Life

The definition of life is the subject of intense debate in the literature (see e.g. Cleland & Chyba Reference Cleland and Chyba2002; Kolb Reference Kolb2007; Lazcano Reference Lazcano2008). For the purpose of our discussion we consider a series of requirements that should characterize, by definition, any form of life in the universe, focusing on properties relevant for the cross-feedback between life and its environment. With this pragmatic approach, we define life, terrestrial and non-terrestrial, with the following series of requirements.

At the most basic level, life is an active network of chemical reactions, the metabolism, leading to the synthesis and/or cleavage of functional molecular structures organized in cells. In conjunction with covalent bonding, hydrogen bonding is essential for building up any possible molecular structure of biochemical interest (see e.g. Jeffrey & Saenger Reference Jeffrey and Saenger1991). Biochemical processes inside cells require a liquid medium/solvent; owing to the special properties of the water molecule (see e.g. Bartik et al. Reference Bartik, Bruylants, Locci, Reisse, Gargaud, López-García and Martin2011), we restrict our attention to water-based life, although we acknowledge the possibility of other chemistries that could form the basis of life under some circumstances (Schulze-Makuch & Irwin Reference Schulze-Makuch and Irwin2008; Budisa & Schulze-Makuch Reference Budisa and Schulze-Makuch2014). Cells must be able to grow and reproduce by means of a set of instructions, the genetic information, recorded in molecular form. At higher level of internal organization, complex life is composed of a coordinated network of differentiated cells specialized in different functions. Life inevitably undergoes Darwinian evolutionFootnote ¹ , a gradual modification of the genetic instructions transmitted during reproduction, driven by long-term adaptation to ambient conditions.

At variance with the life that we know, non-terrestrial life could feature a different set of molecular structures and/or biochemical processes, and/or a different way of organizing/transmitting the genetic information, and/or any other possible difference at a higher level of complexity, as long as such differences are consistent with the above defining requirements.

Complex life

Analysis of the huge record of terrestrial evolutionary pathways indicates that unicellular organisms are not able to exploit all the potential resources offered by the environment. Multicellularity evolved many times on Earth, possibly as a response to environmental conditions (e.g. Grosberg & Strathmann Reference Grosberg and Strathmann2007). By analogy, we assume that, given sufficient time and appropriate ambient conditions, multicellularity would also emerge outside Earth. Several lines of evidence indicate that oxygen metabolism is an essential requirement of complex life (Catling et al. Reference Catling, Glein, Zahnle and McKay2005). The general lack of anaerobic metazoans (see however Danovaro et al. Reference Danovaro, Dell'Anno, Pusceddu, Gambi, Heiner and Kristensen2010) is probably due to the fact that only the oxygenic metabolism is sufficiently efficient to satisfy the energetic requirements that maintain the functional capabilities of complex life. There are some other terminal electron acceptors that could, in principle, fulfil the role that oxygen plays in earth-based life, and that might allow non-oxygen-based complex life to evolve on other planets. However, the chemical characteristics and high availability of oxygen in the universe makes it the most likely basis for the metabolism of complex life (Catling et al. Reference Catling, Glein, Zahnle and McKay2005). We therefore assume that oxygen metabolism is essential for any form of complex life. We refer to Lane (Reference Lane2014) for a discussion on the bioenergetic constraints on the evolution of complex life.

Since this work is focused on the relationship between ambient temperature and life, we focus our attention to organisms whose internal temperature, depends directly on and varies with ambient temperature. In terrestrial life these organisms are called poikilotherms because they feature a broad range of internal temperatures (e.g. Precht et al. Reference Precht, Christophersen, Hensel and Larcher1973). Since we are interested in complex life, we focus on multicellular poikilotherms, such as plants (although note that a few plants have a limited form of endothermy, e.g. Minorsky Reference Minorsky2003), invertebrates and ectothermic vertebrates. We omit homeotherms from our discussion because homeotherms are able to maintain a narrow range of internal temperature over a broad range of ambient temperatures (e.g. Ruben Reference Ruben1995) and this capability makes hard to establish thermal limits of habitability. Poikilotherms represent a necessary step along the Darwinian pathway that has led to the emergence of homeotherms on Earth. Since homeotherms must evolve from poikilotherms, a planet must have some regions that are within the range of habitability for poikilotherms for homeothermy to emerge. In this sense, the limits of planetary habitability for poikilotherms are relevant for complex life in general, including homeotherms. This conclusion is reinforced by the fact that poikilotherms, such as plants, lie at the base of the food chain of homeotherms. Homeotherms have emerged only relatively late, a few 100 Myr ago (Hillenius & Ruben Reference Hillenius and Ruben2004), while multicellular poikilotherms have been present for at least 1 Gyr (Grosberg & Strathmann Reference Grosberg and Strathmann2007). If these evolutionary timescales are sufficiently general, multicellular poikilotherms could be the most representative form of complex life in exoplanets.

