Assessment of Isoprene as a Possible Biosignature Gas in Exoplanets with Anoxic Atmospheres

2.2.1. The extent of formation of isoprene by life on Earth

Isoprene is produced by a very large number of evolutionarily diverse organisms, including algae, animals, bacteria, fungi, plants, and protists (Gelmont et al., 1981; Moore et al., 1994; Kuzma et al., 1995; Sharkey, 1996; Fall and Copley, 2000; Bäck et al., 2010; King et al., 2010; Exton et al., 2013). The majority (∼90%) of the global production of isoprene is from terrestrial plants, mostly by tropical trees and shrubs (Sharkey et al., 2008) (see Fig. 2 for an overview of the isoprene cycle in the atmosphere). Animals are responsible for the release of a significant fraction of the remaining 10% of isoprene's yearly global emissions. Production of isoprene was extensively studied in many animal species, but the majority of research was done on isoprene production in rodents and humans (Sharkey, 1996). For example, nursing mice and rats emit substantial amounts of isoprene (Sharkey, 1996). Isoprene is also the most abundant hydrocarbon in the exhaled breath of humans (Gelmont et al., 1981; Sharkey, 1996; King et al., 2010).

In addition to plants and animals, many bacteria, both aerobic and anaerobic, produce isoprene. The true extent of isoprene synthesis in prokaryotes is still difficult to estimate, as only a few phyla have been tested for isoprene production (e.g., Proteobacteria, Actinobacteria, and Firmicutes) (Kuzma et al., 1995; Schöller et al., 1997, 2002; Fall and Copley, 2000; Alvarez et al., 2009). Bacteria from the genus Bacillus, both terrestrial and marine, were shown to be the highest producers of isoprene among tested prokaryotes (Kuzma et al., 1995; McGenity et al., 2018). Some Bacillus species are also the only bacteria known so far to naturally produce isoprene completely anaerobically (see Section 2.2.2) (Fall et al., 1998).

The endogenous production of isoprene in archaea has not been widely investigated, and isoprene has not yet been found to be produced by archaea.

In summary, isoprene production on the Earth is not only abundant but also widespread and present in a large number of evolutionarily diverse organisms, from bacteria to mammals, and is made by at least two, evolutionarily distinct metabolic pathways (Supplementary Appendix A2). No other volatile secondary metabolite has a larger evolutionary reach than isoprene.

2.2.2. Biosynthesis of isoprene

Isoprene biosynthesis has only been extensively studied in plants. In plants, isoprene synthase (IspS; PDB ID: 3n0g; EC 4.2.3.27) is responsible for the catalysis of the last step in the isoprene biosynthesis pathway—the elimination of pyrophosphate from the isoprene precursor dimethylallyl pyrophosphate (DMAPP) and the release of isoprene (Fig. 5) (Köksal et al., 2010).

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FIG. 5.

Biological production of isoprene. Isoprene synthase is an Mg²⁺- or Mn²⁺- dependent terpenoid synthase that catalyzes the cleavage of inorganic diphosphate from the isoprene precursor DMAPP to yield isoprene. DMAPP, dimethylallyl diphosphate.

The mechanisms of biosynthesis of isoprene in non-plant species are largely unknown despite confirmed widespread isoprene production by a diverse host of organisms. Early studies suggested that mammals synthesize isoprene in the liver through a different pathway than plants (Deneris et al., 1985; Sharkey, 1996). For more detail, see Supplementary Appendix A2.

Interestingly, despite plentiful evidence for bacterial production of isoprene, bacterial isoprene synthase has been only partially characterized and is believed to be evolutionarily unrelated to the plant isoprene synthase (Sivy et al., 2002; McGenity et al., 2018). Isoprene production has been detected in fungi (Berenguer et al., 1991) and animals even if they too, like bacteria, do not seem to have plant isoprene synthase homologs. We conducted a bioinformatic search of genomic databases for sequences similar to plant isoprene synthase sequences and confirmed that no homologues of plant isoprene synthase have been found in bacteria, archaea, fungi, or animals. This confirms that isoprene synthetic pathways have evolved independently at least twice.

Impressively, all species belonging to the three domains of life (Bacteria, Archaea, and Eukarya) possess isoprenoid biosynthetic pathways. This means that all species are capable of producing complicated natural compounds containing the isoprene “motif,” even though not all species release isoprene as an isolated molecule (Supplementary Appendix Table A1) (Firn, 2010). For details on isoprenoid biosynthetic pathways, see Supplementary Appendix A2.

Although on Earth life that produces isoprene is aerobic (O₂-dependent) or facultatively anaerobic (e.g., Escherichia coli or Bacillus subtilis), the biosynthesis of isoprene does not require molecular oxygen (unlike, e.g., the biosynthesis of sterols). This means that isoprene could be, in principle, made by strictly anaerobic organisms, in anoxic atmospheres. The synthesis of isoprene by recombinant anaerobic bacteria and archaea is known (Beck et al., 2014; Murphy et al., 2017). For example, the methanogenic and anaerobic archaea Methanosarcina acetivorans is capable of efficient isoprene production on heterologous expression of isoprene synthase from plants (Murphy et al., 2017). There are also a small number of studies of native anaerobic isoprene production in natural environments. A few anaerobic bacteria, such as Bacillus cereus 6A1 and Bacillus lichenformis 5A24, have been shown to naturally produce isoprene anaerobically, and in substantial quantities, with production rates of 40–60 nmol/(g·hour) (Fall et al., 1998), comparable to that of terrestrial plants as demonstrated in Section 4.1.2, where we discuss in detail the global production rate achievable for an Archean anoxic biosphere comprising purely isoprene-producing prokaryotes.

Indeed, the capability for isoprene biosynthesis appears to be independent of aerobic metabolism. Such few laboratory studies on anaerobic production of isoprene establish the precedent that alien life could, in principle, discover an anaerobic biosynthetic pathway to produce isoprene, even on planets that have atmospheres very different than the Earth's (e.g., H₂-dominated). We note that H₂-dominated atmospheres are not detrimental for life and that life can survive and actively reproduce in an H₂-dominated environment (Seager et al., 2020). There is, however, the question of sufficient evolutionary incentive for production of huge amounts of isoprene by an anaerobic biosphere. We discuss this problem next.

The reasons that the Earth's aerobic biosphere makes isoprene in such impressively large amounts is not known, and it is not yet known what are the evolutionary pressures that govern isoprene production by life on the Earth (Sharkey and Monson, 2017). It is, however, likely that the functions of isoprene for life on Earth are many and are not limited to one single dominant role (see Section 2.2.3 below for discussion of various biological functions of isoprene). The biological functions of isoprene may be related to ultraviolet (UV) shielding and reactive-UV-radical protection (as evidenced by plants' response to UV, heat etc.); isoprene might also be used as a signaling molecule (Harvey and Sharkey, 2016; Zuo et al., 2019). It is impossible to predict what biological functions a specialized secondary metabolite such as isoprene could have in an anaerobic setting. One could speculate that the protective role of isoprene against UV radiation and/or other stressors could be universal to all life, even an anaerobic one, and therefore could justify its abundant production in an anoxic world, especially as the anoxic world would have no ozone layer to protect against UV.

