iBook The Future of the Universe - 4. The Price of Doing Nothing

4. The Price of Doing Nothing

Cost (noun). The price to be paid. Cost (verb intransitive). Result in the loss of. (from The Concise Oxford English Dictionary) If our descendants do absolutely nothing about the aging of the Sun, then the future is clear: all life on and inside Earth will die. Indeed, all that will remain after the Sun has become a red-giant will be a sterile and heat-blasted Earth. Venus will possibly survive against destruction in the Sun’s red-giant envelope, but Mercury is definitely doomed, and it will be consumed. The fate of our future desolate Earth will be to orbit in endless silence around a slowly fading white dwarf star. In this chapter we will describe some of the costs of allowing the Sun to become a luminous and bloated red-giant. It is one possible future for our Solar System that we shall explore over the following pages, but it is not an inevitable future. Our descendants do, in fact, have a choice concerning their destiny. The Habitability Zone Earth is located in a very specific ‘sweet zone’ within our Solar System. Indeed, Earth is heated by solar radiation to just the right level that liquid water can exist on its surface. It is neither too hot nor too cold over most of Earth’s surface. If Earth had formed much closer in toward the Sun, then all the oceans would have rapidly boiled away; if Earth had formed much further out from the Sun, then all of the oceans would have frozen. Venus and Mars are the possible alternatives to present-day Earth; one too hot for oceans, the other (now) too cold.1 The region within the Solar System where liquid water can exist on the surface of a planet with an atmosphere such as that surrounding Earth is known as 113 114 Rejuvenating the Sun and Avoiding Other Global Catastrophes the habitability zone. At a distance d astronomical units from the Sun the surface temperature of a planet Tsurface expressed in Kelvins will be2 Tsurface = TGHE +278 1−A Lt d2AU 1/4 (4.1) where TGHE is the greenhouse heating effect due to the atmosphere, A is the atmospheric albedo, is the emissivity of the planet,3 and L(t) is the luminosity of the Sun at time t expressed in terms of the Sun’s present luminosity4 [that is, L(t = 4.5 billion years) = 1]. The inner boundary of the habitability zone is determined by the boiling point of water, while the outer boundary corresponds to the distance at which water will freeze. Accordingly, at the present time within our Solar System the inner and outer boundaries for which 373 > Tsurface > 273 are 0.6 < d (AU) < 1.1 [derived from Equation (4.1) with A = 0.2 and = 0.8]. More detailed calculations, including model atmospheres that take active weathering reactions (which regulate the atmospheric CO2 concentration) into account,5 find that the habitability zone for our Solar System is actually shifted outward, falling somewhere between 0.95 < d < 1.4. This latter range makes sense in that the habitability zone straddles Earth’s orbit, but excludes both Venus and Mars as being too hot and too cold, respectively, for liquid water to exist at the present time. The idea of a habitability zone can be applied to any parent star,6 but as seen in Chapter 3, the luminosity of a star varies according to its mass [see Equation (3.12)]. The boundaries of the habitability zone will, therefore, be shifted inward for stars less massive than the Sun, and shifted outward for stars more massive than the Sun. Although no Earth-like extraterrestrial planet has so far been detected around another Sun-like star, a study by Brian Jones and co-workers7 has investigated the orbital stability of hypothetical Earth-like planets within the habitability zones of stars known to have accompanying Jupiter-type planets. Among the systems that were studied it was found that the stars CrB and 47 UMa could, in principle, have Earth-like planets in stable orbits situated in the habitability zone. Such planets could, again in principle, be capable of supporting life. Darren The Price of Doing Nothing 115 Williams and co-workers8 have also looked at the possibility of hypothetical moons in orbit around known extrasolar, Jupiter-like planets falling within a system’s habitability zone. They find that the planets in the 47 UMa and 16 Cyg B systems could possibly support moons with liquid water at their surfaces (provided, that is, the moons are large enough to maintain an atmosphere). The extrasolar planetary system HD 69830 is of particular interest with respect to both the deduced structure of the planets and the location of the planets around the parent star. HD 69830 is about 12.5 pc away, has a mass of 0.86 M , and hosts three Neptune-mass planets. Extensive computer modeling9 has led to the suggestion that the innermost of the planets – with a mass about 15 times that of Earth and an orbital radius of 0.08 AU – has a rocky composition. In many ways, it is a super-sized Earth. The outermost planet, which is probably more similar to our Neptune in structure (i.e., a rocky/ice core surrounded by an extensive gas envelope), has an orbital radius of 0.63 AU, and this places it close to the inner edge of the habitability zone for the system. Recent observations with the Spitzer Infrared Telescope also indicate that the system sports what appears to be an asteroid belt in the region between 0.3 to 0.5 AU from HD 69830. This is actually an infrared emission excess due to small dust grains that the Spitzer telescope observations record, but since the system is estimated to be at least several billion years old, the dust is most probably a product of numerous asteroid collisions. With three planets moving in circular orbits – one of which is located near the habitability zone and an asteroid belt – HD 69830 shares many properties with our Solar System, and life on a large moon in orbit around the outermost planet might be possible (see Figure 4.1). The Ocean on Europa Europa is the second innermost of the four large Galilean moons that orbit Jupiter. It is about the same size as Earth’s Moon, but rather than being a purely rocky body, Europa has an outer ice surface that caps a global ocean. The exact internal structure of Europa is not known, but various models indicate that it has an iron/iron-sulphide-rich core occupying about 30 percent of its 116 Rejuvenating the Sun and Avoiding Other Global Catastrophes interior.10 Most of the remaining interior is taken up by a silicate mantle, but the outermost few hundred kilometers appear to be composed of a global, possibly salty ocean covered by a solid-ice veneer perhaps a few kilometers in thickness. Equation (4.1) indicates that at 5.2 AU from the Sun the surface temperature of Europa is something like 120 K, well below the freezing point of water or brine (which freezes at a lower temperature because of its salt content). And yet, Europa has a global ocean! How is this possible? First, there is little doubt that there is a global ocean, since the Galileo spacecraft clearly detected a peculiar magnetic anomaly when it flew past Europa in December 1996. The most reasonable explanation of the recorded anomaly is that Europa has a near-surface conducting layer, and this is where the brine comes in. Next, of course, the question to answer is why hasn’t the ocean frozen, since Europa formed along with the rest of the Solar System some 4.56 billion years ago. The reason why the ocean still exists is, in fact, remarkable, and it reminds us that liquid water can be found in locations well outside of the habitability zone defined – admittedly conservatively – above. The ocean of Europa hasn’t frozen because of a tidal heating effect related to the non-circular orbit of Europa and the corresponding periodic stretching and relaxing that it undergoes in the strong gravitational field of Jupiter. This flexing and relaxing actually heats the outer part of its rocky mantle, and it is this heat that keeps the ocean from freezing. Although there is little doubt that there is some form of global ocean under Europa’s outer ice cap, it is far from clear if it can support life. It is likely that all the basic chemical ingredients to support primitive life are present in Europa, but by far the greater problem is how any life forms might produce the energy needed for their survival. Certainly the outer ice cap precludes photosynthesis from operating, so other chemosynthesis forms of energy generation will presumably need to apply. One possibility is that Europa might support isolated colonies of animals similar to those found around hydrothermal vents in Earth’s deep