The multi-path development of multicellularity on Earth had first to undergo prokaryotic to eukaryotic cell evolution, which may have taken place only once in Earth history, possibly as a stochastic endosymbiosis between two prokaryotes (e.g. Lane Reference Lane2014; Koonin Reference Koonin2015). Recently, an archaeal phylum has been found to show traits that may have facilitated the symbiosis (Spang et al. Reference Spang, Saw, Jørgensen, Zaremba-Niedzwiedzka, Martijn, Lind, van Eijk, Schleper, Guy and Ettema2015). The modality of the transition to eukaryotes affects the probability and timescale of subsequent multicellular development. We assume that the minimum timescale is driven by the oxygenation of the atmosphere (see the section ‘Long term habitability’).

In discussing the relationship between ambient temperature and habitability we need to exclude organisms with the technological capability of creating habitable conditions in an otherwise hostile environment. In any case, these organisms could not evolve in hostile conditions, because their evolutionary history would have included forms that did not have such technological capability. Therefore, the limits of habitability that we discuss are also relevant for the potential emergence of any technically able organism.

Habitability

Here we summarize the conceptual framework used to specify the concept of habitability. It is worth emphasizing that the conditions of habitability do not guarantee, per se, the emergence of life in a given planet (see e.g. Cleaves & Chalmers Reference Cleaves and Chalmers2004).

Thermal limits for multicellular poikilotherms

The thermal limits for terrestrial plants, invertebrates and ectothermic vertebrates known at the present time can be summarized as follows. Lower limits for invertebrates and ectothermic vertebrates lie between ~−2 and ~0°C (Clarke Reference Clarke2014). A general figure adopted as the high temperature limit of ectothermic metazoans is 47°C (Pörtner Reference Pörtner2002). For instance, the average upper limit for insects is evaluated as 47.4°C (Addo-Bediako et al. Reference Addo-Bediako, Chown and Gaston2000) and the limit for freshwater invertebrates at ~46°C (Clarke Reference Clarke2014). Also terrestrial and marine invertebrates generally conform to these limits. Possible exceptions are represented by a few species of nematodes that tolerate a temporary temperature peak of 60°C (Steel et al. Reference Steel, Verdoodt, Čerevková, Couvreur, Fonderie, Moens and Bert2013). This is line with the result that metazoans may tolerate temperatures beyond 47°C, but only for a short time (Schmidt-Nielsen Reference Schmidt-Nielsen1997). Previous claims of much higher thermal limits of a marine invertebrate, Alvinella Pompeiana, have been dismissed by a recent study, which indicates an upper limit ~50°C (Ravaux et al. Reference Ravaux, Hamel, Zbinden, Tasiemski, Boutet, Léger, Tanguy, Jollivet and Shillito2013). As far as plants are concerned, the lower thermal limits of angiosperms are similar to those of ectothermic animals, T _L ≥ 0°C, but the tolerance at high temperature is higher, with T _L ≤ ~65°C (Clarke Reference Clarke2014). The higher limit is conservative, since the thermal tolerance of Dichantelium lanuginosum, the plant that holds the high temperature record, is mediated by a mutualistic fungus and a mycovirus. In absence of such mediation, the plant can only grow up to 38°C (Márquez et al. Reference Márquez, Redman, Rodriguez and Roossinck2007). Considering the uncertainties in these type of determinations, we adopt a representative interval 0°C ≤ T _L ≤ 50°C for multicellular poikilotherms. As we discuss below in the section ‘Implications for the generation of atmospheric biosignatures’, these limits are consistent with one of the requirements of the definition of exoplanet habitability, namely the potential generation of biosignatures in the planetary atmosphere.

Thermal performance curves (TPCs)

The rates of metabolism, growth, development, or other biological rates, offer a way to measure the thermal performance of an individual organism, or a population, as a function of ambient temperature. The TPCs obtained with these methods share a common behaviour, well described by curves that rise up to a maximum at some optimal temperature and then fall steeply once this optimal temperature is surpassed (Schulte Reference Schulte2015; Vasseur et al. Reference Vasseur, DeLong, Gilbert, Greig, Harley, McCann, Savage, Tunney and O'Connor2015). In spite of the presence of differences in the slopes of the TPCs versus temperature, or location of the optimal temperature, the same general shape of TPCs is found at different levels of biological complexity, including molecular structures, cells, organisms and populations. The same behaviour is shared by different terrestrial species, often developed along independent evolutionary pathways. This common behaviour supports the existence of universal mechanisms of thermal response. We consider the existence of such mechanisms at different levels of complexity, starting from the molecular level.

Thermal response at the molecular level

Mechanisms of thermal response are well known at the atomic and molecular level. For instance, the polarity of water decreases, as the temperature increases, leading to a decline of the dielectric constant (Carr et al. Reference Carr, Mammucarib and Fosterb2011). This behaviour affects the interaction of water with dissolved biomolecules, in particular lipids, but also proteins and nucleic acids (McKay Reference McKay2014).

