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Photosynthesis in the Milky Way
Plant Science 178 (2010) 485–490
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Review
Photosynthesis in the Milky Way Werner von Bloh ∗ , Christine Bounama, Siegfried Franck Potsdam Institute for Climate Impact Research (PIK), P.O. Box 601203, 14412 Potsdam, Germany
a r t i c l e
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Article history: Received 18 December 2009 Received in revised form 11 February 2010 Accepted 16 February 2010 Available online 24 February 2010 Keywords: Habitable zone Extrasolar planets Rare Earth Hypothesis
a b s t r a c t The habitable zone around a given central star is defined as the region within which an Earth-like planet might enjoy the moderate surface temperatures required for advanced life forms. At present, there are several models calculating the habitable zone. One class of models utilises climate constraints for the existence of liquid water on a planetary surface. Another approach is based on an integrated Earth system analysis that relates the boundaries of the habitable zone to the limits of photosynthetic processes. Within the latter approach, the evolution of a photosynthesis-sustaining habitable zone (pHZ) around mainsequence stars can be straightforwardly calculated. The average number of Earth-like planets harbouring primitive and complex life (plants and animals) is calculated by estimating the pHZ for both life forms and using the formation rate of Earth-like planets in the Milky Way. The number of planets bearing complex life is at least two orders of magnitude lower than the number for primitive life forms. The maximum appearance of complex life forms was 1.5 Gyr before present (∼2.5 million in the Milky Way) and is now declining. Based on the habitable zone approach one can conclude that complex life forms might be not really “rare” in the Milky Way today. © 2010 Elsevier Ireland Ltd. All rights reserved.
Contents 1. 2.
3. 4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modelling the Earth system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The global carbon cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. The photosynthesis-based biosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The photosynthesis-sustaining habitable zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimating the number of habitable planets in the Milky Way and the rare Earth factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Is there life beyond planet Earth? This is one of the fundamental questions which humankind tries to answer through scientific research. The extra-terrestrial life debate spans from the ancient Greek world of Democritus through the 18th century European world of Immanuel Kant to the recent discoveries of extrasolar planets. The first detection of a Jupiter-sized planet around 51 Peg in 1995 changed the knowledge about extrasolar planetary systems from fiction to facts. Up to now, more than 400 extrasolar planets have been discovered [1]. So-called super Earths [2], i.e., rocky planets up to 10 Earth masses, have already been detected [3], including a first candidate for a habitable planet around a red dwarf (Gliese 581d) [4].
∗ Corresponding author. Fax: +49 331 2882600. E-mail address: [email protected] (W. von Bloh). 0168-9452/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.plantsci.2010.02.013
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The definition of habitability is closely related to the very definition of life. Up to now, we only know terrestrial life, and therefore the search for extra-terrestrial life is the search for life, as we know it from our home planet. Life can be defined as a self-sustained system of organic molecules in liquid water immersed in a source of free energy [5]. It is well known that organic molecules are rather common in the solar system and even in interstellar clouds. There is also no problem to find any source of free energy for extraterrestrial life. Therefore, the existence of liquid water is the central point in the search for extra-terrestrial life and in the definition of habitability. Nevertheless, it is evident that liquid water and basic nutrients are essential but not sufficient requirements for life. A rather general characterization of habitability has been generated, based on the possibility of photosynthetic biomass production under large-scale geodynamic conditions [6–8]. Thus not only the availability of liquid water on a planetary surface is taken into account but also the suitability of CO2 partial pressure.
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A habitable zone can also be defined for a galaxy [9]. The boundaries of the so-called galactic habitable zones (GHZ) are set by two requirements: the availability of material to build a habitable planet and adequate seclusion from cosmic threats. The inner regions of the galaxy suffer from orbital instabilities, radiation bursts and cometary perturbations. The outer regions are safer, but because of the lower metallicity, terrestrial planets are typically smaller there. The galactic habitable zone in the Milky Way has been identified as an annular region (roughly around the sun’s location) between 23,000 and 29,000 light years from the galactic centre that widens with time and is composed of stars that formed between 8 and 4 billion years (Gyr) ago [10]. 2. Modelling the Earth system It is necessary to employ an integrated Earth system model in order to determine the photosynthesis-based habitability of an Earth-like planet beginning just after planetary formation up to the final end of its existence. Such a model must consist of the components solid Earth, hydrosphere, atmosphere, and biosphere. It couples the increasing solar luminosity, the silicate-rock weathering rate, and the global energy balance to estimate the partial pressure of atmospheric and soil carbon dioxide, the mean global surface temperature, and the biological productivity as a function of time. The crucial point is the long-term balance between the CO2 sink in the atmosphere–ocean system and the metamorphic (platetectonic) sources. The respective features of the Earth system model are described in some detail below. 2.1. The global carbon cycle The carbon cycle is the main process for the regulation of the atmospheric composition and climate with respect to increasing insolation [11–13]. The main sink of atmospheric carbon dioxide is provided by silicate rock weathering playing a crucial role in Earth’s climate. The overall chemical reactions for the weathering process are
Fig. 1. The global carbon cycle as part of the general volatile exchange between mantle and surface reservoirs.
