captures carbon for biomass building,

$$\begin{equation} {\rm H_2O + CO_2 \rightarrow CH_2O +O_2}, \end{equation} \tag{ 6 }$$

where CH₂O represents sugars. O₂ is Earth's most robust biosignature gas because it is very hard to conceive of geochemical processes that would generate a high partial pressure of oxygen in an atmosphere with CO₂ in it at Earth's atmospheric temperature, making the probability that oxygen is a "false positive" signal very low (Selsis et al. 2002; Segura et al. 2007; Hu et al. 2012). It is, however, easy to explain why life produces oxygen in an oxidized environment. In order to build biomass in an oxidized environment, where carbon is tied up as carbonates or CO₂, living organisms have to generate a highly oxidized by-product in order to reduce CO₂ to biomass. The most plausible oxidized species is molecular oxygen itself. For more subtleties about why building biomass in an oxidizing environment results in a Type II biosignature gas that is more oxidized than the equilibrium atmospheric components, see the detailed discussion in Bains & Seager (2012).

Other potential-oxidized Type II biosignature gases might include volatiles that are oxidized forms of nitrogen (nitrogen oxides) or halogens (molecular halogens, halogen oxides, or halates; see Haas 2010 regarding chloride photosynthesis), all other common elements that could form volatile chemicals are completely oxidized in Earth's surface environment. The oxidized forms of nitrogen or halogens are less likely Type II biosignature gases than oxygen itself, as they are all more reactive (and hence damaging to life) than molecular oxygen, require more energy to generate from environmental chemicals, or both.

On a planet with a reduced atmosphere, we can generally state

$$\begin{eqnarray} &&{\rm H_2O + CH_4 \rightarrow CH_2O + H_2}, \end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray} &&{\rm CO_2 + H_2O + NH_3 \rightarrow CH_2O.N + H_2}, \end{eqnarray} \tag{ 8 }$$

etc. Here, the right-hand side has CH₂O as an approximate storage molecule. Because H₂ is the by-product gas—already abundant in an H-rich atmosphere—there are no useful Type II by-product candidate biosignature gases. For further discussion on biosignature gases in a H₂-rich atmosphere see Seager et al. (2013).

We define Type III biosignatures as chemicals produced by life for reasons other than energy capture or the construction of the basic components of life. Type III biosignature gases have much more chemical variety as compared to Type I or Type II biosignature gases because they are not the products of reactions that are executed for their thermodynamic effect out of chemicals that exist in the environment. Rather, Type III biosignature gases have a wide variety of functions, including defense against the environment or against other organisms, signaling, or internal physiological control. Like Type II biosignature gases, energy is required to generate Type III biosignature gases.

There are a wide range of Type III biosignatures, including sulfur compounds (e.g., DMS, OCS, CS₂; see Domagal-Goldman et al. 2011), hydrocarbons, halogenated compounds (e.g., CH₃Cl; see Segura et al. 2005, CH₃Br), and a variety of volatile organic carbon chemicals (including isoprene and terpenoids). These products are sometimes called the products of secondary metabolism. See Seager et al. (2012) for a summary.

The most interesting aspect of secondary metabolism gas by-products as a biosignature class is the much more diverse range of molecules than produced by gas products from energy extraction (the Type I biosignature gases). Just as importantly, Type III biosignatures are not as prone to confusion by abiotic false positives as Type I biosignatures. As specialized chemicals, most are not naturally occurring in the atmosphere. Because they require energy and specific catalysis to be produced, Type III biosignature gases are unlikely to be made geologically in substantial amounts, and so are unlikely to be present in the absence of life. In general, the more complicated a molecule is (i.e., the more atoms it has) and the further from fully oxidized or reduced the molecule is, the less are produced by geological sources as compared to more simple molecules. For example, volcanoes produce large quantities of CO₂, somewhat smaller amounts of CH₄, small amounts of OCS, trace amounts of CH₃SH, and none of isoprene. The downside to Type III biosignatures is that because they are usually such specialized compounds they typically are produced in small quantities that do not accumulate to levels detectable by remote sensing.

Type III biosignatures are not directly tied to the environment and therefore could be produced by life on any exoplanet.

Biosignature gases can be transformed into other chemical species abiotically. The resulting product might also not be natural occurring in a planet's atmosphere and therefore also a sign of life. We call these abiotically altered products "bioindicators" and consider them a separate subclass of each of the above three types of biosignature gases.

O₃ is a canonical bioindicator derived from the Type II biosignature O₂ (Leger et al. 1993). O₃ is a photochemical product of O₂ (governed by the Chapman cycle; Chapman 1930). As a nonlinear indicator of O₂, O₃ can be a more sensitive test of the presence of O₂ under low atmospheric O₂ conditions (Leger et al. 1993). Other bioindicators that have been described in the literature include ethane (a hydrocarbon compound) from biogenic sulfur gases (Domagal-Goldman et al. 2011) and hazes generated from CH₄ (Haqq-Misra et al. 2008).

3.1.1. Type I Biomass Model Derivation

The biomass surface density for Type I biosignatures can be estimated by conservation of energy. We may equate the required energy rate for organism survival to the energy generation rate from an energy-yielding reaction. The organism survival energy requirements come from an empirical measurement of so-called minimal maintenance energy rate that depends only on temperature (Tijhuis et al. 1993). We describe the minimal maintenance energy rate, $P_{m_e}$, in units of kJ g⁻¹ s⁻¹ (i.e., power per unit mass)⁸ later in this section. The energy yield rate comes from the Gibbs free energy of the energy-yielding reaction times the rate at which a group of organisms processes the reaction. The Gibbs free energy of the reaction is denoted by ΔG, in units of kJ mole⁻¹. The metabolic by-product gas production rate per unit mass is described by R in units of mole g⁻¹ s⁻¹. The conservation of energy per unit mass and time is then described by

$$\begin{equation} P_{m_e} = \Delta G R. \end{equation} \tag{ 9 }$$

The equation tells us that under the assumption that the energy yield ΔG is used only for maintenance, the by-product gas production rate per unit mass R can be constrained if $P_{m_e}$ is known. The by-product gas production rate is what we have been calling the biosignature gas surface flux.

The biomass surface density is the parameter of interest and so we break down R into a biomass surface density Σ_B and a biosignature gas source flux F_source

$$\begin{equation} R = \frac{F_{\rm source}}{\Sigma _B}, \end{equation} \tag{ 10 }$$

where Σ_B is the biomass surface density in g m⁻². The biosignature gas source flux F_source (in units of mole m⁻² s⁻¹) describes the surface flux emitted as the metabolic by-product and is also used as an input in a computer model of an exoplanet atmosphere. An important point for exoplanet atmospheres is that F_source cannot be directly converted into a detectable gas concentration that makes up a spectral feature—any source flux coming out of a planet surface is usually modified by atmospheric chemical reactions including photochemical processes. In atmosphere modeling, a photochemistry model is needed to translate the source flux into the amount of gas that accumulates in an exoplanet atmosphere. (False positives in the form of geologically produced source fluxes must be also be considered; see Section 6.5.)

The biomass estimate follows from Equations (9) and (10),

$$\begin{equation} \Sigma _B \simeq \Delta G \left[ \frac{F_{\rm source}}{ P_{m_e}} \right]\!{.} \end{equation} \tag{ 11 }$$

The free parameter in this biomass estimate equation is the biosignature gas source flux F_source, because the Gibbs free energy is known and minimal maintenance energy rate is empirically adopted (Section 3.1.2). A caveat is that both ΔG and $P_{m_e}$ depend on temperature.

Σ_B is an apparent minimum biomass surface density estimate because F_source may be weakened to a net biosignature gas surface flux if some of the gas is consumed by other organisms. See Section 6.3 for a discussion.

We review the point that ΔG depends on gas concentration. The energy available to do work depends on the concentration of both the reactants and products via

$$\begin{equation} \Delta G= \Delta G_0 +RT \ln (Q_t). \end{equation} \tag{ 12 }$$

Here, ΔG₀ is the "standard free energy" of the system (Equation (1)), i.e., the free energy available when all the reactants are in their standard state, one molar concentration (for solutes) or one atmosphere pressure (for gases). R in this context is the universal gas constant and T is temperature. The reaction quotient Q_t is defined as

$$\begin{equation} Q_t = \frac{[A]^n [B]^m}{[X]^o[Y]^p}, \end{equation} \tag{ 13 }$$

for the reaction

$$\begin{equation} oX + pY \rightarrow nA + mB, \end{equation} \tag{ 14 }$$

where, e.g., [X] is the concentration or partial pressure of species X. In general, care must be taken for the Type I biomass calculations described in this paper as relates to the appropriate ΔG. Most of our ΔG are taken from Amend & Shock (2001).

The biosignature gas source flux, F_source, can now be used as a free parameter in exoplanet model atmosphere calculations, whereby, again, the purpose of the biomass estimate from Equation (11) is to ensure the biomass surface density underlying the source flux is physically reasonable.

3.1.2. The Minimal Maintenance Energy Consumption Rate, $P_{m_e}$

We now turn to discuss the microbial minimal maintenance energy consumption rate, $P_{m_e}$, in more detail. Although $P_{m_e}$ is not yet a familiar quantity in exoplanets research, it is both measured empirically and tied to thermodynamics. $P_{m_e}$ is a fundamental energy flux central to the biomass estimate. $P_{m_e}$ is the minimal amount of energy an organism needs per unit time to survive in an active state (i.e., a state in which the organism is ready to grow). An empirical relation has been identified by Tijhuis et al. (1993) that follows an Arrhenius law

$$\begin{equation} P_{m_e} = A \exp \left[ \frac{-E_A}{RT} \right]. \end{equation} \tag{ 15 }$$

Here, E_A = 6.94 × 10⁴ J mol⁻¹ is the activation energy, R = 8.314 J mol⁻¹ K⁻¹ is the universal gas constant, and T in units of kelvin is the temperature. The constant A is 3.9 × 10⁷ kJ g⁻¹ s⁻¹ for aerobic growth and 2.2 × 10⁷ kJ g⁻¹ s⁻¹ for anaerobic growth (Tijhuis et al. 1993). Here, per g refers to per gram of wet weight of the organism. Note that we have explicitly converted from Tijuis' $P_{m_e}$ units of kJ (mole C)⁻¹ yr⁻¹ in bacterial cells to kJ g⁻¹ s⁻¹ per organism by dividing the $P_{m_e}$ values by a factor of 60 (molecular weight of carbon (=12) × the ratio of dry weight to carbon (=2) × the ratio of wet weight to dry weight in bacteria (=2.5)).

The $P_{m_e}$ maintenance energy rate equation (Equation (15)) is species independent (Tijhuis et al. 1993) and also applicable for different microbial culture systems (Harder 1997). The equation is not intended to be very precise, the confidence intervals are 41% and 32% for aerobic and anaerobic growth, respectively (Tijhuis et al. 1993).

$P_{m_e}$ as measured is not strictly a minimal energy requirement. $P_{m_e}$ is in fact the minimal energy needed for a bacterial cell to keep going under conditions under which it is capable of growth. The $P_{m_e}$ is measured during growth, and is extrapolated to growth =0. This extrapolated $P_{m_e}$ is nevertheless not the same as "maintenance energy" for non-growing cells. Growing cells have a variety of energy-required mechanisms "turned on" which non-growing cells will turn off to save energy, such as the machinery to make proteins, break down cell walls, and so on. $P_{m_e}$ as a maintenance energy rate therefore separates out the baseline energy components from the energy needed to actually build biomass. $P_{m_e}$ is therefore the minimal energy needed to maintain active biomass.⁹ See Hoehler (2004) for a more detailed review of the different types of "maintenance energy" and their relationship to organism growth.

The $P_{m_e}$ (Equation (15)) is an Arrhenius equation and it is natural to ask why the microbial maintenance energy rate follows Arrhenius' law. Organisms use energy for repair and replacement of damaged molecular components. Molecular damage is caused by non-specific chemical attack on the components of the cell by water, oxygen, and other reactive small molecules. The rate of such reactions is no different than other chemical reactions—well described by an Arrhenius equation. In aggregate, therefore, the overall rate of breakdown of the macromolecular components of the cell is expected to follow Arrhenius' law. Arrhenius' law describes chemical reaction rates (indeed any thermally activated process) and has two reaction-specific parameters A and E_A. For two stable molecules to react, chemical bonds need to be broken. E_A, the activation energy of a reaction, represents the energy needed to break the chemical bonds. In uncatalyzed reactions, E_A comes from the thermal energy of the two reacting molecules, which itself follows from the Boltzmann velocity distribution. The probability that any two colliding molecules will have a combined energy greater than E_A is exp [ − E_A/RT]. The parameter A is an efficiency factor that takes into account that molecules have to be correctly oriented in order to react.