A key aspect of the mechanisms of thermal response is the kinetic energy of atoms/molecules, which is governed by the temperature, T. The initial rise of TPC can be understood in terms of the kinetic energy of the reactants taking part to biochemical processes. The observed behaviour often obeys to the Arrhenius law, k ~ e ^–(Ea/T), where k is the rate of reaction and E _a the activation energy (Arrhenius Reference Arrhenius1915). The higher the temperature, the higher the reaction rate because the reactants are more likely to collide with enough energy to allow the reaction to occur. However, at some point the rise of kinetic energy would tend to randomize molecular structures by violent motion, leading to denaturation of the molecular structures. At this point, a rise of temperature would lead to a fast decline of the thermal performance. The gradual rise and fast decline of the TPCs are in qualitative agreement with such expectations, even though the detailed shapes require more complex explanations (Schulte Reference Schulte2015). It is logical to assume that the same behaviour is also shared by non-terrestrial life of the type we have defined, i.e. life based on chemical processes taking place between molecular structures (see the section ‘Definitions’). Of course, the quantitative thresholds of temperature will depend on the particular molecular structures developed by different forms of life. Even so, broad quantitative thresholds with general validity can be inferred by studying the binding energies of biomolecules.

Thermal response at the unicellular level

Unicellular organisms on Earth, and in particular prokaryotes, have developed several strategies of thermal adaptation. The upper threshold for prokaryotes can be as high as 122°C (Methanopyrus kandleri), while it is ~60°C (and possibly 70°C) for unicellular eukaryotes, such as algae and yeasts. The low limit of T _L can be as low as −20°C for unicellular prokaryotes and eukaryotes. Broadly speaking, the strategies of high temperature adaptation of thermophilic prokaryotes rely on relatively rigid membranes and proteins, while low temperature adaptation of cryophilic prokaryotes are based on relatively loose, more flexible, membranes and proteins (Cavicchioli & Thomas Reference Cavicchioli, Thomas and Schaechter2003). Extant extremophiles use only one of such strategies at a time, i.e. either increasing or decreasing the molecular rigidity, even though the simultaneous presence of both strategies of adaptation is not impossible on biophysical grounds (Schulte Reference Schulte2015). The rigidity and flexibility of molecular structures can be changed, for instance, by varying the proportion of hydrophobic cores, hydrogen bonds and thermophilic amino acids (Cavicchioli & Thomas Reference Cavicchioli, Thomas and Schaechter2003). One may wonder why multicellular life does not benefit of the broader thermal thresholds developed in the framework of the unicellular world. A possible explanation is that the changes of rigidity at the molecular level, with respect to some optimal value, might hinder the integration of higher level structures. For instance, changes of membrane fluidity can affect the functioning of proteins embedded in the mitochondrial membranes and can also diminish the rate of adenosine triphosphate (ATP) production due to leakage of protons through the membrane (Schulte Reference Schulte2015). Another possibility, that we now discuss, is that some of the functions required to integrate processes across cells in multicellular organisms may have a lower maximum temperature threshold than the cellular and subcellular functions of unicellular life.

Thermal response at the multicellular level

Synopsis

A comprehensive mechanistic understanding of the effects of temperature on biological processes is still lacking, particularly at the higher levels of biological complexity (Schulte Reference Schulte2015). In spite of this, the intimate nature of the main mechanisms of thermal response at work in terrestrial life suggests that the same mechanisms would also be at work in other forms of chemical life outside Earth, if any. For water-based life, that we consider here, we argue that the water freezing point, T ~ 0°C for the range of pressures we consider in this work, is a universal lower bound because the kinetic energy of Brownian motion cannot be harvested by molecular motors below the water solidification point. The upper bound would be set by the temperature at which thermal energy denatures the molecular structure most sensitive to heat. Since the number of molecular structures potentially limiting the thermal tolerance must increase with increasing complexity of the organism, the thermal tolerance narrows as complexity increases. Oxygenic metabolism, apparently necessary for the development of complex life, sets tighter thermal limits than other high level functions typical of multicellular life. Taken together, the above conclusions strongly suggest that the thermal limits for complex life will be generally narrower than those implied by the liquid water interval usually adopted in studies of habitability. In lack of better indications, we adopt the thermal limits 0°C ≤ T _L ≤ 50°C, representative of terrestrial multicellular poikilotherms, as a criterion of long-term habitability of complex life outside Earth. The fact that such limits are shared by multicellular poikilotherms emerged from independent evolutionary pathways on Earth is consistent with this assumption. As long as the evolutionary pathway from simple cells to complex multicellular organisms is a universal feature of life, the habitability requirements for multicellular poikilotherms can be taken as a precondition for the development of more advanced forms of complex life, such as homeotherms, for which it is harder to define thermal limits.

Mean global temperature and habitability in the AMHZ

The solid green curves in Figs. 1 and 2 indicate the isotherm lines where the mean global orbital temperature of the planet surface, T _m, is constant. The isotherms highlight the trend of T _m with S and N _atm. One can see that T _m tends to rise both with increasing insolation S and increasing N _atm (i.e. increasing strength of the greenhouse effect). As a result, the isotherms are generally tilted. However, the slope of the isotherms changes in different regimes of N _atm. At high N _atm the slopes are relatively large, whereas at low N _atm they are generally small. This behaviour is particularly clear for the isotherm T _m = 50°C (green curve close to the inner edge), for which the separation between these two regimes lies at N _atm ~ 3–5 × 10² g cm⁻² (see Fig. 1). At high N _atm, the isotherm gets closer to the star if the atmospheric mass decreases. At low N _atm, the atmospheric radiative transport becomes negligible and a decrease of N _atm does not help to keep habitable a planet with high insolation.