boundary layer theory of convection [15] with water dependent viscosity [16]. 2.2. The photosynthesis-based biosphere Nearly all life depends on photosynthesis using light as a source of energy. Photosynthetic organisms, in particular, are the basis for nearly all life on Earth and produce some of the strongest indicators of life in abundances that can be detected astronomically [17]. In particular, the detection of oxygenic photosynthesis is most relevant for the direct determination of life on extrasolar terrestrial planets. The terrestrial planet finder (TPF) and Darwin space missions of NASA and ESA are planning to detect O2 or its photolytic product O3 as a biosignature of life built up by oxygenic photosyn-
CO2 + CaSiO3 → CaCO3 + SiO2 CO2 + MgSiO3 → MgCO3 + SiO2 . The total process of weathering embraces (i) the reaction of silicate minerals with carbon dioxide, (ii) the transport of weathering products, and (iii) the deposition of carbonate minerals in sediments. The main feedback loop stabilizing the planetary climate is maintained by the weathering process: An increase of the luminosity leads to a higher mean global temperature causing an increase in weathering. Then more CO2 is extracted from the atmosphere weakening the greenhouse effect. Overall the temperature is lowered and homeostasis is achieved. On geological time scales, however, the deeper parts of the Earth are considerable sinks and sources for carbon and the tectonic activity as well as the continental area change markedly [14]. In addition to the usual carbonate–silicate geochemical cycle, subduction of large amounts of carbon into the mantle with descending slabs and the degassing of carbon from the mantle at mid-ocean ridges has to be taken into account. The global carbon cycle is sketched in Fig. 1. In the framework of a geodynamic-equilibrium approach for the global carbon cycle at longer time scales of about hundred thousands of years, a balance is proposed between the CO2 sink in the atmosphere–ocean system and the metamorphic source [11]. The main driving forces and feedbacks acting in the Earth system are depicted in Fig. 2. The metamorphic sources can be determined by calculating the temperature of the planetary mantle according to
Fig. 2. Earth system box model. The arrows indicate the different driving forces and feedback mechanisms. The bold arrows mark the main feedback loop stabilizing planetary climate.
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thesis [18]. But there is also non-oxygenic photosynthesis in, e.g., sulfur bacteria not considered here. Photosynthetic fixation leads to build up of organic material consuming CO2 from the atmosphere. On the other hand organic material is decomposed and CO2 is remobilised: h
CO2 + H2 OCH2 O + O2 Carbon isotope composition of photosynthetic products indicates that the enzyme Rubisco prefers the lighter isotope 12 C over 13 C and therefore oxygenic photosynthesis controlled the global distribution of carbon in the atmosphere–ocean system for at least 3.5 Gyr and gave an imprint on the isotopic signature of the carbon reservoirs [19]. Direct evidence of oxygenic photosynthesis is given by the steep rise of oxygen in the atmosphere 2.2 Gyr ago [20]. According to Wolstencroft and Raven [21] oxygenic photosynthesis is not ruled out for central stars distinct from our Sun. They concluded that photosynthesis on other planets is plausible for different types of parent stars with different radiation spectra. The productivity of the photosynthesis-based biosphere is a function of various parameters such as water supply, photosynthetic active radiation, nutrients, atmospheric carbon dioxide content, and surface temperature. As a first approximation biological productivity is considered to be solely a function of the global averaged mean surface temperature Tsurf and the CO2 partial pressure in the atmosphere pCO2 . Biosphere productivity vanishes for temperatures Tsurf ≤ 0◦ C and Tsurf ≥ 100◦ C and CO2 partial pressures below 10−5 bar as the presumed minimum value for C4 -photosynthesis [22,23]. The upper limit of the temperature tolerance is valid for primitive thermophilic life only, complex life has an upper temperature tolerance of 30–50 ◦ C [24]. The evolution of the biosphere and its adaptation to even lower CO2 partial pressures are not taken into account. Only biosphere on continents is considered because only the land biota has an influence on the weathering processes. The question pertaining to what extent the biota are actually able to play a key role in stimulating the weathering sink is crucial for an understanding of the dynamic properties of the overall Earth system. Vascular plants are particularly effective at rock weathering. Cyanobacteria of some algae weather rock in desert conditions — as so-called resurrection forms of life. In a study [25] accounting for the accumulation of weathered ions in vegetation and soil, experimental sandboxes with red pine stands had weathering rates amplified by a factor of 10 for Ca2+ and 18 for Mg2+ , relative to plots with moss and lichen cover. An overall factor of ∼ 7 for vascular plants has been used [26]. 3. The photosynthesis-sustaining habitable zone In general, the habitable zone around a main-sequence star can be defined as the region within which an Earth-like planet have moderate surface temperatures needed for advanced life forms. Main-sequence stars are stars getting their energy mainly by fusing hydrogen in their cores. During stellar evolution the luminosity of a star increases. The luminosity of the Sun, e.g., increases by 10% in one billion years. Stars with higher masses than our Sun have a higher luminosity and evolve more rapidly. The habitable zone has been more specifically related to the existence of liquid water at a planetary surface [27–29]. The socalled zero age main sequence habitable zone [30], i.e., at the time the star starts hydrogen fusion, is shown as a function of stellar mass in Fig. 3. The habitable zone moves outwards with increasing stellar mass due to an increase in luminosity. Based on the Earth system model described in the previous section, the habitable zone can be determined in a different way.
Fig. 3. The zero age main sequence habitable zone (HZ) as a function of central-star mass (in solar masses M ). The distance to the central star is measured in astronomical units (AU), the mean distance between the Earth and the Sun. As the mass of the central star increases the habitable zone moves outwards due to an increase in stellar luminosity. The long-dashed lines delineate the probable terrestrial planet accretion zone. The dotted line is the orbital distance for which an Earth-like planet in a circular orbit would be locked into synchronous rotation (tidal locking) (picture taken from [30]).