It is likely that more endogenous isoprene production among archaea and other anaerobic organisms awaits discovery. We hope that this article stimulates further research into this understudied aspect of isoprene biology.

2.2.3. Biological functions of isoprene

The biological roles of isoprene have mostly been studied in plants, as plants are responsible for more than 90% of isoprene production on the Earth. The consensus is that isoprene protects the photosynthetic apparatus of tree leaves from heat stress, especially the sudden changes in temperature caused by varying exposure to sunlight (Sharkey et al., 2008), although other functions have been proposed (Laothawornkitkul et al., 2008; Vickers et al., 2009; Velikova et al., 2012; Jones et al., 2016; Sharkey and Monson, 2017). A range of observations supports this thermal protection role for isoprene (Logan et al., 2000; Peñuelas et al., 2005; Taylor et al., 2019), although its mechanism of action is not known.

The function of isoprene in bacteria, fungi, or animals is far less studied than its function in plants. In a facultative anaerobe bacterium B. subtilis, isoprene synthesis is elevated as a response to hydrogen peroxide treatment (Xue and Ahring, 2011; Hess et al., 2013) or in response to non-optimal growth conditions (e.g., elevated temperature and salinity) (Xue and Ahring, 2011). It has also been suggested that isoprene might play a role as a signaling molecule in the regulation of spore development of B. subtilis (Wagner et al., 1999; Fall and Copley, 2000; Sivy et al., 2002). The role of isoprene as an interspecies signaling molecule was also postulated. Isoprene could also act as a repellant for microbe-grazing springtails (hexapods) (Michelozzi et al., 1997; Fall and Copley, 2000; Gershenzon, 2008). Despite the fact that animals produce significant amounts of isoprene, our knowledge of its biological function in animals is still limited.

2.3.1. Destruction by ⋅OH radicals and O₂

Isoprene's reaction with ⋅OH is the first step in a series of reactions that end with aerosol formation (Fig. 6) (e.g., Zhang et al., 2000). The rate coefficient for the destruction of isoprene by reaction with ⋅OH is k = 10.0 ± 1.2 × 10⁻¹¹ cm³/(molecule·s) at 294 K (Zhang et al., 2000). The ⋅OH radical can attack different positions of the isoprene molecule to create intermediate sets of radicals with the general formula:

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FIG. 6.

A mechanistic diagram for the reactions of ^•OH with isoprene and the subsequent ^•C₅H₈[OH] radical reactions with O₂. The dots indicate the location of the radicals. The dashed lines indicate the delocalized electrons. The four isoprene intermediates (left side) immediately react with O₂, resulting in six different radicals (right side). The six radicals react with other trace atmospheric components to form aerosols. Figure adapted from the work of Zhang et al. (2000).

In an anoxic atmosphere, ⋅OH will still be present (from H₂O photodissociation) but at much lower levels than in an oxygenic atmosphere (Hu et al., 2012). Therefore, the fate of ^⋅C₅H₈[OH] radicals, in the absence of oxygen, will depend on the trace constituents of a given atmosphere. To our knowledge, the reaction network for ^⋅C5H8[OH] is not known for anoxic conditions; therefore, as with the other products of isoprene destruction, we neglect its chemistry to focus on the prospects for isoprene buildup, with the understanding that this approximation may lead to underestimates of the isoprene concentration at a given isoprene surface flux since we neglect the possibility of isoprene recombination and/or UV shielding from isoprene photochemical products.

In the Earth's atmosphere, the intermediate ^⋅C₅H₈[OH] radicals then react with O₂. The product oxidized isoprene radicals (^⋅C₅H₈[OH][O₂]) subsequently react with NO_x ^⋅ species in the atmosphere and other reactive trace gases, contributing to the overall destruction rate of isoprene (Zhang et al., 2000; Fan and Zhang, 2004). We ignore the subsequent reactions of isoprene radicals for anoxic atmospheres where oxygen is not present.

2.3.2. Destruction by O₃

Isoprene can react directly with O₃ with the rate coefficient k = 9.6 ± 0.7 × 10⁻¹⁸ cm³/(molecule·s) at 286 K (Karl et al., 2004). We include the destruction rate of isoprene by O₃ for completeness; the reaction rate is several orders of magnitude smaller than the dominant pathways (reaction with ⋅OH, O^⋅).

2.3.3. Destruction by O^⋅ radicals

Isoprene can react directly with O^⋅ with the rate coefficient k = 3.5 ± 0.6 × 10⁻¹¹ cm³/(molecule·s) at 298 K (Paulson et al., 1992).

2.3.4. Destruction by H^⋅ radicals and H₂ molecules

To our knowledge, there are no data published on the reactivity of isoprene with hydrogen (H^⋅) radicals. Although there are plenty of documented reactions of H^⋅ radicals with ethene, propene, and butene (Linstrom and Mallard, 2001), it is beyond the scope of this work to extrapolate from these reactions to isoprene. Further experimental work is needed to confirm or rule out the possibility of efficient conversion of isoprene with H^⋅ radicals in H₂-dominated conditions. It is also not known whether any of the ^⋅C₅H₈[OH] radicals, formed on reacting with ⋅OH, can efficiently react with H^⋅ radicals in an H₂-dominated environment to revert back to isoprene and water.

Hydrogenation of isoprene (or isoprene units) by using molecular hydrogen, which results in saturation of a double bond, is a standard reaction used in human industry. However, such reactions require higher than habitable temperatures (>400 K), catalysts and meticulous environments (Abdelrahman et al., 2017). It is also unknown whether lightning might be a catalyst for such reactions to occur in the atmosphere.

2.3.5. Destruction through UV radiation

The general chemical formula for photodissociation of isoprene is:

where hν is the energy of a photon. To the best of our knowledge, the quantum yield of isoprene photolysis is also not well known. We take a conservative approach and assume the quantum yield of 1, which means that any high-energy UV photon that is absorbed by an isoprene molecule will dissociate it. ^§

2.3.6. Destruction by life

Apart from the atmospheric sinks of ⋅OH, O₂, and UV photolysis, ∼4% (20 Tg/year) of the yearly production of isoprene is directly consumed as a carbon source by a variety of soil microorganisms (Cleveland and Yavitt, 1998; Shennan, 2005). Although on Earth the biological sink of isoprene is small, it may be reasonable to assume that any atmosphere that is enriched with isoprene will have a sizable population of living organisms utilizing isoprene as a carbon source, further contributing to its removal from the atmosphere. The efficiency of biologically driven removal of isoprene will be largely dependent on the unique biochemistry and ecology of life inhabiting the planet. The impact of the potential biological destruction of isoprene has, therefore, not been included in our model.