The colour coding of Figs. 1 and 2 shows that, when the mean global temperature gets close to the assigned thermal thresholds, the mean fraction of planet surface that is habitable during an orbital period, tends to vanish. The mean global orbital habitability is determined by the fraction of time that each latitude strip spends inside or outside the assigned temperature limits. In the examples shown in Fig. 5, the mean habitability h ₀₅₀ depends on the zones reaching T (φ) > 50°C at low latitude (bottom panels) and the zones with T (φ) < 0°C at high latitude (top panels).

‘Liquid water’ versus ‘complex life’ habitable zone

In Fig. 1 we compare the maps of habitability obtained for the liquid water index, h _lw (left panel), and the complex life index, h ₀₅₀ (right panel), for the same set of Earth-like parameters. The outer edge of habitability is identical in both cases because the lower temperature limit is 0°C for both indices. The outer edge shifts to lower values of S with increasing N _atm because the greenhouse effect becomes stronger and the condition T > 0°C is satisfied at lower insolation. As far as the inner edge is concerned, the results obtained for the two indices are instead quite different. When N _atm increases, the inner edge shifts to low S for the h ₀₅₀ index (right panel) and to high S for the h _lw index (left panel). In this latter case, based on the liquid water criterion, the behaviour of the inner edge is due to the rise of the water boiling point with increasing p. However, the region to the left of the RG limit (red line) does not comply with the requirement of long-term habitability. Instead, in the case of the complex life index h ₀₅₀, most of the habitable zone lies to the right of RG limit, in line with the requirement of long-term habitability.

Comparison with the habitable zone of land-dominated planets

Planets dominated by land, rather than oceans, may avoid the RG instability up to high values of insolation thanks to their low atmospheric water vapour content. For such water-limited (‘dry’) planets the inner edge of the habitable zone lies closer to the star than the classic inner edge (Abe et al. Reference Abe, Abe-Ouchi, Sleep and Zahnle2011; Zsom et al. Reference Zsom, Seager, de Wit and Stamenkovic2013). Although the study of land-dominated planets is beyond the purpose of the present work, the comparison between the results obtained with the h _lw and h ₀₅₀ indices illustrates how biological limits prevent the presence of complex life at high values of insolation even in absence of the RG instability. Indeed, Figs. 1 and 3 indicate that the h ₀₅₀ inner edge for complex life is significantly more distant from the star than the h _lw inner edge, which is representative of the boiling point in absence of the RG instability. The extended limits of inner edge of dry planets (Abe et al. Reference Abe, Abe-Ouchi, Sleep and Zahnle2011; Zsom et al. Reference Zsom, Seager, de Wit and Stamenkovic2013) can be suitable for extremophiles, but not for complex life. It is worth mentioning that evapotranspiration from vegetation, if present, could trigger a hydrological cycle and favour the presence of a moist atmosphere also on a sandy planet without oceans (Cresto Aleina et al. Reference Cresto Aleina, Baudena, D'Andrea and Provenzale2013).

Fig. 3. Insolation limits S _min and S _max (upper curves) and width ΔS = S _max–S _min (lower curves) of the AMHZ as a function of N _atm for different indices of habitability and levels of pCO₂. Left: comparison of the results obtained using the h _lw (dotted light-blue curves, computed up to S _eff = 2) and h ₀₅₀ (solid green curves) indices for a planet with pCO₂ = 380 ppmv. The outer edge of h _lw is the same as for h ₀₅₀. Right: effects of variations of pCO₂ using the h ₀₅₀ index. Blue dot-dashed curves: pCO₂ = 10 ppmv. Green solid curves: Earth reference value pCO₂ = 380 ppmv. Red dashed lines: pCO₂ = 38 000 ppmv. Black dotted lines: insolation S at the initial main sequence (bottom) and at 4.58 Gyr (top) for a planet at 1 AU around a sun like star.

Variations of atmospheric composition

Figure 2 illustrates the effect of variations of the CO₂ partial pressure on the habitability map calculated with the index h ₀₅₀. In the left panel, pCO₂ is raised by a factor of 100 compared with the Earth's reference value pCO₂ = 380 ppmv, while in the right panel pCO₂ is decreased to get a value of 10 ppmv, representative of the minimum value for plants with C₄ photosynthesis systems (Caldeira & Kasting Reference Caldeira and Kasting1992). In the first case the whole AMHZ is displaced to lower S values due to the higher strength of the greenhouse effect. The effect becomes stronger at high values of atmospheric columnar mass. In the case of low pCO₂ (right panel) the AMHZ is displaced to higher values of S. At this very low value of pCO₂ the slope of isotherms becomes almost negligible, and the temperature, habitability, position and width of the HZ are determined by S, being weakly dependent on N _atm.

Variations of insolation affect not only the temperature, but also the amount of water vapour, which changes at different locations inside AMHZ. By adopting a representative value of relative humidity, r = 0.6, the ESTM calculates p(H₂O) as a function of planet surface temperature. The water vapour pressure model is predicted to rise from the outer edge to the inner edge due to the temperature dependence of the water vapour saturation pressure. As an example, for an Earth-like planet with N _atm = 1033 g cm⁻² and pCO₂ = 380 ppmv, the ESTM predicts that the mean global p(H₂O) increases from ~3.5 mbar at T _m = 0°C (S _eff = 0.934) to ~72 mbar at T _m = 50°C (S _eff = 1.187).