3.1.3. Type I Biomass Model Validation

Tests of the biomass model for Type I biosignature gases aim to both validate the model and understand the intended range of model accuracy. Because our end goal is to estimate whether the flux of gas necessary to generate a spectral signature is plausible, we aim only for an order of magnitude estimate of the biomass that is producing the biosignature gas of interest.

The first test is to check our basic assumption of conservation of energy in Equation (9) that the maintenance energy rate ($P_{m_e}$) is approximately equal to the redox energy yield rate (R_labΔG), via lab-measured rate values. We consider the biosignature gases and corresponding reactions described below and compare the maintenance energy rate to the redox energy yield rate, along with the values for R_lab, ΔG, and $P_{m_e}$ at the temperature, T, considered (each of these three quantities are temperature-sensitive). To validate using Equation (9), we have averaged the validation results from different literature studies. In other words, we used the appropriate concentration, pH, and temperature for the ΔG and the appropriate temperature for $P_{m_e}$ with the validation result shown in the last column in Table 4. To provide overview values for each individual parameter, Table 4 also shows averaged values for each of R_lab and ΔG.

Table 4. Type I Biomass Model Validation for Select Biosignature Gases

Gas	Rlab	ΔG	T	$P_{m_e}$	Approx. $\frac{R_{\rm lab} \Delta G}{P_{m_e}}$	$\frac{R_{\rm lab} \Delta G}{P_{m_e}}$
	(mole (g−1 s−1))	(kJ mole−1)	(K)	(kJ (g−1 s−1))
N2O	3.36 × 10−8	443.7	302	...	...	...
NO	5.36 × 10−9	355.9	302	...	...	...
N2O/NO	8.73 × 10−8	...	302	2.2 × 10−5	3.2	0.62
H2S a	8.17 × 10−5	27.2	338	4.2 × 10−4	5.3	5.2
H2S b	6.57 × 10−3	13.4	374	4.8 × 10−3	19	19
H2S c	1.13 × 10−6	31.8	308	3.8 × 10−5	0.95	4.8
CH4	4.7 × 10−5	191.8	338	4.2 × 10−4	21	21

Notes. The maintenance energy production rate $P_{m_e}$ should be comparable to the lab production rate fluxes times the free energy R_labΔG. Averaged values for each literature study are given for R_lab, Δ_G, and $P_{m_e}$ (T is within a few degrees for each row), with the approximate validation using these averages given in Column 6. The actual validation given in Column 7 is an average of individual values (not shown) of R_lab, Δ_G, and $P_{m_e}$. The biosignature gas-producing reactions are listed in the text but can be summarized as N₂O: produced via ammonia oxidation, H₂S a and b: sulfur reduction with H₂, H₂S c: S₂O₃ disproportionation to H₂S, and CH₄: produced via methanogenesis (see the text in Section 3.1.3) for details.

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We consider four different Type I biosignature gas-generating reactions. These reactions are selected because they involve the reaction of geochemically available starting materials, have well-characterized microbial chemistry, and for which sufficient F_field and R_lab measurements are available.

The first reaction is ammonia oxidation to nitrogen oxides, described by

$$\begin{eqnarray} &&{\rm 2 NH_4^+ + 2 O_2 \rightarrow N_2O + 3 H_2O + 2H^+} \\ &&\nonumber {\rm 4 NH_4^+ + 5 O_2 \rightarrow 4 NO + 6 H_2O + 4H^+}. \end{eqnarray} \tag{ 16 }$$

We note that the oxidation of ammonia is only a relevant route for production of N₂O in an environment containing molecular oxygen. In both laboratory systems and real ecosystems, organisms oxidize ammonia to N₂O and to NO at the same time, the ratio depending on oxygen availability and other environmental factors. To validate our estimates of gas flux based on energy requirements, we therefore have to account for an organism's production of N₂O and NO, as the production of both of these gases contributes materially to the organism's energy budget. For ammonia oxidation, we summed the R_labΔG for NO and N₂O generation for each experiment and calculated the geometric mean of those summed values.

Our second, third, and fourth validation examples are for H₂S, a gas produced by many biological reactions. As examples, we choose the reduction of elemental sulfur (at two different temperatures),

$$\begin{equation} {\rm H_2 + S \rightarrow H_2S}, \end{equation} \tag{ 17 }$$

and the disproportionation of thiosulfate,

$$\begin{equation} {\rm S_2O_3^{2-} + H_2O \rightarrow HSO_4^{2-} + H_2S}. \end{equation} \tag{ 18 }$$

These two reactions can use geochemically produced substrates, and hence are not dependent on pre-existing biomass.

We choose as a fifth example methanogenesis, via the reduction of CO₂ by H₂ to produce CH₄. Methanogenesis is a key energy-capturing reaction in hydrothermal environments, and a reaction which relies only on geochemical inputs,

$$\begin{equation} {\rm CO_2 + 4H_2 \rightarrow 2H_2O + CH_4}. \end{equation} \tag{ 19 }$$

Methanogenesis is discussed at length in Sections 5.2 and 5.3.

The validation results—that the lab-based redox energy yield rate compares to the maintenance energy rate within an order of magnitude—are shown in Table 4 (rightmost column). The results show a reasonable confirmation of our application of the minimal maintenance energy concept to biosignature gas production rates to within about an order of magnitude with one exception. An order of magnitude is expected because of uncertainties in the individual factors: $P_{m_e}$ a factor of two, the gas flux typically a factor of two, and the biomass measurement and conversion values a factor of two.

We pause to discuss the relevance of validating the $P_{m_e}$ equation against lab production rates, given that Tijhuis et al. (1993) already used laboratory measurements in the original paper. The Tijhuis et al. (1993) equation for $P_{m_e}$ (Equation (15)) was developed from studies in which all the inputs and outputs from energy metabolism were completely characterized, so that the energy balance of the organisms could be calculated exactly. The organisms' growth rate was also controlled, so that the energy consumption at zero growth ($P_{m_e}$) could be inferred directly from the data. In our application we wish to infer the biomass from a single measure of gas output, from organisms whose rate of growth is not known. We therefore needed to validate that such an extrapolation of the application of the $P_{m_e}$ concept is valid.

Based on the lab and $P_{m_e}$ comparison in Table 4, the rate of production of gas in growing cultures of organism in the laboratory is higher than that predicted by the $P_{m_e}$ calculations. This is expected. $P_{m_e}$ is the minimal maintenance energy—the energy needed to maintain the cell in a state ready to grow. Actual growth requires additional energy to assemble cell components. This extra energy demand in turn requires that the cell produce more Type I metabolic waste products per unit mass than is expected from the $P_{m_e}$ calculations. The amount of the excess will depend on specifics of the growth conditions (e.g., what nutrients are supplied to the organisms), the organisms growth rate, and specifics of its metabolism. Thus, Table 4 is consistent with our model, showing that organisms use at least the $P_{m_e}$ of energy in cultures capable of active growth.

Now we comment more specifically on the actual validation numbers in Table 4. Two of the test validation results are too high, at a factor of 20 when they should be close to unity. Based on this high value and reasons described further below, the Type I biomass model should only be used for temperatures below ∼343 K, because the Tijhuis et al. (1993) $P_{m_e}$ equation was derived from measurements taken between 283 and 338 K (with one measurement at 343 K). Both of the anomalously high values in Table 4 are for cultures grown at the upper end of this temperature range. It is possible that at such extreme temperatures organisms require more energy for stress and damage response than predicted from culture at lower temperature. We note that the deviation of $P_{m_e}$ as compared to ΔGR_lab may also be reflected in the temperature dependencies: $P_{m_e}$ follows an exponential with T, whereas ΔG changes linearly with T (Equation (1)).

As a second test of the Type I biomass model, we check the biomass estimate equation (11), specifically that the quantity of interest, the biomass surface density (Σ_B) is reasonable based on the field fluxes, and ΔG and $P_{m_e}$. In other words, for this second test, we ask if the surface biomass (estimated via Equation (11)) is reasonable by comparison with Earth-based biomass surface densities for the microbial redox energy equation and environment in question. For the N₂O and H₂S examples given above, we find biomass surface densities are below 0.0024 g m⁻², as shown in Table 5, well within a plausible biomass surface density (Section 1.3).

Table 5. Type I Biomass Model Validation for Biomass Surface Density for Select Biosignature Gases

Gas	$P_{m_e}$	ΔG	T	Ffield	ΣB
	(kJ (g−1 s−1))	(kJ mole−1)	(K)	(mole (m−2 s−1))	(g m−2)
N2O/NO	4.1 × 10−5	−472.0	303	5.22 × 10−9	2.4 × 10−2
H2S a	1.1 × 10−3	−46.7	338	2.08 × 10−10	9.3 × 10−6
H2S b	1.1 × 10−2	−48.3	373	2.08 × 10−10	9.4 × 10−7
H2S c	9.5 × 10−5	−23.9	307	2.08 × 10−10	5.1 × 10−5

Notes. The biomass surface density is computed by the Type I biomass model equation (11) using the geometric means of the maximum values of the field fluxes F_field. The biomass surface density should be reasonable as compared to terrestrial values described in Section 1.3.

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We did not validate CH₄ for surface biomass density because maximum local field fluxes of methane are not meaningful for comparison with other gas fluxes in our analysis. Extremely high CH₄ fluxes can be generated from anaerobic biomass breakdown (fermentation), but these represent the rapid breakdown on biomass that has been accumulated over much wider areas and over substantial time. As an extreme example, sewage processing plants can generate substantial methane, but only because they collect their biomass from an entire city. This flux does not therefore represent a process that could be scaled up to cover a planet.

We also did not validate the biosignature gas NH₃ because no natural terrestrial environment emits detectable amounts of ammonia on a global scale. NH₃ is sometimes generated by the breakdown of biomass, especially protein-rich biomass or nitrogen-rich excretion products, but NH₃ represents a valuable source of nitrogen, which is taken up rapidly by life. Because ammonia is very soluble in water, any residual NH₃ not taken up by life remains dissolved in water and does not generate any significant amount of NH₃ gas in the atmosphere.

We conclude this subsection by summarizing that the Type I biomass model is a useful estimate to about an order of magnitude. This is validated from our use of the minimum maintenance energy $P_{m_e}$ as compared to lab flux values (ΔGR_lab). We also showed that a reasonable biomass surface density is derived using the field flux values in the main Type I biomass equation (Equation (11)).

We do not propose a biomass model for Type II biosignature gases and here we explain why. Type II biosignature gases are produced as a result of biomass building. Once the biomass is built, there is no further Type II biosignature gas produced, to a reasonable approximation.

If one wanted to estimate a Type II biosignature gas flux, one would have to estimate the turnover rate of the biomass, which itself depends on seasonality, burial rates, predation, fire clearance, and many other factors. If a turnover rate, Tr, could be determined, then the flux of a Type II biosignature gas would be Tr × s, where s is the stoichiometrically determined amount of biosignature gas needed to generate a gram of biomass. For plants, for example (∼80% water, ∼20% dry weight; of that dry weight 45% is carbon), the stoichiometry of carbon fixation is

$$\begin{equation} {\rm CO_2 + H_2O \rightarrow CH_2O + O_2}, \end{equation} \tag{ 20 }$$

(in other words, one mole of carbon fixed gives one mole of oxygen released), and so s = 5.6 × 10⁻³ moles O₂ g⁻¹ wet weight of plant.

For our present purposes, in the absence of any good framework for estimating exoplanet Tr, we omit biomass models for Type II biosignature gases.

Type III biosignature gases have no physically based biomass model because Type III biosignatures are not linked to the growth or maintenance of the producing organism. Because the amount of biosignature gas produced is arbitrary from the point of view of its overall metabolism, there can be no quantitative biomass model for Type III biosignature gases.

We therefore instead construct a biomass estimate from a framework based on terrestrial Type III biosignature gas fluxes. While tying the biomass estimate to the specifics of terrestrial metabolism is unsatisfactory, it is still more general than the conventional adoption of Earth-like environmental flux rates which assume both terrestrial metabolism and terrestrial ecology. With our Type III biomass estimate approach, we can scale the biosignature gas source flux to different biomass densities that are not achieved on Earth.