2.3.7. Aerosol and haze formation

On Earth, isoprene radical-induced aerosols are a major source of secondary organic aerosols. The production of haze is also the primary pathway for isoprene destruction on the Earth (e.g., Seinfeld and Pandis, 2016). For example, the blue haze of some forest-covered mountains (Claeys et al., 2004) is a product of isoprene radical-induced aerosols.

In the context of anoxic atmospheres, hazes and aerosols would be different from those found in the Earth's atmosphere, with haze composition depending on the molecules and radicals available to react with isoprene and isoprene's destruction products.

3.1.1. UV-Vis cross-section

The isoprene UV-Vis cross-section is shown in Fig. 7. The data have been taken from Dillon et al. (2017) and are used for calculating the UV photolysis rate (see Section 3.3). The isoprene UV-Vis absorption peaks at 218 nm with σ _peak = 7.93 ± 0.02 × 10⁻¹⁷/(cm²/molecule) and covers a wavelength range of 118–278 nm.

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FIG. 7.

Isoprene UV-Vis absorption cross-section taken from (Dillon et al., 2017). The axes show absorption cross-section (cm²/molecule) versus wavelength (μm). The peak absorption of isoprene UV-Vis is at 218 nm. UV-Vis, ultraviolet-visible. Color images are available online.

3.1.2. IR cross-sections and uncertainty estimates

The isoprene IR absorption cross-sections are shown in Fig. 8. The data are measured by Brauer et al. (2014) and are collected and calibrated by the “HITRAN online Absorption Cross Sections Database” (Gordon et al., 2017).

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FIG. 8.

Isoprene high-resolution IR cross-sections at standard pressure and temperature in log-log scale from 1.3 to 18 μm. Shown in green are isoprene cross-sections, as collected by Brauer et al. (2014) and calibrated by HITRAN (Gordon et al., 2017). Shown in blue are the isoprene cross-sections with a uniform uncertainty of 3 × 10⁻²² cm²/molecule. Shown in orange is the estimated wavelength-dependent uncertainty based on methods described in the work of Chu et al. (1999). The uncertainties represent the 95% confidence interval of the data. Marked in gray are the five regions of isoprene spectral features that we consider to evaluate the detectability of isoprene (1.6–1.7, 2.1–2.5, 3.1–3.7, 5.4–7.9 and 9–12 μm). We omit assessment of the spectral features in other regions due to high uncertainties and omit features longer than 12 μm due to high instrumental noise from the JWST MIRI LRS Instrument (Batalha et al., 2017). IR, infrared; JWST, James Webb Space Telescope. Color images are available online.

The isoprene cross-section datasets are measured at standard pressure for 278 K, 298 K, and 323 K with a 1/8 cm⁻¹ resolution. In this study, we opt to only use the 298 K data to assess the detectability of isoprene because it has the least uncertainties. More specifically, measurements at standard pressure and temperature do not require heating/cooling of the experimental setup, and will, therefore, have the least variation between the source and background reference spectra. As a side note, the methodology for the consideration of the noise floor differs between the 298 K data and the 278 K/323 K data. As a result of this difference in treatment, it is not possible to reliably extrapolate the measured cross-sections to temperatures beyond those measured. Including all three measurements with different noise floor treatments may introduce additional uncertainties to our models.

Unlike absorption cross-sections calculated from molecular line lists, the uncertainties of absorption cross-sections calculated from lab-measured transmission spectra cannot be ignored, especially for data points with opacities that approach the instrument noise floor.

We estimated the wavelength-dependent uncertainties (95% confidence interval of the measured data) as described in Eq. 4 in the work of Chu et al. (1999) as follows:

where U is the expanded uncertainty, a is the absorption-cross section, and B, C, and D are coefficients unique for each molecule. The uncertainty U is the 95% confidence interval. We compare the wavelength-dependent uncertainties with a uniform 3 × 10⁻²² cm²/molecule noise floor, as described in the work of Brauer et al. (2014) and approximately validate this method by finding the same averaged value. Therefore, both methods are sufficient to identify which data points we can trust and which may be no different than noise, but in general, the uncertainty of the wavelength-dependent method scales with the cross-section values (uncertainties for the largest peaks are larger than the uniformed uncertainty, and uncertainties for the small peaks near the noise floor are smaller than the uniformed uncertainty).

We note that the specific values of the B, C, and D coefficients for isoprene are not measured by Chu et al. (1999); they are not provided in the original work of Brauer et al. (2014) and are also missing in the NIST spectral database (Linstrom and Mallard, 2001). We, therefore, adopt the values of B = 1.6 × 10⁻⁴, C = 1.1 × 10⁻⁹, D = 2.7 × 10⁻¹⁴ from C₄H₆ (1-3-butadiene). Although we expect this substitution to introduce some additional uncertainty, it is the most appropriate approximation; C₄H₆ is structurally similar to isoprene (2-Methyl-1,3-butadiene), though it has one less methyl group.

3.1.3. Isoprene spectral features

Isoprene has 33 fundamental IR-active vibrational modes, associated with several functional groups containing carbon–carbon and carbon–hydrogen bonds. The fundamental vibrational modes of isoprene have previously been assigned from both measured and theoretically calculated spectra (Panchenko and De Maré, 2008; Brauer et al., 2014).

We assess the detectability of isoprene in the context of JWST's observation capabilities (see Sections 3.4 and 4.2). We have divided the isoprene spectral features into five wavelength regions: 1.6–1.7, 2.1–2.5, 3.1–3.7, 5.4–7.9, and 9–12 μm. We omitted spectral features in other regions due to the high measurement error-bars and omitted spectral features above 12 μm due to the high instrumental noise of JWST Mid-Infrared Instrument Low-resolution Spectrometer beyond 12 μm (Batalha et al., 2017).

Isoprene cross-section features in the 1.6–1.7 and 2.1–2.5 μm regions are formed by rovibrational overtones of the 3.1–3.7 μm region bands. Features in these two regions lack reliable experimental measurements (Brauer et al., 2014), and detectability of these two spectral features should be taken with some caution. This article motivates future measurements and theoretical simulations of isoprene spectra in the visible and near-IR, as it would expand the assessment of isoprene detection by using more readily available instruments that cover these spectral regions.

Isoprene spectral features in the 3.1–3.7 μm region primarily comprise the following two features: (1) the narrow bands around 3.2 μm, which are composed of the ν₁ and ν₂ asymmetric stretching modes; (2) the broader bands (3.3–3.7 μm), which are composed of the ν₃ (symmetric stretch), ν₄ (asymmetric stretch), and ν₂₄ (deformation) modes (Brauer et al., 2014). These two features arise from the stretching modes of X = C-H (sp² hybridized) and X-C-H (sp³ hybridized), where X denotes another atom (other than H).