Width of the habitable zone

In Fig. 3 we plot the insolation limits of habitability, S _min and S _max (curves at the top of the figures) and the width of the AMHZ, ΔS = S _max–S _min (curves at the bottom) as a function of N _atm for different model parameters. In the left panel we compare the results obtained with the liquid water criterion (dotted light-blue curves) and the complex life h ₀₅₀ index (solid green curves) for a planet with Earth-like atmospheric composition. With the h _lw index the inner edge S _max and the width ΔS rise significantly when N _atm > 200 g cm⁻². The complex life index h ₀₅₀ yields instead a gradual decline of S _max and a modest increase of ΔS with increasing N _atm. In the right panel we show the impact of variations of pCO₂ on the insolation limits calculated with the index h ₀₅₀. The limits of insolation tend to decrease with increasing N _atm. The variations become stronger as pCO₂ increases from 10 ppmv (blue, dashed-dotted line), to the reference Earth value 380 ppmv (green solid curve) and finally up to 38 000 ppmv (red, dashed curve). Variations of the inner edge as a function of N _atm are quite complex because the greenhouse effect in the proximity of the inner edge is governed not only by variations of N _atm and CO₂, but also by water vapour, whose partial pressure is temperature dependent. Variations of the outer edge versus N _atm are more regular, probably because water vapour plays a negligible role at low temperatures. At the bottom of Fig. 3 we plot the width of the AMHZ, ΔS = S _max–S _min, for the same three values of pCO₂. In general, ΔS increases with increasing pCO₂. However, in the curve pCO₂ = 38 000 ppmv, the strong slope of the inner edge results in a decrease of ΔS at N _atm > 2000 g cm⁻².

Mean temperature and temperature excursions

The mean global orbital temperature T _m gives a broad indication of which type of life, classified according to its thermal tolerance, might be present at different locations in the plane (S, N _atm). In the proximity of the inner and outer edge T _m is close to the upper and lower thermal limits of terrestrial multicellular poikilotherms, respectively. If such limits are universal, we may expect a dearth of poikilotherm species adapted to such extremes, while thermophilic and cryophilic extremophiles would find favourable conditions near the inner and outer edge, respectively. In the proximity of the outer edge, the effective habitability for poikilotherms would be low because their thermal performance rises slowly at T ≥ 0°C. At high temperature the capability of hosting multicellular poikilotherms would depend on the optimal temperature of different species potentially present in the planet. For each species the habitability would drop steeply after the thermal optimum, owing to the fast decline of TPCs at T > T _opt.

Besides the mean temperature T _m, latitudinal and seasonal excursions of temperature will affect the distribution of different forms of life according to their thermal tolerance. To show these effects we calculate the mean orbital profiles of surface temperature as a function of latitude, T (φ), by integrating the temperature matrix T (φ, t _s) during one orbital period. Similarly, we calculate the mean orbital habitability H ₀₅₀ (φ) by integrating h ₀₅₀ during one orbital period. In the top panels of Fig. 4 we show T (φ) (left panels) and H ₀₅₀ (φ) (right panels) for a sequence of ESTM simulations selected along a line of constant atmospheric columnar mass, N _atm = 1033 g cm⁻², inside the AMHZ of Fig. 1 (right panel). A similar example is shown in the lower panels, but by combining a decreasing amount of CO₂ for increasing S, the exact sequence of profiles depending on how S and f _gh are combined (see the section ‘Time interval of complex life habitability’). In any case, in the proximity of the outer edge of habitability (blue solid curves) only an equatorial zone of the planet lies above the water freezing point (cyan horizontal line in the left panel), and the habitability H ₀₅₀ (φ) drops at high latitudes. In the proximity of the inner edge the equator is too hot and only the polar regions are habitable (black, dashed-dotted curves).

Fig. 4. Effects of variations of insolation on the mean orbital latitude profile of surface temperature, T (φ) (left panels), and habitability, H ₀₅₀ (φ) (right panels), for an Earth-like planet with atmospheric columnar mass, N _atm = 1033 g cm⁻². Top panels: model predictions at constant f _GH = pCO₂/(380 ppmv) = 1 with insolation S = 0.92, 1.00, 1.15 and 1.22 (blue solid, green dotted curves, dashed magenta and black dashed-dotted curves, respectively). Bottom panels: predictions for a planet in which pCO₂ decreases as the insolation increases. The blue, green, magenta, and black curves correspond to (S, f _GH) = (0.77, 100), (0.90, 10), (1.00, 1), and (1.22, 0.026), respectively. The mean orbital global temperature of each T (φ) profile is shown with a horizontal line of the same colour.

The mean orbital temperature-latitude profiles T (φ) inside the AMHZ can be steep or flat, depending on the location of the planet in the plane (S, N _atm). These latitude profiles become flatter with increasing N _atm because the efficiency of the horizontal transport tends to rise with increasing N _atm (e.g. Vladilo et al. Reference Vladilo, Silva, Murante, Filippi and Provenzale2015). The profiles also tend to become flatter with increasing S, as in the examples of Fig. 4, because the latent heat component of the horizontal transport rises because pH₂O increases at high temperature. For flat temperature profiles, life at different latitudes would show little diversity as far as the thermal response is concerned. Conversely, a large meridional gradient of temperature would favour the emergence of a diversity of life forms, each one adapted to the mean temperature of its own latitude zone. In each latitude strip, the temperature will vary around its mean orbital value T (φ) as a result of seasonal excursions.