3.3.1. Type III Biomass Estimate

In lieu of a quantitative, physical biomass model, we adopt a comparative approach for a biomass estimate. We use the biosignature source fluxes and production rates of Type III metabolites of Earth-based organisms.

We estimate the biomass surface density by taking the biosignature gas source flux F_source (in units of mole m⁻² s⁻¹) divided by the mean gas production rate in the lab R_lab (in units of mole g⁻¹ s⁻¹), as in Equation (10),

$$\begin{equation} \Sigma _B \simeq \frac{F_{\rm source}}{R_{\rm lab}}. \end{equation} \tag{ 21 }$$

Recall that the source flux is measured in the field on Earth (and in that context called F_field) but assumed or calculated for exoplanet biosignature gas detectability models (and called F_source). See Table 1 for a list of select Type III field fluxes and Table 2 for a list of select Type III lab rates. As described in Section 1.2, we take the geometric mean of the maximum for the Type III R_lab rates F_field values from different studies.

The caveat of the Type III biomass estimate explicitly assumes that the range of R for life on exoplanets is similar to that for life in Earth's lab environment.

3.3.2. Type III Biomass Estimate Validation

We now turn to a validity check of the Type III biomass estimate. To validate, we compare the flux rates of Type III biosignature gases observed in the field (F_field) with the production rate of Type III gases from laboratory culture (R_lab) of pure organisms. The field rates give a flux per unit area, and the laboratory rates give a flux rate per unit mass. Also, the lab rates are from single species, whereas the field rates are from an ecology. We wish to confirm that comparison of the two predicts a physically plausible biomass per unit area to explain the field flux. We use the values for F_field and R_lab as given in Table 6.

Table 6. Type III Biomass Estimate Validation

Molecule	Ffield	Rlab	$\Sigma _B = \frac{F_{\rm field}}{R_{\rm lab}}$
CH3Cl	2.90 × 10−12	6.17 × 10−11	0.0047
COS	1.68 × 10−11	2.70 × 10−14	620
CS2	3.96 × 10−12	2.61 × 10−14	150
DMS	5.83 × 10−12	3.64 × 10−07	1.6 × 10−5
Isoprene	8.38 × 10−9	9.00 × 10−10	9.3

Notes. The biomass surface density, Σ_B as generated from the Type III biomass in Equation (21). Here, F_field are Earth values—the geometric mean of the maximum fluxes from values reported in the literature, taken from Table 1. R_lab are Earth lab values, the maximum fluxes from literature studies, and are taken from Table 2.

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Most of the Type III biomass surface density values (as shown in Table 6) are well within the values of biomass density seen in natural ecosystems (Section 1.3). We can therefore say that using laboratory fluxes is a reasonable way to approximately estimate the biomass necessary to generate biosignature gas fluxes. We emphasize approximate, because the biomass densities are somewhat high for Type III organism biomass densities.

The biomass surface density validation for COS is somewhat large at 622 g m⁻². The problem with COS is that it is both given off and absorbed by ecosystems, often by the same ecosystem at different times. The net field flux may therefore be poorly defined, perhaps representing the release of stored gas. In addition, COS is usually only produced by organisms in response to attack by other organisms such that COS is produced in large quantities in soils but produced in much smaller quantities in lab cultures. The same argument applies to CS₂ and also gives rise to a somewhat large biomass. In any case, COS and CS₂ are examples of how the Type III biomass model based on scaling is approximate only.

The biomass surface density validation for DMS is much lower than the other Type III biomass estimates in Table 6. All of the molecules in the table except DMS are produced at a cost to the organism for carbon and energy in order to perform specific signaling or defense functions. DMS, in contrast, is a product of the consumption of DMSP. DMSP is produced in response to stress and then is broken down enzymatically to DMS by zooplankton. In the lab, DMSP is often fed to the phytoplankton at a level unavailable in the natural environment, and the phytoplankton consume the DMSP at a very high rate likely leading to the high lab DMS production rates, and hence the low biomass surface density estimate.

We aim to calculate the source flux F_source or in photochemistry model jargon, the production rate P of a gas species of interest. The production rate is tied to the loss rate L and the steady-state gas concentration [A], via

$$\begin{equation} P = L[A]. \end{equation} \tag{ 22 }$$

The source flux is described by

$$\begin{equation} F_{\rm source} = \int _z P(z) + \Phi _{\rm dep}, \end{equation} \tag{ 23 }$$

where z is altitude and Φ_dep is the deposition flux described later below.

The derivation of the production rate (source flux) equation is as follows. In steady state,

$$\begin{equation} \frac{d[A]}{dt} = P - L[A] = 0, \end{equation} \tag{ 24 }$$

where [A] is the number density of species A (in units of molecule m⁻³), P is the production rate of species A (in units of molecule m⁻³ s⁻¹), and L is the loss rate of species A in (in units of s⁻¹). By rearranging Equation (24), we have P = L[A]. We also note that the loss rate is often described by its inverse, the lifetime of an atmospheric gas

$$\begin{equation} t = \frac{1}{L}. \end{equation} \tag{ 25 }$$

The loss rate can be described in more detail. The loss rate can be due to reactions with other species B, as in

$$\begin{equation} L[A] = K_{AB}[A][B], \end{equation} \tag{ 26 }$$

where K_AB is the second-order reaction rate in units of m³ molecule⁻¹ s⁻¹. Values of K_AB are presented in Table 7 for gases studied in this paper. The loss rate can also be due to photochemical dissociation of species A, as in

$$\begin{equation} L[A] = J[A] = \int _{\lambda } q_{\lambda } I_{\lambda } \exp ^{-\tau _\lambda } \sigma _{\lambda }[A]d\lambda, \end{equation} \tag{ 27 }$$

where J is the photodissociation loss rate, q_λ is the quantum yield, I_λ is the stellar intensity, $\exp ^{-\tau _\lambda }$ is the attenuation by optical depth τ_λ, σ is the photodissociation cross section of the species A, and λ is wavelength. Photodissociation is most relevant high in the atmosphere typically above mbar levels to which stellar UV radiation can penetrate from above.

Gases can be lost from the atmosphere by deposition to the ground. This loss is at the surface only (and numerically is treated as a lower boundary condition), in contrast to the photochemical loss rate reactions which take place throughout the upper atmosphere. Dry deposition is deposition onto a surface (either solid land or liquid water oceans) and wet deposition is deposition into water (rain) droplets (Seinfeld & Pandis 2000).

The deposition velocity at the planetary surface can be described by

$$\begin{equation} \Phi _{\rm dep} = nv_d, \end{equation} \tag{ 28 }$$

where Φ is the molecular loss flux at the surface due to dry deposition, n is the number density (in units of molecules m⁻³) at the surface of the species under consideration, and v_d is the dry deposition velocity (in units of m s⁻¹). The wet deposition is relevant for water-soluble gases and is not usually described as a velocity but as a process that occurs throughout the layer where water condenses (on Earth the troposphere) (Hu et al. 2012). Where photochemical reactions are slow, the deposition rate (the rate of loss to the ground) can control the atmospheric concentration of gas. Surface deposition consists of two processes: transfer of a gas between the atmosphere and the surface and removal of the gas from the surface. The rate of transfer from the atmosphere to the surface is proportional to the concentration difference between the atmosphere and the surface. Thus, once transferred to the surface, the gas has to be chemically removed, or the surface will saturate with gas, there will be no more transfer—the deposition rate will be zero. The values of wet and dry deposition velocities can be measured on Earth (e.g., Sehmel 1980), but the wet and dry deposition rates for various gases are highly variable and therefore averages tend to be used in models.

Caution must be taken, however, in applying Earth-based averages to exoplanets. The chemistry that removes many of Earth's atmospheric gases at the surface, such as methane, ammonia, OCS, and methyl chloride from Earth's atmosphere are biochemical, not geochemical. Life actively consumes these gases. So deposition rates on exoplanets may be very different from those in the terrestrial atmosphere. We discuss this in more detail in the context of CH₄ and NH₃ in Sections 5.2 and 5.1, respectively. In summary, caution should be taken when extrapolating the Earth-measured values to planetary applications. Notably, if the surface is saturated with a specific molecule, the surface uptake of the molecule may be reduced to zero.

The production rate are written in terms of the two different loss rates (and considering Φ_dep as a surface boundary condition),

$$\begin{equation} P = [A](J + K_{AB}[B]). \end{equation} \tag{ 29 }$$

The production rate is here assumed to be from biological sources, but when considering false positives, the geological source should also be considered.

For biosignature gases that are minor chemical perturbers in the atmosphere, the biosignature lifetime can be estimated based on the dominant loss rate via Equation (26). The simplified example for one species A gets more complicated for the case where there are several terms in the loss rate and when the production rate also includes other chemical reactions, and this is where the photochemistry model calculation is required. The steady-state concentration [B] is unknown and calculating [B] is one reason why a full photochemical model is needed to go beyond estimates.

The full photochemical model is presented in Hu et al. (2012). The photochemical code computes a steady-state chemical composition of an exoplanetary atmosphere. The system can be described by a set of time-dependent continuity equations, one equation for each species at each altitude. Each equation describes chemical production, chemical loss, eddy diffusion and molecular diffusion (contributing to production or loss), sedimentation (for aerosols only), emission and dry deposition at the lower boundary, and diffusion-limited atmospheric escape for light species at the upper boundary. The code includes 111 species, 824 chemical reactions, and 71 photochemical reactions.

Starting from an initial state, the system is numerically evolved to the steady state in which the number densities no longer change. Because the removal timescales of different species are very different, an implicit inverse Euler method is employed for numerical time stepping. The generic model computes chemical and photochemical reactions among all O, H, N, C, and S species, and formation of sulfur and sulfate aerosols. The numerical code is designed to have the flexibility of choosing a subset of species and reactions in the computation. The code therefore has the ability to treat both oxidized and reduced conditions, by allowing selection of "fast species." For the chemical and photochemical reactions, we use the most up-to-date reaction rate data from both the National Institute of Standards and Technology (NIST) database (http://kinetics.nist.gov) and the JPL publication (Sander et al. 2011). UV and visible radiation in the atmosphere is computed by the δ-Eddington two-stream method with molecular absorption, Rayleigh scattering, and aerosol Mie scattering contributing to the optical depth.

We developed the photochemistry model from the ground up from basic chemical and physical principles and using both established and improved computer algorithms (see Hu et al. 2012 and references therein). We tested and validated the model by reproducing the atmospheric composition of Earth and Mars. For one of the tests, we simulated Earth's atmosphere starting from an 80% N₂ and 20% O₂ atmosphere and temperature profile of the US Standard Atmosphere 1976. Important atmospheric minor species are emitted from the lower boundary by standard amounts (e.g., reported by the IPCC), including CO, CH₄, NH₃, N₂O, NO_x, SO₂, OCS, H₂S, and H₂SO₄. We validate that vertical profiles predicted by our photochemical model of O₃, N₂O, CH₄, H₂O, OH, HO₂, NO, NO₂, and HNO₃ match with various balloon and satellite observations, and the surface mixing ratios of OH, O₃, SO₂, and H₂S also match with standard tropospheric values (see Hu et al. 2012, for details). As another test, we reproduce the chemical composition of the current Mars atmosphere, in agreement with measured compositions (e.g., Krasnopolsky 2006) and previous one-dimensional photochemistry model results (e.g., Zahnle et al. 2008). In particular, the code correctly illustrates the effect of HO_x catalytic chemistry that stabilizes Mars' CO₂-dominated atmosphere, predicting an O₂ mixing ratio of ∼1500 ppb.

We compute synthetic spectra of the modeled exoplanet's atmospheric transmission and thermal emission with a line-by-line radiative transfer code (Seager et al. 2000; Miller-Ricci et al. 2009; Madhusudhan & Seager 2009). Opacities are based on molecular absorption with cross sections computed based from the HITRAN 2008 database (Rothman et al. 2009), molecular collision-induced absorption when necessary (e.g., Borysow 2002), Rayleigh scattering, and aerosol extinction computed based on Mie theory. The transmission is computed for each wavelength by integrating the optical depth along the limb path, as outlined in, e.g., Seager & Sasselov (2000). The planetary thermal emission is computed by integrating the radiative transfer equation without scattering for each wavelength (e.g., Seager 2010).

