by Livio, Mario
Out of Hoyle’s numerous accomplishments, I want to concentrate here on only a few of his contributions to one particular topic: nuclear astrophysics. Hoyle’s work in this area has become one of the main pillars on which our modern understanding of stars and their evolution rests. Along the way, he solved the puzzle of how the atoms of carbon, the anchor of complexity and life as we know it, formed in the universe. To fully appreciate the significance of Hoyle’s achievement, however, we first need to understand the background against which he produced his masterwork.
Prologue to the History of Matter
On one of the walls of almost every science classroom in the United States, you can find a chart of the periodic table of the elements (figure 19). Just as our language consists of words constructed from the letters of the alphabet, all ordinary matter in the cosmos is composed of these elements. Elements are those substances that cannot be further broken down or modified by simple chemical means. Dmitry Mendeleyev, a Russian chemist, is generally credited with having noticed (in the mid–nineteenth century) the periodic regularities that are the basis of the periodic table, and with having the foresight to predict the characteristics of elements that had yet to be discovered to complete the table. In many ways, the periodic table is a symbolic representation of the progress achieved since Empedocles’ and Plato’s famous fire, air, water, and earth as the basic constituents of matter. As an amazing aside, the smallest reproduction of the periodic table was engraved in 2011 onto a human hair belonging to chemist Martyn Poliakoff of the University of Nottingham in the United Kingdom. The engraving was done at the university’s nanotechnology center. (The hair was then returned to Poliakoff as a birthday gift.)
Figure 19
The periodic table currently consists of 118 elements (the latest, ununoctium, was identified in 2002), of which 94 occur naturally on Earth. If you think about it for a moment, this is a fairly large number of primary building blocks, and consequently, it was only a matter of time before someone would ask, Where did all of these chemical elements come from? Or: Could these rather complex entities have simpler origins?
Someone actually did pose these questions even before the publication of the periodic table. In two papers published in 1815 and 1816, the English chemist William Prout hypothesized that the atoms of all the elements were in fact condensations of different numbers of hydrogen atoms. Astrophysicist Arthur Eddington combined the general idea of Prout’s hypothesis with some experimental results on nuclei by physicist Francis Aston to formulate his own conjecture. Eddington proposed in 1920 that four hydrogen atoms could somehow combine to form a helium atom. The small difference between the total mass of the four hydrogen atoms and the mass of one helium atom was supposed to be released in the form of energy, through Einstein’s celebrated equivalence between mass and energy, E = mc2 (“E” denotes energy, “m” is mass, and “c” is the speed of light). Eddington estimated that in this way the Sun could shine for billions of years by converting only a few percent of its mass from hydrogen into helium. Less widely known is the fact that the French physicist Jean-Baptiste Perrin expressed very similar ideas around the same time. A few years later, Eddington further speculated that stars such as the Sun could provide natural “laboratories” in which nuclear reactions could somehow transform one element into another. When some physicists at the Cavendish Laboratory objected that the Sun’s internal temperature was insufficient to make two protons overcome their mutual electrostatic repulsion, Eddington is famously said to have advised them to “go and find a hotter place.” The hypothesis of Eddington and Perrin marked the birth of the idea of stellar nucleosynthesis in astrophysics: the notion that at least some elements could be synthesized in the hot interiors of stars. As you might have guessed from the above, Eddington was one of the strongest champions of Einstein’s theory of relativity (especially general relativity). On one occasion, physicist Ludwik Silberstein approached Eddington and told him that people believed that only three scientists in the entire world understood general relativity, Eddington being one of them. When Eddington didn’t answer for a while, Silberstein encouraged him, “Don’t be so modest,” to which Eddington replied, “On the contrary. I’m just wondering who the third might be.” Figure 20 shows Eddington with Einstein at Cambridge.
Figure 20
To continue the story of the formation of the elements, we need to remind ourselves of some of the very basic properties of atoms. Here is an extraordinarily brief refresher. All ordinary matter is composed of atoms, and all atoms have at their centers tiny nuclei (the atomic radius is more than 10,000 times the nuclear radius), around which electrons move in orbital clouds. The constituents of the nucleus are protons and neutrons, which are very similar in mass (a neutron is slightly heavier than a proton), each of them being about 1,840 times more massive than an electron. While neutrons bound in stable nuclei are stable, a free neutron is unstable—it decays with a mean lifetime of about fifteen minutes into a proton, an electron, and a virtually invisible, very light, electrically neutral particle called an antineutrino. Neutrons in unstable nuclei can decay in the same fashion.
The simplest and lightest atom that exists is the hydrogen atom. It consists of a nucleus that contains only one proton. A single electron revolves around this proton in orbits the probability for which can be calculated using quantum mechanics. Hydrogen is also the most abundant element in the universe, constituting about 74 percent of all the ordinary (known as baryonic) matter. Baryonic matter is the stuff that makes up stars, planets, and human beings. Moving from left to right along rows in the periodic table (figure 19), in each step, the number of protons in the nucleus increases by one, as does the number of orbiting electrons. Since the number of protons is equal to the number of electrons (and they carry opposite electric charges that are equal in magnitude), atoms are electrically neutral in their unperturbed state.