Seasonal variations are induced by the eccentricity of the orbit, e, which can be measured in exoplanets, and by the tilt of the rotation axis, ε, which can be parameterized in the climate simulations. In Fig. 5 we show examples of the seasonal excursions of surface temperature of an Earth-like planet with four possible combinations of insolation and atmospheric columnar mass inside the AMHZ. In each panel the seasonal excursions are displayed by superposing instantaneous temperature-latitude profiles calculated at different phases of one orbital period (thin curves). One can see that the seasonal variability is negligible in the equatorial belt, but increases towards the poles. At a given latitude the seasonal excursions are larger at low N _atm (left panels) than at high N _atm (right panels) because the atmospheric columnar mass damps variations of surface temperature. Also variations of the axis tilt and geographical distribution of continents/oceans, not discussed here, would affect the temperature excursions. Variations of the axis tilt would affect the temperature excursions at high latitude and only modestly at low latitude.

Fig. 5. Latitude-temperature profiles of an Earth-like planet in four representative locations of the AMHZ. Top panels: locations in the proximity of the outer edge, with mean global orbital temperature T _m = 5°C (dashed line in upper panels). Bottom panels: locations in the proximity of the inner edge, with T _m = 45°C (dashed line in lower panels). The values of insolation, S, and atmospheric columnar mass, N _atm, are indicated in each panel. Thin curves: seasonal evolution of T (φ) during one orbital period. Thick curves: mean orbital temperature, T (φ). Adopted orbital eccentricity: e = 0.0167; rotation axis tilt: ε = 22.5°.

Seasonal excursions affect the potential geographical distribution of different forms of life. Latitude zones with strong seasonal excursions would be expected to favour the emergence of organisms with capability of seasonal migration and/or organisms that can function at a wide range of different body temperatures, such as terrestrial eurytherms. Equatorial regions and, more in general, planets with high atmospheric mass would be expected to favour the emergence of organisms only capable of living in a narrow temperature range, such as terrestrial stenotherms. At the present time, the lack of understanding of the origin of terrestrial homeotherms prevents conclusions about the existence of a relationship between ambient temperature conditions and the emergence of homeothermy. Terrestrial homeotherms may have evolved in response to inter-specific competition (Lovegrove Reference Lovegrove2012), rather than in response to ambient conditions.

Surface radiation dose

The planet atmosphere shields the life potentially present on the planet surface from the biological damage induced by ionizing radiation of astrophysical origin (see Appendix). The shielding from cosmic rays can be used to assess the habitability of the planet according to the value of atmospheric columnar mass N _atm and to the radio tolerance of different types of organisms. Based on the discussion in the Appendix, we adopt here 100 mSv yr⁻¹ as an illustrative limit of long-term irradiation tolerable by complex life. From the results obtained by Atri et al. (Reference Atri, Hariharan and Grießmeier2013) for an Earth-like planetary magnetic moment, a surface radiation dose of 100 mSv yr⁻¹ corresponds to an atmospheric columnar mass N _atm ~ 200 g cm⁻². The shaded region in Figs. 1 and 2 indicate the range of low atmospheric column densities that yield a radiation dose in excess of 100 mSv yr⁻¹. The N _atm threshold depends on the planetary magnetic moment, as shown in the figure: the orange and light yellow shaded areas indicate the thresholds obtained for an Earth-like magnetic field and for a planet without magnetic field, respectively. The results of such calculations are quite independent of the exact chemical composition of the atmosphere (Atri et al. Reference Atri, Hariharan and Grießmeier2013). These results indicate that in the shaded areas of low N _atm of the AMHZ the high radiation dose may favour genetic mutations, accelerating the pace of Darwinian evolution, or may lead to the reinforcement of biological mechanisms aimed at repairing the damages induced by ionizing radiation. The high radiation dose may combine with other ambient conditions discussed above, such as the latitudinal and/or seasonal temperature excursions, to produce a variety of possible combinations of ambient conditions that differentiate the type of habitability at different locations in the AMHZ. For instance, a planet with N _atm ~ 400 g cm⁻² would experience, at the same time, high seasonal excursions of surface temperature (see the above discussion of Fig. 5) and a relatively high surface dose of radiation, ~20–40 mSv yr⁻¹. These ambient conditions would favour the emergence of species with large capability of thermal adaptation and radio tolerance. Conversely, the right panels of Fig. 5 show examples with small temperature excursions and low radiation dose resulting from the relatively high atmospheric column density (N _atm = 5725 g cm⁻²). These ambient conditions may favour the emergence of species without particular requirements in terms of radio tolerance and adapted to a narrow range of temperatures in each latitude strip. Altogether, this latter situation would probably be less dynamic, in terms of Darwinian evolution, in comparison with the case of low N _atm and high radiation dose discussed above.