The temperature profiles for the simulated atmospheres are self-consistently computed with the gray-atmosphere assumption (Guillot 2010). Opacities of CO₂, H₂O, CH₄, O₂, O₃, OH, CH₂O, H₂O₂, HO₂, H₂S, SO₂, CO, and NH₃ are considered, if they are needed in the atmospheric scenario under consideration. For the gray-atmosphere temperature profiles, we have assumed isotropic irradiation, and applied the convection correction if the radiative temperature gradient is steeper than the adiabatic lapse rate. We have assumed for all cases the planetary Bond albedo is 0.3; in other words, we have implicitly assumed a cloud coverage of 50% (assuming cloud albedo to be 0.6). For consistency, we account for the effect of clouds on the planetary reflection and thermal emission spectrum by a weighted average of spectra with and without clouds as in Des Marais et al. (2002).

We emphasize that the precise temperature–pressure structure of the atmosphere is less important than photochemistry for a first-order description of biosignature gases.

We now describe our metric for a "detection" that leads to a required biosignature gas concentration. For now, the detection has to be a theoretical exercise using synthetic data. We determine the required biosignature gas concentration based on a spectral feature detection with an SNR = 10. Specifically, we describe the SNR of the spectral feature as the difference between the flux in the absorption feature and the flux in the surrounding continuum (on either side of the feature) taking into account the uncertainties on the data,

$$\begin{equation} {\rm SNR} = \frac{\left| F_{{\rm out}} - F_{{\rm in}} \right|}{\sqrt{\sigma ^2_{F_{{\rm out}}} + \sigma ^2_{F_{{\rm in}}}}}, \end{equation} \tag{ 30 }$$

where $F_{{\rm in}} \pm \sigma _{F_{{\rm in}}}$ is the flux density inside the absorption feature and $F_{{\rm out}} \pm \sigma _{F_{{\rm out}}}$ is the flux density in the surrounding continuum, and σ is the uncertainty on the measurement.

The uncertainties of the in-feature flux and continuum flux are calculated for a limiting scenario: an Earth-sized planet orbiting a noiseless Sun-like star at 10 pc observed (via direct imaging) with a 6 m diameter telescope mirror operating within 50% of the shot noise limit and a quantum efficiency of 20%. The integration time is assumed to be 20 hr. We note that collecting area, observational integration time, and source distance are interchangeable depending on the time-dependent observational systematics.

We propose ammonia, NH₃, as a biosignature gas in a H₂-rich exoplanet atmosphere. NH₃ is a good biosignature gas candidate for any thin H₂-rich exoplanet atmosphere because of its short lifetime and lack of production sources. NH₃ as a biosignature gas is a new idea, and one that is specific to a non-Earth-like planet. On Earth, NH₃ is not a useful biosignature gas because, as a highly valuable molecule for life that is produced in only small quantities, it is rapidly depleted by life and unable to accumulate in the atmosphere.

The biosignature idea is that ammonia would be produced from hydrogen and nitrogen, in an atmosphere rich in both,

$$\begin{equation} {\rm 3H_2 + N_2 \rightarrow 2 NH_3}. \end{equation} \tag{ 31 }$$

This is an exothermic reaction which could be used to capture energy. We propose that in a H₂-rich atmosphere, life can catalyze breaking of the N₂ triple bond and the H₂ bond to produce NH₃, and capture the energy released. In a H₂-rich environment, life could use the reduction of N₂ to capture energy—in contrast to life on Earth which solely fixes nitrogen in an energy-requiring process. Energy capture would yield an excess of ammonia over that needed by life to build biomass, and so the excess would accumulate in the atmosphere as a Type I biosignature gas.

A catalyst is required to synthesize ammonia from hydrogen and nitrogen gas because the reaction in Equation (31) does not occur spontaneously at temperatures below 1300 K, at which temperature the formation of ammonia is strongly thermodynamically disfavored. On Earth, the industrial production of NH₃ by the above reaction is called the Haber process: an iron catalyst is used at high pressure (150–250 bar) to allow the reaction to happen at 575–825 K at which temperature the formation of ammonia is thermodynamically favored (Haber 1913). The Haber process is the principal industrial method for producing ammonia.¹⁰ More efficient catalysts are known, which can catalyze the formation of ammonia from elemental nitrogen and hydrogen gases at 500 K and standard pressure (Yue et al. 2006; Avanier et al. 2007). Others catalyze the formation of ammonia from nitrogen gas and a proton (Yandulov & Schrock 2003; Shilov 2003; Weare et al. 2006) or from an activated nitrogen molecule and hydrogen gas (Nishibayashi et al. 1998), in water at room temperature and pressure. The final step of combining a room temperature nitrogen reduction catalyst with a room temperature hydrogen-splitting catalyst has not been achieved in the lab but is believed to be a realistic goal (Weare et al. 2006). Such a combined catalyst would make NH₃ from H₂ and N₂ and would generate energy (heat) from the reaction.

Life on Earth does not use the "Haber" reaction. This might be because the appropriate catalysts have not evolved. It might be because the rare environments in which H₂ is available provide other more easily accessible sources of energy (such as methanogenesis; Section 5.2). On Earth life inputs energy to break the N₂ triple bond, and the fixed nitrogen is a valuable resource representing an investment of energy and so is avidly taken up by other Earth life. Haber life using the Haber chemistry in an atmosphere with plenty of N₂ would produce generous amounts of NH₃, more than enough for the rest of life to use, enabling NH₃ to accumulate in the atmosphere as a biosignature gas.

To check the viability of NH₃ as a biosignature gas, we follow the steps listed in Section 3. For background, we consider a planet of Earth mass and size, a 290 K surface temperature and with a 1 bar atmosphere composed of 25% H₂ and 75% N₂ by volume, and including carbon species via a CO₂ emission flux from the planet's surface. NH₃ has significant opacity in the 10.3–10.8 μm band in a thermal emission spectrum. A mixing ratio of 0.1 ppm is radiatively significant for a 1 bar atmosphere in this band in a H₂–N₂ atmosphere (Figure 2) according to our detection metric (Section 4.3). We next determine the NH₃ surface source flux required for the gas to accumulate in the atmosphere to the 0.1 ppm concentration level. For this, we compute the photochemical equilibrium steady-state composition (results shown in Figure 3) with the ammonia surface source flux as a free parameter (Section 4.1). The dominant loss mechanism of NH₃ is due to photolysis (or reaction with OH; each process breaks the NH₃ bond) with some NH₃ eventually being converted to N₂. We adopt an NH₃ deposition velocity of 0 m s⁻¹, assuming that the surface is saturated in NH₃. (See below for a further discussion of deposition removal rate assumptions and related consequences.) The resulting NH₃ surface source flux is 5.0 × 10¹⁵ molecule m⁻² s⁻¹. We note that this planet has a column-averaged mixing ratio of 0.4 ppm of NH₃, and to meet a surface temperature of 290 K, the semimajor axis would be 1.1 AU. We also point out that NH₃ concentrates mostly in the lower atmosphere, and decreases very rapidly with altitude above 15 km (Figure 3) because of the high-altitude destruction rates. To compute ΔG we used T = 290 K, and reactant and product concentrations at the surface in terms of partial pressures of N₂ = 0.75, H₂ = 0.25, and NH₃ = 6.6 × 10⁻⁷.

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We next estimate the biomass surface density. Using the biomass equation (Equation (11)) with the NH₃ source flux of 5.0 × 10¹⁵ molecule m⁻² s⁻¹ (or 8.4 × 10⁻⁹ mole m⁻² s⁻¹), ΔG = 75.0 kJ mole⁻¹ at 300 K, and $P_{m_e} = 7.0 \times 10^{-6}$ kJ g⁻¹ s⁻¹, we find a biomass surface density of 8.9 × 10⁻² g m⁻². We therefore consider the NH₃ production flux to be viable in our Haber World scenario. The global annual biogenic NH₃ surface emission in the Haber World would be about 6700 Tg yr⁻¹. This is much higher than Earth's natural NH₃ emission at 10 Tg yr⁻¹ (Seinfeld & Pandis 2000). Comparing NH₃ production on the Haber World and on Earth, however, is not valid. We are postulating that production of NH₃ on the Haber World is a major source of metabolic energy for life. A better emission rate comparison is to the biosignature gas O₂ from Earth's principal energy metabolism, photosynthesis. Earth's global oxygen flux is 500 times larger than the Haber World's NH₃ surface emission, at about 2 × 10⁵ Tg yr⁻¹ (Friend et al. 2009).

Deposition rates require more description, because on Earth deposition is the dominant atmospheric removal process for NH₃, yet we argue the deposition rates to play a minor role for NH₃ atmospheric removal on the Haber World. On Earth, ammonia is taken up avidly by life in soil and in water. On our proposed Haber World, life is a net producer of ammonia, not a net consumer, and so water (as raindrops or ocean) and soil would saturate with ammonia. Wet and dry deposition rates would therefore be limited to chemical consumption, the rates of which would depend on specifics of the surface chemistry. We therefore assume that the deposition rates are much less than atmospheric loss rates and this is considered in the photochemical calculation. A larger deposition rate implies a larger NH₃ emission flux and therefore a larger biomass to maintain the biosignature. When deposition is the dominant removal process, the relation between the source flux and the steady-state mixing ratio of NH₃ is linear. A Haber World with Earth-like NH₃ deposition rates (10⁻³ m s⁻¹) requires a NH₃ source flux of about 3.0 × 10¹⁷ molecule m⁻² s⁻¹ and a surface emission flux 100 times higher than the zero-deposition rate case. The biomass is also 100 times higher, and at Σ_B ∼ 9 g m⁻² is still a reasonable value.

The molecule HCN can be considered a bioindicator gas in the specific situation where HCN is detectable but its formation components, NH₃ and CH₄ (or any other dominant carbon source, such as CO or CO₂) are not. More specifically, in a H₂-rich atmosphere, if NH₃ and CH₄ are emitted at comparable rates, HCN will be produced with little NH₃ and CH₄ remaining in the atmosphere above the convective layer (or above the first several scale heights from the surface; Hu et al. 2012). It can therefore be expected that if emissions of methane and ammonia are both elevated, the mixing ratio of HCN in the atmosphere can be as high as 1 ppmv and then become detectable via its prominent spectral feature at ∼3 μm. In other words, HCN can be an indicator of surface NH₃ emission, even if NH₃ itself is depleted and not detectable due to atmospheric photochemistry. The photochemical pathway of HCN under such conditions is described in detail in Hu et al. (2012). In general, in an atmosphere with enough NH₃ or N₂ and CH₄, the formation of HCN is inevitable in anoxic environments (Zahnle 1986). Also of potential interest, HCN is the second most common N-bearing species in the Haber World.

In terms of false positives for NH₃, the NH₃ biosignature gas concept is not changed in the massive atmosphere case with high surface pressure. As long as the surface conditions are suitable for liquid water, NH₃ will not be created by uncatalyzed chemical reactions. False positives may still exist such as chemical or biological breakdown of abiotic molecules. An additional false positive for NH₃ could be generated by non-life-compatible surface temperatures: at 820 K with surface iron, NH₃ could be generated by the conventional Haber process. These false positive statements hold for a rocky planet with a thin atmosphere; other cases such as planets with a massive atmosphere where NH₃ could be generated kinetically at extremely high pressures, or planets with icy interiors where NH₃ is outgassed during planetary evolution, have to be assessed on a case-by-case basis (see Seager et al. 2013).

In summary, we propose NH₃ as a biosignature gas on a planet with a N₂–H₂ composition. NH₃ should be photodissociated and therefore its presence would be indicative of biogenic production. We have nicknamed this planet "cold Haber World" because life would have to perform the Haber process chemistry using a highly efficient catalyst, low temperature to break both the N₂ triple bond and the H₂ bond, rather than the elevated temperature and relatively inefficient catalyst used in the industrial "hot" Haber process.

We revisit methane as a biosignature gas on early Earth to estimate the biomass surface density required for primary producers to generate a remotely detectable CH₄ concentration.