Isoprene spectral features in the 5.4–7.9 μm region comprise the following two features: (1) the narrow features around 6.5 μm, which are composed of the symmetric and asymmetric stretching modes (ν₈ and ν₉) associated with the C = C double bond; (2) the features in the 6.6–7.9 μm region that are composed of the ν_10–13 and ν₂₄ modes associated with deformation and scissoring rovibrational motions (Brauer et al., 2014).

Isoprene spectral features in the 9–12 μm region comprise several bands associated with the wagging modes of the carbon–hydrogen functional groups (ν₂₆, ν₂₇, and ν₂₈), and one associated with the rocking motion of the X = C-H functional group (ν₁₇ mode) (Brauer et al., 2014).

3.1.4. Haze extinction cross-section

We anticipate that abundance of isoprene, a hydrocarbon, in an atmosphere could lead to the presence of a haze layer in the atmosphere similar to the haze layer induced by organic molecules described in the work of Arney et al. (2018). The presence of a haze layer may hinder detection of isoprene spectral features and should be quantified.

Studying the effects of isoprene-induced haze requires wavelength-dependent refractive indices and haze particle size distribution, but neither is available for isoprene as studies regarding reactions of the isoprene-induced radicals (or products of isoprene reactions described in Section 2.3) are limited. Isoprene-induced haze on the Earth does not have measurements in IR thus far, and in any case, the Earth's isoprene-induced haze is an oxygenated product not likely to be the same as the isoprene-induced haze on an anoxic exoplanet. Therefore, we estimate the isoprene-induced haze extinction cross-section by using wavelength-dependent refractive index measurements and haze particle-size distributions of other hydrocarbons in a reducing environment.

We adopt the wavelength-dependent refractive indices of Titan's methane-induced haze (measured by Khare et al., 1984), or tholins, as a proxy for that of isoprene-induced hazes. In our solar system, Titan (Khare et al., 1984), Pluto (Zhang et al., 2017), and Venus have extensive haze layers in their atmosphere. The composition of Pluto's haze is yet to be confirmed. The Venusian haze is not known, but it is likely to contain high concentrations of sulfur-containing molecules derived from SO₂ and H₂SO₄ (Takagi et al., 2019). Therefore, Titan's atmospheric haze is the closest analogue to isoprene haze on habitable exoplanets; both are hydrocarbon-induced haze. To show that our results are not specific to the case of Titan tholins, we compare our results with those using refractive indices of HCN (Khare et al., 1994), C₂H₂ (Dalzell and Sarofim, 1969), and octane (Anderson, 2000).

We approximated the mean size distribution as a Gaussian distribution with a mean particle size equal adopted from the works of He et al. (2018) and Hörst et al. (2018), who measured the diameters of haze particles for different temperatures and metallicities. For CO₂-dominated and N₂-dominated atmospheres, we used a mean size of 89 nm and a standard deviation of 25 nm, which is approximated from the 300 K, 1000 × metallicity case from the work of He et al. (2018). For H₂-dominated atmospheres, we used a mean size of 53.8 nm and a standard deviation of 16 nm, which is approximated from the 300 K, 10,000 × metallicity case from the work of He et al. (2018). We choose to use a Gaussian distribution approximation rather than using the original measurement to avoid overfitting the data for isoprene.

Finally, we used miepython ^** to calculate the isoprene-induced haze's extinction cross-section with the assumed wavelength-dependent refractive indices and haze particle-size distribution. The cross-section is averaged from 1000 radii sampled from the Gaussian distribution. For simplicity, we assumed the haze particle to be spherical and we assumed the mean size and size distribution to be constant as a function of height.

3.3.1. Astronomical scenarios

We consider stellar irradiation environments corresponding to the modern Sun and an M5V star (“M dwarf star”) with a visual magnitude of 10.

The semimajor axes of the planets are taken to be 1.6, 1.0, and 1.3 AU if orbiting a Sun-like star, and 0.042, 0.026, and 0.034 AU if orbiting an M dwarf star for H₂-dominated, N₂-dominated, and CO₂-dominated atmosphere, respectively. The semimajor axes are chosen to maintain a surface temperature of 288 K (Hu et al., 2012).

We calculate photochemical models for an Earth analog planet (1 Earth-mass, 1 Earth-radius). We follow the work of Hu et al. (2012) in projecting these photochemical models to the scenario of a massive super-Earth with 10 Earth-mass and 1.75 Earth-radius, by assuming the molecular mixing ratio to be a function of pressure, which is invariant of surface gravity. The preference for the larger planet is beneficial for observation with near-future space telescopes for mass measurement with radial velocity and atmosphere characterization with both transmission (e.g., more likely to retain a reducing, H₂-dominated atmosphere) and secondary eclipse spectroscopy (e.g., higher planet/star flux ratio).

3.3.2. Atmospheric scenarios

We consider three different atmosphere scenarios according to their redox state: a reducing H₂-dominated atmosphere, an intermediate redox state N₂-dominated atmosphere, and a weakly oxidizing CO₂-dominated atmosphere. We only consider anoxic atmospheres, because it is already well known from the Earth's atmosphere that isoprene cannot accumulate in an O₂-dominated atmosphere. The exact composition and vertical mixing ratio profile for the starting atmosphere scenarios that we use as seeding conditions for calculating vertical mixing ratio profiles with varying surface flux are shown in Supplementary Appendix A1 (and originally come from Sousa-Silva et al., 2020) for details on the H₂-dominated and CO₂-dominated atmosphere scenarios. The physical concept behind the H₂-dominated atmosphere scenario is that the planet outgassed H₂ during planet formation and managed to either maintain its H₂ atmosphere or has interior reservoirs with planetary processes to replenish it (Table 1).

3.3.3. Atmosphere temperature, pressure, and abundances

Using the six starting simulation scenarios (three atmosphere scenarios for the Sun-like star and three for the M dwarf star) as seeds, we calculate the mixing ratio profile of isoprene with varying surface flux by using the photochemistry code from the work of Hu et al. (2012) for each scenario. The vertical mixing strength (Eddy diffusion profile) of an atmosphere archetype is linearly scaled from the ratio of the Earth atmosphere's mean molecular mass and the atmosphere archetype. We adopt the eddy diffusion coefficients scaling factors of 6.3, 1.0, and 0.68 for the H₂-, N₂-, and CO₂-dominated atmospheres from the work of Hu et al. (2012), which is based on the scale height of the atmosphere archetypes.

The surface pressure of the planet is set to 1 bar, and the surface temperature is set to 300 K. In the troposphere, the temperature decreases with altitude based on a dry adiabatic lapse rate. The tropopause is set to 160 K for the H₂-dominated atmospheres, 180 K for the CO₂-dominated atmospheres, and 200 K for the N₂-dominated atmospheres. The different tropopause temperatures used for each atmosphere reflect the different efficiencies of gases as coolants in the upper atmosphere. H₂ is a more effective coolant than N₂, so the stratosphere of H₂-dominated atmospheres will be colder than N₂-dominated atmospheres.

