STARS, THE PERIODIC TABLE, AND ε
I believe a leaf of grass is no less than the journey-work of the stars.
Walt Whitman
STARS AS ‘NUCLEAR FUSION REACTORS’
How old is the Earth? It is now pinned down, by measurements of radioactive atoms, to 4.55 billion years. Compelling arguments for its great antiquity were, however, already being advanced in the nineteenth century. Geologists, gauging the rate at which erosion and sedimentation shaped our terrain, assessed the Earth’s age as at least a billion years: Darwinians concurred with this, from their estimates of how many generations of gradually evolving species must have lived before us. On the other hand, the great physicist Lord Kelvin calculated that all the Sun’s internal heat would leak out, and it would deflate, in only one per cent of that time. He gloomily averred that: ‘Inhabitants of the Earth cannot continue to enjoy the light and heat essential to their life, for many millions of years longer, unless sources now unknown to us are prepared in the great storehouse of creation.’ Twentieth-century science has taught us that such a source indeed exists, stored in the nuclei of atoms. H-bombs are frightening testimony to the energy latent in the nucleus.
The Sun is fuelled by conversion of hydrogen (the simplest atom, whose nucleus consists of one proton) into helium (the second-simplest nucleus, consisting of two protons and two neutrons). Attempts to harness fusion as a power source (‘controlled fusion’) have so far been stymied by the difficulty of achieving the requisite temperatures of many millions of degrees. It is even more of a problem to confine this ultra-hot gas physically in a laboratory – it would obviously melt any solid container – and it has instead to be trapped by magnetic forces. But the Sun is so massive that gravity holds down the overlying cooler layers, and thereby ‘keeps the lid on’ the high-pressure core. The Sun has adjusted its structure so that nuclear power is generated in the core, and diffuses outward, at just the rate needed to balance the heat lost from the surface – heat that is the basis for life on Earth.
This fuel has kept the Sun shining for nearly five billion years. But when it starts to run out, in another 5 billion years or so, the Sun’s core will contract, and the outer layers expand. For a hundred million years – a brief interval relative to its overall lifetime – the Sun will brighten up and expand into the kind of star known as a ‘red giant’, engulfing the inner planets and vaporizing any life that remains on Earth. Some of its outer layers will be blown off, but the core will then settle down as a white dwarf, shining with a dull blue glow, no brighter than a full moon today, on the parched remains of the Solar System.
Astrophysicists have computed what the inside of our Sun should be like, and have achieved a gratifying fit with its observed radius, brightness, temperature and so forth. They can tell us confidently what conditions prevail in its deep interior; they can also calculate how it will evolve over the next few billion years. Obviously these calculations can’t be checked directly. We can, however, observe other stars like the Sun that are at different stages in their evolution. Having a single ‘snapshot’ of each star’s life is not a fatal handicap if we have a large sample, born at different times, available for study. In the same way, a newly landed Martian wouldn’t take long to infer the life-cycle of humans (or of trees), by observing large numbers at different stages. Even among the nearby stars, we can discern some that are still youngsters, no more than a million years old, and others in a near-terminal state, which may already have swallowed up any retinue of planets that they once possessed.
Such inferences are based on the assumption that atoms and their nuclei are the same everywhere. Newton’s great insight was to link the roles of gravity here on Earth and in celestial orbits. Yet even he only addressed the motions within our Solar System. It took much longer to realize that gravity applied in other stars, and even in other galaxies. In ancient times, the celestial sphere was believed to be made of a special substance, ‘quintessence’, purer than the earth, air, fire and water of our terrestrial realm. Until the mid-nineteenth century, there were no clues as to what the stars were made of. The use of prisms to disperse light into a rainbow of different colours revealed that light from the Sun, and from other stars, contained the hues characteristic of well-known atoms on Earth. The ingredients of starstuff were no different from the atoms here on the ‘sub-lunary sphere’.
Astrophysicists can compute, just as easily as the Sun’s evolution, the life-cycle of a star that is (say) half, twice, or ten times the mass of the Sun. Smaller stars burn their fuel more slowly. In contrast, stars ten times as heavy as the Sun – the four blue Trapezium stars in the constellation of Orion, for instance – shine thousands of times more brightly, and consume their fuel more quickly. Their lifetimes are much shorter than the Sun’s, and they expire in a more violent way, by exploding as supernovae. They become, for a few weeks, as bright as several billion suns. Their outer layers, blown off at 20,000 kilometres per second, form a blast wave that ploughs into the surrounding interstellar gas.