CH₄ has long been considered a prime biosignature gas for Earth-like exoplanets (Hitchcock & Lovelock 1967) and especially for early Earth analogs (Des Marais et al. 2002). An early Earth analog prevalence of CH₄ theory is motivated by the early faint young Sun paradox. A few billion years ago, the Sun was 20%–30% fainter than today, specifically with 26% lower luminosity 4 Gyr ago, based on asteroseismology-constrained stellar evolution models (Bahcall et al. 2001). Yet, there is no evidence that Earth was frozen over during that time. A reduced greenhouse gas is a good, viable explanation for keeping Earth warmed despite the much cooler Sun (Sagan & Mullen 1972). The greenhouse gas CH₄ is a favored greenhouse gas explanation (Kiehl & Dickinson 1987; Haqq-Misra et al. 2008). Methane at 1000 times today's atmospheric concentration would have been sufficient to keep the Earth warm (i.e., concentrations of 1600 ppmv instead of 1.6 ppmv) (Pavlov et al. 2000; Haqq-Misra et al. 2008, and references therein). Moreover, accumulation of atmospheric CH₄ to levels much higher than Earth's would have been possible in the anoxic environment of early Earth. CH₄ could have accumulated to 1000 ppmv levels in the weakly reducing early Earth atmosphere because the CH₄ loss rate was so much smaller, owing to the lack of O₂. In more detail, the dominant removal rate of methane in an oxidized atmosphere is due to reaction with atmospheric OH. OH is produced via photochemistry, from both O₃ (itself a photochemical by-product of O₂) and H₂O (Seinfeld & Pandis 2000).

To consider the biomass required on any methanogenesis world, we must work with surface fluxes generated only by primary production methanogenesis. Overlooked or unstated for early Earth in past work is that most of Earth's biogenic methane production today is from fermentation of biomass. This biomass available for fermentation is almost entirely produced via photosynthesis. For an early Earth analog, before the rise of oxygenic photosynthesis, there is likely no large reservoir of biomass for fermentation. We note that on early Earth itself, there should have been a small reservoir of biomass, from, for example, anoxic photosynthesis. For exoplanets, we want to consider biologically produced methane from an ecosystem that uses methanogenesis as a primary energy source. In such a methanogenesis world, there would be biomass for fermentation, but the amount of methane produced by fermentation would be minor compared to the amount of methane produced from energy capture.

The methanogens of interest are those that convert H₂ and CO₂ to CH₄ in the process of extracting energy from the environment. These methanogens do not require biomass to feed upon and today live in anoxic environments, including hydrothermal vents at the deep sea floor, subterranean environments, and hot springs.

The methanogens of interest produce CH₄ by using carbon from CO₂ from inorganic sources,

$$\begin{equation} {\rm H_2 + CO_2 \rightarrow CH_4 + H_2O}. \end{equation} \tag{ 32 }$$

At the deep-sea floor, H₂ is released from rocks by hot water emitted from hydrothermal vents (serpentinization). CO₂ is available dissolved in seawater. In other Earth environments, H₂ is also produced as a by-product of biological metabolism, and CO₂ is available as gas in air or dissolved in water. The metabolic by-products from methanogenesis are CH₄ and H₂O.

We now turn to the biomass estimate for CH₄ as the biosignature from a primary producing methanogenesis ecology on an early Earth analog exoplanet. We take early Earth (Earth-size, Earth-mass with a 1 bar atmosphere) to be an anoxic, N₂-dominated atmosphere with CO₂ mixing ratios of 1% and 20% (Ohmoto et al. 2004), the time period before the rise of oxygen (an Archaen atmosphere, 3.8–2.5 Gyr ago). For the planets to have surface temperatures of 290 K, they would be at 1.2 AU for the 1% CO₂ atmosphere and 1.3 AU for the 20% CO₂ atmosphere. Using our detection metric (Section 4.3), we find a detectable CH₄ mixing ratio to be 200 ppm in the 3.1–4 μm band. See Figure 4 for the chemical composition of the 1% CO₂ atmosphere.

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Although we consider the effect of clouds on weakening the spectral features in the exoplanet spectrum, we do not treat formation of hydrocarbons that have more than two carbon atoms. The formation of hydrocarbons that have more than two carbon atoms should only have minor impact on our estimate of required biomass, because the most abundant hydrocarbons that have more than two carbon atoms, C₃H₈, has still five orders of magnitude lower mixing ratio at the steady state than C₂H₆ in N₂ atmospheres (Pavlov et al. 2001). The formation of hydrocarbon haze (commonly hydrocarbons with more than five carbon atoms), a point we do not address in this paper, may impact the energy budget of the planet and therefore the surface temperature (Haqq-Misra et al. 2008).

A CH₄ source flux of 7.0 × 10¹⁴ molecules m⁻² s⁻¹ (1.2 × 10⁻⁹ mole m⁻² s⁻¹) and 5.0 × 10¹⁴ molecules m⁻² s⁻¹ (8.3 × 10⁻¹⁰ mole m⁻² s⁻¹) is required to reach the 200 ppm CH₄ concentration in the 1% and 20% CO₂ atmospheres, respectively. To compute the ΔG value, we used the reactant and product molecule concentrations at the surface in terms of partial pressures as follows. For the CO₂ case of 0.01, we used H₂ = 3.9 × 10⁻⁵, CH₄ = 2.2 × 10⁻⁴, H₂O = 0.01, and this results in a ΔG = 47.4 kJ mole⁻¹. In the CO₂ of 0.20 case, we used H₂ = 1 × 10⁻⁵, CH₄ = 2.5 × 10⁻⁴, and H₂O = 0.01, and this results in a ΔG = 41.2 kJ mole⁻¹.

Using the above values, together with $P_{m_e} = 7.0 \times 10^{-6}$ kJ g⁻¹ s⁻¹ for the minimal maintenance energy rate for anaerobic microbes at 290 K, the biomass estimate is 7.8 × 10⁻³ g m⁻³ and 4.9 × 10⁻³ g m⁻³, for the 1% and 20% CO₂ atmospheres, respectively, globally averaged values. This is a reasonable biomass as compared to terrestrial microbial biomass surface density values (Section 1.3). In this scenario, methanogenic organisms would dominate a biosphere where methanogenesis is the main energy source for life, just as on Earth photosynthetic organisms (including plants and water-based photosynthesizes) dominate the biosphere because photosynthesis is the dominant energy source for life.

For an early Earth analog "slime world," the critical question is whether H₂ would be a limiting input for methanogenesis on a planet with Earth-like atmospheric conditions (see Equation (32)). For the methanogenesis world, a global CH₄ flux of about 750 Tg yr⁻¹ is required to reach the detectability threshold (this global CH₄ flux is the value corresponding to the CH₄ production rate calculated above). To investigate, we look at fluxes of hydrogen gas from Earth's hydrothermal systems and levels of hydrogen gas in hydrothermal fluids. Fluxes of hydrogen from hydrothermal systems on Earth can be as high as 1.8% of the total gases (see, e.g., Gerlach 1980; Le Guern et al. 1982; Taran et al. 1991). If this flux of H₂ is extrapolated to the global fluxes by comparison with fluxes of H₂S and SO₂ (Halmer et al. 2002), it would imply global H₂ fluxes of between 0.8 and 1.6 Tg yr⁻¹.¹¹ If all of the hydrogen were used in methanogenesis that would result in 3.2–6.4 Tg yr⁻¹ methane.

If the H₂ needed to support the required rate of methanogenesis comes from volcanism alone—as in the case of modern Earth—a methanogenesis world with an Earth-like atmosphere, requires about 100 times more hydrogen flux outgassing than on present-day Earth. This high H₂ flux outgassing could be sustained by either a more reduced mantle (Holland 1984; Kasting et al. 1993), more serpentization, and/or more volcanism than on the present-day Earth.

The required large amounts of H₂ could be also produced from atmospheric photochemistry, in the absence of atmospheric oxygen, enabling a biochemical cycle to sustain surface methanogenesis. In our photochemistry code, atmospheric H₂ forms from photolysis of CH₄. The net accumulation of CH₄ results from the difference in production and loss of CH₄, being computed self-consistently with the appropriate mass balance. A form of this methanogenesis scenario was describe previously in Kharecha et al. (2005). In this biochemical cycle, a reasonable quantity of H₂ is required only at the onset of the evolution of methanogenesis.

We note that methane can reach high abundances through abiotic means especially if the mantle is reduced. More work is needed on false positives in the hope of finding a way to distinguish biotic and abiotic methane, or at least to assign a probability to the chance of methane being biotic.

We finish the early Earth methanogenesis scenario with an emphasis on the deposition velocity as a loss rate. For CH₄, we have considered a zero deposition velocity, with the concept that a slime world covered in methanogens has a CH₄-saturated surface. We also assume that this world has few CH₄-consuming organisms compared to the CH₄-producing organisms. In other words, the rationale is that on a methane slime world, living organisms are net producers of CH₄ at the surface and would not destroy CH₄—the surface would likely be saturated in CH₄ making the deposition rate zero. On Earth, CH₄ deposited to the surface is rapidly oxidized by life to CO₂, so deposition is efficient, although only a minor contribution to the CH₄ loss rate. If we treat the N₂–CO₂ atmosphere with an Earth-like CH₄ deposition rate (for CH₄ on Earth typically 10⁻⁶ m s⁻¹), then CH₄ is prevented from accumulating to 200 ppm, but instead is at a lower concentration, at values of 15 ppm. A deposition velocity could be non-zero due to life other than the methanogens consuming CH₄; but see the discussion in Section 6.1.

To summarize this subsection, we have revisited methane as a biosignature gas on early Earth. We have found the biomass surface density needed to sustain a detectable CH₄ biosignature gas from primary production is reasonable at ∼5 × 10⁻³ g m⁻². Although volcanism alone is unlikely to provide the amount of H₂ needed to sustain methanogenesis at the level required for CH₄ detection, an atmospheric photolysis of CH₄ can recycle the H₂ to provide sufficient flux.

As a second case study, we apply our biomass model to the methane flux on Mars. CH₄ has been detected in the atmosphere of Mars with three independent instruments (Formisano et al. 2004; Krasnopolsky et al. 2004; Mumma et al. 2009). The Martian CH₄ detection is difficult to reconcile with present understanding of the planet and some believe the ground-based CH₄ detection may be a result of observational artifacts (see the references in the summary review by Atreya et al. 2011). The Martian CH₄ may be the result of geochemical outgassing or atmospheric photochemistry (Bar-Nun & Dimitrov 2006). A more intriguing, if speculative CH₄ source, is Martian life (Krasnopolsky et al. 2004). In this subsection, we show that the minimum required biomass density is plausible for the measured CH₄ fluxes.

Averaged CH₄ levels are 5–30 ppbv in the spring and summer mid-latitudes on Mars, depending on location, local time of day, and season (Formisano et al. 2004; Geminale et al. 2008, 2011; Mumma et al. 2009). There are pronounced local hot spots for methane concentration, hence presumably for CH₄ production. Different CH₄ observational studies, however, find hot spots in different regions (e.g., compare Mumma et al. 2009; Geminale et al. 2011), so we use global averages for our case study. The photochemical loss rate for the 5–30 ppb average level of CH₄ is 1–2 × 10⁹ molecules m⁻² s⁻¹ (Wong et al. 2004; Krasnopolsky et al. 2004)

If Martian organisms were producing CH₄, they would be reducing atmospheric CO₂ with mantle-derived material, most plausibly H₂, so that the methane we observe would be the product of methanogenesis. We can calculate the free energy available from the reaction

$$\begin{equation} {\rm 4H_2 + CO_2 \rightarrow CH_4 + 2H_2O}, \end{equation} \tag{ 33 }$$

and hence estimate the biomass present in the soil that might account for the observed methane flux. The Gibbs free energy ΔG for methanogenesis under Martian daytime maximum temperature range (250–265 K) is calculated assuming the 15 ppb CH₄ surface flux, a likely surface hydrogen concentration of 15 ppm (Krasnopolsky & Feldman 2001), a CO₂ partial pressure of 0.95, and an H₂O partial pressure of 3 × 10⁻⁴. ΔG is 85.2–77.5 kJ mole⁻¹. $P_{m_e} \simeq 7 \times 10^{-8}$ and ≃ 5 × 10⁻⁷ for temperatures at 250 K and 265 K, respectively. Combined with the surface flux above the CH₄ hot spots of the 1–2 × 10⁹ molecules m⁻² s⁻¹ (Wong et al. 2004; Krasnopolsky et al. 2004), we find from Equation (11) surface biomass density of Σ_B ≃ 10⁻⁶–10⁻⁷. This a very small biomass surface density as compared to terrestrial biofilm values (Section 1.3), and hence the Martian CH₄ production by microbial life appears physically plausible.