oceans. We do not currently know if life has gained a toehold in Europa’s ocean, but spacecraft missions may provide us with an answer within the next three or four decades. In the meantime there is a place on Earth – Lake Vostok in Antarctica – which The Price of Doing Nothing 117 might provide us with a few clues as to what future Europa landers might find. Lake Vostok is several hundred meters deep, but more importantly, it is buried under some 4-km of ice. The icecap is estimated to be at least 500,000 years old, and it has been suggested that the lake may have preserved life forms that are significantly different from those found anywhere else on Earth. An active coredrilling project has been conducted at the Lake Vostok site, and the bore-hole is estimated to be very close (a few tens of meters) to breaking through into the liquid layer. The final penetration effort, however, is currently on hold, as engineers try to ensure that no, or at least a minimum, of pollutants (i.e., the drilling fluid) are introduced into the pristine waters of the lake. A Brief Aside: Utilizing Europa If no life forms are detected within Europa’s ocean, then one good use for this vast brine resource would be to ‘seed’ it with appropriately engineered (genetically engineered, in this case) halophiles— equivalents of the salt-loving extremophiles found, for example, in the Dead Sea in Israel. If such seeding and successful breeding can be nurtured, then a potentially massive food resource could be cultivated. Moon Life The current models accounting for the formation of moons orbiting large gas-giant planets, such as Jupiter, suggest that they form in naturally occurring circumplanetary disks. There is no specific reason, therefore, why the Jupiter-mass planets being discovered around other Sun-like stars shouldn’t also have moons. The question concerning how far moon-based life might evolve is completely open at the present time. In the case of Europa one might reasonably imagine that microbial life could have evolved, but it is not at all clear if intelligent life, capable of, say, manipulating its environment or even colonizing an entire planetary system is possible. 118 Rejuvenating the Sun and Avoiding Other Global Catastrophes Synchronization and the Moon Effect Figure 3.9, in the last chapter, indicates that stars can form with masses as small as a few tenths of a solar mass, and it is also known that these stars can support planetary systems. The low temperature, low luminosity, M dwarf star Gliese 581 is one especially intriguing example of a low-mass [0.3 M ] star that has three known planetary companions. The system holds great interest since one of the planets is a so-called ‘super-Earth’ planet. The planet is about 1.5 times larger than the Earth (five times more massive) and orbits Gliese 581 in just under 13 days. Although located very close to Gliese 581 (at a distance of 0.07 AU) the planet is nonetheless in the system’s habitability zone, and Stephane Udry, of the Geneva Observatory, and co-workers have recently suggested that the planet might have regions where surface water could exist. Even though the system is estimated to be some 4.3 billion years old, it is unlikely that the ‘super-Earth’ companion to Gliese 581 supports any life (or, for that matter, any extensive oceans). The reason for this latter statement is exemplified by our Moon, which is in synchronous rotation around Earth. Due to the close proximity of the Moon and Earth, and the fact that the Moon and Earth are not perfect spheres, the Moon’s spin rate has been brought into equalization with its orbital motion. This is why we always see the same face of the Moon from Earth. Since low-mass stars are also low luminosity stars, their habitability zones are located close in toward the star. Indeed, the habitability zones will be so close to the parent stars that planetary synchronization will inevitably come about. For our Moon synchronization is not a problem, but for a planet with an atmosphere the effect will most certainly be catastrophic. Since one hemisphere of the planet will always face the parent star it will be continuously warmed, while the other hemisphere will be constantly cooled by radiating its energy into outer space. The outcome of such extreme heating and cooling is not absolutely clear, but most meteorologists suggest that the atmosphere will eventually freeze out. This being said, some researchers have argued that stable atmospheres capable of supporting regions of surface water might still form around The Price of Doing Nothing 119 synchronized planets. Detailed numerical modeling indicates that planets located within the habitability zones of stars less massive than 0.5 M will be synchronized, and we have therefore taken this to be the lower stellar mass limit for supporting a habitable planet. The main-sequence lifetime of a 0.5 M star is about eight times greater than that of the Sun’s, so habitable planets in orbit around these stars have a naturally extended lifetime. The Upper Limit Stars are observed to form with masses perhaps as high as 100 times that of the Sun. Such stars are very rare, but they do form. Where, then, might we place the upper limit to the mass of a star capable of supporting planets on which intelligent life might evolve? As discussed in Chapter 1 the mass limit can be set (to a first approximation) according to the main-sequence lifetime of the star being longer than the time required for human beings to have appeared on Earth: TUS = 4.5 billion years. According to Equation (2.1), this sets a limit of about 1.3 M on the mass of a star capable of supporting intelligent life. Life may well evolve on planets within the habitability zones of stars outside of the chosen mass range of 0. 5 to 1.3 M but at this stage it can be assumed that such life is most likely microbial in nature rather than of an advanced form capable of space exploration. Although massive stars have relatively short main-sequence lifetimes this does not preclude the possibility of them having planets. The very high luminosities associated with such stars dictate that the planets cannot be too close in – or else they would literally boil away – but there is some limited, albeit controversial, evidence that they do at least form. Not only is there evidence that planets form around massive stars, there is also – again controversial – evidence that massive stars can consume their planetary progeny. This latter possibility is based upon recent interpretations of the ‘outburst’ observed from the star V838 Monocerotis (Figure 4.2). V838 Mon is a binary system composed of two ∼8 M stars situated between 6 to 10 kpc away from the Sun. In early 2002 the system underwent a series of distinct outbursts in brightness 120 Rejuvenating the Sun and Avoiding Other Global Catastrophes over a period of about 100 days. Three outbursts were actually recorded, with each event lasting about 25 days. As a consequence of this sudden increase in brightness a pulse of light spread outward from V838 Mon into space, illuminating in its path the surrounding interstellar medium as seen in the dramatic Hubble Space Telescope image reproduced in Figure 4.2 A number of distinctly different explanations for the origin of the outbursts have been published, but Alon Retter (Penn State University) and co-workers11 have argued that the three outbursts were the result of one of the stars in V838 Mon consuming three Jupiter-sized planets. Detailed numerical modeling suggests that as a consequence of devouring the first planet, the host star expanded and this resulted in the envelope entrapment and eventual consumption of the next two planets. Provided this model for the outburst of V838 Mon is the correct one (the debate still rages), it tells us that not only can planets form around massive stars, but that planets can also form in binary star systems. A Moving Habitability Zone As the Sun’s luminosity steadily increases with time, Equation (4.1) tells us that the surface temperature of the different planets must also increase, thereby shifting the habitability zone outward and deeper into the Solar System. Using the solar evolution model described in Chapter 3 [see Table 3.2], the location of the hot, inner boundary for the habitability zone is shown in Figure 4.3. Here we have used Equation (4.1), which while oversimplified for the problem to be discussed is nonetheless representative of the point. And the point is, as the Sun ages, so the inner (hot) boundary of the habitability zone is swept into the outer reaches of the Solar System and, indeed, once the