Here the so-called photosynthesis-sustaining habitable zone (pHZ) for an Earth-like planet is the region around a star within which the global averaged mean surface temperature Tsurf of the planet stays between 0◦ C and 100◦ C and the atmospheric CO2 partial pressure pCO2 is higher than 10−5 bar (10 ppmv), i.e., suitable for photosynthesis-based life (biological productivity > 0): pHZ := {R|(PCO2 (R, t), Tsurf (R, t)) > 0},
(1)
where R is the distance to the central star. The specific parameterization of the biological productivity plays a minor role in the calculation of the pHZ. Habitability is linked to the photosynthetic activity of the planet. The term “Earth-like” explicitly implies the occurrence of plate tectonics as a necessary condition for the operation of the carbonate–silicate cycle as the mechanism to compensate for the gradual brightening of the central star during its “life” on the main sequence. The geodynamical evolution of the considered Earth-like planet provides an even stronger constraint. The volcanic input of CO2 to the atmosphere is decreasing over time while the continental area (available for weathering) is increasing. In principle, it is possible to calculate the pHZ for any value of central-star mass [7]. As an illustration, the results for central-stars of 0.8, 1.0, and 1.2 masses of our Sun (M ), respectively, are presented in Fig. 4. While the inner limit of the pHZ moves outward with time, the outer limit moves inwards after 3.6 Gyr. After 6.5 Gyr no photosynthesis-sustaining habitability can be found. The following effects limit the pHZ: 1. Stellar lifetime on the main sequence decreases strongly with mass. After all hydrogen in the core is consumed the star leaves the main sequence and turns into a red giant with an increase in luminosity by a factor of 1000–10,000. Using simple scaling laws [32], the central hydrogen burning period H is estimated to be shorter than 0.8 Gyr for a star with a mass larger than 2.2 solar masses. Therefore, there is no point in considering central stars with masses larger than 2.2 solar masses because an Earth-like planet may need ∼0.8 Gyr of habitable conditions for the origin of life [33]. Smaller numbers for the time span required for the emergence of life have been discussed, for instance 0.5 Gyr [34]. Performing calculations with H < 0.5 Gyr, one obtains qualita-
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Fig. 4. Graphs of the width and position R of the pHZ derived from the geodynamic model for three different stellar masses M (0.8, 1.0, 1.2M ). The distance to the central star is measured in astronomical units (AU), the mean distance between the Earth and the Sun. tmax is the maximum life span of the biosphere limited by geodynamic effects. H indicates the hydrogen burning time on the main sequence limiting the life span of more massive stars.
tively similar results, but the upper limit of central-star masses is shifted to 2.6M . 2. When a star leaves the main sequence, there clearly remains no habitable conditions for an Earth-like planet previously in the pHZ. This limitation is relevant for stellar masses in the range between 1.1 and 2.2M . There might be habitable conditions for 108 –109 yr at the red giant branch for Earth-like planets more distant from the central star suitable for the origin of life [35,36]. 3. In the stellar mass range between 0.6 and 1.1M , the maximum life span of the biosphere is determined exclusively by planetary geodynamics, which is independent of distance to the central star. So one obtains the limitation t < tmax , where tmax = 6.5 Gyr. 4. There have been discussions about the habitability of tidally locked planets. Similar to the moon orbiting the Earth in synchronous rotation tidally locked planets are facing one hemisphere constantly to their central star. This limitation is relevant for central-star masses lower than 0.6 solar masses where the outer boundary of the pHZ is below the tidal-locking radius. Global climate models of tidally locked planets have indicated that Earth-like planets should not be necessarily precluded from habitability [37], but complex life is not very likely due to the harsh environmental conditions. 4. Estimating the number of habitable planets in the Milky Way and the rare Earth factor In the previous section we discussed several factors limiting habitability in extrasolar planetary systems. In the following the pHZ concept is used to calculate the number of planets harbouring photosynthesis-based life in the Milky Way. Additionally we try to distinguish between primitive unicellular life and complex multicellular life. In the 1960s, astronomer Frank Drake developed an formula to predict in a statistic way how many intelligent civilizations might exist in the Milky Way. It is a string of factors, when multiplied together, giving an estimate of such a number where are some of the
individual factors are highly speculative. Nevertheless, it is possible to determine the number of habitable extra-terrestrial planets with the help of a segment of the Drake formula to 50 million [31]. The same conclusion was reached with the help of a time-dependent calculation [38]. Both models were based on a parameterization of a uniform biosphere consisting of primitive photosynthesis-based life. “Complex life” is defined as multicellular organisms that have the ability to perform photosynthesis. It left fossil records in the Cambrian Explosion. Such a biosphere is mainly composed of land plants (due to food net relations a prerequisite for animals) that can amplify weathering. Additionally, we assume toxic effects of very high atmospheric carbon dioxide. In 2000 Ward and Brownlee came up with the Rare Earth Hypothesis [39]. They argue that complex life – plants and animals – may be very rare, perhaps unique, in the Universe, while primitive life is common and widespread. They based this hypothesis on two observations on Earth. First, microbial life existed as soon as Earth’s environment made it possible, and this nearly invincible form of life flourished over most of Earth history, populating a broad range of hostile terrestrial environments. Second, the existence of larger and more complex life occurred only in restricted environments, and the evolution and survival of this more fragile variant of terrestrial life seems to require a highly fortuitous set of circumstances that could not be expected to exist commonly on other planets. Appearing at about the time of the Cambrian explosion (the Big Bang of biology), complex life exists on Earth only for the last 0.5 Gyr. Compared to the age of our planet of about 4.6 Gyr this is just a short period. Lineweaver et al. [10] modelled the evolution of the galactic habitable zone. The model suggests that ∼75% of the stars that could potentially harbour complex life in the Milky Way are older than the Sun and that their average age is ∼5.5 Gyr. The number of habitable Earth-like planets in the Milky Way at a certain time t harbouring primitive (i = 1) and complex (i = 2) life forms can also be determined with the help of a convolution integral [38] from the planet formation rate (PFR) and the probability phab , i that a stellar system hosts a habitable Earth-like planet at time t after its formation. The probability is zero if the lifetime of the central star on the main sequence is exceeded. To calculate the planet formation rate it is necessary to estimate the rate of star formation. The question of the star formation history has been the subject of a number of studies. While some authors favour a smooth and constant star formation history, others favour a bursty star formation history fluctuating around a constant mean [40–43]. However, cosmological simulations result in an exponentially decaying star formation rate with intermittent spikes [44]. Based on observational data, the star formation rate for the universe can be fitted to an exponentially increasing function for the first 2.6 Gyr after Big Bang followed by an exponential decline [45]. Star metallicity as an ingredient for the formation of Earth-like planets can be calculated from this fit for star formation rate. In astrophysics metals are defined as elements heavier than H and He and are built up during cosmological evolution through thermonuclear processes. Therefore the metallicity can be calculated as an integral of the star formation rate. Then the planet formation rate (PFR) can be parameterized in the following way: PFR = 0.5 · fGHZ · SFR · pE (),
(2)
where pE is the probability that Earth-like planets are formed and fGHZ is the fraction of stars within the galactic habitable zone. Here we assume as an upper limit that 10% of all stars are in the galactic habitable zone [10]. The pre-factor 0.5 reflects the assumption that 50% of the stars are in the range of 0.1–1.2, M including red dwarfs and Sun-like stars. The function pE () is an increasing function of metallicity . In contrast to Linewearver [45] we neglected
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Fig. 6. Evolution of the number of habitable Earth-like planets in the Milky Way harbouring complex life (solid line) and primitive life (dashed line). The vertical dotted lines denote the time of Earth’s origin and the present time, respectively.
