Photosynthesis on Earth-like planets

This scenario corresponds to a tidally locked exoplanet orbiting a star, which is expected to be ubiquitous for planets in the habitable zone of dwarf stars (Barnes Reference Barnes2017). It is conceivable that some of the best-known planets discovered in recent times such as Proxima b (Anglada-Escudé et al. Reference Anglada-Escudé, Amado, Barnes, Berdiñas, Butler, Coleman, de La Cueva, Dreizler, Endl, Giesers, Jeffers, Jenkins, Jones, Kiraga, Kürster, López-González, Marvin, Morales, Morin, Nelson, Ortiz, Ofir, Paardekooper, Reiners, Rodríguez, Rodríguez-López, Sarmiento, Strachan, Tsapras, Tuomi and Zechmeister2016) and the seven planets around TRAPPIST-1 (Gillon et al. Reference Gillon, Triaud, Demory, Jehin, Agol, Deck, Lederer, de Wit, Burdanov, Ingalls, Bolmont, Leconte, Raymond, Selsis, Turbet, Barkaoui, Burgasser, Burleigh, Carey, Chaushev, Copperwheat, Delrez, Fernandes, Holdsworth, Kotze, Van Grootel, Almleaky, Benkhaldoun, Magain and Queloz2017) might belong to this category. As the nightside would always face away from the star, it cannot support photosynthesis on its own because it does not receive stellar radiation. However, the existence of an exomoon can, perhaps, enable photosynthesis at full moon on the planetary nightside provided that (7) is satisfied.

Figure 1 shows the maximum separation between the planet and the moon (d) that still permits photosynthesis to occur on the nightside at full moon as a function of the stellar temperature for different exomoon sizes^{Footnote 1}. As the moon size gets smaller, d also decreases along expected lines. When the stellar temperature is lowered, fewer PAR photons are received, causing d to decrease in order to compensate for the reduction in PAR flux. We have also plotted the Roche limit (d _L) for an Earth-like planet under the assumption that its exomoon has a mean density comparable to the Moon; for fluid satellites, d _L is expressible as

(8)$$ d_{\rm L} \approx 2.46 R_{\rm planet} \left({\rho_{\rm planet} \over \rho_{\rm moon}}\right)^{1/3}, $$

where R _planet is the planet's radius, while ρ_planet and ρ_moon are the densities of the planet and its moon, respectively (Murray and Dermott Reference Murray and Dermott1999). The significance of the Roche limit stems from the fact that d < d _L would lead to disruption of the exomoon due to tidal forces exerted by the planet.

Fig. 1. The maximum separation (d) between the planet and the moon (in units of $R_\oplus$) for photosynthesis to occur on the nightside of the planet at full moon, as a function of the stellar temperature (in K). The various curves correspond to d for different exomoon sizes. The horizontal red line corresponds to the Roche limit for an Earth-analogue assuming that the exomoon's composition is similar to that of Earth's moon.

If we substitute d = d _L in (7), we can determine the lower bound on the radius of the exomoon as a function of the stellar temperature. The resulting criterion has been plotted in Fig. 2. This figure implies that the minimum exomoon radius must be approximately half the radius of the Earth's moon. As no exomoons have been conclusively identified so far^{Footnote 2}, the frequency of large exomoons as a function of the star spectral type remains unknown. However, theoretical considerations suggest that compact exoplanetary systems around low-mass star (e.g. TRAPPIST-1) have a low likelihood of hosting exomoons (Kane Reference Kane2017).

Fig. 2. The minimum moon radius (in $R_\oplus$) required in order to enable photosynthesis to occur on the nightside of a tidally locked planet, as a function of the stellar temperature (in K). The parameters for Earth's moon (the black dot) are shown for reference.

There is another vital issue that must be taken into account. If the exomoon's orbit is not stable, any photosynthesis driven by it will be transient in nature. Hence, it is important for the exomoon to be able to survive over long timescales without escaping the planet or being disrupted. The issue of the orbital stability of exomoons is complex because it is sensitive to the initial spin period of the planet, the tidal dissipation factor of the planet, the mass of the exomoon, the initial moon–planet and planet–star separation, the orientation of their orbital planes and the spectral type of the host star among other factors.