Atmospheric composition and water vapour content

Variations of pCO₂ affect the type of life potentially present in the planet. In particular, the photosynthesis requires CO₂ and this fact can be used to set a lower threshold to the possible values of pCO₂. On Earth, plants with C3 and C4 photosynthetic systems require a minimum pCO₂ of ~150 and 10 ppmv, respectively, while the photosynthesis of (some) cyanobacteria requires a minimum pCO₂ of 1 ppmv (Caldeira & Kasting Reference Caldeira and Kasting1992; O'Malley-James et al. Reference O'Malley-James, Greaves, Raven and Cockell2013 and references therein). The lowest possible value for the plant photosynthesis, pCO₂ = 10 ppmv, can be considered as a representative limit for efficient oxygenic production by means of photosynthesis. Since the presence of oxygen is required for the existence of aerobic metabolism and complex life, the inner edge of the AMHZ calculated at pCO₂ = 10 ppmv (right panel of Figs. 2 and 3), is illustrative of the minimum inner edge (maximum insolation) for a planet hosting complex life.

Also variations of humidity affect life, in particular when they are associated with variations of temperature. Therefore the expected rise of water vapour with increasing temperature will vary the characteristics of habitability inside the AMHZ. In the proximity of the outer edge life should be adapted to cold, dry conditions, while in the proximity of the inner edge to damped, warm conditions.

Time interval of complex life habitability

As we discussed above, long-term habitability is a necessary (even though not sufficient) condition to allow the long-term existence of a biosphere and the ensuing evolution to complex life forms. The stellar evolutionary tracks provide a relation between the age of the star, t*, and its luminosity that we can use to calculate the time span of habitability. For instance, we can convert the range of insolation ΔS _hab = S _max–S _min, calculated at constant N _atm between the edges of the habitable zone, into a maximum time of habitability

$$\Delta t_{{\rm hab}}(N_{{\rm atm}}) = t ^\ast (S_{{\rm max}})- t ^\ast(S_{{\rm min}}).$$

With this definition, Δt _hab is positive during the MS phase of hydrogen burning, when the stellar luminosity is characterized by a steady, gradual rise. The actual fraction of habitable surface will change with time, depending on the instantaneous value of N _atm and S _eff. Therefore, a more meaningful quantity can be provided by weighting each time step with the corresponding value of mean habitability h (h ₀₅₀ or h _lw) at each location i inside the AMHZ. In this way, we obtain an effective time of habitability

$$\tau_{{\rm hab}}(N_{{\rm atm}}) = \sum _ih_i\;\delta t_i^{^\ast} $$

where δt _i * is the time increment corresponding to a constant increment of insolation, δS. The increment δt _i * is not constant because it depends on the rate of luminosity evolution of the star, which changes with time. For instance, for our adopted sun track, the luminosity rate increases from ~0.05 L _sun Gyr⁻¹ at the first stage on the MS, to the current ~0.08 L _sun Gyr⁻¹, and will reach ~0.35 L _sun Gyr⁻¹ towards the end of the MS. Since the rate of growth of the luminosity increases with age, the early stages of MS will experience longer intervals of habitability τ _hab for a given interval ΔS _hab than the late stages of MS.

In Fig. 6 we show calculations of Δt _hab and τ _hab performed at different values of N _atm for 3 values of CO₂ in an otherwise Earth-like atmospheric composition. The planet is assumed to lie at 1 AU from the central, sun-like star. One can see that the times of habitability become larger with increasing N _atm and increasing pCO₂. From this figure we can constrain the values of N _atm and pCO₂ that yield an effective time of habitability compatible with our requirement of long-term habitability. Assuming τ _hab > 2 Gyr (see the section ‘Definitions’) we obtain a lower limit N _atm > 300 g cm⁻² for an Earth-like value of pCO₂ (green curves). In this framework, a 3-fold decrease of the Earth's atmospheric mass would have made impossible the emergence of complex life on our planet. For the case pCO₂ = 38 000 ppmv (red curves) we obtain N _atm > 70 g cm⁻². This example of high CO₂ indicates that a low-mass atmosphere could still guarantee a long-term habitability, but with a surface dose of radiation well above 100 mSv yr⁻¹, i.e. non optimal for complex life as we know it. The case with pCO₂ = 10 ppmv (blue curves) indicates that an atmosphere with low pCO₂ could sustain long-term habitability only if the total columnar mass of the atmosphere is sufficiently high, N _atm > 1500 g cm⁻². In this case, the surface dose would be safely below 100 mSv yr⁻¹.

Fig. 6. Time span of habitability calculated with the ‘complex life’ index h ₀₅₀ for an Earth-like planet with different values of atmospheric columnar mass, N _atm, and CO₂ partial pressure, pCO₂. Times are calculated using the main sequence evolution of a sun-like star (Bressan et al. Reference Bressan, Marigo, Girardi, Salasnich, Dal Cero, Rubele and Nanni2012), assuming that the planet lies at 1 AU from the star. Dashed curves: maximum time of habitability, Δt _hab. Solid curves: effective time of habitability, τ _hab. Blue, green and red curves: pCO₂ = 10, 380, and 38 000 ppmv, respectively. Horizontal line: representative time required for the emergence of complex life. The red curves are truncated where the insolation of the outer edge becomes lower than the minimum insolation at the initial main sequence (Fig. 3). See the text.