Fig. 5. The star formation rate (SFR) and the Earth-like planet formation rate (PFR) recalculated from [45]. The vertical dotted lines denote the time of Earth’s origin and the present time, respectively.
the effect of the formation of hot Jupiters. High metallicity yields a high probability of forming hot Jupiters thought to destroy Earthlike planets during inward migration. A giant planet migration does not preclude the formation of Earth-like planets [46]. The star formation rate and the resulting planet formation rate for Earth-like planets are plotted in Fig. 5. The probability that a stellar system hosts a habitable Earthlike planet harbouring primitive (phab , 1) and complex (phab , 2) life forms at time t can be estimated with the help of an integral summing up the probabilities that an Earth-like planet is in the pHZ around a central star with mass M over all relevant star masses. Stellar masses in the Milky Way are distributed according to a power law [47], the orbital distribution of Earth-like planets is uniform on a logarithmic scale [48,49]. For determining the pHZ for complex life the upper tolerance temperature for non-vanishing biological productivity is set to 30◦ C. Primitive life is robust at unlimited high CO2 concentrations, while complex life dies with high atmospheric partial pressure due to poisoning effects [50]. Here we assume a value of 10−2 bar (10,000 ppmv), double the maximum Phanerozoic concentration. Complex life has an additional amplifying effect on weathering assumed to be 5 times higher than for primitive life [51]. The estimated number of habitable Earth-like planets in the Milky Way bearing primitive and complex life is shown in Fig. 6. If the pHZ approach is the only necessary condition for the appearance and maintenance of these two life forms then the number of planets hosting complex life is only a factor ∼ 270 lower than for primitive life. There was a maximum of these planets about 1.5 Gyr ago (∼2.5 mill. in the Milky Way) and their number is then declining [52]. Complex life occurred about ∼ 6 billion years later than
primitive life. The maximum number of planets bearing primitive life (∼ 690 mill. in the Milky Way) was about the time of Earth’s origin [38] and is then declining. Based on the simple Earth system model one could conclude that complex life forms might be not really “rare” in the Milky Way. This could be a false conclusion because there are many other limiting factors that up to now are difficult to model but surely influence the appearance and maintenance of complex life. The habitability of an Earth-like planet depends also on other circumstances. The presence of a large moon seems to be necessary to stabilize the planet’s obliquity [53] in order to have a stable climate. The presence of a giant planet is important to shield the planet from comets and to scatter asteroids to the planet early on to deliver volatiles [54]. The abundance of long-lived isotopes as a primary source of internal heat is necessary for the operation of plate tectonics, which drives the planetary temperature thermostat. Nevertheless, complex life has to be more rare than primitive life, at least by two orders of magnitude. This factor originates by the photosynthesis-sustaining habitable zone approach only. All the other rare Earth factors will diminish the number of habitable Earth-like planets in the Milky Way, but up to now, they are difficult to model and/or to quantify. References [1] The Extrasolar Planets Encyclopaedia web page, maintained by J. Schneider, http://exoplanet.eu (accessed January 2010). [2] D. Valencia, D.D. Sasselov, R.J. O’Connell, Radius and structure models of the first super-earth planet, Astrophys. J. 656 (2007) 545–551. [3] D. Charbonneau, A super-Earth transiting a nearby low-mass star, Nature 462 (2009) 891–894. [4] M. Mayor et al., The HARPS search for southern extra-solar planets, XVIII. An Earth-mass planet in the GJ 581 planetary system, Astron. Astrophys. 507 (2009) 487–494. [5] D.E. Koshland Jr., The seven pillars of life, Science 295 (2009) 2215–2216. [6] S. Franck, A. Block, W. von Bloh, C. Bounama, H.-J. Schellnhuber, Y. Svirezhev, Reduction of biosphere life span as a consequence of geodynamics, Tellus 52B (2000) 94–107. [7] S. Franck, W. von Bloh, C. Bounama, M. Steffen, D. Schönberner, H.-J. Schellnhuber, Determination of habitable zones in extrasolar planetary systems: where are Gaia’s sisters? J. Geophys. Res. 105(E1) (2000) 1651–1658. [8] W. von Bloh, C. Bounama, M. Cuntz, S. Franck, The habitability of super-Earths in Gliese 581, Astron. Astrophys. 476 (2007) 1365–1371. [9] G. Gonzalez, D. Brownlee, P. Ward, The galactic habitable zone: galactic chemical evolution, Icarus 152 (2001) 185–200. [10] C.H. Lineweaver, Y. Fenner, B.K. Gibson, The galactic habitable zone and the age distribution of complex life in the Milky Way, Science 302 (2004) 59–62. [11] J.C.G. Walker, P.B. Hays, J.F. Kasting, A negative feedback mechanism for the long-term stabilization of Earth’s surface temperature, J. Geophys. Res. 86 (1981) 9776–9782.