Temperatures above the troposphere are set to be constant, that is, no temperature inversion (see Supplementary Appendix A1 for the temperature-pressure profiles for the three-atmosphere archetypes). This assumption may be violated for hazy atmospheres, where absorption of UV photons by high-altitude haze may drive an inversion, analogous to ozone in the modern Earth's atmosphere. We expect our results to be relatively insensitive to the stratospheric temperature since the ultimate limit on accumulation of isoprene comes from UV photolysis. Nevertheless, we performed a sensitivity test of the resulting transmission spectra by replacing the temperature-pressure profile with that of the Earth's temperature-pressure profile. We find that there is negligible difference in the transmission spectra resulting from the two different temperature-pressure profiles.

We exclude trace gases that do not exceed 100 ppb at any altitude from our spectral model, because their absorption does not contribute enough variation to the atmosphere spectra and they are unlikely to be detectable without significant instrumentation advancements that are capable of reaching a < 1 ppm noise floor.

3.4.1. Transmission spectra

The SEAS transmission spectrum code calculates the radiative transfer of stellar radiation passing through each layer of the transiting planet atmosphere. Next, we detailed the exact step to calculate the effective height of the atmosphere and the transit depth for each wavelength.

where A(λ)_i is the total wavelength-dependent absorption for the i th layer, j denotes each molecule, n is the number density, σ(λ) is the wavelength-dependent absorption cross-section, P is the pressure, T is the temperature, l is the path length, z denotes the total number of layers above the i th layer that the stellar radiation passes through, and m denotes the total number of molecules.

We note that the cross-sections of haze particles have units of (cm²/particle) and, therefore, the particle density is calculated from the gas number density and has a unit of (particle/cm³). The particle density of isoprene-induced haze at a given layer is calculated by dividing the particle vapor density with the average particle mass. The particle vapor density is the product of the air density, the mixing ratio of isoprene, and an assumed haze-to-isoprene mass fraction (see Section 3.2).

To consider the detection of isoprene via transmission spectra, we first assessed model scenarios in which the atmospheres have no clouds or haze. This result represents an upper bound on the detectability of the isoprene features in transmission (Section 4.2). Next, we study how detection will be hindered if haze is included (Section 4.3).

3.4.2. Secondary eclipse thermal emission spectroscopy

The SEAS thermal emission code is similar to those described in the works of Seager (2010) and Sousa-Silva et al. (2020) and uses the same temperature-pressure profiles, mixing ratio profiles, and molecular-cross sections as in the transmission code.

The emission code integrates the blackbody radiation for each wavelength from the surface and up through each layer of the atmosphere, as the radiation is absorbed and reemitted by gases in each layer. The surface is set to be a pure black body, and the top layer is set to be transparent. We do not consider scattering in the current emission code. The final spectrum is calculated by integrating the emerging flux by the cross-sectional area of the planet. To add the presence of clouds, we consider 50% cloud coverage by averaging between a cloudy and cloud-free spectrum.

4.1.1. Isoprene remains a trace gas at Earth's production rate

At the Earth's isoprene production rate of 3 × 10¹⁰ molecules/(cm²·s), isoprene remains a trace gas in all of the three exoplanet atmosphere scenarios, at <1 ppb (column-averaged mixing ratio) (Table 2). At surface fluxes lower than 1 × 10¹¹ molecules/(cm²·s), isoprene is concentrated near the surface where it is created. Any isoprene that diffuses to the upper atmosphere is readily destroyed. To illustrate this finding, the column-averaged mixing ratio of isoprene at four different altitudes for a CO₂-dominated atmosphere of an exoplanet transiting an M dwarf star is shown in Fig. 9.

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FIG. 9.

Column-averaged mixing ratios of isoprene and other major atmospheric gases in a CO₂-dominant atmosphere orbiting an M dwarf star as a function of isoprene surface flux. Dominant atmosphere species and isoprene-reacting radicals are plotted in various colored dash lines. The isoprene column-averaged mixing ratios (in units of ppm) for different isoprene surface fluxes [i.e., biological production rate; in units of molecules/(cm²·s)] are shown by a solid black curve. The abundance of isoprene at 0–10 km from the surface overlap with the solid black curve and is additionally indicated by the light gray stars. The abundances of isoprene at 10–20, 20–30, and >30 km from the surface are shown in different shades of gray and are additionally shown by different types of triangles. For low surface fluxes, isoprene remains a trace gas throughout the atmosphere (<ppm levels) with abundances increasing linearly with surface fluxes. For surface fluxes above 3 × 10¹⁰ molecules/(cm²·s), isoprene abundance rapidly increases. For isoprene surface fluxes above 3 × 10¹¹ molecules/(cm²·s), isoprene abundance at the upper atmosphere (where most transmission spectral features originate) reaches the same level as surface abundance. Color images are available online.

Isoprene may remain a trace gas even at higher production rates than on the Earth, because large isoprene sinks may exist on planets different from the Earth. The sinks could realistically include life that has evolved to consume the abundant isoprene; photochemical destruction pathways as yet-unknown in anoxic atmospheres; and/or higher deposition rates than those that exist on the Earth.

As a trace gas, isoprene is not detectable via transmission spectroscopy even with far-future space telescopes. In Section 4.2.1, we explore the potential to detect isoprene as a trace gas via thermal emission spectroscopy by using JWST.

4.1.2. Maximum isoprene production estimate

For isoprene to accumulate to higher levels than a trace gas, it must be produced by life at rates hundreds, if not thousand times, the global production rate on the Earth (Fig. 9). In this section we establish that high isoprene production niche environments exist on the Earth, up to one million times the Earth's globally averaged isoprene production rate (Section 2.2).

One such niche is a modern tropical environment, where isoprene production is optimal for trees, the main producer of isoprene on the Earth due to their widespread abundance. In the Amazon rainforest, African rainforest, and Southeast Asia, the isoprene production rate averages >1 mg/(m²·s) with core areas averaging >10 mg/(m²·s) (McFiggans et al., 2019). In comparison, the global averaged isoprene production rate on the Earth is ∼3 × 10⁻⁵ mg/(m²·s) [converted from 500 Tg/year, or ∼3 × 10¹⁰ molecules/(cm²·s)]. For 12% of the Earth's habitable history [e.g., during Phanerozoic eon (the past 541 million years)], the Earth had a pole-to-pole tropical climate (e.g., during Carnian Pluvial Event; Royer et al., 2004; Dal Corso et al., 2012). Therefore, in a hypothetical scenario where the Earth's total land mass (∼30% of total surface area) is filled completely with isoprene producers and attains the 1 mg/m² production rate, it is possible for the global average to reach 0.3 mg/(m²·s), or 3 × 10¹⁴ molecules/(cm²·s). However, although trees are the main producer of isoprene on the Earth, we cannot ignore the fact that trees are also the main producer of oxygen and the presumed condition for isoprene to accumulate is an anoxic atmosphere.