Sasaki and Barnes (Reference Sasaki and Barnes2014) carried out numerical simulations and found that stars with stellar mass $M_\star < 0.4 M_\odot$ were unlikely to host exomoons over Gyr timescales for a wide range of bulk compositions for the planet–moon system. On the other hand, numerical results from Piro (Reference Piro2018) indicate that stars with $M_\star < 0.5 M_\odot$ might be able to retain their moons over timescales of ~ 10⁹ yrs if the planet was initially situated outside the habitable zone before potentially migrating inwards. This inward migration could have occurred for the planets of the TRAPPIST-1 system (Unterborn et al. Reference Unterborn, Desch, Hinkel and Lorenzo2018) and other planetary systems detected by the Kepler mission (Winn and Fabrycky Reference Winn and Fabrycky2015).

Photosynthesis on Earth-like moons

The second scenario we consider is a large exomoon with an Earth-like atmosphere (albeit not necessarily the same size) orbiting a gas giant planet in the habitable zone (Williams et al. Reference Williams, Kasting and Wade1997; Heller et al. Reference Heller, Williams, Kipping, Limbach, Turner, Greenberg, Sasaki, Bolmont, Grasset, Lewis, Barnes and Zuluaga2014). In this setting, starlight reflected from the giant planet would illuminate the moon during its night and enable photosynthesis; the relevant geometry for this case has been illustrated in Cockell et al. (Reference Cockell, Raven, Kaltenegger and Logan2009).

We can estimate the constraints on the planet–moon separation by making use of (7) and carrying out an analysis along the lines of section 3.1. However, it is important to appreciate a couple of distinctions. Recall that, as per our notation, R _P now refers to the radius of the gas giant, which we shall measure in units of Jupiter's radius (R _J). Second, by using (8), we find that the Roche limit is d _L ≈ 1.53 R _planet after supposing that the densities of the giant planet and the habitable exomoon are similar to that of Jupiter and Earth, respectively.

However, this is not the only constraint on the planet–moon separation (d). Assessing the habitable zone for an exomoon is a complex endeavour because it depends not only on the properties of the classical circumstellar habitable zone (e.g. stellar flux) but also the eccentricity of the moon's orbit, its inclination to the ecliptic, its rheology, the mass of the giant planet and the value of d to name a few (Heller et al. Reference Heller, Williams, Kipping, Limbach, Turner, Greenberg, Sasaki, Bolmont, Grasset, Lewis, Barnes and Zuluaga2014; Dobos and Turner Reference Dobos and Turner2015; Forgan and Dobos Reference Forgan and Dobos2016; Dobos et al. Reference Dobos, Heller and Turner2017). In view of this complexity, it is difficult to identify a realistic lower bound on d. However, when the stellar insolation received by the planet–moon system is similar to that incident on the Earth, a cut-off of d _min ≈ 10 R _planet appears to be reasonable (Heller and Barnes Reference Heller and Barnes2015; Zollinger et al. Reference Zollinger, Armstrong and Heller2017). When d < d _min, the planet is susceptible to a runaway greenhouse effect for ${\cal O}(10^8)$ yr, and could therefore end up losing much of its water inventory during this period (Heller and Barnes Reference Heller and Barnes2015).

The maximum planet–moon separation that permits photosynthesis at night on the exomoon by way of reflected light from the giant planet is plotted in Fig. 3. At all stellar temperatures, we find that d > d _min. Hence, it would seem as though there exist regions of parameter space where the exomoon is situated sufficiently far from the planet so as to remain habitable while simultaneously able to receive enough PAR to power photosynthesis via reflected light.

Fig. 3. The maximum separation (d in units of R _J) between a giant planet and an Earth-like moon for photosynthesis on the moon at night (via reflected light from the planet), as a function of the stellar temperature (in K). The various black curves correspond to d for different radii of the giant planet. The red curves (for the corresponding planetary sizes) depict the cut-off distances for d that must be exceeded in order to ensure that the moon is habitable.

However, there is another factor that needs to be taken into consideration. As the habitable zones of low-mass stars are located at close-in distances, any exomoons in this region are subject to strong tidal torques from the star. Numerical models indicate that exomoons in habitable zones around stars with $M_\star \lesssim 0.2 M_\odot$ are unlikely to be habitable because of stellar perturbations, and even those around stars with $0.2 M_\odot < M_\star \lesssim 0.5 M_\odot$ may experience considerable stellar gravitational effects (Heller Reference Heller2012; Zollinger et al. Reference Zollinger, Armstrong and Heller2017).