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Plant Science journal homepage: www.elsevier.com/locate/plantsci
Review
Photosynthesis in the Milky Way Werner von Bloh ∗ , Christine Bounama, Siegfried Franck Potsdam Institute for Climate Impact Research (PIK), P.O. Box 601203, 14412 Potsdam, Germany
a r t i c l e
i n f o
Article history: Received 18 December 2009 Received in revised form 11 February 2010 Accepted 16 February 2010 Available online 24 February 2010 Keywords: Habitable zone Extrasolar planets Rare Earth Hypothesis
a b s t r a c t The habitable zone around a given central star is defined as the region within which an Earth-like planet might enjoy the moderate surface temperatures required for advanced life forms. At present, there are several models calculating the habitable zone. One class of models utilises climate constraints for the existence of liquid water on a planetary surface. Another approach is based on an integrated Earth system analysis that relates the boundaries of the habitable zone to the limits of photosynthetic processes. Within the latter approach, the evolution of a photosynthesis-sustaining habitable zone (pHZ) around mainsequence stars can be straightforwardly calculated. The average number of Earth-like planets harbouring primitive and complex life (plants and animals) is calculated by estimating the pHZ for both life forms and using the formation rate of Earth-like planets in the Milky Way. The number of planets bearing complex life is at least two orders of magnitude lower than the number for primitive life forms. The maximum appearance of complex life forms was 1.5 Gyr before present (∼2.5 million in the Milky Way) and is now declining. Based on the habitable zone approach one can conclude that complex life forms might be not really “rare” in the Milky Way today. © 2010 Elsevier Ireland Ltd. All rights reserved.
Contents 1. 2.
3. 4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modelling the Earth system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The global carbon cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. The photosynthesis-based biosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The photosynthesis-sustaining habitable zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimating the number of habitable planets in the Milky Way and the rare Earth factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Is there life beyond planet Earth? This is one of the fundamental questions which humankind tries to answer through scientific research. The extra-terrestrial life debate spans from the ancient Greek world of Democritus through the 18th century European world of Immanuel Kant to the recent discoveries of extrasolar planets. The first detection of a Jupiter-sized planet around 51 Peg in 1995 changed the knowledge about extrasolar planetary systems from fiction to facts. Up to now, more than 400 extrasolar planets have been discovered [1]. So-called super Earths [2], i.e., rocky planets up to 10 Earth masses, have already been detected [3], including a first candidate for a habitable planet around a red dwarf (Gliese 581d) [4].
∗ Corresponding author. Fax: +49 331 2882600. E-mail address: [email protected] (W. von Bloh). 0168-9452/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.plantsci.2010.02.013
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The definition of habitability is closely related to the very definition of life. Up to now, we only know terrestrial life, and therefore the search for extra-terrestrial life is the search for life, as we know it from our home planet. Life can be defined as a self-sustained system of organic molecules in liquid water immersed in a source of free energy [5]. It is well known that organic molecules are rather common in the solar system and even in interstellar clouds. There is also no problem to find any source of free energy for extraterrestrial life. Therefore, the existence of liquid water is the central point in the search for extra-terrestrial life and in the definition of habitability. Nevertheless, it is evident that liquid water and basic nutrients are essential but not sufficient requirements for life. A rather general characterization of habitability has been generated, based on the possibility of photosynthetic biomass production under large-scale geodynamic conditions [6–8]. Thus not only the availability of liquid water on a planetary surface is taken into account but also the suitability of CO2 partial pressure.
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A habitable zone can also be defined for a galaxy [9]. The boundaries of the so-called galactic habitable zones (GHZ) are set by two requirements: the availability of material to build a habitable planet and adequate seclusion from cosmic threats. The inner regions of the galaxy suffer from orbital instabilities, radiation bursts and cometary perturbations. The outer regions are safer, but because of the lower metallicity, terrestrial planets are typically smaller there. The galactic habitable zone in the Milky Way has been identified as an annular region (roughly around the sun’s location) between 23,000 and 29,000 light years from the galactic centre that widens with time and is composed of stars that formed between 8 and 4 billion years (Gyr) ago [10]. 2. Modelling the Earth system It is necessary to employ an integrated Earth system model in order to determine the photosynthesis-based habitability of an Earth-like planet beginning just after planetary formation up to the final end of its existence. Such a model must consist of the components solid Earth, hydrosphere, atmosphere, and biosphere. It couples the increasing solar luminosity, the silicate-rock weathering rate, and the global energy balance to estimate the partial pressure of atmospheric and soil carbon dioxide, the mean global surface temperature, and the biological productivity as a function of time. The crucial point is the long-term balance between the CO2 sink in the atmosphere–ocean system and the metamorphic (platetectonic) sources. The respective features of the Earth system model are described in some detail below. 2.1. The global carbon cycle The carbon cycle is the main process for the regulation of the atmospheric composition and climate with respect to increasing insolation [11–13]. The main sink of atmospheric carbon dioxide is provided by silicate rock weathering playing a crucial role in Earth’s climate. The overall chemical reactions for the weathering process are
Fig. 1. The global carbon cycle as part of the general volatile exchange between mantle and surface reservoirs.