The habitability times calculated above should be regarded as a lower limit to the true times of habitability if the atmospheric properties evolve in a such a way to compensate the gradual rise of insolation (possibly as a product of the presence of life, see e.g. Watson & Lovelock Reference Watson and Lovelock1983). For instance, it has been suggested that the atmospheric background pressure may decrease during the evolution of S, possibly due to biological N₂ fixation and organic matter burial (Li et al. Reference Li, Pahlevan, Kirschvink and Yung2009). In this case, the ensuing smaller pressure broadening of greenhouse gases may extend the inner edge. In the case of the Earth this possibility has been questioned by the archean pressure measurements by Som et al. (Reference Som, Catling, Harnmeijer, Polivka and Buick2012), more consistent with an almost constant surface pressure for Earth. More likely, an active tectonic can help to widen the HZ by adjustment of the CO₂ level via the carbonate-silicate cycle (e.g. Kasting et al. Reference Kasting, Whitmore and Reynolds1993; Selsis et al. Reference Selsis, Kasting, Levrard, Paillet, Ribas and Delfosse2007; Kopparapu et al. Reference Kopparapu, Ramirez, Kasting, Eymet, Robinson, Mahadevan, Terrien, Domagal-Goldman, Meadows and Deshpande2013). The CO₂ abundance is expected to fade with increasing S due to the rise of surface weathering with increasing temperature. The decrease of CO₂ can delay the onset of the greenhouse instability at the inner edge (Kasting Reference Kasting1988; Goldblatt & Watson Reference Goldblatt and Watson2012). However, pCO₂ should not fade below the above mentioned minimum thresholds for photosynthesis, i.e. pCO₂ ~ 10 ppmv for plants with C4 photosynthesic systems.

If the carbonate-silicate cycle is at work, the gradual decrease of pCO₂ in the course of the planet evolution would yield a milder evolution of the latitude profiles of surface temperature and habitability. To illustrate this effect, in the bottom panels of Fig. 4 we show how the mean orbital profiles T (φ) and H ₀₅₀ (φ) would evolve when a rise of insolation (S _eff = 0.77, 0.90, 1.00, 1.22) is coupled to a decrease of pCO₂ (f _GH = 100, 10, 1, 0.1, respectively). One can see that the mean orbital temperature and habitability show less dramatic differences with respect to the case of constant pCO₂ (f _GH = 1) shown in the upper panels of the same figure.

Evolutionary tracks of complex life habitability

By adopting a proper stellar evolutionary track we can explore the surface temperature and habitability as a function of planet age. Examples of application of this technique are presented in Fig. 7, where we show the evolution of h ₀₅₀ and T _m versus S and t* for several representative climate models. Each of the five curves shown in figure corresponds to a constant value of N _atm between 30 and 8000 g cm⁻², as specified in the legend. An Earth-like atmospheric composition, with a reference value pCO₂ = 380 ppmv, was adopted in all cases. The results show that the initial and final times of habitability are a strong function of N _atm. For planets with massive atmospheres the habitability starts and finishes relatively early, even though the time span of habitability (Fig. 6) is relatively large. For planets with low-mass atmospheres the habitability starts at much later stages and lasts for a relatively short time. It is not clear whether such a late start would be compatible with the emergence of life. For instance, in the case of the Earth, life emerged during the first Gyr after the formation of the Solar System and the conditions for the emergence of life may have faded at a later stage. For an Earth-like planet with present age 4.58 Gyr but different values of atmospheric mass, the epoch of habitability would have already passed for N _atm > 4000 g cm⁻², while the right conditions would not have yet been met for N _atm < 200 g cm⁻², but these low values would imply a harsh radiation environment. Of course, as discussed for the time interval of habitability, also the actual initial and final times of habitability will depend on possible changes of the chemical composition and total mass of the atmosphere. For instance, by adopting present-day values of N _atm and pCO₂, Fig. 7 indicates that an Earth twin would not be habitable for a long initial period, while we know that the primordial Earth was habitable since the archean. This is the well-known ‘faint young sun paradox’ that can be solved assuming a high initial value of pCO₂ (see e.g. Kasting Reference Kasting1993). An example is shown in Fig. 8.

Fig. 7. Evolution of the mean global and orbital habitability h ₀₅₀ (left panel) and temperature T _m (right panel) as a function of planet insolation (bottom horizontal axis) and stellar age (top horizontal axis) for an Earth-like planet orbiting a sun-like star at a = 1 AU. The stellar evolutionary track is taken from Bressan et al. (Reference Bressan, Marigo, Girardi, Salasnich, Dal Cero, Rubele and Nanni2012). The curves correspond to the 5 values of atmospheric columnar mass, N _atm, indicated in the panels. The dotted vertical lines indicate the age of arrival on the main sequence time, t = 0.048 Gyr (the track includes the pre-MS evolution), and the current age, t ₀ = 4.58 Gyr, respectively, the solid vertical line is the reference minimum τ _hab of 2 Gyr. The size of the squares on the right panel are proportional to the value of the habitability index h ₀₅₀.

Fig. 8. Same as Fig. 7, but for fixed p = 1 bar, and pCO₂ = 10 (blue), 380 (green), 380 × 100 (red) ppmv. The crosses on the green line correspond to the four models in the top panels of Fig. 4.