Sun enters its asymptotic giant branch phase, even the icy moons of Saturn will begin to evaporate. The simplified model calculations appear to indicate that Earth’s oceans will begin to boil away in about 7 billion years. In fact, the situation is more urgent than that and the oceans will, in fact, enter a significant evaporation phase in about 1 billion years. The reason for the accelerated demise of the oceans is due to the evolution of Earth’s atmosphere,12 which is not taken into account The Price of Doing Nothing 121 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 012345 Distance (AU) )nusM(ssaM Habitability zone Mercury 16 Cyg B 47 UMa HD69830 HD183263 ρ CrB Jupiter Figure 4.1. The habitability zone for stars in the range 0.8 to 1.2 times the mass of the Sun. The inner planets within our Solar System are shown (circles), the location of the planets within a selection of extrasolar systems (triangles) are also indicated. Based upon the calculations by Kasting and co-workers.5 Figure 4.2. The light echo of V838 Monocerotis. A burst of light from V838 Mon has illuminated the dust in the surrounding interstellar medium. (Image courtesy of the Hubble Space Telescope Institute and NASA) 122 Rejuvenating the Sun and Avoiding Other Global Catastrophes 0.1 1 10 100 11.6 11.8 12 12.2 12.4 Time (Gyr) K273=Trof]UA[d Saturn Earth Mars Jupiter Figure 4.3. Evolution of the inner hot edge of the habitability zone within our Solar System. Note that the boundary line [calculated according to Equation (4.1)] is the actual surface temperature of the planet, assuming that it has no atmosphere and ocean. Earth’s dry surface temperature will reach 100 oC (372 K) in about 7 billion years; the surface of Mars will reach this temperature about 200 million years later. The moons of Jupiter and Saturn will first fall in the 100 oC heating zone in about 8 billion years from now as the Sun ascends the giant branch. in the calculations leading to Figure 4.3. Likewise, life will have been killed off long before Earth’s equilibrium temperature reaches 100oC. Indeed, only the most extreme of bacterial life forms – the so-called extremophiles13− can survive and potentially thrive in environments where the temperature exceeds 40oC for prolonged periods of time. There is a clear symmetry to the story of life on Earth when we compare the deep future to the distant past: microorganisms were the very first life forms to appear on Earth, and they will be the very last to die. The Beginning of the End Although it is the Sun’s increasing energy output (that is, its luminosity) that will eventually cause Earth’s oceans to evaporate and kill off even the hardiest of life forms, it will be the Sun’s increasing size that will destroy Mercury. In about 8 billion years from now, when the Sun begins to ascend the red-giant branch (points 3 to 4 in Figure 3.10), it will swell up to engulf the entire orbit of Mercury, which orbits the Sun at a distance of 83 solar radii. The Price of Doing Nothing 123 Inevitably, as the Sun’s radius expands outward, Mercury will find itself moving through an increasingly dense gas. The planet will then begin to accrete material from the Sun’s envelope, and it will begin to experience the drag effects associated with its motion through the Sun’s extended atmosphere. As we shall see below, Mercury will be rapidly destroyed as it falls deeper and deeper into the Sun’s envelope. For a short few years it will circle the Sun like a glowing meteor, with its vast bulk eventually being broken apart and ablated into its constituent atoms. If the accretion rate of material by Mercury from the Sun’s envelope is written as Macc, then the characteristic time for its orbit to decay will be Tdecay ≈ MMerc/Macc, where MMerc is the mass of Mercury.14 The accretion rate can be estimated as being of the order of the cross-sectional area of Mercury ( = R2 M) multiplied by the density of the Sun’s envelope at the orbit of Mercury ( env) multiplied by Mercury’s orbital velocity VMerc. Mercury’s orbital speed is VMerc = 48 km/s, its radius is RM = 2,440 km, and its mass is MMerc = 3.3 x 1023 kg. Taking an envelope density15 of env = 10−4 kg/m3, an orbital decay time of Tdecay ≈ 100 years is indicated for Mercury. The orbital decay time will probably be more rapid than this estimate because we haven’t included the effects of gravitation, which will tend to increase the accretion rate.16 Therefore, once the Sun starts to climb the red-giant branch, Mercury will begin to spiral inward on its orbit, speeding ever more rapidly toward a fiery destruction. The Fate of Venus and Earth Although Mercury is doomed once the Sun becomes a red-giant, it appears that Venus and Earth, at least as physical entities, will survive. The ultimate fate of these planets, however, will reside in the amount of mass lost by the Sun during both its red-giant and asymptotic giant branch phases. The more mass our future Sun ejects into space the more likely it is that Venus and Earth will be spared from a fiery obliteration. The reason for this dramatic escape is due to the fact that as the Sun loses mass, so the orbital radius of each of the planets will increase, carrying them 124 Rejuvenating the Sun and Avoiding Other Global Catastrophes 0 50 100 150 200 250 12 12.1 12.2 12.3 12.4 Time (Gyr) )nusR(suidaR Mercury Venus Earth Figure 4.4. Changes in the Sun’s radius with age. Mercury will be consumed by the Sun in about 8 billion years from now. Note that in this particular set of calculations both Venus and Earth survive against destruction because the Sun loses mass (about 0.2 M as it ascends the giant branch. [Solar model based upon calculations by Sackmann, Boothroyd, and Kraemer, ApJ. 418, 457–468 (1993)] beyond the reaches of the Sun’s bloated envelope (as shown in Figure 4.4). At the present time Earth’s orbital radius (1 AU) is equivalent to 215 R . Detailed computer models predict that the Sun will expand to somewhere between 200 to 250 times its present size during its red-giant phase which, without orbital migration, suggests that Earth will be destroyed. The change in Earth’s orbital radius as a result of the Sun losing mass can be determined by assuming that Earth conserves its orbital angular momentum.17 In this fashion, Earth’s orbital radius a(t) can be related to the Sun’s mass M (t) at some future time t, as a(t) = a(0) M (0)/M (t), where a(0) and M (0) are the values of Earth’s orbital radius and the Sun’s mass at some specified starting time t = 0 (i.e. now). For Earth to survive against the extreme expansion predicted for the Sun’s outer red-giant envelope we require a(t)/a (0) ≈ 250 R /215 R = 1.16 at the time that the Sun reaches the red-giant tip (Point 4 in Figure 3.10). In other words, the Sun’s mass must decrease by a factor of M (t)/M (0) = 0.86 for Earth to be sure of escaping consumption. For Venus to survive, a(t)/a (0) ≈ 250 R /155 R = 1.61, and correspondingly, M (t)/M (0) = 0.62. Observations clearly indicate that solar-mass stars do lose about 0.2 to 0.3 M during their red-giant branch phases. Earth, it The Price of Doing Nothing 125 therefore appears, is probably safe from physical destruction during the red-giant branch and asymptotic giant branch phases of the Sun’s evolution. The detailed computational models of solar evolution, however, are not currently in agreement as to whether the Sun will lose enough mass for Venus to survive. Calculations by Peter Schrder18 and co-workers at the University of Sussex, for example, predict that the future mass-loss of the Sun will result in the survival of Earth, but not of Venus. The Outer Planets Moving into the outer Solar System, beyond the orbit of Mars, the Sun’s increasing luminosity is not likely to have any great effect upon the internal structure of the Jovian planets. Both Jupiter and Saturn have massive hydrogen and helium envelopes, and these can adjust without any great structural changes to accommodate the increased energy output received from the aging Sun. Examples of the possible future atmospheric states of Jupiter and Saturn can be found among the extrasolar planets. Indeed, many of the extrasolar planets have exceptionally small orbits, and this means that they are heated to temperatures in excess of those experienced by the planets in our Solar System. The most extreme case known is that for the 1.45 Jupiter mass planet OGLE-TR-56b, which has an orbital radius of 0.0225 AU. This planet orbits its parent star in an incredible 1.2 days at a distance 17 times closer than Mercury orbits our Sun, resulting in a surface temperature of about 1,500 K. In the few cases where measurements have been made, the hot Jupiter-like planets appear to have diameters that barely differ from those of their cooler counterparts orbiting at much greater distances from their parent stars. It is upon this basis that we would not expect Jupiter or Saturn to experience any extensive internal changes as the Sun ages. This being said, it is highly likely that the appearance of their upper cloud decks will change dramatically. The enhanced solar heating will warm the atmosphere, driving stronger zonal winds and altering the details of the photochemical reactions responsible for producing the various colored spots, ovals, and bands. 