The basis of photosynthesis

The photosynthetic machinery inherent to organisms on Earth is intricate and characterized by its complex biochemistry and physiology. Hence, it is not immediately obvious a priori as to which features found in Earth-based photoautotrophs would also be manifested on other habitable worlds. For this reason, we will focus on highlighting only a few generic features of photosynthesis, with an emphasis on oxygenic photosynthesis, which might exhibit some degree of universality. Comprehensive reviews of this subject can be found in Hohmann-Marriott and Blankenship (Reference Hohmann-Marriott and Blankenship2011), Blankenship (Reference Blankenship2014), Nelson and Junge (Reference Nelson and Junge2015) and Fischer et al. (Reference Fischer, Hemp and Johnson2016).

In its most basic form, the net reaction of photosynthesis is expressible as follows:

(9)$$ {\rm CO}_2 + 2{\rm H}_2{\rm X}\mathrel{\mathop{\longrightarrow} \limits_{\rm pigments}^{h\nu }} {\rm CH}_2{\rm O} + {\rm H}_2{\rm O} + 2{\rm X}. $$

In the above equation, H₂X denotes the reducing agent (i.e. electron donor) that undergoes biochemical oxidation to yield electrons that are utilized in subsequent biochemical reactions. Examples of reducing agents used in photosynthesis include H₂S, H₂ and H₂O; for the latter, note that O₂ is the metabolic waste product. The product CH₂O essentially represents a reduced carbon compound (e.g. sugar) where the energy is stored. The net reaction is endergonic in nature, owing to which the input of light energy (exemplified by hν) is necessary.

In a recent review, Schwieterman et al. (Reference Schwieterman, Kiang, Parenteau, Harman, DasSarma, Fisher, Arney, Hartnett, Reinhard, Olson, Meadows, Cockell, Walker, Grenfell, Hegde, Rugheimer, Hu and Lyons2018) posited that three basic stages ought to be operational in a generic photosynthetic apparatus (reaction centre (RC)). The photosynthetic reactions are initiated via the photoelectric effect and are reliant on the absorption of photons by a suitable pigment to produce electrons in an excited state. Given sufficient energies, the electrons are ejected from the molecule, thus leaving behind an electron hole. The ejected electron must be replaced, which can happen either through cyclical or non-cyclical electron transfer mechanisms. In the case of the latter, the ejected electron is replaced when the biomolecule(s) in the photosystem under question oxidizes the reducing agent (H₂X) and yields the metabolic product X. The energy inherent to the ejected electron is used for two purposes: the oxidation of the reducing agent and the synthesis of reduced carbon compounds (which act as repositories for the captured energy) via redox reactions.

An important point to recognize here is that the photon energy is not directly used for photolysis of the reductant. Instead, as noted above, the oxidation of the reducing agent requires the biomolecule(s) comprising the photosystem to be more oxidizing than the former. Bearing this fact in mind, we turn our attention to the potential reductants. The redox potentials for H₂/2H⁺ and H₂S/S⁰ are − 0.42 V and − 0.24 V, respectively, at neutral pH (Hohmann-Marriott and Blankenship Reference Hohmann-Marriott and Blankenship2011). In contrast, the redox potential for the H₂O/O₂ pair is + 0.815 V (Hohmann-Marriott and Blankenship Reference Hohmann-Marriott and Blankenship2011). In other words, it is relatively easier to extract electrons from strong reductants such as H₂ and H₂S. Hence, it is not surprising that microbes reliant on these reductants possess comparatively simpler photosynthetic machinery, i.e. they have only a single photosystem (PSI or PSII). It is commonly supposed that the anoxygenic photosynthesis (with its single photosystem) evolved on Earth earlier than its oxygenic counterpart (which has two photosystems), but the evidence favouring this hypothesis has been challenged as of late (Cardona Reference Cardona2019).