For a purely anoxic environment, we assume an Archean biosphere that comprises anaerobic, isoprene-producing prokaryotes such as those found in lab studies (Fall et al., 1998) (see Section 2.2 for details), which is capable of naturally producing isoprene in high quantities with average production rates of 50 nmol/(g·hour). By using an average bacteria density of 1 g/cm³ (Loferer-Krößbacher et al., 1998) and assuming a global biomass layer of 1 cm thick covering all of the Earth's total land mass (∼30% total surface area), it is possible for the global average to reach 2.5 × 10¹³ molecules/(cm²·s).

With these assumptions, we show that the high isoprene production rates required for isoprene to accumulate in the upper atmosphere can be supported by species on Earth and the theoretical upper limit to isoprene production rate is 10⁴ that of the Earth's current production rate. Therefore, it is plausible to explore the detection of isoprene under these conditions.

4.1.3. Isoprene run-away

Very high surface fluxes of isoprene will send isoprene accumulation into a run-away state (Fig. 9). In a run-away phase, isoprene rapidly accumulates in the upper atmosphere to high levels, up to hundreds of ppm. The run-away is a result of “photochemical self-shielding” whereby the isoprene production flux saturates its UV-driven sinks, resulting in a dramatic increase in lifetime and hence accumulation. This run-away phenomena has been discussed for abiotic CO (Kasting et al., 1983, 1984, 2014; Zahnle, 1986; Kasting, 2014), has been alluded to for CH₄ (Segura et al., 2005), and has been observed by us for other biosignature gases (Huang et al., unpublished data; Sousa-Silva et al., 2020). We plan a detailed study in the work of Ranjan et al. (unpublished data). In this subsection, we consider the case where isoprene has entered a run-away phase, a scenario in which the abundance of isoprene in the upper atmosphere reaches a similar level to the abundance of isoprene in the lower atmosphere.

The run-away phase is important, because it shows that cases exist in which isoprene can populate the upper exoplanet atmosphere such that it can be detected via transmission spectroscopy in simulations of the JWST. Recall that transmission spectra are only sensitive to the upper atmosphere. The lower atmosphere has extremely long path lengths for light to travel through it, making the atmosphere optically thick, which, in turn, results in featureless spectra.

The most favorable atmosphere scenario for isoprene accumulation is a CO₂-dominated atmosphere because CO₂ shields isoprene more strongly from UV irradiation than N₂-dominated atmosphere or H₂-dominated atmosphere do.

The run-away effect is highly dependent on the quantity of UV flux from the host star. UV fluxes from Sun-like stars are significantly (more than 1000 times) higher than UV fluxes from M dwarf stars. Isoprene is unlikely to enter the run-away phase for planets orbiting Sun-like stars. There, the production rate required is around 3 × 10¹⁴ molecules/(cm²·s) for a CO₂-dominated atmosphere, approaching the maximum isoprene production rate even in niche environments on the Earth. In contrast, for planets orbiting M dwarf stars, isoprene's transition to the run-away phase occurs around 3 × 10¹¹ molecules/(cm²·s) for a CO₂-dominated atmosphere and 1 × 10¹² molecules/(cm²·s) for an H₂-dominated or N₂-dominated atmosphere. The surface flux required to enter the run-away phase is within 1–2 orders of magnitude of the Earth's globally averaged surface isoprene flux of 2.7 × 10¹⁰ molecules/(cm²·s). With isoprene surface fluxes above 3 × 10¹¹ molecules/(cm²·s), but below 3 × 10¹² molecules/(cm·s), the corresponding atmosphere volume mixing ratio is 100 ppm or greater, and isoprene can accumulate in the upper atmosphere. At isoprene surface fluxes above 3 × 10¹² molecules/(cm²·s), the corresponding atmosphere column-averaged volume mixing ratio is 1000 ppm (0.1%) or greater. There are sufficient isoprene molecules in the atmosphere to balance photochemical destruction, thus allowing isoprene molecules to diffuse to the upper atmosphere; the resulting mixing ratio profile is well mixed such that isoprene has a constant mixing ratio up to 50 km above the surface.

Therefore, if life produces enough isoprene to enter a run-away phase, isoprene can accumulate to become a major atmospheric gas. In this case, life will have re-engineered the atmosphere, reminiscent of cyanobacteria's oxygenation of the Earth's atmosphere. We note that the run-away hypothesis ignores potential unknown chemical or surface sinks in anoxic atmospheres that would limit the accumulation of isoprene in the atmosphere. Therefore, realistic situations might require further investigation (see e.g., Ranjan et al., unpublished data).

4.2.1. Detecting isoprene as a trace gas is challenging

As a trace gas, isoprene molecules are concentrated near the surface. We did not find any transmission spectra scenario in which isoprene can accumulate above the troposphere for a surface flux below 1 × 10¹² molecules/(cm²·s). Our spectra simulations confirmed that the isoprene spectral features are <10 ppm in transit depth, smaller than JWST's assumed noise floor. Therefore, it is not possible to detect isoprene as a trace gas via transmission spectroscopy.

We additionally explore whether isoprene can be detected via secondary eclipse thermal emission spectroscopy (emission spectroscopy) for planets transiting an M dwarf star. In emission spectroscopy, spectral features scale with the temperature gradient and, in general, detection might be more promising than for transmission spectroscopy.

For the terrestrial exoplanet atmosphere scenarios we considered in this study, the largest change in temperature occurs in the lower atmosphere layers, from the planet surface to “tropopause.” Therefore, in scenarios where isoprene is a trace gas and concentrated near the surface, it is worth investigating detection via emission spectroscopy.

Since isoprene accumulates best in CO₂-dominated atmospheres, we modeled this case. We found that in a CO₂-dominated atmosphere, secondary eclipse detection for a planet transiting an M dwarf star is possible given a surface flux of 1 × 10¹¹ molecules/(cm²·s), which is three times that of the Earth's isoprene surface flux (Fig. 10). Detection of isoprene in H₂- and N₂-dominated atmospheres is possible given a surface flux of 1 × 10¹² molecules/(cm²·s). For a planet with a habitable surface temperature of ∼300 K, the peak thermal emission is between 10 and 15 μm. There is only one very broad spectral feature of isoprene that lies in this spectral region, between 9 and 12 μm.

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FIG. 10.