126 Rejuvenating the Sun and Avoiding Other Global Catastrophes In similar fashion to their gas-giant cousins, the icy giant planets Uranus and Neptune will ride out the effects of the Sun’s increasing luminosity essentially unscathed. Again, the main observational changes will be cosmetic and relate to the extra heating of their upper cloud decks and outer atmosphere. For a short few hundred million years – some 7.5 billion years from now – Uranus will be located in the Solar System’s habitability zone (see Figure 4.3). During this time an interesting possibility for terraforming arises. More correctly perhaps, one should say aquaforming in the case of Uranus, since the idea here is to generate a water world—literally, a planet encircled by a deep global ocean. Alain Le´ger of the Institu d’Astrophysique Spatiale in Orsay, France, and co-workers have suggested that among the extrasolar planetary systems, a family of ‘ocean-planets’ might well exist.19 These worlds will be smaller in mass than Uranus, by a factor of about two, but will have a similar internal structure. Essentially, and in contrast to Uranus, what they lack is an extensive hydrogen atmosphere. Le´ger and co-workers have found that ice-rich planets with masses of between 6 to 8 times that of Earth, situated in the habitability zone of their parent star, can develop global oceans up to about 100 km in depth. Models for the interior structure of Uranus are not especially well constrained at the present time, but it does appear that the planet has a central rocky core and an extensive icy mantle. Indeed, the icy mantle accounts for about 80 percent of the mass of Uranus (a total of 11.5 Earth masses of material), and the core accounts for a further 7 percent (about 1 Earth mass of material). To trim Uranus down to an aquaforming mass, something like 6 Earth masses of material will have to be removed from the planet’s atmosphere. This removal might be in the form of direct mining, since the extracted hydrogen, helium, oxygen, and nitrogen could be used in numerous industrial processes (see Chapter 6). The mass removal process could also be more dramatic (and wasteful) with the excavation being driven by multiple impacts from Kuiper Belt objects specifically maneuvered into position. An appropriately aquaformed Uranus could support structures such as the supramundane platforms described by Paul Birch (see Note 40 in Chapter 2), and it could provide a near inexhaustible supply of fluids for an intensive hydroponics industry. The Price of Doing Nothing 127 Orbital Engineering Irrespective of what the numerical calculations for the Sun’s future evolution predict, our future descendants will likely feel that the planet Venus is worth saving, especially if it has already been successfully terraformed. Likewise, our descendants may feel that Earth itself requires an additional safety zone, such that it is placed well beyond the outer reaches of the (non-engineered) red-giant Sun’s envelope. There are, in fact, ways in which this outward orbital migration might be achieved. In addition to reacting to any mass lost by the Sun, planetary orbits can be adjusted via repeated close gravitational encounters with smaller objects. Don Korycansky and co-workers20 have outlined, for example, a scenario by which orbital energy can be transferred from Jupiter to Earth, thereby increasing Earth’s orbital radius. And, as suggested above, a similar process of orbital engineering might be used to aquaform Uranus. In the Korycansky, et al scheme, a ∼100-km diameter asteroid or Kuiper Belt body is used as an energy transfer object. The idea is that the smaller body first gains energy via a gravitational slingshot encounter with Jupiter. That gained energy is then deposited into Earth’s orbital motion by an appropriately controlled close, leading limb flyby. By repeating this process every 6,000 years or so for the next billion years the Korycansky team believes that Earth can be maneuvered into an increasingly large orbit such that its equilibrium temperature [as given by Equation (4.1)] remains constant throughout the Sun’s main-sequence lifetime. Accordingly,21 in a billion years from now, Earth’s orbital radius will need to have increased to 1.045 AU; 4 billion years from now Earth’s orbital radius will need to be 1.225 AU. Korycansky and co-workers point out that ‘’Any serious proposal for planetary engineering, or any large-scale alteration of the Solar System, raises important questions of responsibility.“20 Absolutely! They also point out that their proposal has a number of potential problem points. The transfer of energy from one object to another via gravitational assists is well understood, and it is already a routine part of spacecraft navigation. The problem, however, is if Earth is gaining orbital energy from Jupiter, and thereby moving slowly outward, Jupiter is losing orbital energy 128 Rejuvenating the Sun and Avoiding Other Global Catastrophes and slowly moving inward. Because of Jupiter’s size, it doesn’t actually move very far – about 0.01 AU closer to the Sun over the Sun’s main-sequence lifetime. This inward shift is small, but Jupiter is very close to the outer edge of the main-belt asteroid region and, consequently, the inward drift might destabilize the orbits of numerous asteroids. It is possible, therefore, that the orbital migration program might enhance the NEA population of asteroids and consequently increase the asteroid impact problem. In addition, it is not clear what happens to Earth’s Moon in the Korycansky scenario. Since the Moon’s gravitational influence is vital for stabilizing the obliquity of Earth’s spin-axis, its loss could result in dramatic and chaotic swings in the climate.22 The fate of the planets Venus and Mars are not presently resolved in the scenario outlined by Korycansky and co-workers, but presumably the basic process could be multiplied to adjust their orbits as well. However, one starts to feel a little uncomfortable at the sheer complexity of trying to simultaneously manipulate the orbital radii of three of the terrestrial planets in such a fashion that Solar System stability is maintained and unwanted collisions do not occur. The Korycansky scheme, as currently outlined, would require about a million close Earth flybys by a ∼100-km diameter object; one slip, and Earth is sterilized as effectively as not increasing Earth’s orbit at all. With this possibility of catastrophic disaster in mind, Colin McIness has suggested23 that a large reflective sail (Figure 4.5), suitably stabilized near Earth, could be used to increase the size of Earth’s orbit through the action of solar radiation pressure. This method avoids having to coordinate the numerous close flybys that the gravity-assist scenario calls for and alleviates the chances of a catastrophic impact by accident. The McInnes scenario requires the construction of a 5 x 1016 m2, 8 μm thick, 1015-kg mass metallic solar sail from an 9-km diameter M type (i.e., a nickel-iron rich) asteroid. Such a sail (which corresponds to a disk of radius 19.2 Earth radii), if maintained at a standoff distance of 300 Earth radii, could enlarge Earth’s orbit to 1.5 AU over a time interval of about 6 billion years. Leonid Shkadov24 has outlined an even grander scale use for very large solar sails and suggests that the entire orbit of the Solar System about the galactic center could be controlled. Another use for such reflectors – also called class A stellar engines – is, of course, to deflect nearby stars The Price of Doing Nothing 129 Figure 4.5. An artist’s rendering of the Cosmos-1 space sail. Developed for the Planetary Society, an unfortunate launch-rocket malfunction resulted in the space sail never reaching an operational orbit. In the future, however, solar sails will probably be employed to manipulate the orbit of asteroids, comets, and Kuiper Belt objects. Image by Rick Sternbach and the Planetary Society. from passing too close to our Solar System’s Oort Cloud, thereby triggering a potentially deadly cometary shower (see Chapter 2). The orbital manipulation of diverse objects within the Solar System will presumably play an important part in our distant descendants’ strategy toolkit for long-term survival. The gravitational assist method, for example, could be exploited to not only avoid Earth’s heat death, but to aid in the terraforming of Mars by (initially) nudging its orbit closer in toward the Sun. Likewise, the process could be used to clear potentially impacting asteroids from near-Earth space, or maneuver asteroids, Jupiter-family comets, and Kuiper Belt objects into orbits where they could be more easily (and safely) mined for their resources. The orbital shepherding of these same objects might also produce ‘useful’ planetary impacts. The bulk of Venus’s overburdened atmosphere, for example, could be removed by repeated large body impact, thereby allowing the terraforming process to begin. 