For the time being, let us adopt the notion that anoxygenic photosynthesis would have evolved more readily on other worlds because the presence of stronger reductants (e.g. H₂S) would impose less stringent constraints on the oxidizing biomolecules in the photosystem. However, at this juncture, we encounter a potential bottleneck imposed by geology, namely, the available fluxes of these reductants. On Earth, the geological fluxes of electron donors for photosynthesis were probably limited, which in turn may have yielded a net primary productivity (NPP) that was ~3 orders of magnitude smaller than the present-day value (Ward and Shih Reference Ward and Shih2019; Ward et al. Reference Ward, Rasmussen and Fischer2019). Once water could be utilized as an electron donor, the bottleneck on NPP was possibly eliminated; other factors such as nutrients (e.g. phosphorus) would have limited the NPP instead.

Therefore, unless other worlds have a much higher inventory of volcanogenic reducing agents, it is likely that higher NPP is typically achievable by the use of water as an electron donor. However, as mentioned earlier, the redox potential for the water–oxygen pair is very high with respect to other reducing agents commonly employed in anoxygenic photosynthesis. Hence, several authors have suggested that intermediate reducing agents such as Fe²⁺ and Mn²⁺, especially the latter, may have served as transitional electron donors (Fischer et al. Reference Fischer, Hemp and Johnson2016; Meadows et al. Reference Meadows, Reinhard, Arney, Parenteau, Schwieterman, Domagal-Goldman, Lincowski, Stapelfeldt, Rauer, DasSarma, Hegde, Narita, Deitrick, Lustig-Yaeger, Lyons, Siegler and Grenfell2018); for instance, the redox potential for the Fe²⁺/Fe³⁺ pair at neutral pH is ~0.2 V (Hohmann-Marriott and Blankenship Reference Hohmann-Marriott and Blankenship2011). The oxidation of water in photoautotrophs on Earth is facilitated by the water-oxidizing complex (WOC) situated in photosystem II (PSII). The core of the WOC is a manganese cluster (Mn₄CaO₅), whose oxidation states, thermodynamics and kinetics are described in Vinyard et al. (Reference Vinyard, Ananyev and Dismukes2013), Wiechen et al. (Reference Wiechen, Najafpour, Allakhverdiev and Spiccia2014) and Nelson and Junge (Reference Nelson and Junge2015).

All oxygenic photoautotrophs on Earth rely upon the manganese cluster (in the WOC) for the purpose of evolving molecular oxygen. Hence, it is natural to wonder whether other variants of the WOC are feasible. Although no such examples appear to exist in photoautotrophs, several alternatives have been artificially designed in the laboratory. Some of the alternatives to manganese in the WOCs include copper (Cu), nickel (Ni), ruthenium (Ru) and iridium (Ir); reviews of this rapidly growing subject can be found in Blakemore et al. (Reference Blakemore, Crabtree and Brudvig2015), Li et al. (Reference Li, Güttinger, Moré, Song, Wan and Patzke2017), Suen et al. (Reference Suen, Hung, Quan, Zhang, Xu and Chen2017) and Zhang and Sun (Reference Zhang and Sun2019). Molecular catalysts synthesized using these elements enable the ‘splitting’ of water to yield molecular oxygen as follows:

(10)$$ 2 {\rm H_2O \rightarrow O_2 + 4 H^+ + 4 e^-} $$

In principle, therefore, it is conceivable that WOCs reliant on the likes of copper or nickel clusters instead of manganese might evolve on other planets and moons.

When it comes to light-harvesting pigments, it is important to distinguish between the antenna pigments that absorb photons (of different wavelengths) and transmit them to the RC pigment, which can donate electrons by absorbing photons of a particular wavelength and undergoing excitation across the band gap (Kiang et al. Reference Kiang, Siefert, Govindjee and Blankenship2007). The colour and biosignatures produced by photosynthetic organisms are dependent not only on the RC pigment but also on the antenna pigments. It is not easy to determine over what wavelengths pigments will optimally absorb radiation because it is governed by the oxidation state of the pigment macrocycle as well as the functional groups and proteins surrounding the macrocycle. The peak absorption wavelengths for light-harvesting pigments range from ~0.7 to 1.0 μm for bacteriochlorophylls to ~0.4 and ~0.7 μm for chlorophylls (Schwieterman et al. Reference Schwieterman, Kiang, Parenteau, Harman, DasSarma, Fisher, Arney, Hartnett, Reinhard, Olson, Meadows, Cockell, Walker, Grenfell, Hegde, Rugheimer, Hu and Lyons2018). Another notable light-harvesting pigment, bacteriorhodopsin, exhibits a peak of ~0.6 μm (DasSarma and Schwieterman Reference DasSarma and Schwieterman2018).