The Martian surface is believed to be sterile, in part because the surface atmospheric pressure is incompatible with the existence of liquid water at any temperature and in part because the surface is unshielded from extremely destructive radiation from space (solar UV and X-rays and cosmic rays; Dartnell 2011). Water, if it exists near the surface, will be present as ice. Viking's finding of a complete lack of organic molecules in the top few centimeters of soil supports the sterility of the surface (Biemann et al. 1976, 1977). A few tens of centimeters of regolith would shield organisms from radiation (Pavlov et al. 2002). However, orbital radar suggests that water is frozen to a depth of several kilometers in most sites on Mars (reviewed in Kerr 2010), so Martian life must either be more deeply buried than current radar penetration, or be living in highly concentrated brines at depths of 1–3 km. The column-integrated density of ∼10⁻⁶–10⁻⁷ g m⁻² of biomass would therefore be present not as surface life but living in rock interstices. This density is well below that of the density of such rock-dwelling microbial communities on Earth (Pedersen 1993 and references therein).

In summary, we have applied our biomass model to the putative methane detections on Mars. We found that if the CH₄ is produced by methanogenesis only a very small biomass surface density is required, Σ_B ≃ 10⁻⁶–10⁻⁷ g m⁻². Martian methane could be generated by microorganisms living in subsurface rocks. Our model predicts that the amount of biomass needed to generate the proposed methane flux is plausible for a rock-based microbial community. By itself, a biomass surface density prediction does not rule out methanogenesis as the cause of the atmospheric CH₄.

The gas H₂S is generated by bacteria on Earth, and also by volcanism. The majority of Earth's H₂S emission is from life (Watts 2000). With our biosignature framework, we can calculate a consistent biosphere based on sulfur-metabolizing organisms and estimate how much biomass is required to generate a detectable amount of H₂S. Although detection of H₂S will be very difficult due to water vapor contamination of H₂S features, and just as seriously H₂S has a serious risk of false positive through volcanic production, the biomass estimate turns out to be reasonable.

H₂S would be very difficult to detect in a future exoplanet atmosphere spectrum, mostly because there are no spectral features that are not heavily contaminated by water vapor spectral features. In the UV, H₂S absorption features are mixed in with those of SO₂ and elemental sulfur, both of which are likely to be present in the atmosphere with H₂S (http://www.atmosphere.mpg.de/enid/2295/; for specific UV cross sections see the references in Hu et al. 2012). At visible wavelengths, there are no prominent spectral features. In the infrared (IR), at 30–80 μm, a huge amount of H₂S would be needed to differentiate from water vapor spectral features. Even so, the H₂S features may cause a quasi-continuum absorption lowering the thermal emission flux below a reasonable detection threshold. There might be a way to detect H₂S in a spectrum that spans UV to IR: it might be plausible to detect total sulfur via UV spectral characteristics, infer from this a relative absence of SO₂, and then infer from an IR signature that there was a significant flux of H₂S (or DMS) from the ground. This is implausibly demanding of instrumentation, but not in theory impossible.

H₂S is commonly regarded as a poor biosignature gas because it is released by volcanoes. In general, we consider an atmospheric gas a potential biosignature gas if it is present in such large quantities that, in the context of other atmospheric gases, has no likely geological origin.

We nonetheless now turn to explore H₂S as a biosignature gas based on its biomass estimate. On a highly reduced planet, organisms could gain energy from reducing sulfate to H₂S, but in this environment H₂S would likely be the dominant volcanic sulfur gas as well. On an exoplanet with a more oxidized crust and atmosphere, we can imagine an ecosystem of sulfur disproportionators as the primary producers.

Microorganisms can disproportionate sulfur compounds of intermediate oxidation state, including thiosulfate, sulfite, and elemental sulfur, into H₂S and sulfate (Finster 2008). H₂S would be released as a biosignature gas. For example, the sulfite reducers include microorganisms in the genus Desulfovibrio and Desulfocapsa that obtain energy from the disproportionation of sulfite (Kramer & Cypionka 1989). The equation of the disproportion of sulfite in the ocean is

$$\begin{equation} 4 {\rm HSO_3^{-} \rightarrow 3SO_4^{2-} + 2H^+ + H_2S}. \end{equation} \tag{ 34 }$$

Note that the accumulation of sulfite and sulfate in an ocean would make the ocean acidic, and at acidic pH levels, H₂S will exist in solution primarily as H₂S molecules, which will exchange readily with the atmosphere (unlike a neutral or basic ocean, where S(II) would exist as HS⁻ or S^{2 −} which are not volatile).

To continue to explore H₂S as a biosignature gas, in our biomass estimate framework, we take an Earth-size, Earth-mass planet with a 1 bar exoplanet atmosphere composed almost entirely of N₂ with a minor H₂O concentration (like Earth above the cold trap but much drier below the cold trap) and a small amount of CO₂ (1 ppm), assuming volcanic emission. We consider detection at IR wavelengths, where absorption of H₂S might only be detected when the planet has a relatively dry troposphere (10⁻⁶ mixing ratio throughout the troposphere), meaning that there will be reduced contamination of H₂S spectral features by water vapor. Even for an extremely high H₂S emission (3000 times Earth's volcanic emission) on a desiccated planet, we have estimated an H₂S concentration of 10 ppm for detection via thermal emission in the 45–55 μm range according to our detection metric (Section 4.3). The H₂S surface flux required is 3000 times Earth's volcanic emission (10¹⁷ molecules m⁻² s⁻¹). The SO₂ surface flux (used by the sulfur disproportionators) is scaled up accordingly (two times the H₂S surface flux). To compute the ΔG value, we used the reactant and product molecule concentrations at the surface in terms of partial pressures as follows: SO₂ = 2.9 × 10⁻⁷ and H₂S =9.4 × 10⁻⁶, and we assumed the ocean was saturated with sulfate (1.1 mole liter⁻¹) with an ocean pH of 3 (i.e., 10⁻³ mole). This results in a ΔG = 71.3 kJ mole⁻¹.

To summarize, using Equation (11) and the values $P_{m_e} = 7.04 \times 10^{-6}$ kJ g⁻¹ s⁻¹ at 290 K, F_source = 3.0 × 10¹⁷ molecule m⁻² s⁻¹ (or 5.0 × 10⁻⁷ mole m⁻² s⁻¹), and ΔG = −71.3 kJ mol⁻¹, we find a surface biomass density of about 5.1 g m⁻². The total flux produced on an Earth-sized exoplanet would be 4.0 × 10⁵ Tg yr⁻¹. This total flux is very high, on the order of 10⁵ times more than H₂S produced on Earth, and similar to the benchmark values for primary production of carbon on Earth.

A further challenge with H₂S as a biosignature (or even as a geosignature) has to do with atmospheric photochemistry. As soon as H₂S (or SO₂) is released into the atmosphere at an amount greater than 10–100 times Earth's current H₂S or SO₂ surface flux, a blanket of aerosols or condensates form. These aerosols or condensates are present at optically thick amounts, potentially masking any H₂S or SO₂ spectral features, depending on the particle size distribution.

As a side note we explain why we consider sulfur dioxide, SO₂, is a failed potential biosignature gas, even though it is a gas produced by life. SO₂ as a Type I biosignature would result from the oxidation of sulfur or sulfides, via the reaction

$$\begin{eqnarray} &&{\rm S_2^- + 3[O] + 2H^+ \rightarrow SO_2 + H_2O} \end{eqnarray} \tag{ 35 }$$

$$\begin{eqnarray} &&{\rm S + 2[O] \rightarrow SO_2}, \end{eqnarray} \tag{ 36 }$$

where [O] represents an oxidizing agent, such as Fe^{3 +} or O₂. The resulting SO₂ would almost certainly be dissolved in water as sulfite; in an oxidized environment further energy would be generated from oxidizing sulfite to sulfate

$$\begin{equation} {\rm SO_3^{2-} + [O] \rightarrow SO_4^{2-}}. \end{equation} \tag{ 37 }$$

So, if the environment is sufficiently oxidizing to allow energy generation from sulfide oxidation, the end product is likely to be sulfate, not SO₂. Furthermore, because SO₂ is geologically generated, it would be hard to distinguish from biogenic SO₂. If there are oxidants available for life (i.e., there are oxidants available for life to use to oxidize sulfides for energy), then the crust and upper mantle will also be oxidized, and SO₂ will be a major volcanic gas.

In summary, H₂S is a potential biosignature gas as seen from the view of a biomass estimate, in a reduced atmosphere where H₂S can accumulate. In general, H₂S is ruled out as detectable or identifiable as a biosignature gas because of its weak or H₂O-contaminated spectral features and because of geological false positives.

We now turn to the Type III biosignature gases, using methyl chloride CH₃Cl as the example. On Earth, CH₃Cl is thought to generated mostly by land soils (by plants; Keppler et al. 2005), changed from an earlier view that phytoplankton in the open ocean contributed most of Earth's CH₃Cl. On Earth, CH₃Cl has a global production rate of between 2 and 12 Tg yr⁻¹ (see Table 1, and references therein). Averaged over Earth's land mass, the CH₃Cl translates into a source flux of 3.2 × 10⁻¹² mole m⁻² s⁻¹. This value of source flux does not produce a detectable biosignature gas in the "Earth as an exoplanet spectrum," where CH₃Cl has a mixing ratio of 1 ppb. For an Earth-like atmosphere around a low-UV quiet M dwarf, CH₃Cl can accumulate up to 1 ppm (Segura et al. 2005).

For an Earth-like exoplanet atmosphere spectrum, CH₃Cl is a difficult biosignature gas to detect because of its overlap with other spectral features, notably O₃ or CO₂. As reported in Segura et al. (2005), the CH₃Cl spectral feature at 9.3–10.3 μm coincides with the O₃ 9.6 μm band, and would be difficult to identify, necessitating detection of CH₃Cl features at 13–15 μm or a weaker feature near 7 μm. Under the conditions of a UV-quiet M star with low OH concentration, Segura et al. (2005) have shown that CH₃Cl in an Earth-like atmosphere orbiting a quiet M dwarf can accumulate to 1 ppm. In an N₂ atmosphere with little CO₂, CH₃Cl would be easier to detect, but still difficult owing to even a tiny amount of atmospheric CO₂.

With our framework for biomass estimates, we ask the question, "what biomass surface density of CH₃Cl-producing life is required to generate a detectable CH₃Cl biosignature gas?" We answer the question for present-day Earth and for early-Earth conditions before the rise of atmospheric O₂. We take a planet of Earth's size and mass with an Earth-mass atmosphere. The temperature profiles are self-consistently computed with photochemistry, and the semimajor axis of the planet is adjusted so that the surface temperature is kept at about 300 K.

For a planet with the present-day Earth atmosphere concentration, our detection metric (Section 4.3) finds a 20 ppm mixing ratio at 13–14 μm on the short-wavelength wing of the 15 μm CO₂ band (note that in Earth's atmosphere, the CO₂ concentration is low enough not to fully saturate the 15 μm wing). The concentration of 20 ppm is 20,000 times more than Earth's current atmospheric concentration of CH₃Cl, a value of 0.001 ppm. See Figure 5.

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The Type III biomass equation scales linearly (Equation (21)), so for all other atmospheric conditions being equal to the present-day Earth, the biomass must therefore be 20,000 times higher than the present day. By adopting the scaling relationship, we also assume that the 20 ppm concentration of CH₃Cl is not enough to feed back on the dominant destructing molecule [OH] concentration or to significantly effect the temperature–pressure profile.

Is it reasonable to imagine a world with a planet biomass surface density of CH₃Cl-generating life 20,000 times higher than on Earth? If the conventional view that CH₃Cl is produced overwhelmingly by oceanic plankton is adopted, then densities of tens of kilograms of phytoplankton per m⁻² in the oceans would be required. If the more recent view that land plants are a major source of CH₃Cl, then a 20,000-fold increase in biomass requires all the planet's land be covered with plants at a density not even achieved in the most intensively farmed land in the most favorable conditions. Neither seem plausible. We can only escape from this conundrum if we assume that a much larger fraction of organisms on an exoplanet produce CH₃Cl, or they produce it at a much higher rate than organisms on Earth. We have no reason for making such assumptions.