Simulated secondary eclipse thermal emission spectra for an H₂-dominated (left) and N₂-dominated (right) atmosphere of an exoplanet transiting an M dwarf star with an isoprene surface flux of 1 × 10¹² molecules/(cm²·s). The simulated atmosphere uses input and parameters as listed in Section 3. We show the planet-to-star flux ratio versus wavelength in μm (top) and the statistical significance of a modeled atmosphere versus wavenumber in cm⁻¹ (bottom). The horizontal axes are applied to both the top and bottom panel. In the top panel, we show the simulated atmospheres with and without isoprene as represented by the green and orange curves, respectively. The best fit blackbody curves are shown in blue. Simulated observations of atmospheres with isoprene are represented by the black error bars. In the bottom panel, we show the statistical significance of a simulated atmosphere with isoprene as compared with the black body fit, in units of σ-interval. The green line represents the 5-σ statistical significance threshold. Color images are available online.

Unfortunately, given a spectral resolution of R, approximately 10–20, although we could detect isoprene, it would be hard to distinguish isoprene from other molecules that could be absorbing in this spectral region. Future 30-meter diameter aperture ground-based telescopes with dedicated instruments that focus on the N-band and using a spectral resolution of R > 100 will be able to identify the individual, narrow spectral features that made up the broad 9–12 μm spectral features if given generous observation time (100+ transits).

4.2.2. Detection of isoprene as a major atmospheric gas

We assess the detection of isoprene via transmission spectra for isoprene in the run-away phase via transmission spectra. For exoplanets with anoxic atmospheres orbiting M dwarf stars, the high isoprene accumulation scenario occurs given an isoprene production rate of at least 1 × 10¹² molecules/(cm²·s) for any atmosphere scenario we studied. We found that at this high production rate, isoprene can accumulate to a column average mixing ratio of 100–1000 ppm and the isoprene spectral features would be prominent compared with those of other molecules, potentially allowing isoprene to be identified (Fig. 11).

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FIG. 11.

Upper panel: Simulated spectra of exoplanets with H₂-dominated atmospheres transiting an M dwarf star for a range of isoprene surface fluxes from 0 to 1 × 10¹³ molecules/(cm² s). The y-axis shows transit depth (ppm), and the x-axis shows wavelength (μm). The spectra are simulated from 0.3 to 23 μm, covering the wavelength span of most of JWST's observation modes. The yellow, green, and blue region shows the spectral coverage of NIRSpec and the red region shows that of MIRI LRS. At low surface mixing ratios, the isoprene spectral features are not prominent as isoprene is mostly concentrated near the surface and rapidly decays as a function of altitude. Isoprene features are not noticeable until the surface flux is above 1 × 10¹¹ molecules/(cm²·s). Above 1 × 10¹² molecules/(cm²·s), increasing the surface flux of isoprene rapidly increases the amount of isoprene in the atmosphere and significantly increases the strength of isoprene's transmission spectral features. Lower panel: Comparison of isoprene cross-sections (Brauer et al., 2014) with cross-sections of dominant molecules (except H₂, its absorption is mainly in the form of collision-induced absorption) in the atmosphere such as H₂O, CO, CH₄, and CO₂ (Gordon et al., 2017). Color images are available online.

For terrestrial exoplanets transiting the 10th magnitude M5V dwarf star, only the H₂-dominated atmospheres (with surface pressure set to 1 bar and surface temperature set to 300 K) are detectable with JWST in transmission spectroscopy in near- to mid-IR, as they have a large scale height due to the low mean molecular weight. In this scenario, isoprene can be detected if it is produced at fluxes above 3 × 10¹² molecules/(cm²·s), or 100 times that of the Earth's isoprene production rate. Isoprene has many spectral features; we find that detection can be achieved with 20 transits by using any of the four modes of JWST (NIRSpec G140M, G235M, G 395M, and MIRI LRS) we assessed (Fig. 12).

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FIG. 12.

Upper panel: Simulated H₂-dominated atmosphere observation using JWST for a 10 M _Earth, 1.75 R _Earth super-Earth transiting an M dwarf star given 20 transit observations per instrument (80 transits in total). The y-axis shows transit depth (ppm), and x-axis shows wavelength (μm). The simulated observation spans the wavelength range of the NIRSpec and MIRI instruments. We compare a model with no isoprene surface flux (blue line, green error-bar) and a model with 5 × 10¹² molecules/(cm²·s) (orange line, red error-bar). The error bars are 95% confidence intervals for each model uniformly binned to a spectral resolution of R = 10. For this comparison, we take the isoprene cross-section as is and did not account for lab measurement error estimates. The error bar is attributed from observational noise only to more accurately reflect observation simulation. Lower panel: Difference between the two simulated spectra showing the spectral features of isoprene peaks. We show that within each instrument, there are more than more than 20 ppm transit depth differences between the two models; therefore, it is possible to achieve statistical significance and detect isoprene. Color images are available online.

For N₂-dominated and CO₂-dominated atmospheres, we did not find a scenario in which the atmosphere is detectable via transmission spectroscopy with JWST without investing 100 transits per observation mode. Although it is theoretically possible to accumulate 100 transits for a planet orbiting a late M dwarf star over 5 years (the cryogenic lifetime of JWST), it is unrealistic given the competitive nature of the telescope observation time. We, therefore, conclude that detection of isoprene in a non-H₂-rich atmosphere should only be considered plausible for exoplanet dedicated future observatories with far better collecting power.

For exoplanets transiting a Sun-like star, we found that no atmosphere scenarios are detectable via transmission spectroscopy because the ratio of planet to star radius, or (R_planet/R_star)², was too small, resulting in too small a transit depth even for H₂-dominated atmospheres.

Assessing the detectability of isoprene as a major atmospheric gas via secondary eclipse thermal emission spectroscopy is at present problematic due to our assumption of an isothermal atmosphere above the 0.01 bar (10³ Pa) level (an assumption in our photochemistry model; Hu et al., 2012). Secondary eclipse thermal emission spectra can, in principle, arise in the lower atmosphere, which in our model does have a temperature gradient. However, when isoprene is a major atmosphere gas, above column-averaged mixing ratio of 100 ppm, there are enough isoprene molecules to saturate the atmosphere and render it opaque from the surface to near or above the 0.01 bar level. Since the atmosphere is isothermal above 0.01 bar, the result is a featureless spectrum: a blackbody curve of much lower temperature than the surface temperature (Supplementary Appendix Fig. A2). Correction for this would require adapting the photochemistry model to use a self-consistent temperature-pressure profile, which is beyond the scope of this work.

4.2.3. Isoprene identification is hindered by methane

Detecting isoprene on an exoplanet atmosphere is challenging, requiring either very high isoprene production rate and/or long observation times. Another layer of challenge is that isoprene identification can be hindered by methane, unlike other biosignature gases we proposed: PH₃, which have distinguishable features around 4.5 μm (Sousa-Silva et al., 2020), and NH₃, which have distinguishable features around 1.5, 2 μm (Huang, et al., unpublished data). Therefore, we report on isoprene spectral distinguishability because, as observing capabilities improve in the future, the ultimate limiting factor for isoprene detection will remain the spectral strength, location, and distinguishability of its features, and these are immutable.