In spite of the fact that no convincing alternatives to tetrapyrrole-based pigments (e.g. chlorophylls) have been identified thus far, it is difficult to estimate what factors will govern the peak absorbance of pigments on other worlds. This issue was explored by Kiang et al. (Reference Kiang, Siefert, Govindjee and Blankenship2007) wherein it was suggested that the peak absorbance of exo-pigments might occur near: (a) the wavelength associated with the maximum value of the incident photon flux density or (b) the longest wavelength that permits the resonance transfer of excitation energy and energy funnelling in antenna and RC pigments. If we focus on (a), it is apparent that the peak absorbance will be shifted towards longer wavelengths on M-dwarfs as the peak photon flux density of these stars occurs in the near-infrared. There is also an extra complication introduced by atmospheric transmission, which will depend on the chemical composition and bulk properties of the atmosphere. As the latter is empirically unknown for habitable exoplanets (or exomoons) at this stage, we will restrict ourselves to Earth-like worlds.

Alternatives to conventional oxygenic photosynthesis

As we have seen in the preceding paragraph, it is conceivable that near-IR photons might be employed by photoautotrophs deriving their energy from K- and M-dwarfs. It should also be recalled that the wavelength of photons does not directly influence the oxidation of water. Instead, it is the redox potential of the RC in PSII that dictates whether water oxidation is feasible or not; the corresponding redox potential is estimated to be ~1.26 V (Rappaport et al. Reference Rappaport, Guergova-Kuras, Nixon, Diner and Lavergne2002). In principle, by chaining a number of photosystems together, it is theoretically possible to use photons of longer wavelengths to achieve the oxidation of water and the synthesis of reduced carbon compounds (Hill and Bendall Reference Hill and Bendall1960; Hill and Rich Reference Hill and Rich1983; Kiang et al. Reference Kiang, Segura, Tinetti, Govindjee, Blankenship, Cohen, Siefert, Crisp and Meadows2007). However, in doing so, it is important to appreciate that other consequences such as lowered quantum yield may arise as a result.

Hence, a ${\cal N}$-photosystem series utilizing wavelengths up to λ_max can supply the same energy input as the two photosystems (PSI and PSII) of oxygenic photosynthesis, where the relationship between λ_max and ${\cal N}$ is given by Wolstencroft and Raven (Reference Wolstencroft and Raven2002); Kiang et al. (Reference Kiang, Segura, Tinetti, Govindjee, Blankenship, Cohen, Siefert, Crisp and Meadows2007):

(11)$$ {\cal N} \approx 2\left({\lambda_{\rm max}} \over {0.7 {\rm \mu m}}\right). $$

For the ${\cal N}$-photosystem series, the minimum photon flux must be adjusted from Φ_c to $({\cal N}/2) \Phi _{\rm c}$ (Wolstencroft and Raven Reference Wolstencroft and Raven2002). We can repeat the same calculation in section 2 with the modified flux and the adjusted upper wavelength limit. By doing so, we find that the analogue of (7) is

(12)$$ \left({A_{\rm P} \over 0.2}\right)\left({R_{\rm P} \over R_\oplus}\right)^2 \left({d \over 60R_\oplus}\right)^{-2} \left({T_\star \over T_\odot}\right)^{-1} {\cal G}(T_\star) \gtrsim 0.5, $$

where the new function ${\cal G}(T_\star )$ is defined as

(13)$$ {\cal G}(T_\star) \approx {2 \over {\cal N}} {\int\;}_{\!\!\! 2x_1(T_\star)/ {\cal N}}^{x_2(T_\star)} {x'^2\,{\rm d} x' \over \exp\left(x'\right) - 1}. $$

It is possible to use the above equation to obtain the analogues of the results from section 3. Obtaining the appropriate plots is straightforward, and our basic qualitative conclusions are not much affected, owing to which we provide only one example here. For ${\cal N} = 3$ and ${\cal N} = 4$, the equivalent of Fig. 2 is plotted in Fig. 4. The chief differences between higher-order photosystem schemes and conventional oxygenic photosynthesis, with its PSI and PSII, are twofold. First, for ${\cal N} = 3$ and ${\cal N} = 4$, we see that the dependence of the moon size on the temperature is weak. Second, we find that the minimum moon size is lowered by a factor of ≲2, implying that it must be only ~20% the size of Earth's moon. Thus, by linking a higher number of photosystems, even moons slightly larger than Enceladus (whose radius is $\sim 0.04R_\oplus$) might permit oxygenic photosynthesis to function on the planet's nightside under ideal circumstances.