On 24 February 1987 a Canadian astronomer, Ian Shelton, was carrying out routine observations with his Chilean assistant at the Las Campanas Observatory in northern Chile. They noticed an unfamiliar glow in the Southern sky, bright enough to be seen with the unaided eye, that had not been visible on the previous night. This proved to be much the nearest supernova to be observed in modern times. During the few weeks of its peak brilliance, and during its gradual fading in the subsequent years, it has been monitored by all the techniques of modem astronomy, allowing theories of these immense explosions to be tested. It is the only supernova whose precursor star was already known: old photographic plates show, at the site of the supernova, a blue star of about twenty solar masses.
Supernovae represent cataclysmic events in the life of the stars, involving some ‘extreme’ physical processes; so supernovae naturally fascinate astronomers. But only one person in ten thousand is an astronomer. What possible relevance could these stellar explosions thousands of light-years away have to all the others, whose business lies purely on or near the Earth’s surface? The surprising answer is that they are fundamental to everyone’s environment. Without them, we would never have existed. Supernovae have created the ‘mix’ of atoms that the Earth is made of and that are the building blocks for the intricate chemistry of life. Ever since Darwin, we’ve been aware of the evolution and selection that preceded our emergence, and of our links with the rest of the biosphere. Astronomers now trace our Earth’s origins back to stars that died before the Solar System formed. These ancient stars made the atoms of which we and our planet are composed.
ALCHEMY IN THE STARS
Atoms exist in nature in ninety-two varieties, as represented in the ‘periodic table’. The place of each atom in the table depends on the number of protons in its nucleus. The table starts with hydrogen at number 1, and goes up to uranium at 92. The nuclei of atoms contain not only protons but particles of another kind, called neutrons. A neutron weighs slightly more than a proton, but has no electric charge. Atoms of a particular element can exist in several variants, called isotopes, with different numbers of neutrons. For example, carbon is number 6 in the periodic table: its nucleus contains six protons. The most common form (known as 12C) contains six neutrons as well; but there are also isotopes with seven and eight neutrons (known as 13C and 14C respectively). Uranium is the heaviest naturally occurring element; still heavier nuclei, with charges up to 114, have been made in laboratories. These super-heavy elements are unstable to fission. Some, like plutonium (number 94 in the table), have a lifetime of thousands of years; those numbered beyond 100 can be manufactured in experiments that collide nuclei together, but decay after a transient existence.
When a big star’s central hydrogen has all been converted into helium (number 2), the core is pulled inwards, squeezing it hotter until the helium can itself react – helium nuclei have twice the electric charge of hydrogen, so they need to collide faster in order to overcome the fiercer electric repulsion, and this demands a higher temperature. When the helium is itself used up, the star contracts and heats up still more. Stars like the Sun never achieve hot-enough cores to permit these transmutations to go very far, but the centres of heavier stars, where gravity is more powerful, reach a billion degrees. They release further energy via the build-up of carbon (six protons), and then by a chain of transmutations into progressively heavier nuclei: oxygen, neon, sodium, silicon, etc. The amount of energy released when a particular nucleus forms depends on a competition between the nuclear force that ‘glues’ its constituent protons and neutrons together, and the disruptive effects of electric forces between the protons. An iron nucleus (twenty-six protons) is more tightly bound than any other; energy must be added (rather than being released) to build up still heavier nuclei. A star therefore faces an energy crisis when its core has been transmuted into iron.
The consequences are dramatic. Once the iron core gets above a threshold size (about 1.4 solar masses), gravity gains the upper hand and the core implodes down to the size of a neutron star. This releases enough energy to blow off the overlying material in a colossal explosion – creating a supernova. Moreover, this material has, by then, an ‘onion skin’ structure: hydrogen and helium are still burning in the outer regions, but the hotter inner layers have been processed further up the periodic table. The debris thrown back into space contains this mix of elements. Oxygen is the most common, followed by carbon, nitrogen, silicon and iron. The calculated proportions, when we take account of all types of star and the various evolutionary paths they take, agree with those observed on Earth.
Iron is only the twenty-sixth element in the periodic table, and at first sight the heavier atoms might seem a problem because it takes an input of energy to synthesize them. But intense heat in the collapse, and the blast wave that blows off the outer layers, together produce small traces of the elements in the rest of the periodic table, right up to uranium at number 92.