When compared with the expected major gases in habitable terrestrial planet atmospheres, isoprene broad band (R approximately 10–20) spectral features are distinguishable from molecules such as H₂O, CO₂, CO, NH₃, and H₂S (see Supplementary Appendix Fig. A3). However, distinguishing isoprene from CH₄ will be challenging and requires further discussion. The column-averaged mixing ratio of methane in the six simulation scenarios is in the range between 1 and 100 ppm (see Supplementary Appendix Fig. A1 for detailed mixing ratio profile). For H₂-dominated atmospheres, CH₄ should be readily present (Seager et al., 2013). In CO₂-dominated atmospheres where CH₄ may not exist, isoprene contamination by CH₄ will not be an issue though other hydrocarbons might still confuse isoprene identification (see Section 5.2 for further discussion).

In an idealistic world with no observational constraints, the spectral features of all molecules are unique. Given the limitation of numbers of photons, however, instruments always have a finite spectral resolution. For detection of habitable exoplanet atmospheres, we must further trade spectral resolution in favor of increasing the (SNR) by binning the data after the data are obtained. We find that the data need to be binned to a relatively low spectra resolution of R = 10–20 to reach statistical significance (as demonstrated in Fig. 12).

At resolution lower than R = 20, distinguishing between isoprene spectral features and methane spectral features at shorter than 4 μm is not possible. Both methane and isoprene share the C-H stretch feature and its overtones; thus, if methane is present in significant quantities, the isoprene 1.6–1.7, 2.1–2.5, and 3.1–3.7 μm features will be masked by methane. In contrast, the 5.4–7.9 μm features and the 9–12 μm features do not overlap with methane spectral features (Fig. 13). Therefore, to confidently detect isoprene in H₂-dominated atmospheres, the identification of both the 5.4–7.5 μm features and the 9–12 μm features is required, therefore requiring the use of both NIRSpec and MIRI, potentially more than doubling the number of transit observations required (since there are fewer photons at longer wavelengths).

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FIG. 13.

Comparison of isoprene (orange) and methane (blue) cross-sections binned to R = 20. The axis shows cross-section (cm⁻²·molecule⁻¹) versus wavelength (μm). Cross-sections for isoprene are measured by Brauer et al. (2014). Cross-section for methane is calculated by using HITRAN line lists with standard pressure and temperature (Gordon et al., 2017). The small panel shows a zoomed-in version of the isoprene-methane-shared spectral feature at 3.1–3.7 μm. We show that distinguishing between isoprene and methane spectral features at 3.1–3.7 μm is still possible at a spectral resolution of R = 20. Distinction between isoprene and methane at spectral resolution lower than this limit is not possible, and, therefore, detection of isoprene's 3.1–3.7 μm feature requires sufficient spectral resolution. We also show that isoprene's 5.4–7.5 μm features and the 9–12 μm features do not overlap with methane's spectral features, so detection of these two features can be done with a lower spectral resolution. Color images are available online.

5.1.1. Limitations with using absorption cross-sections from lab-measured spectra

Using cross-sections calculated from lab-measured data “as is” without estimating uncertainties for high isoprene mixing ratios can result in atmospheric spectra that are saturated and show artificially strong, wide, and featureless absorption bands (see Supplementary Appendix Fig. A4), which lead to inconclusive detection predictions. This effect is unphysical, because in some wavelength ranges, the true cross-section values are likely much smaller than the instrumental noise floor. The Brauer et al. (2014) wavelength-independent uncertainty is approximately four orders of magnitude weaker than the strongest absorption peaks of isoprene. Based on Beer-lambert law, for transmission spectroscopy, the cross-section uncertainty will also need to be eight orders of magnitude weaker than the strongest absorption peaks to avoid the unphysical effect. Therefore, we recommend future lab-based measurements of the isoprene cross-sections to focus on measuring the strength of the weak absorption features, or location of the spectra where there are no spectral peaks, so that it is possible to differentiate between real, but weak transitions and the noise floor.

A possible work-around method is to subtract the uncertainties from the data, leaving only the strongest peaks. However, we disfavor discarding cross-section values below an arbitrary value because it can remove weak, but real, absorption lines. Although individually these weak lines are negligible, collectively they can drastically change the overall opacity, and subsequently conclusions on the potential for detection. We show in Supplementary Appendix Fig. A4 how such an unphysical noise floor cut-off can artificially remove the weak features of isoprene and re-engineer the spectrum and associated detectability of isoprene.

In addition, we encourage the measurement of isoprene spectra to cover a broad temperature/pressure range relevant for exoplanet atmospheres. A broader coverage as compared with the current standard temperature and pressure measurements would allow extrapolation of isoprene cross-sections to conditions that are more appropriate for the upper atmosphere of a variety of exoplanets. Calculating molecular line lists by using ab initio theoretical quantum mechanical methods is computationally demanding (e.g., Tennyson and Yurchenko, 2012), often requiring years of work even for a small molecule, and it is not currently possible to obtain accurate theoretical cross-sections for isoprene due to the complexity of the molecule (see Sousa-Silva et al., 2019 for a more in-depth discussion on alternatives). However, we emphasize that our SEAS model is sufficiently versatile to be able to quickly update its predictions on isoprene detectability whenever improved cross-sections for isoprene become available.

5.1.2. Limitations to isoprene reaction rates

In this work, we have only focused on the reaction of isoprene with UV and the dominant radical species O^⋅ and ⋅OH. The photochemistry of isoprene with other, potentially relevant radicals, such as H^⋅, Cl^⋅, and ^⋅C_nH_m is insufficiently studied. Inclusion of these radicals may potentially increase the isoprene destruction rate. Our models may not include all chemical reactions that are relevant to anoxic, temperate terrestrial planets. Therefore, more detailed studies of anoxic atmospheric chemical reaction networks are required.

Many M dwarf stars have frequent, strong flares. Flares introduce intense packets of UV radiation capable of destroying biosignature gases, including isoprene (Segura et al., 2010; Tilley et al., 2019). Recent work by Günther et al. (2019) has found 30% of late M dwarf stars and 5% of early M dwarf stars display active flaring events. Future photochemistry models, therefore, will require consideration of flaring activities and addressing how flaring activities impact habitability and accumulation of biosignature gases.

5.1.3. Limitations to understanding isoprene induced haze

No one has yet addressed the formation of isoprene-induced hazes in anoxic planetary atmospheres. On Earth, isoprene destruction rapidly leads to haze formation. Further studies on constraining the isoprene-haze mass ratio and mean particle size in anoxic planetary atmospheres are needed because sub-micron haze particles can heavily mute transmission spectral features at wavelengths up to 4 μm, as demonstrated in Section 4.3.

In addition, high-altitude hazes in an anoxic atmosphere could act as a UV shielding mechanism for biosignature gases, therefore increasing the probability of their accumulation (Segura et al., 2005; Seager et al., 2013).