We now turn back to Earth's past, prior to the oxidation of Earth's atmosphere, with solar-like EUV conditions, where the CO₂ concentration was thought to be as high as 1% to 20% by volume (Ohmoto et al. 2004). In an atmosphere with so much CO₂, CH₃Cl is much harder to detect than on present-day Earth because of overlap with the 15 μm CO₂ feature, the CH₃Cl feature at 10 μm must be considered. A CH₃Cl concentration of 1000 ppm would be needed (and barely detectable according to our detection metric), for either the 1% or 20% CO₂ atmosphere, requiring a surface biosignature gas source flux of 3.5 × 10¹⁹ m⁻² s⁻¹ (or 5.8 × 10⁻⁵ mole m⁻² s⁻¹). Although our photochemistry code does not yet self-consistently treat halogentated compounds, we computed this surface source flux by considering the loss rates: the source flux, F_source, is the production rate P integrated over an atmosphere column, and P is related to the loss rate L, (recall Section 4.1)

$$\begin{eqnarray} F_{\rm source} &=& \int _z P = \int _z {[\rm CH_3Cl]}(z) L(z) \nonumber \\ &=& \int _z {\rm [CH_3Cl]}(z) {\rm [OH]}(z) K_{\rm CH_3Cl,OH}(z), \end{eqnarray} \tag{ 38 }$$

where [OH] is the main reactive molecule that destroys CH₃Cl. The loss rate scales linearly with [OH], as long as the concentration of CH₃Cl does not affect [OH]. For values of reaction rate K, see Table 7.

The estimate of the surface biomass density required for a surface source flux of 3.5 × 10¹⁹ molecules m⁻² s⁻¹ can be found using the estimate for the Type III biosignature gases (Equation (21)). For CH₃Cl, we find Σ_B = 9.4 × 10⁵ g m⁻² higher than any reasonable biomass surface density. The uncertainties in the Type III biomass estimate, however, should be considered.

To summarize this subsection, Type III biosignature gases are not produced in large quantities on Earth because they are specialized chemicals, each produced by a small number of species. Furthermore, collisional destruction by OH is rapid. Type III biosignature gases have shown to be detectable in low-UV environments, which as a consequence have less OH. We have shown that in order to reach detectable levels on present-day Earth, we can scale up the biomass estimates based on the concentration of the atmospheric gas required for detection, although in the case of CH₃Cl this results in an implausible biomass surface density.

The biomass estimates are limited to an order of magnitude for Type I biosignatures, and about two orders of magnitude for Type III biosignature gases.

Estimates of the Type I biomass are dependent on $P_{m_e}$ whose constants are known to 40% 1σ (Tijhuis et al. 1993), and $P_{m_e}$ is very sensitively dependent on temperature, due to an exponential term (Equation (15)). Small changes in surface temperature estimates can have very large effects on $P_{m_e}$. Of equal importance is that chemical reaction rates also exponentially increase with temperature.¹² For the same change in temperature, the rate of destruction (and hence production) of a gas F_source, and the minimal maintenance energy rate $P_{m_e}$ have opposite, although not necessarily balanced, effects on our estimate of biomass, via the Type I biomass equation (11). The effect of temperature uncertainty needs to be further investigated. A more minor contribution to the inaccuracy of Type I biosignature gases is that the energy released in a reaction (captured ΔG) varies with pH, and reactant and product concentrations, none of which are known for exoplanet environments.

The Type III biomass estimate is uncertain because it is not constrained by thermodynamics. The accuracy-limiting assumption for the Type III biomass estimate is that exoplanet biosignature gas production rates are the same as those found in Earth's lab-based maximum production rates.

Unlike applied physics, we do not know everything about biology, we do not know everything about Earth, and we do not know everything about atmospheric chemistry. In other words, the model is not 100% accurate and we must live with uncertainty in the biomass estimates. The point is that the biomass estimate should be used to answer the question, "Is the proposed biosignature gas plausible?" and not for any kind of precise prediction of biomass surface densities.

A question arises as to the terracentricity of the biomass estimates, and whether or not we have interchanged the conventionally used Earth-based surface biofluxes with an Earth-based biomass model estimate.

For the Type I biosignature gases we argue no, because thermodynamics is universal. The Type I biosignature biomass model uses a prefactor A and an activation energy E_A for the minimum maintenance energy rate $P_{m_e}$ equation. These parameters are lab-measured values for Earth-based microbes. A critical question is to what extent are A and E_A specific to Earth life. A simple argument is that the particular repair mechanisms and molecular turnover involved in maintaining an organism are specific to Earth life, which is very unlikely to be exactly replicated on other worlds. There are stronger arguments, however, that the energy rate is more broadly applicable: $P_{m_e}$ follows Arrhenius' law, we think because the rate of molecular component damage (and hence repair rate) is no different than other chemical reactions—well described by an Arrhenius equation. E_A, the activation energy of a reaction, represents the energy needed to break chemical bonds during the chemical reaction. In uncatalyzed reactions, E_A comes from the thermal energy of the two reacting molecules, which itself follows from the Boltzmann velocity distribution. The probability that any two colliding molecules will have a combined energy greater than E_A is exp [ − E_A/RT]. The parameter A is an efficiency factor that takes into account that molecules have to be correctly oriented in order to react. Thus, the basic physics of the Arrhenius equation is general to all chemistry.

The argument for applying the Arrhenius equation to calculating $P_{m_e}$ starts with the point that terrestrial life is composed of many of the possible structures in CHON chemistry. The principal way that random chemical attack breaks those molecules down is through hydrolysis (attack by water) or oxidation (attack by oxygen) if oxygen is present. The A and E_A terms in the equation for $P_{m_e}$ represent those relevant to the breakage of the most fragile of metabolites (as more stable molecules will not need to be repaired). Although the specific chemicals in non-terrestrial metabolism could be quite different from those on Earth, the nature of the chemical bonds will be similar. In particular, non-terrestrial biochemistry will be made up of chemicals that are moderately stable at ambient temperature and pressure, but not too stable. Thus, the overall distribution of molecular stability in a non-terrestrial metabolism is likely to be similar to that in terrestrial metabolism, even if the chemical specifics differ. As a consequence, it is reasonable to propose that the rate of breakdown of those metabolites, and the rate at which energy is needed to repair them (i.e., $P_{m_e}$) will be of a similar order of magnitude as the rate of breakdown and energy requirement seen on Earth. Therefore, A and E_A are likely to be based on chemical principles and therefore similar to those calculated for Earth.

Turning to the terracentricity of the production rates for Type III biosignature gases, they are derived from lab measurements of each organism and are likely to be specific to those organisms. The rates may, however, be plausible indications of the Type III fluxes to be expected from non-terrestrial life because the gas production represents investment of energy and mass for a specialized biochemical function. The maximum flux rates used here represent the maximum investment that organisms make in these Type III gases, given essentially unlimited energy and nutrient resources in a lab environment. We speculate that it is unlikely that non-terrestrial life would be more wasteful of resources through making any Type III biosignature gas at rates orders of magnitude greater than those used in this study.

The biomass surface density limits we use as a reference point are based on Earth data, and so are terracentric. We believe that adopting Earth values is an acceptable approximation in our model, as what limits Earth life in environments with abundant nutrition is the physics of mass transfer, not the specifics of how Earth life evolved. This, however, should be validated by future research.

We do not argue the biosignature biomass model estimates are accurate; rather we emphasize the goal of the biomass model estimate is the nature of the order of magnitude for a first-order assessment of the plausibility of a given biosignature gas candidate.

A serious criticism against the biomass estimate is lack of an ecology context. An ecology will contain organisms that consume gases as well as produce them. Hence, the concern is that potential biosignature gases will be destroyed by life in the same ecosystem, rendering the biomass estimates invalid. Indeed, the biomass estimate must be a minimum biomass estimate because there is no guarantee that biosignature gas flux (F_source) is not being consumed by other organisms.

The biomass estimate model is intended as a check on the plausibility of a specific gas as a biosignature gas. It is not intended to be a prediction of the ecology of another world. If the biomass estimate is low, then we have confirmed that the gas is plausible as a biosignature, given the caveats presented in Sections 6.1 and 6.2 and discussed throughout this paper. In this low biomass estimate case, even if the planetary ecology has a mix of gas-producing and gas-consuming organisms, a net production of the gas from a moderate biomass is quite plausible. If the biomass estimate is too high, the gas is not a plausible biosignature gas in any ecology. For the intermediate case where a large but not unreasonable biomass is needed to generate a detectable biosignature, the decision on whether the gas is a plausible biosignature is more complicated, and will depend on the context: geochemistry, surface conditions, atmospheric composition, and other factors.

In the future when we have spectra with candidate biosignature gas detections, in most cases we will assign a probability and not a certainty to a biosignature gas candidate. The biomass estimate, in the context of an ecology, will be just one of the input factors to the probability assessment. We give an example here to sketch out other factors to consider, which also bear weight on the ecology. The example is the question, how would we interpret the detection of 500 ppm CH₃Cl in the atmosphere of an anoxic, Earth-like planet (well above the detectable amount according to our detection metric and assumed future telescope capabilities)? Our biomass model predicts that we would need a highly implausible surface biomass density to generate such an atmospheric concentration through metabolism. Volcanic chemistry on Earth produces traces of methyl chloride, but only as a tiny fraction of emitted gases, making a volcanic source seems also highly improbable. Conceivably, the CH₃Cl could be an industrial waste gas from a technological civilization, but in the absence of other signs of civilization this is also improbable. In this abstract sense, the conundrum of the intermediate biomass estimate has no solution, but the plausibility of a biosignature gas is still addressable through Bayesian statistics in principle, if the prior probabilities of the different assumptions about geochemical sources, biological sources, or technological sources can be estimated. Our biomass model provides a numerical approach to quantifying the assumptions made concerning the potential biological production of a biosignature gas. Further work will integrate this into a model of our confidence that the detection of the gas represents a detection of life.

In an atmosphere more massive than Earth's 1 bar atmosphere, the biomass surface density estimates could be different, depending on the biosignature gas loss rate mechanism. In an atmosphere where the photochemical loss rates dominate, the biosignature source flux and hence biomass is the same as for a less-massive atmosphere. In an atmosphere where the deposition rate is the dominant loss mechanism, the biosignature source flux and hence biomass surface density will scale linearly with planetary atmosphere mass. These conclusions are under the caveat that the surface pressure and temperature do not cause unusual chemistry (e.g., supercritical fluid or high chemical kinetic rates).

The biosignature source flux (i.e., production rate) is balanced by the loss rate, as described in Equation (22). Photochemical removal is only effective at and above the mbar pressure level in the atmosphere, because the UV radiation typically penetrates only down to the mbar level. The loss rate is therefore unaffected by how much atmosphere there is below the mbar pressure level: the mbar level can be "sitting on top of" a small atmosphere or a very large one. Hence, the loss rate is the same (all other factors being equal) regardless of the total mass of the atmosphere. The loss rate is balanced by the source flux and hence the source flux needed to maintain a given concentration of gas in an atmosphere is unaffected by the mass of the atmosphere (assuming that there is no new, non-photochemical loss of gas at much higher pressures). Thus, against loss from photochemistry, the surface biomass density required to maintain a given gas concentration is the same regardless of atmospheric mass for any planet of a given surface area.

Loss by deposition, in contrast to loss by photochemical removal, occurs at the planetary surface. The loss rate at the surface is proportional to the number density of the biosignature gas at the surface (see Equation (28)) The number density of any well-mixed species scales as the surface pressure for an ideal gas atmosphere in hydrostatic equilibrium. We can estimate the surface gas concentration n_ref by considering a uniformly mixed atmosphere and integrating over a vertical atmosphere column under hydrostatic equilibrium,

$$\begin{equation} \int _{p_0}^{p_{\rm ref}} dp = {-} \int _{0}^{z_{\rm ref}} g \rho dz, \end{equation} \tag{ 39 }$$

where p is pressure and g is surface gravity. Here, we integrate from p = 0, z = 0 at the top of the atmosphere down to a reference pressure p_ref at a reference altitude. Integrating the above equation, we have

$$\begin{equation} p_{\rm ref} = g m_{\rm atm}, \end{equation} \tag{ 40 }$$

where m_atm is the atmospheric mass in a vertical column of 1 m² cross-sectional area. We can therefore define n_atm by rewriting the column-integrated mass of the atmosphere in terms of number density and the mean molecular mass of the atmosphere μ_atmm_H (where μ is the mean molecular weight and m_H is the mass of the hydrogen atom,

$$\begin{equation} X_i n_{\rm ref} = X_i \frac{p_{\rm ref}}{kT} = \frac{g m_{\rm atm}}{kT}, \end{equation} \tag{ 41 }$$

where X_i is the mixing ratio of the gas under consideration.