THE GALACTIC ECOSYSTEM
The first stars formed about ten billion years ago from primordial material that contained only the simplest atoms – no carbon, no oxygen, and no iron. Chemistry would then have been a very dull subject. There could certainly have been no planets around these first stars. Before our Sun even formed, several generations of heavy stars could have been through their entire life-cycles, transmuting pristine hydrogen into the basic building blocks of life and flinging them back into space via strong winds or explosions. Some of these atoms found themselves in an interstellar cloud resembling the Orion Nebula, where, about 4.5 billion years ago, a new star condensed, surrounded by a dusty disc of gas, to become our Solar System. Why are carbon and oxygen so common here on Earth, but gold and uranium so rare? The answer involves stars that exploded before our Sun formed. The Earth, and we ourselves, are the ashes from those ancient stars. Our galaxy is an ecosystem, recycling atoms again and again through generations of stars.
The carbon, oxygen and iron atoms in the Solar System are fossils from the dusty cloud from which it formed about 4.5 billion years ago: they were made by heavy stars that had already expelled processed debris by that time. These ‘pollutants’ constituted only two per cent of the mass: hydrogen and helium were still overwhelmingly the dominant atoms. Heavy atoms are, however, overrepresented on Earth, because hydrogen and helium are volatile gases that escaped from all the inner planets. In contrast, the giant planet Jupiter is, like the Sun, mainly hydrogen and helium. It was formed from the cooler outer part of the disc that surrounded the newly formed Sun, and its own gravity was enough to retain these lightweight atoms.
Older stars than the Sun would have formed before our galaxy had undergone so much ‘pollution’; their surfaces should therefore be deficient in heavy elements compared with the Sun. Starlight has a complicated spectrum, in which each kind of atom imprints a distinctive set of colours. (Streetlights have, for instance, familiarized us with the yellow light of sodium, and the characteristic blue of mercury vapour.) All the heavier atoms, indeed, tend to be less abundant in the oldest stars, corroborating this general scheme of galactic history. Helium, in contrast, is very abundant even in the oldest stars, and the reason, discussed in the next chapter, leads us back to the first few minutes after the Big Bang.
NUCLEAR EFFICIENCY: ε = 0.007
Accounting for the proportions of the different atoms – and realizing that the Creator didn’t need to turn ninety-two different knobs – is a triumph of astrophysics. Some details are still uncertain, but the essence depends on just one number: the strength of the force that binds together the particles (protons and neutrons) that make up an atomic nucleus.
Einstein’s famous equation E = mc2 tells us that mass (m) is related to energy (E) via the speed of light (c). The speed of light thus has fundamental significance. It fixes the ‘conversion factor’: it tells us how much each kilogram of matter is ‘worth’ in terms of energy. The only way that mass can be converted 100 per cent into energy is if it can be brought together with an equal mass of antimatter – something that (fortunately for our survival) doesn’t exist in bulk anywhere in our galaxy. Just one kilogram of antimatter would yield as much energy as a large electrical power station generates in ten years. But ordinary fuels such as gasoline, or even explosives such as TNT, release only about a billionth of the material’s ‘rest mass energy’. Such materials involve chemical reactions, which leave the nuclei of atoms unchanged and just reshuffle the orbits of their electrons and the linkages between the atoms. But the power of nuclear fusion is awesome because it is millions of times more efficient than any chemical explosion. The nucleus of a helium atom weighs 99.3 per cent as much as the two protons and two neutrons that go to make it. The remaining 0.7 per cent is released mainly as heat. So the fuel that powers the Sun – the hydrogen gas in its core – converts 0.007 of its mass into energy when it fuses into helium. It is essentially this number, ε, that determines how long stars can live. Further transmutations of helium all the way up to iron release only a further 0.001. The later stages in a star’s life are therefore relatively brief. (They are even briefer because, in the hottest stellar cores, extra energy drains away invisibly in neutrinos.)
The amount of energy released when simple atoms undergo nuclear fusion depends on the strength of the force that ‘glues’ together the ingredients in an atomic nucleus. This force is different from the two forces I have discussed so far, namely gravity and electricity, because it acts only at very short range, and is only effective on the scale of an atomic nucleus. We don’t directly experience it, in contrast to the way that we can ‘feel’ electrical and gravitational forces. Within an atomic nucleus, however, this force grips the protons and neutrons together strongly enough to combat the electrical repulsion that would otherwise make the (positively charged) protons fly apart. Physicists call this force the ‘strong interaction’.
This ‘strong’ force, the dominant force in the microworld, holds the protons in helium and heavier nuclei together so firmly that fusion is a powerful enough energy source to provide the prolonged warmth from the Sun that was a prerequisite for our emergence. Without nuclear energy, the sun would deflate within about ten million years, as Kelvin realized a century ago. Because the force only acts at short range, it becomes less effective in the larger and heavier nuclei: this is why the nuclei heavier than iron become less tightly bound rather than more so.