boundary layer theory of convection [15] with water dependent viscosity [16]. 2.2. The photosynthesis-based biosphere Nearly all life depends on photosynthesis using light as a source of energy. Photosynthetic organisms, in particular, are the basis for nearly all life on Earth and produce some of the strongest indicators of life in abundances that can be detected astronomically [17]. In particular, the detection of oxygenic photosynthesis is most relevant for the direct determination of life on extrasolar terrestrial planets. The terrestrial planet finder (TPF) and Darwin space missions of NASA and ESA are planning to detect O2 or its photolytic product O3 as a biosignature of life built up by oxygenic photosyn-
CO2 + CaSiO3 → CaCO3 + SiO2 CO2 + MgSiO3 → MgCO3 + SiO2 . The total process of weathering embraces (i) the reaction of silicate minerals with carbon dioxide, (ii) the transport of weathering products, and (iii) the deposition of carbonate minerals in sediments. The main feedback loop stabilizing the planetary climate is maintained by the weathering process: An increase of the luminosity leads to a higher mean global temperature causing an increase in weathering. Then more CO2 is extracted from the atmosphere weakening the greenhouse effect. Overall the temperature is lowered and homeostasis is achieved. On geological time scales, however, the deeper parts of the Earth are considerable sinks and sources for carbon and the tectonic activity as well as the continental area change markedly [14]. In addition to the usual carbonate–silicate geochemical cycle, subduction of large amounts of carbon into the mantle with descending slabs and the degassing of carbon from the mantle at mid-ocean ridges has to be taken into account. The global carbon cycle is sketched in Fig. 1. In the framework of a geodynamic-equilibrium approach for the global carbon cycle at longer time scales of about hundred thousands of years, a balance is proposed between the CO2 sink in the atmosphere–ocean system and the metamorphic source [11]. The main driving forces and feedbacks acting in the Earth system are depicted in Fig. 2. The metamorphic sources can be determined by calculating the temperature of the planetary mantle according to
Fig. 2. Earth system box model. The arrows indicate the different driving forces and feedback mechanisms. The bold arrows mark the main feedback loop stabilizing planetary climate.
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thesis [18]. But there is also non-oxygenic photosynthesis in, e.g., sulfur bacteria not considered here. Photosynthetic fixation leads to build up of organic material consuming CO2 from the atmosphere. On the other hand organic material is decomposed and CO2 is remobilised: h
CO2 + H2 OCH2 O + O2 Carbon isotope composition of photosynthetic products indicates that the enzyme Rubisco prefers the lighter isotope 12 C over 13 C and therefore oxygenic photosynthesis controlled the global distribution of carbon in the atmosphere–ocean system for at least 3.5 Gyr and gave an imprint on the isotopic signature of the carbon reservoirs [19]. Direct evidence of oxygenic photosynthesis is given by the steep rise of oxygen in the atmosphere 2.2 Gyr ago [20]. According to Wolstencroft and Raven [21] oxygenic photosynthesis is not ruled out for central stars distinct from our Sun. They concluded that photosynthesis on other planets is plausible for different types of parent stars with different radiation spectra. The productivity of the photosynthesis-based biosphere is a function of various parameters such as water supply, photosynthetic active radiation, nutrients, atmospheric carbon dioxide content, and surface temperature. As a first approximation biological productivity is considered to be solely a function of the global averaged mean surface temperature Tsurf and the CO2 partial pressure in the atmosphere pCO2 . Biosphere productivity vanishes for temperatures Tsurf ≤ 0◦ C and Tsurf ≥ 100◦ C and CO2 partial pressures below 10−5 bar as the presumed minimum value for C4 -photosynthesis [22,23]. The upper limit of the temperature tolerance is valid for primitive thermophilic life only, complex life has an upper temperature tolerance of 30–50 ◦ C [24]. The evolution of the biosphere and its adaptation to even lower CO2 partial pressures are not taken into account. Only biosphere on continents is considered because only the land biota has an influence on the weathering processes. The question pertaining to what extent the biota are actually able to play a key role in stimulating the weathering sink is crucial for an understanding of the dynamic properties of the overall Earth system. Vascular plants are particularly effective at rock weathering. Cyanobacteria of some algae weather rock in desert conditions — as so-called resurrection forms of life. In a study [25] accounting for the accumulation of weathered ions in vegetation and soil, experimental sandboxes with red pine stands had weathering rates amplified by a factor of 10 for Ca2+ and 18 for Mg2+ , relative to plots with moss and lichen cover. An overall factor of ∼ 7 for vascular plants has been used [26]. 3. The photosynthesis-sustaining habitable zone In general, the habitable zone around a main-sequence star can be defined as the region within which an Earth-like planet have moderate surface temperatures needed for advanced life forms. Main-sequence stars are stars getting their energy mainly by fusing hydrogen in their cores. During stellar evolution the luminosity of a star increases. The luminosity of the Sun, e.g., increases by 10% in one billion years. Stars with higher masses than our Sun have a higher luminosity and evolve more rapidly. The habitable zone has been more specifically related to the existence of liquid water at a planetary surface [27–29]. The socalled zero age main sequence habitable zone [30], i.e., at the time the star starts hydrogen fusion, is shown as a function of stellar mass in Fig. 3. The habitable zone moves outwards with increasing stellar mass due to an increase in luminosity. Based on the Earth system model described in the previous section, the habitable zone can be determined in a different way.
Fig. 3. The zero age main sequence habitable zone (HZ) as a function of central-star mass (in solar masses M ). The distance to the central star is measured in astronomical units (AU), the mean distance between the Earth and the Sun. As the mass of the central star increases the habitable zone moves outwards due to an increase in stellar luminosity. The long-dashed lines delineate the probable terrestrial planet accretion zone. The dotted line is the orbital distance for which an Earth-like planet in a circular orbit would be locked into synchronous rotation (tidal locking) (picture taken from [30]).