Fig. 4. The minimum moon radius (in $R_\oplus$) necessary for facilitating photosynthesis on the nightside of a tidally locked planet, as a function of the stellar temperature (in K). The unbroken, dotted and dashed curves correspond to the limits for conventional oxygenic photosynthesis (PSI and PSII), 3-photon and 4-photon oxygenic photosynthesis schemes, respectively; the associated maximum wavelengths are ~0.7, ~1.05 and ~1.4 μm, respectively, as seen from (11). The black dot corresponds to the parameters for Earth's moon and is shown for reference.

Now, let us turn our attention to variants of photosynthesis beyond those found on Earth. This subject has received comparatively little attention because of the lack of direct empirical evidence. We focus on a single example for the sake of simplicity, namely, ‘hydrogenic photosynthesis’. Studies of exoplanets indicate that many of them may possess substantial hydrogen–helium atmospheres (Batalha et al. Reference Batalha, Rowe, Bryson, Barclay, Burke, Caldwell, Christiansen, Mullally, Thompson, Brown, Dupree, Fabrycky, Ford, Fortney, Gilliland, Isaacson, Latham, Marcy, Quinn, Ragozzine, Shporer, Borucki, Ciardi, Gautier, III, Haas, Jenkins, Koch, Lissauer, Rapin, Basri, Boss, Buchhave, Carter, Charbonneau, Christensen-Dalsgaard, Clarke, Cochran, Demory, Desert, Devore, Doyle, Esquerdo, Everett, Fressin, Geary, Girouard, Gould, Hall, Holman, Howard, Howell, Ibrahim, Kinemuchi, Kjeldsen, Klaus, Li, Lucas, Meibom, Morris, Prša, Quintana, Sanderfer, Sasselov, Seader, Smith, Steffen, Still, Stumpe, Tarter, Tenenbaum, Torres, Twicken, Uddin, Van Cleve, Walkowicz and Welsh2013; Venturini and Helled Reference Venturini and Helled2017). On such worlds, Bains et al. (Reference Bains, Seager and Zsom2014) analysed the prospects for hydrogenic photosynthesis, whose net reaction is given by

(14)$$ {\rm CH_4} + {\rm H_2O} \rightarrow {\rm CH_2O} + 2{\rm H_2}, $$

and it is more instructive to break it down into half-reactions as follows:

(15)$$ \eqalign{ & {\rm CH_4} + {\rm H_2O} \rightarrow {\rm CH_2O} + 4{\rm H^+} + 4{\rm e^-} \cr & 4{\rm H^+} + 4{\rm e^-} \rightarrow 2{\rm H_2}. } $$

Bains et al. (Reference Bains, Seager and Zsom2014) proposed that hydrogenic photosynthesis was more advantageous than oxygenic photosynthesis on worlds with hydrogen-dominated atmospheres because the energetic costs in synthesizing a given quantity of biomass are nearly an order of magnitude smaller relative to oxygenic photosynthesis, and the longest wavelength that permits this variant of photosynthesis is ~ 1.5 μm; in contrast, for conventional photosynthesis the maximum wavelength is around 750 nm (Nürnberg et al. Reference Nürnberg, Morton, Santabarbara, Telfer, Joliot, Antonaru, Ruban, Cardona, Krausz, Boussac, Fantuzzi and Rutherford2018). If we take the latter factor into account and presume that the minimum photon flux for hydrogenic photosynthesis is comparable to Φ_c, we find that (7) is transformed into

(16)$$ \left({A_{\rm P} \over 0.2}\right)\left({R_{\rm P} \over R_\oplus}\right)^2 \left({d \over 60R_\oplus}\right)^{-2} \left({T_\star \over T_\odot}\right)^{-1} {\cal K}(T_\star) \gtrsim 0.5, $$

where the new function ${\cal G}(T_\star )$ is defined as

(17)$$ {\cal K}(T_\star) \approx {\int\;}_{\!\!\! x_1(T_\star)/2}^{x_2(T_\star)} {x'^2\,{\rm d} x' \over \exp\left(x'\right) - 1}. $$

We can repeat the analysis in section 3 using the above two formulae, but we shall not address this topic further as the calculations are fairly straightforward.