The element following hydrogen in the periodic table is helium, which has two protons in its nucleus. In addition, the helium nucleus also contains two neutrons (which carry no net electric charge). Helium is the second most abundant element, making up about 24 percent of the cosmic ordinary matter. Atoms of the same chemical element have the same number of protons, and this number is called the atomic number of that element. Hydrogen has the atomic number 1, helium is 2, iron is 26, uranium is 92. The total number of protons and neutrons in the nucleus is called the atomic mass. Hydrogen has the atomic mass of 1; helium, 4; carbon (which has six protons and six neutrons), 12. Nuclei of the same chemical element can have different numbers of neutrons, and those are called isotopes of that element. For instance, neon (which has ten protons), can have isotopes with ten, eleven, or twelve neutrons in the nucleus. The common notation for these different isotopes is 20Ne, 21Ne, and 22Ne. Similarly, hydrogen (one proton, or 1H) also has in nature an isotope usually called deuterium (one proton and one neutron in the nucleus, or 2H), and an isotope called tritium (one proton and two neutrons, or 3H).
Returning now to the central problem of the synthesis of the different elements, the physicists of the first half of the twentieth century were faced with a series of questions related to the periodic table. First and foremost: How were all of these elements formed? But also: Why are some elements, such as gold and uranium, extremely rare (hence, their high price!), while others, such as iron or oxygen, are much more common? (Oxygen is about a hundred million times more common than gold.) Or: Why are stars composed mostly of hydrogen and helium?
Since their inception, ideas about the process of the formation of the elements have been linked intimately to those on the enormous energy sources of stars. Recall that Helmholtz and Kelvin proposed that the Sun’s power comes from slow contraction and the associated release of gravitational energy. However, as Kelvin had clearly demonstrated, this reservoir could provide for the Sun’s radiation for only a limited time: no more than a few tens of millions of years. This limit was disturbingly at odds with geological and astrophysical evidence
that was pointing with increasing accuracy to ages of billions of years for both the Earth and the Sun. Eddington was fully aware of this glaring discrepancy. In his address to the British Association for the Advancement of Science meeting in Cardiff, Wales, on August 24, 1920, he made the following prescient statement:
Only the inertia of tradition keeps the contraction hypothesis alive—or rather, not alive, but an unburied corpse. But if we decide to inter the corpse, let us frankly recognize the position in which we are left. A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the subatomic energy which, it is known, exists abundantly in all matter [emphasis added].
Despite his enthusiasm for the idea that stars could derive their power from four hydrogen nuclei fusing together to assemble a helium nucleus, Eddington had no specific mechanism for this process to actually take place. In particular, the problem of the mutual electrostatic repulsion, mentioned above, had to be solved. Here is the obstacle: Two protons (the nuclei of hydrogen atoms) repel each other electrostatically because both have positive electric charges. This Coulomb force (named after the French physicist Charles-Augustin de Coulomb) has a long range, and it is therefore the dominant force between protons at distances larger than the size of the atomic nucleus. Within the nucleus, however, the strong, attractive nuclear force takes over, and it can overcome the electric repulsion. Consequently, in order for protons in the cores of stars to fuse together as envisioned by Eddington, they need to have sufficiently high kinetic energies in their random motions to overcome the “Coulomb barrier” and allow them to interact via the attractive nuclear force. The apparent snag in Eddington’s hypothesis was that the temperature calculated for the center of the Sun was not high enough to impart protons with the necessary energy. In classical physics, this would have been a death sentence for this scenario; particles with insufficient energy to overcome such a barrier just cannot make it. Fortunately, quantum mechanics—the theory that describes the behavior of subatomic particles and light—came to the rescue. In quantum mechanics, particles can behave like waves, and all processes are inherently probabilistic. Waves are not precisely localized like particles but are spread out. In the same way that some parts of an ocean wave crashing against a seawall can splash to the other side, there is a certain (albeit small) probability that even protons with insufficient energy to overcome their Coulomb barrier would still interact. Using this quantum mechanical effect of “tunneling” through barriers, physicist George Gamow and, independently, the two teams of Robert Atkinson and Fritz Houtermans, and Edward Condon and Ronald Gurney, demonstrated in the late 1920s that under the conditions prevailing in stellar interiors, protons could indeed fuse.