Here the so-called photosynthesis-sustaining habitable zone (pHZ) for an Earth-like planet is the region around a star within which the global averaged mean surface temperature Tsurf of the planet stays between 0◦ C and 100◦ C and the atmospheric CO2 partial pressure pCO2 is higher than 10−5 bar (10 ppmv), i.e., suitable for photosynthesis-based life (biological productivity > 0): pHZ := {R|(PCO2 (R, t), Tsurf (R, t)) > 0},
(1)
where R is the distance to the central star. The specific parameterization of the biological productivity plays a minor role in the calculation of the pHZ. Habitability is linked to the photosynthetic activity of the planet. The term “Earth-like” explicitly implies the occurrence of plate tectonics as a necessary condition for the operation of the carbonate–silicate cycle as the mechanism to compensate for the gradual brightening of the central star during its “life” on the main sequence. The geodynamical evolution of the considered Earth-like planet provides an even stronger constraint. The volcanic input of CO2 to the atmosphere is decreasing over time while the continental area (available for weathering) is increasing. In principle, it is possible to calculate the pHZ for any value of central-star mass [7]. As an illustration, the results for central-stars of 0.8, 1.0, and 1.2 masses of our Sun (M ), respectively, are presented in Fig. 4. While the inner limit of the pHZ moves outward with time, the outer limit moves inwards after 3.6 Gyr. After 6.5 Gyr no photosynthesis-sustaining habitability can be found. The following effects limit the pHZ: 1. Stellar lifetime on the main sequence decreases strongly with mass. After all hydrogen in the core is consumed the star leaves the main sequence and turns into a red giant with an increase in luminosity by a factor of 1000–10,000. Using simple scaling laws [32], the central hydrogen burning period H is estimated to be shorter than 0.8 Gyr for a star with a mass larger than 2.2 solar masses. Therefore, there is no point in considering central stars with masses larger than 2.2 solar masses because an Earth-like planet may need ∼0.8 Gyr of habitable conditions for the origin of life [33]. Smaller numbers for the time span required for the emergence of life have been discussed, for instance 0.5 Gyr [34]. Performing calculations with H < 0.5 Gyr, one obtains qualita-
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Fig. 4. Graphs of the width and position R of the pHZ derived from the geodynamic model for three different stellar masses M (0.8, 1.0, 1.2M ). The distance to the central star is measured in astronomical units (AU), the mean distance between the Earth and the Sun. tmax is the maximum life span of the biosphere limited by geodynamic effects. H indicates the hydrogen burning time on the main sequence limiting the life span of more massive stars.
tively similar results, but the upper limit of central-star masses is shifted to 2.6M . 2. When a star leaves the main sequence, there clearly remains no habitable conditions for an Earth-like planet previously in the pHZ. This limitation is relevant for stellar masses in the range between 1.1 and 2.2M . There might be habitable conditions for 108 –109 yr at the red giant branch for Earth-like planets more distant from the central star suitable for the origin of life [35,36]. 3. In the stellar mass range between 0.6 and 1.1M , the maximum life span of the biosphere is determined exclusively by planetary geodynamics, which is independent of distance to the central star. So one obtains the limitation t < tmax , where tmax = 6.5 Gyr. 4. There have been discussions about the habitability of tidally locked planets. Similar to the moon orbiting the Earth in synchronous rotation tidally locked planets are facing one hemisphere constantly to their central star. This limitation is relevant for central-star masses lower than 0.6 solar masses where the outer boundary of the pHZ is below the tidal-locking radius. Global climate models of tidally locked planets have indicated that Earth-like planets should not be necessarily precluded from habitability [37], but complex life is not very likely due to the harsh environmental conditions. 4. Estimating the number of habitable planets in the Milky Way and the rare Earth factor In the previous section we discussed several factors limiting habitability in extrasolar planetary systems. In the following the pHZ concept is used to calculate the number of planets harbouring photosynthesis-based life in the Milky Way. Additionally we try to distinguish between primitive unicellular life and complex multicellular life. In the 1960s, astronomer Frank Drake developed an formula to predict in a statistic way how many intelligent civilizations might exist in the Milky Way. It is a string of factors, when multiplied together, giving an estimate of such a number where are some of the
individual factors are highly speculative. Nevertheless, it is possible to determine the number of habitable extra-terrestrial planets with the help of a segment of the Drake formula to 50 million [31]. The same conclusion was reached with the help of a time-dependent calculation [38]. Both models were based on a parameterization of a uniform biosphere consisting of primitive photosynthesis-based life. “Complex life” is defined as multicellular organisms that have the ability to perform photosynthesis. It left fossil records in the Cambrian Explosion. Such a biosphere is mainly composed of land plants (due to food net relations a prerequisite for animals) that can amplify weathering. Additionally, we assume toxic effects of very high atmospheric carbon dioxide. In 2000 Ward and Brownlee came up with the Rare Earth Hypothesis [39]. They argue that complex life – plants and animals – may be very rare, perhaps unique, in the Universe, while primitive life is common and widespread. They based this hypothesis on two observations on Earth. First, microbial life existed as soon as Earth’s environment made it possible, and this nearly invincible form of life flourished over most of Earth history, populating a broad range of hostile terrestrial environments. Second, the existence of larger and more complex life occurred only in restricted environments, and the evolution and survival of this more fragile variant of terrestrial life seems to require a highly fortuitous set of circumstances that could not be expected to exist commonly on other planets. Appearing at about the time of the Cambrian explosion (the Big Bang of biology), complex life exists on Earth only for the last 0.5 Gyr. Compared to the age of our planet of about 4.6 Gyr this is just a short period. Lineweaver et al. [10] modelled the evolution of the galactic habitable zone. The model suggests that ∼75% of the stars that could potentially harbour complex life in the Milky Way are older than the Sun and that their average age is ∼5.5 Gyr. The number of habitable Earth-like planets in the Milky Way at a certain time t harbouring primitive (i = 1) and complex (i = 2) life forms can also be determined with the help of a convolution integral [38] from the planet formation rate (PFR) and the probability phab , i that a stellar system hosts a habitable Earth-like planet at time t after its formation. The probability is zero if the lifetime of the central star on the main sequence is exceeded. To calculate the planet formation rate it is necessary to estimate the rate of star formation. The question of the star formation history has been the subject of a number of studies. While some authors favour a smooth and constant star formation history, others favour a bursty star formation history fluctuating around a constant mean [40–43]. However, cosmological simulations result in an exponentially decaying star formation rate with intermittent spikes [44]. Based on observational data, the star formation rate for the universe can be fitted to an exponentially increasing function for the first 2.6 Gyr after Big Bang followed by an exponential decline [45]. Star metallicity as an ingredient for the formation of Earth-like planets can be calculated from this fit for star formation rate. In astrophysics metals are defined as elements heavier than H and He and are built up during cosmological evolution through thermonuclear processes. Therefore the metallicity can be calculated as an integral of the star formation rate. Then the planet formation rate (PFR) can be parameterized in the following way: PFR = 0.5 · fGHZ · SFR · pE (),
(2)
where pE is the probability that Earth-like planets are formed and fGHZ is the fraction of stars within the galactic habitable zone. Here we assume as an upper limit that 10% of all stars are in the galactic habitable zone [10]. The pre-factor 0.5 reflects the assumption that 50% of the stars are in the range of 0.1–1.2, M including red dwarfs and Sun-like stars. The function pE () is an increasing function of metallicity . In contrast to Linewearver [45] we neglected
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Fig. 6. Evolution of the number of habitable Earth-like planets in the Milky Way harbouring complex life (solid line) and primitive life (dashed line). The vertical dotted lines denote the time of Earth’s origin and the present time, respectively.