130 Rejuvenating the Sun and Avoiding Other Global Catastrophes What is perhaps most remarkable about the scenarios outlined above is that the technology and know-how to complete the tasks described already exists. The material to make working space sails has been developed, and small-scale space sails and inflatable structures have also been successfully deployed in near-Earth orbit. We are literally on the cusp of taking space sail technology into the Solar System now, and the first steps toward the more challenging engineering projects that our descendants will want to make are already being taken. Waving the Flag In addition to the shepherding and orbital manipulation of asteroids, cometary nuclei, Kuiper Belt objects, planets, and perhaps the entire Solar System, our descendants may even build massive solar sails just to advertise humanity’s existence. The same idea, of course, might also occur to extraterrestrial civilizations. Indeed, Luc Arnold of the Observatoire de Haute-Provence in France has suggested25 that SETI searches could be established on the basis of looking for unusual transit features. If, for example, an extragalactic civilization constructs a large solar sail having a triangular shape or a louvered structure, then the light curve produced by the sail each time it passes in front of the system’s parent star would be readily detected by a diligent observer (provided, of course, that the transit geometry was favorable for the observer). With respect to the required resources to build such structures, Arnold comments that a 12,000-km diameter, 1-micrometer thick solar sail made of iron would have a mass of about 1012 kg. While this certainly seems large, it is equivalent to the material contained within a 632-m diameter iron asteroid. Equivalently, as noted by Arnold, 1012 kg roughly corresponds to the annual production of iron on Earth. Once again, what is remarkable about the construction of such massive structures is that the knowhow and the resources to produce them already exist. All that humanity lacks at the present time is the inclination to start the project. The Price of Doing Nothing 131 End Games and Exotic Worlds It is not just the inner Solar System that will be disrupted if our Sun is allowed to become a red-giant. The outer Solar System will also feel the effects of the Sun’s growing luminosity. Although, as we said earlier, the Jovian planets won’t be affected much by the Sun’s increasing luminosity, their many attendant moons will be, since water ice is a major part of their internal makeup. As indicated by Equation (4.1), as the Sun’s luminosity increases, so the heliocentric distance at which water ice begins to rapidly sublimate moves deeper and deeper into the Solar System. Literally, the boundary of an expanding sublimation sphere will sweep through the outer Solar System as the Sun ages to become a red-giant. Inside of this sphere ice will begin to evaporate rapidly. Currently the ice evaporation boundary is situated some 1.5 to 2 AU from the Sun. It is upon reaching this boundary, for example, that we see tails and extended comas begin to appear around cometary nuclei—this coming about because cometary nuclei are predominantly composed of water ice. As the Sun’s luminosity increases, however, the ice evaporation boundary will move deeper into the Solar System. Eventually the Galilean moons of Jupiter will begin to lose their surface ices, the atmosphere of Saturn’s Titan will boil away, and the innermost Kuiper Belt objects, Pluto, and Charon, will begin to develop extensive water vapor exospheres. The bright infrared source IRC +1o216 is one well-studied example of what the future Solar System might look like. This particular proto-planetary nebula has been resolved into a series of high-density concentric shells caused by the thermal pulsing and episodic mass-loss of the central Mira variable star CW Leonis (Figure 4.6). The central star is truly a giant, with a radius estimated to be some 500 times larger than the size of the Sun (it would fill our Solar System out to the orbit of Jupiter), and a luminosity some 7,000 times greater. The CW Leonis system also supports a large surrounding cloud of water vapor. Studied in detail with the Submillimeter Wave Astronomy Satellite (SWAS), it is estimated that the water vapor cloud is composed of some four Earth masses of sublimated ice. The question, of course, is where did all this ice come from? The answer is thought to be from billions of cometlike bodies. Just as in our Solar System, it is believed that CW 132 Rejuvenating the Sun and Avoiding Other Global Catastrophes Figure 4.6. Multiple-shell structure in the extended envelope surrounding the carbon star CW Leonis (IRC +1o216). The system is some 150 pc distant, and the outermost ring has a diameter of about 0.1 pc. The rings are believed to relate to variations in the mass-loss rate of CW Leonis. (Image courtesy of Dr. Nicolas Mauron) Leonis has a surrounding swarm of large cometary bodies—the equivalent of our Kuiper Belt and Oort Cloud – and it is these objects that are in the process of evaporating en mass due to the high luminosity of the central star. During the Sun’s planetary nebula phase it is likely that Earth will be stripped of its rocky mantle to reveal its metal core—a compact nickel- and iron-rich remnant. This pared-down Earth will eventually find itself in a close orbit about the white dwarf Sun. What happens next partly depends upon how strong the magnetic field of the white dwarf Sun is. All white dwarfs are observed to have magnetic fields, but some show field strengths as high as tens of mega-Gauss.26 Under these latter conditions it is possible that an electric current loop can form between the central white dwarf and the stripped-down planetary-core. This is essentially a scaled-up version of the interaction between Jupiter and its moon Io in our Solar System. Looking at the consequences of a white dwarf-conducting planetary core current loop forming, Jianke Li and co-workers27 have suggested that the atmosphere of the white dwarf star will become heated in the regions close to its magnetic poles (Figure 4.7). This extra heating, it is then suggested, will The Price of Doing Nothing 133 Magnetic field line White Dwarf Planet core Atmospheric Electric current heating Orbital separation Figure 4.7. White dwarf planetary core system. The electric current is generated by the conducting planet moving through the white dwarf’s magnetic field lines (a consequence of Ampere’s law). As shown here, the orbit of the planetary core is perpendicular to the plane of the page. When a closed circuit has been formed, both the white dwarf’s atmosphere and the planet are heated. (Diagram based upon Figure 1 of Note 26.) result in observable effects. Indeed, Li and colleagues argue that the observed optical emission from the white dwarf star GD356 might be explained by the presence of a small planetary core companion. In this way, the white dwarf star GD356 might just be a model for Earth’s distant future if no asteroengineering of the Sun is performed. What about the planets in the outer Solar System? Although the atmospheres of Venus and Earth will be stripped by the Sun’s enhanced red-giant wind, it is likely that Jupiter and Saturn will survive mostly intact. Evidence for this possibility was recently discovered by Peter Maxted (University of Keele, in the UK) and co-workers when they studied the white dwarf star WD0137-349. Surprisingly, they found that the white dwarf had a close binary companion. At a distance comparable to that separating Earth and the Moon, the