Other modes of carbon fixation

Hitherto, we have tackled the conditions for photoautotrophy on the nightside of planets and moons. However, even in the case of worlds with permanent nightside that do not receive sufficient photon fluxes, it is crucial to recognize that such worlds might still host fairly diverse biospheres. The primary reason is that photosynthesis does not represent the only route to carbon fixation, i.e. the biosynthesis of organic carbon compounds. To put it differently, there are a number of other carbon fixation pathways that can function in the absence of light.

It is instructive to begin by considering the Earth as an example. Most of the biomass on Earth is contributed by photoautotrophs. In particular, land plants (Embryophyta) are believed to make up more than 80% of Earth's total biomass (Bar-On et al. Reference Bar-On, Phillips and Milo2018). Yet, the contribution of microbes dwelling in deep subsurface habitats is by no means minimal (Colwell and D'Hondt Reference Colwell and D'Hondt2013). It has been estimated that the majority of Earth's prokaryotes (>80% by weight) dwell in such environments and make up ~13% of the total biomass (Bar-On et al. Reference Bar-On, Phillips and Milo2018). Naturally, not all of these microbes are autotrophs, but it is reasonable to presume that most of them do not rely on phototrophy as these habitats do not have access to sufficient fluxes of PAR photons.

Recent estimates indicate that >90% of carbon fixation per year by plants, algae and other microbes occurs via the Calvin–Benson–Bassham (CBB) cycle (Schwander et al. Reference Schwander, Schada von Borzyskowski, Burgener, Cortina and Erb2016), which is also referred to as the reductive pentose phosphate cycle (Berg Reference Berg2011). Aside from the CBB cycle, five other major pathways for carbon fixation have evolved on Earth (Fuchs Reference Fuchs2011). Contemporary studies indicate that they are non-negligible contributors to carbon fixation in Earth's oceans (Hügler and Sievert Reference Hügler and Sievert2011). Of these, four of them are cyclic acetyl-CoA–succinyl-CoA pathways that exhibit structural similarities (Bar-Even et al. Reference Bar-Even, Flamholz, Noor and Milo2012); here, note that CoA signifies coenzyme A. The outlier, and the sixth avenue for carbon fixation, is the reductive acetyl-CoA pathway (also called the Wood–Ljungdahl pathway) – which entails the fixation of two CO₂ molecules and leads to the formation of acetyl-CoA – because of its non-cyclic nature (Ragsdale and Pierce Reference Ragsdale and Pierce2008; Berg Reference Berg2011). Aside from the six naturally occurring routes, a synthetic pathway for carbon fixation involving crotonyl-coenzyme A, ethylmalonyl-CoA and hydroxybutyryl-CoA was demonstrated in vitro (Schwander et al. Reference Schwander, Schada von Borzyskowski, Burgener, Cortina and Erb2016).