Fig. 5. The star formation rate (SFR) and the Earth-like planet formation rate (PFR) recalculated from [45]. The vertical dotted lines denote the time of Earth’s origin and the present time, respectively.
the effect of the formation of hot Jupiters. High metallicity yields a high probability of forming hot Jupiters thought to destroy Earthlike planets during inward migration. A giant planet migration does not preclude the formation of Earth-like planets [46]. The star formation rate and the resulting planet formation rate for Earth-like planets are plotted in Fig. 5. The probability that a stellar system hosts a habitable Earthlike planet harbouring primitive (phab , 1) and complex (phab , 2) life forms at time t can be estimated with the help of an integral summing up the probabilities that an Earth-like planet is in the pHZ around a central star with mass M over all relevant star masses. Stellar masses in the Milky Way are distributed according to a power law [47], the orbital distribution of Earth-like planets is uniform on a logarithmic scale [48,49]. For determining the pHZ for complex life the upper tolerance temperature for non-vanishing biological productivity is set to 30◦ C. Primitive life is robust at unlimited high CO2 concentrations, while complex life dies with high atmospheric partial pressure due to poisoning effects [50]. Here we assume a value of 10−2 bar (10,000 ppmv), double the maximum Phanerozoic concentration. Complex life has an additional amplifying effect on weathering assumed to be 5 times higher than for primitive life [51]. The estimated number of habitable Earth-like planets in the Milky Way bearing primitive and complex life is shown in Fig. 6. If the pHZ approach is the only necessary condition for the appearance and maintenance of these two life forms then the number of planets hosting complex life is only a factor ∼ 270 lower than for primitive life. There was a maximum of these planets about 1.5 Gyr ago (∼2.5 mill. in the Milky Way) and their number is then declining [52]. Complex life occurred about ∼ 6 billion years later than
primitive life. The maximum number of planets bearing primitive life (∼ 690 mill. in the Milky Way) was about the time of Earth’s origin [38] and is then declining. Based on the simple Earth system model one could conclude that complex life forms might be not really “rare” in the Milky Way. This could be a false conclusion because there are many other limiting factors that up to now are difficult to model but surely influence the appearance and maintenance of complex life. The habitability of an Earth-like planet depends also on other circumstances. The presence of a large moon seems to be necessary to stabilize the planet’s obliquity [53] in order to have a stable climate. The presence of a giant planet is important to shield the planet from comets and to scatter asteroids to the planet early on to deliver volatiles [54]. The abundance of long-lived isotopes as a primary source of internal heat is necessary for the operation of plate tectonics, which drives the planetary temperature thermostat. Nevertheless, complex life has to be more rare than primitive life, at least by two orders of magnitude. This factor originates by the photosynthesis-sustaining habitable zone approach only. All the other rare Earth factors will diminish the number of habitable Earth-like planets in the Milky Way, but up to now, they are difficult to model and/or to quantify. References [1] The Extrasolar Planets Encyclopaedia web page, maintained by J. Schneider, http://exoplanet.eu (accessed January 2010). [2] D. Valencia, D.D. Sasselov, R.J. O’Connell, Radius and structure models of the first super-earth planet, Astrophys. J. 656 (2007) 545–551. [3] D. Charbonneau, A super-Earth transiting a nearby low-mass star, Nature 462 (2009) 891–894. [4] M. Mayor et al., The HARPS search for southern extra-solar planets, XVIII. An Earth-mass planet in the GJ 581 planetary system, Astron. Astrophys. 507 (2009) 487–494. [5] D.E. Koshland Jr., The seven pillars of life, Science 295 (2009) 2215–2216. [6] S. Franck, A. Block, W. von Bloh, C. Bounama, H.-J. Schellnhuber, Y. Svirezhev, Reduction of biosphere life span as a consequence of geodynamics, Tellus 52B (2000) 94–107. [7] S. Franck, W. von Bloh, C. Bounama, M. Steffen, D. Schönberner, H.-J. Schellnhuber, Determination of habitable zones in extrasolar planetary systems: where are Gaia’s sisters? J. Geophys. Res. 105(E1) (2000) 1651–1658. [8] W. von Bloh, C. Bounama, M. Cuntz, S. Franck, The habitability of super-Earths in Gliese 581, Astron. Astrophys. 476 (2007) 1365–1371. [9] G. Gonzalez, D. Brownlee, P. Ward, The galactic habitable zone: galactic chemical evolution, Icarus 152 (2001) 185–200. [10] C.H. Lineweaver, Y. Fenner, B.K. Gibson, The galactic habitable zone and the age distribution of complex life in the Milky Way, Science 302 (2004) 59–62. [11] J.C.G. Walker, P.B. Hays, J.F. Kasting, A negative feedback mechanism for the long-term stabilization of Earth’s surface temperature, J. Geophys. Res. 86 (1981) 9776–9782.
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