white dwarf is being orbited every two hours by a brown dwarf companion.28 The mass of the brown dwarf is estimated to be about 55 times greater than that of Jupiter, but the fact that it survived the red-giant and the planetary nebula phase of its white dwarf host is remarkable, and it suggests that giant planets (such as Jupiter in our Solar System) are able to withstand the ravages imposed during the end-phase evolution of their parent 134 Rejuvenating the Sun and Avoiding Other Global Catastrophes stars. As a consequence of losing orbital energy through gravitational wave generation, the brown dwarf in the WD0137–349 system will have a much smaller orbit. Indeed, in the deep future, about 1.5 billion years from now, once the orbital period of the brown dwarf drops to about one hour, then matter transfer to the white dwarf will commence, leading to the formation of a so-called cataclysmic variable.28 A Moving Imperative It was suggested in Chapter 1 that a number of ancient extraterrestrial civilizations may have already experienced the aging of their parent star to the red-giant phase. The number of such civilizations affected since our galaxy formed can be estimated according to the rate at which interstellar matter is being converted into stars per unit time. It is generally taken by astronomers that the current star formation rate SFR(t) within our galaxy amounts to something like 2 M of interstellar material being ‘converted’ into actual stars per year. However, since most stars are less massive than the Sun, this SFR translates into something like one actual star with a mass greater than or equal to the Sun being formed each and every year. In the following calculation it will be assumed that the star formation rate has been constant29 since the galaxy formed and, consequently for us, SFR(t) = constant. Now it is only the stars born after the initial formation of our galaxy that we are interested in, since these are the stars that will have enhanced heavy element abundances. (Recall from Chapter 2 that it is the supernova endphases of massive stars that have very short lifetimes and produce the heavy elements beyond hydrogen and helium that are vital for the formation of planets and living entities.) The gas clouds out of which the oldest stars within our galaxy formed were essentially composed of pure hydrogen and helium. The birthrate function BRF(M, t), which accounts for the total number of stars of mass M that have formed in a given time t, is written in terms of the SFR(t) and the so-called initial mass function IMF(M), such that BRF(M, t) = IMF(M) x SFR(t). The IMF is an expression that describes how the mass distribution of stars is divided. The IMF is actually a complicated function of stellar The Price of Doing Nothing 135 mass, but for stars with masses similar to that of the Sun it can be expressed as a power law with IMF(M) ∼ M−2 35. This indicates that, in general, there are numerically more low-mass stars than massive ones. Figure 4.8 illustrates the variation in the total number of stars formed per year within two specific mass ranges. The total number of stars formed, within the specified mass ranges, over a time interval t will be equal to the areas under the lines shown in the figure (technically this is equivalent to integrating the birthrate function over a given time interval and mass range). Accordingly, the total number of stars formed over the past 12 billion years in the mass range 0.5 to 1.3 M corresponding to those stars that might possibly support advanced life bearing planets, is N(0.5 ⇒ 1.3) ≈ 2.2 x 1010 stars. At this stage, however, what we would like to know is how many of these 22 billion stars have evolved off of the main-sequence to become red-giants. To estimate this number we first need to find the mass of a star that has a mainsequence lifetime equal to that of the age of the galaxy: ms(M) = t(now) = 12 x 109 years. The main-sequence lifetime of a star30 can be expressed purely in terms of its mass, and a star of mass M solar masses has a main-sequence lifetime ms ≈ 1010/M 3 years. In this way it turns out that, our galaxy formed the lowest mass star that N [stars/ yr] t(now) 0.5 ≤ M / M ≤ 1.3 0.94 ≤ M / M ≤ 1.3 TIME [yr] τms(1.3 M ) τms(0.94 M ) Figure 4.8. Schematic variation of the number of stars formed (within a given mass range) against time. The area under the solid line indicates the total number N of stars formed in the mass range from 0.5 to 1.3 M The solid gray shaded area corresponds to those stars that have evolved off the main-sequence to become red-giants. The cross-hatched area corresponds to those stars still on the main-sequence. 136 Rejuvenating the Sun and Avoiding Other Global Catastrophes could have evolved off the main-sequence to become a red-giant has a mass of 0.94 M Again, referring to Figure 4.8, the number of stars born in the mass range 0.94 to 1.3 M is schematically given by the area under the dashed line. A detailed calculation indicates that the number of stars formed over the past 12 billion years with masses between 0.94 and 1.3 M is N(0.94⇒ 1.3) ≈ 4.6 x 109. Remember, these are the stars that will have enhanced heavy element abundances and may harbor life-bearing planets. To finish our calculation we now need to determine how many of the N(0.94 ⇒ 1.3) ≈ 4.6 x 109 stars are still on the mainsequence. The main-sequence lifetime of a 1.3 M star is about 4.5 billion years, so clearly all of the stars that formed with this mass (and greater) shortly after the galaxy itself formed will no longer be main-sequence stars. Indeed, after a time of, say, 6 billion years these stars will have become white dwarfs. Any 1.3 M star formed within 4.5 billion years of the present, however, will still be on the main-sequence. Again, a detailed calculation reveals that the number of stars in the mass range 0.94 to 1.3 M that have formed during the past 12 billion years and are still in their mainsequence phase at the present time is NMS(0.94 ⇒ 1.3) ≈ 3.1 x 109 stars. Finally, therefore, the number of stars in the mass range 0.94 to 1.3 M that have become red-giants since the galaxy formed is NRG(0.94 ⇒ 1.3) = N(0.94 ⇒ 1.3) - NMS(0.94 ⇒ 1.3) = 1.5 x 109 stars. (This corresponds to the gray shaded area in Figure 4.8.) Not all of the 1.5 billion stars with masses between 0.94 and 1.3 M that have become red-giants since the galaxy formed will have had accompanying planets. Modern-day observations31 suggest, however, that at least 15 percent of Sun-like stars have planets with orbital radii of less than 5 AU (the orbital radius of Jupiter in our Solar System). Although the observations also indicate that the occurrence of planets is strongly correlated with the heavy element abundance of the parent star (indicating that the more recently formed stars have a higher probability of harboring planets), it would seem that of order 200 million stars with potential planetary systems will have become red-giants since the galaxy formed. It is not known, of course, whether any of these 200 million systems had planets situated within the habitability zone and whether intelligent life ever evolved. Indeed, we are back at the Drake equation [Equation (1.1)] problem discussed The Price of Doing Nothing 137 in Chapter 1. This being said, Professor Ben Zuckerman, whose original arguments we have essentially followed above,32 suggests that it is likely that somewhere between 1 and 1,000 civilizations will have faced the consequences of their parent star becoming a red-giant. On this basis he also suggests that the galaxy should be ‘’saturated with extraterrestrial creatures.” The existence of Fermi’s Paradox argues that, in spite of Zuckerman’s exuberance, not one of the 200 million stars that might have sustained an advanced civilization, but have now evolved into red-giants, has produced a race that has successfully colonized the galaxy (or else, as the paradox states, they should now be here in our Solar System). This observational situation suggests a number of possible scenarios: 1. Civilizations simply die when their parent star becomes a redgiant. 2. No civilization has ever survived long enough to worry about its parent star becoming a red-giant. 3. Interstellar space travel is not a viable means of survival and escape from a planetary system once its parent star becomes a red-giant. 