THE TUNING OF ε
Nuclear forces are crucial, but how much does their exact strength matter? What would change if ε were, for instance, 0.006 or 0.008 rather than 0.007? At first sight, one might suspect that it wouldn’t make much difference. If ε were smaller, hydrogen would be a less efficient fuel and the Sun and stars wouldn’t live so long, but this in itself would not be crucial – after all, we are here already, and the Sun is still less than halfway through its life. But there turn out to be delicate effects, sensitive to this number, in the synthesis process that transforms hydrogen into the rest of the periodic table.
The crucial first link in the chain – the build-up of helium from hydrogen – depends rather sensitively on the strength of the nuclear ‘strong interaction’ force. A helium nucleus contains two protons, but it also contains two neutrons. Rather than the four particles being assembled in one go, a helium nucleus is built up in stages, via deuterium (heavy hydrogen), which comprises a proton plus a neutron. If the nuclear ‘glue’ were weaker, so that ε were 0.006 rather than 0.007, a proton could not be bonded to a neutron and deuterium would not be stable. Then the path to helium formation would be closed off. We would have a simple universe composed of hydrogen, whose atom consists of one proton orbited by a single electron, and no chemistry. Stars could still form in such a universe (if everything else were kept unchanged) but they would have no nuclear fuel. They would deflate and cool, ending up as dead remnants. There would be no explosions to spray the debris back into space so that new stars could form from it, and no elements would exist that could ever form rocky planets.
At first sight, one might have guessed from this reasoning that an even stronger nuclear force would have been advantageous for life, by making nuclear fusion more efficient. But we couldn’t have existed if ε had been more than 0.008, because no hydrogen would have survived from the Big Bang. In our actual universe, two protons repel each other so strongly that the nuclear ‘strong interaction’ force can’t bind them together without the aid of one or two neutrons (which add to the nuclear ‘glue’, but, being uncharged, exert no extra electrical repulsion). If ε were to have been 0.008, then two protons would have been able to bind directly together. This would have happened readily in the early universe, so that no hydrogen would remain to provide the fuel in ordinary stars, and water could never have existed.
So any universe with complex chemistry requires ε to be in the range 0.006–0.008. Some specific details are still more sensitive. The English theorist Fred Hoyle stumbled on the most famous instance of ‘fine tuning’ when he was calculating exactly how carbon and oxygen were synthesized in stars. Carbon (with six protons and six neutrons in its nucleus) is made by combining three helium nuclei. There is negligible chance of all three coming together simultaneously, and so the process happens via an intermediate stage where two helium nuclei combine into beryllium (four protons and four neutrons) before combining with another helium nucleus to form carbon. Hoyle confronted the problem that this beryllium nucleus is unstable: it would decay so quickly that there seemed little chance of a third helium nucleus coming along and sticking to it before it decayed. So how could carbon ever arise? It turned out that a special feature of the carbon nucleus, namely the presence of a ‘resonance’ with a very particular energy, enhances the chance that beryllium will grab another helium nucleus in the brief interval before it decays. Hoyle actually predicted that this resonance would exist; he urged his experimental colleagues to measure it, and was vindicated. This seeming ‘accident’ of nuclear physics allows carbon to be built up, but no similar effect enhances the next stage in the process, whereby carbon captures another helium nucleus and turns into oxygen. The crucial ‘resonance’ is very sensitive to the nuclear force. Even a shift by four per cent would severely deplete the amount of carbon that could be made. Hoyle therefore argued that our existence would have been jeopardized by even a few percentage points’ change in ε.1
Irrespective of how the elements were made, a change in ε would affect the length of the periodic table. A weaker nuclear force would shift the most tightly bound nucleus (which is now iron, number 26) lower down the periodic table and reduce below ninety-two the number of stable atoms. This would lead to an impoverished chemistry. Conversely, a larger ε could enhance the stability of heavy atoms.
At first sight, a longer ‘menu’ of different abundant atoms would seem to open the way to a more interesting and varied chemistry. But this isn’t altogether obvious – for example, the English language would not be enriched in any important sense if the alphabet had more letters in it. Likewise, complex molecules can exist in endless variety even though there are relatively few common elements. Chemistry would be duller (and complex molecules of the kind essential for life would not exist) if there were no oxygen and iron (numbers 8 and 26 respectively), and especially if carbon (number 6) were not abundant; but little would be added by enhancing the number of abundant elements, or by having a few extra stable elements beyond our natural ninety-two.
The actual mix of elements would depend on ε, but what is remarkable is that no carbon-based biosphere could exist if this number had been 0.006 or 0.008 rather than 0.007.