Despite the dissimilarities among the five pathways aside from the CBB cycle, one of the most striking universal aspects is the central role played by acetyl-coenzyme A (acetyl-CoA). The importance of acetyl-CoA extends beyond its role in carbon fixation pathways because it also regulates mitosis and autophagy, and maintains the balance between cellular anabolism and catabolism (Pietrocola et al. Reference Pietrocola, Galluzzi, Bravo-San Pedro, Made and Kroemer2015). Several hypotheses have, therefore, posited that acetyl-CoA was an essential component of the first metabolic pathway that evolved on Earth (Martin and Russell Reference Martin and Russell2006; Pietrocola et al. Reference Pietrocola, Galluzzi, Bravo-San Pedro, Made and Kroemer2015). Of these five networks, the two most important are the reverse tricarboxylic acid (rTCA) cycle and the Wood–Ljungdahl pathway. A combination of physiological, genomic and bioenergetic arguments have been marshalled (Smith and Morowitz Reference Smith and Morowitz2016; Nunoura et al. Reference Nunoura, Chikaraishi, Izaki, Suwa, Sato, Harada, Mori, Kato, Miyazaki, Shimamura, Yanagawa, Shuto, Ohkouchi, Fujita, Takaki, Atomi and Takai2018; Weiss et al. Reference Weiss, Preiner, Xavier, Zimorski and Martin2018) in conjunction with promising laboratory experiments (Muchowska et al. Reference Muchowska, Varma, Chevallot-Beroux, Lethuillier-Karl, Li and Moran2017; Varma et al. Reference Varma, Muchowska, Chatelain and Moran2018; Muchowska et al. Reference Muchowska, Varma and Moran2019) to suggest these pathways were the first to emerge on Earth; in fact, certain proposals hypothesize that a hybrid of these two networks might have constituted the ancestral metabolic pathway (Braakman and Smith Reference Braakman and Smith2012; Camprubi et al. Reference Camprubi, Jordan, Vasiliadou and Lane2017).

If, for the sake of argument, we suppose that chemoautotrophy – most likely the rTCA cycle, the Wood–Ljungdahl pathway, or some combination thereof – arose first on other habitable worlds, there still remains the question of how photosynthesis subsequently evolved. With regards to this issue, an important point to note is that many components of the photosynthetic apparatus were probably ported over from chemoautotrophs, with notable examples including (i) iron-sulphur proteins, (ii) reduced ferredoxins and quinones and (iii) oxidized electron carriers (e.g. cytochromes and cupredoxins). Hence, it is plausible that (an)oxygenic photosynthesis evolved from chemoautotrophy (Schoepp-Cothenet et al. Reference Schoepp-Cothenet, Van Lis, Atteia, Baymann, Capowiez, Ducluzeau, Duval, Ten Brink, Russell and Nitschke2013; Björn and Govindjee Reference Björn, Govindjee and Björn2015). Moreover, RuBisCO (used in the CBB cycle) exhibits close similarities to other proteins, such as 2,3-diketo-5-methylthiopentyl-1-phosphate enolase, and may have originated from a protein facilitating sulphur metabolism (Björn and Govindjee Reference Björn, Govindjee and Björn2015).

A number of hypotheses have been put forth to explain how, why and where photosynthesis first arose and the connection to prior carbon fixation pathways. Nisbet et al. (Reference Nisbet, Cann, Lee and Dover1995) suggested that photosynthesis evolved from phototaxis, with light from hydrothermal vents providing the selective force. Martin et al. (Reference Martin, Bryant and Beatty2017) proposed that photosynthesis arose to bypass the necessity of flavin-based electron bifurcation to yield reduced ferredoxin utilized in carbon fixation by chemoautotrophs. Martin et al. (Reference Martin, Bryant and Beatty2017) also conjectured that the high fluxes of ultraviolet (UV) radiation at the surface (see Cnossen et al. Reference Cnossen, Sanz-Forcada, Favata, Witasse, Zegers and Arnold2007) hindered the evolution of photosynthesis, and that it emerged instead in the low-intensity IR-dominated regions at hydrothermal vents with Zn-tetrapyrroles constituting the first photopigments. It should, however, be recognized that a number of UV screens potentially existed on early Earth ranging from hazes to biomolecules (Lingam and Loeb Reference Lingam and Loeb2019b), which could have permitted the evolution of photoautotrophy at the surface.

However, when we consider the permanent nightside of tidally locked planets, the reflected light from a moon is the primary source of radiation. As we have seen earlier, this intensity is orders of magnitude lower than the photon flux incident on Earth. Hence, the aforementioned issue arising from high UV radiation is not applicable. Thus, it seems equally feasible that photosynthesis could arise from prior pathways either on the surface (due to the low-intensity radiation) or near black smokers; note that photoautotrophic green sulphur bacteria (Chlorobiaceae) have been detected in the latter environment (Beatty et al. Reference Beatty, Overmann, Lince, Manske, Lang, Blankenship, Van Dover, Martinson and Plumley2005; Raven and Donnelly Reference Raven, Donnelly, de Vera and Seckbach2013).