4. The adoption of star-engineering and stellar rejuvenation processes have negated the red-giant evolution imperative for advanced civilizations to move away from their home worlds. Within the context of the ideas being discussed in this book, it is the fourth scenario that is of particular interest, which is the topic of the next chapter. Notes and References 1. Liquid water cannot exist upon the surface of Mars now because of the low surface pressure provided by its atmosphere. If liquid water were released upon the Martian surface it would rapidly freeze and then sublimate into a gas. Liquid water could have existed on the surface of Mars in the past since its atmosphere was more substantive then. It is possible –and highly likely – that subsurface liquid water exists on Mars to 138 Rejuvenating the Sun and Avoiding Other Global Catastrophes this very day. Indeed, Michael Malin and co-workers [Presentday impact cratering rate and contemporary gully activity on Mars, Science, 314, 1573–1577 (2006)] argue that images obtained with the Mars Global Surveyor satellite indicate that new gully deposits have formed within at least two craters situated in the Centauri Montes and Terra Sirenum regions of Mars. The deposits were certainly formed within the last seven years and are interpreted as being due to the flow of liquid water. 2. Equation (4.1) is derived according to the assumption that Earth is an approximate blackbody radiator. At a distance d from the Sun the energy received at the surface of a planet per second will be Ereceived = P (1 – A)L /(4 d2), where P = is the planet’s cross-section area, P = R2 P, and A is the atmospheric albedo. The amount of energy re-radiated by the planet back into space because it is a blackbody radiator of temperature TP will be given by the Stefan-Boltzmann law, such that Eradiated = 4 RP 2 TP 4 , where is the Stefan-Boltzmann constant and is the emissivity. The equilibrium temperature for the planet, as given by Equation (4.1), is determined under the condition that Eradiated = Ereceived. It should be noted at this stage that the temperature of the planet is not dependent upon how large it is. The additional term TGHE introduced into equation (4.1) accounts for warming due to the so-called greenhouse effect of an atmosphere. The amount of greenhouse warming will depend upon the composition (specifically, the CO2 content) and temperature of the atmosphere. The greenhouse warming for Earth at the present time amounts to TGHE ≈ 25 K. 3. The albedo (A) accounts for how much of the Sun’s energy is reflected back into space before it can heat the planet’s surface. The emissivity ( ) accounts for how efficiently the planet radiates its absorbed energy back into space. In general the albedo and emissivity will vary with temperature, atmospheric and planetary surface composition, and the wavelength of the incident and re-radiated radiation. For a perfect blackbody radiator, A = 0 and =1. 4. We note that L(t = 0) < L(t = 4.5 billion years) [see Table 3.2], and this suggests that solar heating alone would not have been sufficient to stop Earth’s initial oceans from freezing. Since it The Price of Doing Nothing 139 is (arguably) evident that the oceans didn’t freeze, this suggests that there was an additional heating term. It is generally argued that the extra heating was due to a higher greenhouse heating term TGHE in the distant past, when Earth had a richer CO2 atmosphere. For the young Earth, global warming was a good thing. For the current Earth it is a worrying phenomenon, since the Sun is about 45 percent more luminous now than when it first settled onto the main-sequence 4.5 billion years ago. 5. See, for example, the detailed model calculations presented by James Kasting and co-workers in Habitable zones around mainsequence stars. Icarus, 101, 108–128 (1993). A simplified timedependent Earth climate model is considered by Ken Caldeira and James Kasting in, The life span of the biosphere revisited. Nature, 360, 721–723 (1992). 6. The physicist Steven Toulmin once remarked that definitions are like belts. The shorter they are, the more elastic they need to be. Although the definition for the habitability zone is not short, it does warrant a few addendums. One case in point has been described by David Stevenson [Life-sustaining planets in interstellar space? Nature, 400, 32 (1999)]. Stevenson points out that planet formation is a highly dynamic process, and it is conceivable that Earth-mass planets are formed and then ejected from a bound orbit into interstellar space. At first thought this suggests that the planet is doomed and that any atmosphere and/or surface water will rapidly freeze out. The situation, however, is more complex and subtle. Stevenson argues that the slow release of internal heat energy, built up by the accretion process and the decay of radioactive elements, can sustain a liquid layer on an Earth-mass planet for perhaps several billion of years, even if it is situated in the cold depths of interstellar space. Perhaps – even on these exotic, permanently dark worlds – elementary life can evolve and may be even prosper for a short while. 7. B. W. Jones, P. N. Sleep, and J. E. Chambers. The stability of the orbits of terrestrial planets in the habitable zones of 254–262 (2001). The star CrB is slightly less massive than the Sun (M = 0.95 M ) and is estimated to be about 6 billion years old (some 1.5 billion years older than the Sun). The star 47 UMa is 140 Rejuvenating the Sun and Avoiding Other Global Catastrophes slightly more massive than the Sun (M = 1.03 M ) and nearly twice as old, with an estimated age of 7 billion years. 8. D. M. Williams, J. F. Kasting, and R. A. Wade. Habitable moons around extrasolar giant planets. Nature, 385, 234–235 (1997). R. C. Domingos and co-workers [Stable satellites around extrasolar giant planets. Monthly Notices of the Royal Astronomical Society, 373, 1,227–1,234 (2006)] derive analytic expressions for the semi-major axis and eccentricity of stable satellite orbits within exoplanetary systems. 9. Christopher Lovis et al., An extrasolar planetary system with three Neptune-mass planets. Nature, 441, 305–309 (2006). 10. The structure and properties of the four largest moons of Jupiter are described in A. Showman and R. Malhotra, The Galilean satellites, Science, 286, 77 (1999). A number of models describing the possible internal structure of Europa are presented in J. Anderson et al., Europa’s differentiated internal structure: inferences from two Galileo encounters, Science, 276, 1,236 (1997). The surface structure of Europa is described by F. Nimmo and co-workers in Europa’s icy shell: past and present state, and future exploration, Icarus, 177, 293 (2005). 11. Alon Retter et al., The planets capture model of V838 Monocerotis: conclusions for the penetration depth of the planet(s). Monthly Notices of the Royal Astronomical Society, 370, 1,537–1,580, 2006. 12. The key effect that has to be considered at this stage is that of greenhouse warming. As the Sun’s temperature increases so the evaporation rate of Earth’s oceans also increases, and a moist greenhouse effect will develop in which a dense water vapor-laden atmosphere overrides a near boiling ocean. The next phase relates to timescale; if the Sun reaches a luminosity of 40 percent brighter than it is now and the oceans have not fully evaporated, then a runaway greenhouse effect comes into play, trapping heat near to Earth’s surface and pushing the temperature to many hundreds of Kelvins. Earth’s surface may actually melt in some places under the runaway greenhouse scenario. 13. Extremophiles are microorganisms that can survive and thrive, under conditions that would be fatal to most other organisms. The thermophiles, and hyperthermophiles, for example, are The Price of Doing Nothing 141 found in environments where the temperature varies from 50 to 80oC and 80 to 110oC, respectively. These microorganisms thrive, for example, in the deep ocean floor environments surrounding hydrothermal vents, or ‘black smokers.’ Other microorganisms such as the psychropiles can tolerate extreme cold, while the halophiles thrive under high salinity conditions. Peter Ward and Donald Brownlee have attempted to describe the final stages of life on Earth in their interesting, but unnecessarily doom-laden book, The Life and Death of Planet Earth [Owl Books, New York (2002)]. 14. Technically Tdecay provides what is called the e-folding time, which is the characteristic time over which the orbital radius changes by a factor of e = 2.7183. The complete spiral-in destruction time for Mercury would probably correspond to a few e-folding times. 15. The envelope density is estimated from the red-giant models computed by William Rose and Richard Smith [Final evolution of a low-mass star II, Astrophysical Journal, 173, 385–391 (1972)]. We use the model corresponding to a star having a radius of 164 R and luminosity of 2500 L This model atmosphere corresponds to the Sun at the red-giant tip (point 4 in Figure 3.10). 