We can now explain why, when surface deposition is the dominant gas loss mechanism, a larger biosignature surface density is required as an atmosphere mass scales up, even for a fixed atmospheric gas concentration. We see from Equation (41) that the gas number density at the surface scales with the surface pressure p_ref. The deposition velocity scales with the number density and hence surface pressure. With a higher loss rate that scales linearly with surface pressure, a higher source flux (production rate) is required to balance the loss rate. Because biomass scales linearly with source flux, a higher biomass surface density is required.

Type I biosignature gases are fraught with geologically produced false positives because geological processes have the same chemicals to work with as life does. The redox reaction chemical energy gradients exploited by life are thermodynamically favorable but kinetically inhibited. Enzymes are used by life to accelerate the reaction. We can be sure that a chemical reaction that is kinetically inhibited in one environment on Earth could proceed spontaneously somewhere else on the planet (in an environment with a favorable temperature, pressure, and reactant concentrations). Hence, Type I biosignature gases will almost always have a possible geological origin.

Typically astronomers assume that the biosignature gas must be produced in high enough quantities that it could not be confused with a geophysical false positive. But how high of a surface flux could be produced geologically? We plan to model the maximal geofluxes possible for planets of different characteristics (Stamenkovic & Seager, in preparation), with the end goal of assigning a probability to the dominant Type I biosignature gases (H₂S, CH₄, CO, CO₂, N₂O, NO, and NO₂) for being produced as biofluxes versus geofluxes. More progress might also be made with biogeochemical cycles and the whole atmosphere context via other atmospheric diagnostics.

False positives for O₂, the most obvious Type II biosignature gas in an oxidizing environment, are limited and can most likely be identified by other atmospheric diagnostics. For example, photodissociation of water vapor in a runaway greenhouse with H escaping to space could lead up to detectable O₂ levels. This situation could be identified by an atmosphere heavily saturated with water vapor. O₂ could also accumulate in a dry, CO₂-rich planet with weak geochemical sinks for O₂, a case which could be identified via weak H₂O features (Selsis et al. 2002; Segura et al. 2007).

Type III biosignature gases, in contrast to Type I biosignature gases, are less likely to have false positives. Type III biosignature gases are chemicals produced by life for reasons other than energy capture and are not usually naturally existing in the environment. As by-product gases of highly specialized physiological processes, the Type III biosignature gases tend to be larger or more complex molecules than Type I biosignature gases, and are not usually replicated by non-biological processes. In general, the more complicated a molecule is (i.e., the more atoms it has) and the further from fully oxidized or reduced the molecule is, the less are produced by geological sources as compared to more simple molecules. For example, volcanoes produce large quantities of CO₂, somewhat smaller amounts of CH₄, small amounts of OCS, trace amounts of CH₃SH, and none of isoprene. The downside to Type III biosignatures is that because they are usually such specialized compounds they typically are produced in small quantities that do not accumulate to levels detectable by remote sensing.

For Type III biosignature gases, we should therefore depart from requiring huge concentrations in the atmosphere. But, as we have seen, detectable atmospheric concentrations are almost by definition high concentration.

Light isotopes are used to identify biologically produced molecules on Earth. For exoplanets, no planned telescope will allow molecular isotopes to be observationally distinguished from one another. In the distant future when isotopic ratios of molecules are observable, care has to be taken to understand the isotopic distribution of all key molecules in the environment. In particular, the isotopic ratios of the input gases must be different than the biologically output gases. The isotopic ratios of both the input and output gases need to be inventoried, because exoplanets may have varying natural distributions of isotopic ratios not seen on Earth.

The view in biosignature gas studies is to find a biosignature gas that exists in concentrations of orders of magnitude above the naturally occurring values. This picture may supercede the goal to find biosignature gases that are out of redox equilibrium (such as O₂ and CH₄) because while both might exist they might not both be in high enough quantities to be detectable remotely.

For a biosignature gas produced orders of magnitude higher than natural values, how much is too much? We have seen from our H₂S study (Section 5.4) that when H₂S is emitted from the surface at an amount greater than 10–100 times Earth's current H₂S or SO₂ surface flux, a blanket of aerosols or condensates form (Hu et al. 2013). These aerosols or condensates are present at optically thick amounts, masking any H₂S or SO₂ spectral features. The particle size partially dictates the optical properties of the aerosols, and hence which wavelengths the spectral features will be washed out.

Aerosol formation by CH₄ photolysis in N₂–CO₂ atmospheres are expected to be significant when methane reaches 5000 ppmv (Haqq-Misra et al. 2008). There are two effects if aerosol formation is significant. First, aerosols may be a net loss for CH₄, leading to a decreasing marginal gain in atmospheric CH₄ concentration for increasing CH₄ emission. Second, aerosols may impede CH₄ detection. As an aside we point out a basic assumption in the haze formation model used by Haqq-Misra et al. (2008) that could be improved upon a treatment of all hydrocarbons higher than C₄ as solid particles when they might be in the gas phase makes hazes easier to form.

NH₃ emission itself does not lead to aerosol formation, as NH₃ is readily converted to N₂ by photolysis.

The situation for DMS is virtually the same as H₂S and SO₂. Sulfur in the terrestrial atmosphere is likely to end up as aerosols (S₈ and H₂SO₄, for H₂S and SO₂, respectively). The reason is that S₈ and H₂SO₄ are relatively easy to form from sulfur gas compounds, and they have relatively low vapor pressures enabling aerosol formation at Earth atmospheric temperatures (see Seinfeld & Pandis 2000).

If the surface of a planet is not habitable, could the subsurface harbor life? On Earth, there is substantial subsurface life, but its effect on the atmosphere is limited. On Earth, surface life will likely use any product of subsurface life as a food source, generating the characteristic biosignature gas of the surface life. Thus, H₂S or CH₄ emitted by subsurface life on Earth is (largely) oxidized at the surface, and so does not accumulate in the atmosphere.

If the surface is not habitable, however, then any subsurface biological activity will eventually affect the surface, just as surface biology on Earth eventually oxidized the stratosphere. In the absence of surface life, subsurface life biosignature gases will diffuse to the surface and then escape. (The methane on Mars may be an example of this.) If Mars had surface life, then that surface life would "eat" all the methane, and none would accumulate in the atmosphere. Thus, our model is applicable to the biomass of subsurface life as well as surface life, with the caveat that we do not know what a plausible upper boundary on the density of subsurface life is.

There remains the problem that subsurface life will generate gases that are just absorbed by the surrounding material (rock, ice, or water). If life is too deep (as life in the internal oceans of the Gallilean moons would be, if there is any) then biosignature gases would take geological time to reach the surface, and would be chemically transformed by the interposed geology (rocky or icy) in the process. In other words, if life is deep, the rock will only saturate on geological timescales, and over that time any biosignature will be chemically converted to other substances. If life is subsurface but shallow, rocks will become saturated with biosignature gases in a short timescale and the biosignature may then be outgassed to the atmosphere.

It has been speculated that anomalies in the atmosphere of Titan could be signs of surface life. With substantial caveats, we can apply the biomass model to test the plausibility of Titanian life. Acetylene is not detected on the surface of Titan, as reported by Clark et al. (2010), although some models suggest that acetylene should be more abundant on the surface than benzene, which was detected. There is an apparent deficit of acetylene on Titan's surface, because acetylene was detected in Titan's atmosphere. Strobel (2010) modeled the atmosphere of Titan, and predicted a tropospheric deficit of H₂ in Titan's atmosphere, compared to stratospheric levels, implying a downward flux of H₂ of the order of 2 × 10¹⁴ m⁻² s⁻¹. Several authors have speculated this is a sign of life on Titan (see, e.g., Norman 2011; Seager et al. 2012),¹³ deriving energy from either of the following reactions:

$$\begin{eqnarray} &&{\rm C_2H_2 + 2H_2 \rightarrow C_2H_6} \Delta G_0 = -242 \ {\rm kJ\ mole^{-1}} \end{eqnarray} \tag{ 42 }$$

$$\begin{eqnarray} &&{\rm C_2H_2 + 3H_2 \rightarrow 2CH_4 } \Delta G_0 = -375 \ {\rm kJ\ mole^{-1}}. \end{eqnarray} \tag{ 43 }$$

We can test the hypothesis that the acetylene deficit is a biosignature gas using the Type I biomass model. Life on Titan could live on the surface, using liquid methane as a solvent (Bains 2004; McKay & Smith 2005), or near the surface, or in the deep interior using water as a solvent. Life in liquid methane/ethane at ∼100 K must have radically different chemistry from terrestrial life; it is almost inevitable that the biomass model in Equation (11) will not be valid for such different biochemistry. Specifically, we might expect the constant A term in the minimal maintenance energy rate equation (15) to be lower for liquid methane life. The major source of damage for terrestrial biomolecules is attack by water, which will be much slower when the molecules are not dissolved in water. While we have no idea how much smaller A should be, we can, however, still attempt to apply Equation (11) to predict the minimum biomass necessary to generate a biosignature gas. If on Titan the $P_{m_e}$ constant A is smaller than on Earth, then from Equation (15), the minimal maintenance energy rate $P_{m_e}$ will be smaller (at a given temperature), and so from Equation (11) our biomass estimate will be larger.

If hydrogen and acetylene are being consumed by water-based life on Titan today, then that life must be near the surface. Water near the surface would freeze to a eutectic of whatever solutes are present in the internal ocean—as these are unknown, we have assumed a water/ammonia eutectic with a freezing point of 176 K (Leliwa-Kopystyński et al. 2002). The deeply buried "internal ocean" is likely to be warmer, but is too deeply buried to account for a high surface flux of hydrogen (Fortes 2012); however, we include a calculation for a saturated freezing brine at 252 K for comparison.

The flux of H₂ downward is proposed to be 2 × 10¹⁴ m⁻² s⁻¹ = 3.3 × 10⁻¹⁰ mole m⁻² s⁻¹. The surface concentration of acetylene is taken to be 0.15 mM in water (McAuliffe 1966), in the methane/ethane lakes acetylene concentration is taken to be the same as its mixing ratio in the higher atmosphere (Strobel 2010). Hydrogen, methane, and ethane are assumed to be in equilibrium with the atmosphere. Given these constraints, the biomass calculations for the three conditions mentioned above and the two reactions are given in Table 8.

Table 8. Biomass Surface Density Estimates for Titan in Different Surface Environments

Environment	T	ΔG	$P_{m_e}$	Biomass
	(K)	(kJ mole−1)	(kJ g−1 s−1)	(g m−2)
C2H2 + 2H2 → C2H6
Liquid methane/ethane	100	298	1.4 × 10−30	7.1 × 1022
Ammonia/water eutectic	176	288	6.3 × 10−15	1.5 × 107
Freezing brine	252	277	1.0 × 10−8	9.0
C2H2 + 3H2 → 2CH4
Liquid methane/ethane	100	385	1.4 × 10−30	9.1 × 1022
Ammonia/water eutectic	176	421	6.3 × 10−15	2.1 × 107
Freezing brine	252	403	1.0 × 10−8	14

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The values for the biomass predicted for life in liquid methane/ethane are clearly far too high to be in any way acceptable or plausible. We therefore have reason to doubt that life that uses chemistry similar to terrestrial life in liquid methane is generating the hydrogen deficit on Titan. An obvious caveat is that Equation (11) based on terrestrial, carbon/water-based life: life operating at 100 K will have radically different, and probably more fragile, chemistry (Bains 2004), and hence different constants in Equation (15).

Life in near-surface water "only" requires a Titan-covering layer between ∼1 and 1.5 m thick, equivalent to a modern cabbage farm. A Titan-wide layer of life 1.5 m thick implies a near-surface water layer of at least this thickness across the whole moon, or a thicker layer concentrated in specific regions of the moon, One would have thought that evidence of this would have been detected by IR spectrometry, which it is not (Clark et al. 2010). Again our model suggests that near-surface life is not the sink for atmospheric hydrogen.

Only a modest density of living matter is needed to explain the hydrogen flux if life is present in freezing brine. However, if freezing brine is present, it will be buried under a 100 km thick layer of ice. It is unlikely that gases could exchange with the atmosphere through an ice shell of this sort fast enough to explain the apparent deficit of hydrogen in Titan's atmosphere.

This speculative application of the biomass model illustrates that the model can be used to rule out Earth-like life in some circumstances that are quite unlike Earth. As noted in Section 6.2, there is good reason for our model to apply to other biochemistries based on C, O, N, P, and S. If life on Titan is based on radically different chemistry than Earth's biochemistry, then the constants in Equation (15) will be different, and our model will not accurately predict biomass requirements.