16. A similar calculation to the one presented here for Mercury was made for Earth by Samuel Vila [Survival of Earth and the future evolution of the Sun, Earth, Moon and Planets, 31, 313–315 (1984)]. Vila finds that if the envelope of the redgiant Sun does extend to encompass Earth’s orbit, then the e-folding time for orbital decay is about 5,000 years. Again, this is a very short timescale, and destruction of Earth is assured. Goldstein [The fate of Earth in the red-giant envelope of the Sun, Astronomy and Astrophysics, 178, 283–285 (1987)] has presented a more detailed calculation for Earth’s orbital decay time – including gas drag forces – and finds an e-folding time of just a few hundred years—a timescale even more rapid than that found by Vila. It appears that a planet is rapidly destroyed once it begins to encounter the gas envelope of its red-giant parent star. 17. The orbital angular momentum h of a mass m moving with velocity V in a circular orbit of radius a is h = amV. If this is 142 Rejuvenating the Sun and Avoiding Other Global Catastrophes combined with Kepler’s third law, then it turns out that, a M = (h/2 m) 2 = constant, where M is the mass of the object about which the smaller mass m is moving around. The key point about angular momentum is that it is a conserved quantity, meaning that hfinal = hinitial. In this manner the product a(t) M(t) = a(0) M(0) = constant, where t is the time, must hold true. 18. Peter Schroder, Robert Smith, and Kevin Apps [Solar evolution and the distant future of the Earth, Astronomy and Geophysics, 42, 6.26–6.29 (2001)] argue that recent observations indicate modest mass-loss rates during the red-giant phase of solar mass stars. Consequently their solar model expands to destroy Venus. The solar evolutionary calculations published by I-J. Sackmann and co-workers [Our Sun III: present and future, The Astrophysical Journal, 418, 457–468 (1993)], on the other hand, assume a relatively high mass-loss rate during the Sun’s red-giant branch phase and, consequently, Venus survives, as shown in Figure 4.3. 19. Alain Le´ger et al., A new family of planets? Ocean-planets. Icarus, 169, 499–504 (2004). Interestingly, Leger and collaborators point out that the low density of ocean planets dictates that they should be relatively large and, hence, good potential targets for spectroscopic study. This, in turn, suggests that, should they be found, they are attractive candidates for surveys looking for bio-signatures—such as ozone, or O3. Indeed, the Terrestrial Planet Finder (TPF) mission, currently under development by NASA and due for launch circa 2015, is being designed to specifically look for life-related signatures in nearby extrasolar planetary systems. 20. Don Korycansky, G. Laughlin and F. Adams, Astronomical engineering: a strategy for modifying planetary orbits. Astrophysics and Space Science, 275, 349–366 (2001). See also D. Korycansky, Astroengineering, or how to save Earth in only one billion years. Reviews of the Mexican Astronomical Association, 22, 117–120 (2004). 21. With reference to Equation (4.1), the Korycansky scenario requires that the L(t)/d2 term remains constant with time. The Sun’s luminosity on the main-sequence varies approximately as: L(t) = L /(1 – 0.38 t/ ), where = 4.55x 109 years, and where t is expressed in years from the present time. (This formula The Price of Doing Nothing 143 is taken from the Caldeira and Kasting paper introduced in Note 5.). With L(t) specified the required increase in the size of Earth’s orbital radius d(t) can be determined. 22. The yearly weather cycle (winter, spring, summer, and autumn) is driven primarily by the tilt of Earth’s spin axis to the ecliptic (that is, Earth’s orbital plane). This angle, which amounts to some 23.5o, is called the obliquity of the ecliptic. Any change in Earth’s obliquity will result in distinct climate changes, and this is where the Moon comes in as a stabilizing agent. A numerical simulation carried out by J. Laskar and coworkers [Stabilization of the Earth’s obliquity by the Moon. Nature, 361, 615–617 (1993)], for example, indicates that the Earth’s obliquity would vary chaotically and dramatically over many degrees if the Moon did not exist. On the other hand, Darren Williams and co-workers [Low-latitude glaciation and rapid changes in the Earth’s obliquity explained by obliquityoblateness feedback. Nature, 396, 453–455 (1998)] argue that the climate itself can modulate Earth’s obliquity. They reason, for example, that the buildup of massive ice sheets during past glacial cycles has actually reduced Earth’s obliquity. 23. Colin McInness, Astronomical engineering revisited: planetary orbit modification using solar radiation pressure. Astrophysics and Space Science, 282, 765–772 (2002). 24. Leonid Shkadov, Possibility of controlling Solar System motion in the Galaxy. 38th IAF, International Astronautical Congress, Brighton (1987). Paper 1AA-87–613. 25. Luc, F. A. Arnold, Transit light-curve signatures of artificial objects. Astrophysical Journal, 627, 534–539 (2005). On the basis that an artificial transit sail is constructed in the mainbelt asteroid region of our Solar System, the sail would then have to be maneuvered closer in toward the Sun so that transits would both repeat frequently and be visible to a large potential audience. 26. Earth’s magnetic field strength is about 0.5 Gauss, while that of the Sun’s is 1 Gauss. Jupiter supports the strongest magnetic field in the entire Solar System, with field strength of some 8 Gauss. Indeed, decameter radio emission bursts are regularly recorded from Jupiter, and these bursts are synchronized with the orbital period of its moon, Io. It is the motion of Io through 144 Rejuvenating the Sun and Avoiding Other Global Catastrophes Jupiter’s magnetic field that produces the so-called synchrotron radio emissions. 27. Jianke Li, L. Ferrario, and D. Wickramasinghe. Planets around white dwarfs, The Astrophysical Journal, 503, L151–L154 (1998). 28. P. F. L. Maxted et al., Survival of a brown dwarf after engulfment by a red-giant star. Nature, 442, 543–545 (2006). White dwarfs rarely have brown dwarf companions – such pairings occurring in less than 0.5 percent of the systems containing white dwarfs. The WD–0137-349 system will eventually form into a short-period cataclysmic variable, with matter being transferred from the brown dwarf to the white dwarf. A full blown Type I supernova (see Figure 2.13 and Note 13, Chapter 2) will not occur since there isn’t enough mass in the brown dwarf to push the white dwarf beyond the Chandrasekhar limiting mass. Hydrogen-rich matter will accumulate on the white dwarf’s surface, however, and this will periodically undergo runaway thermonuclear reactions to produce a nova-like outburst. 29. The star formation rate in our galaxy has not been constant during the past 12 billion years. It is usually assumed that the SFR decreases exponentially with time, but for our purposes a constant rate will produce the order of magnitude result being sought. 30. Here we have combined the main-sequence lifetime Equation (2.1) with the mass-luminosity Equation (3.12). We have assumed, however, that for solar mass stars the luminosity varies as the mass to the fourth power. The important point about the main-sequence lifetime is that it is shorter for more massive stars. Although the Sun has a main-sequence lifetime of about 10 billion years, a 10 solar mass star has a main-sequence lifetime of about 10 million years. So, although massive stars do have more hydrogen available for consumption, they use it up (in the sense of radiating energy into space) more rapidly. 31. A good technical review is provided by G. Marcy et al., Observed properties of exoplanets: masses, orbits and metallicities. Progress of Theoretical Physics Supplement, No. 158, 1–19 (2005). The percentage of Sun-like stars harboring planets The Price of Doing Nothing 145 within 5 to 6 AU of their parent stars may even be as high as 25 percent. This higher percentage results in there being something like 400 million stars with masses between 0.93 and 1.5 M harboring planets and having left the main-sequence since the Milky Way galaxy formed. A more general review of the properties of exoplanets is given in the April 2007 issue of Astronomy Now Magazine. 32. B. Zuckerman, Stellar evolution: motivation for mass interstellar migration. Quarterly Journal of the Royal Astronomical Society, 26, 56–59 (1985)