Physicists Carl Friedrich von Weizsäcker in Germany, and Hans Bethe and Charles Critchfield in the United States, were the first to elaborate the precise nuclear reactions network through which four hydrogen nuclei coalesce to form a helium nucleus. In a remarkable paper published in 1939, Bethe discussed two possible energy-producing paths in which hydrogen could convert into helium. In one, known as the proton-proton (p-p) chain, two protons first combine to form deuterium—the isotope of hydrogen with one proton and one neutron in its nucleus—followed by the capture of an additional proton that transforms the deuterium into an isotope of helium. The second mechanism, known as the carbon-nitrogen (CN) cycle, was a cyclic reaction in which carbon and nitrogen nuclei acted only as catalysts. The net result was still the fusion of four protons to form one helium nucleus, accompanied by the release of energy. While Bethe thought originally that the CN cycle was the main mode by which our own Sun produces its energy, experiments at the Kellogg Radiation Laboratory at Caltech showed later that it was the p-p chain that mostly powered the Sun, with the CN cycle starting to dominate energy production only in more massive stars.
You have probably noticed that, as its name implies, the CN cycle requires the presence of carbon and nitrogen atoms as catalytic agents. Yet Bethe’s theory fell short of demonstrating how carbon or nitrogen formed in the universe in the first place. Bethe did consider the possibility that carbon could be synthesized from the fusion of three helium nuclei together. (A helium nucleus contains two protons, and a carbon nucleus, six.) However, after completing his calculations, he asserted, “There is no way in which nuclei heavier than helium can be produced permanently in the interior of stars under the present conditions”—that is, with densities and temperatures such as those encountered in most Sun-like stars. Bethe concluded: “We must assume that the heavier elements [than helium] were built up before the stars reached their present state of temperature and density.”
Bethe’s pronouncement created a serious conundrum, since astronomers and Earth scientists were concluding at the time that the different chemical elements had to have, by and large, a common origin. In particular, the fact that atoms such as carbon, nitrogen, oxygen, and iron appeared to have approximately the same relative abundances all across the Milky Way galaxy clearly hinted at the existence of some universal formation process. Consequently, if they were to accept Bethe’s adjudication, physicists had to come up with some common synthesis that could have operated before present-day stars reached their equilibrium.
Just as the theory seemed to be heading toward a paralyzing impasse, the versatile George Gamow (usually known to his colleagues as Geo) and his PhD student Ralph Alpher advanced what appeared to be a brilliant idea: Perhaps the elements could have been formed in the initial, extremely hot and dense state of the universe known as the big bang. The concept itself was genius in its clarity. In the primeval, dense fireball, Gamow and Alpher argued, matter consisted of a highly compressed neutron gas. They referred to this primordial substance as ylem (from the ancient Greek yle and the medieval Latin hylem, both meaning “matter”). As these neutrons started decaying into protons and electrons, all the heavier nuclei could, in principle, be produced by the successive capture of one neutron at a time from the remaining sea of neutrons (and the subsequent decay of those neutrons into protons, electrons, and antineutrinos). Atoms were supposed to march in this way up the periodic table, climbing one step with each consecutive neutron capture. The entire process was assumed to be controlled by the probability for particular nuclei to capture another neutron, and also by the expansion of the universe (discovered in the late 1920s, as we’ll discuss in the next chapter). The cosmic expansion determined the overall decrease of the density of matter with time, and thereby the slowing down of the nuclear reaction rates. Alpher carried out most of the computations, and the results were published in the April 1, 1948, issue of the Physical Review. (April Fool’s Day was Gamow’s favorite publication date.) The always-whimsical Geo noticed that if he could add Hans Bethe (who had nothing to do with the calculations) as a coauthor of the paper, the three names—Alpher, Bethe, Gamow—would correspond to the first three letters of the Greek alphabet: alpha, beta, gamma. Bethe agreed for his name to be included, and the paper is often referred to as the “alphabetical article.” Later in the same year, Alpher collaborated with physicist Robert Herman to predict the temperature of the residual radiation from the big bang, known today as the cosmic microwave background. (Geo, who never abandoned his lifelong interest in punning, joked in his book The Creation of the Universe that Robert Herman “stubbornly refuses to change his name to Delter”—to correspond to delta, the fourth letter in the Greek alphabet.)
As ingenious as the scheme of Alpher and Gamow was, it soon became clear that while nucleosynthesis in a hot big bang could indeed account for the relative abundances of the isotopes of hydrogen and helium (and some lithium and traces of beryllium and boron), it ran into insuperable problems producing the heavier elements. The challenge is easy to understand using a simple mechanical metaphor: It is very difficult to climb a ladder when some of the rungs are missing. In nature, there are no stable isotopes with an atomic mass of 5 or 8. That is, helium has only stable isotopes with atomic masses of 3 and 4; li
thium has stable isotopes with atomic masses of 6 and 7; beryllium’s only truly stable isotope has an atomic mass of 9 (atomic mass 10 is unstable but long lived), and so on. Atomic masses of 5 and 8 are missing. Consequently, helium (atomic mass, 4) cannot capture another neutron to produce a nucleus that would be sufficiently long lived to continue the neutron-capture scheme. Lithium has a similar difficulty because of the gap at atomic mass 8. The mass gaps therefore frustrated further progress along the Gamow and Alpher approach. Even the great physicist Enrico Fermi, who examined the problem in some detail with a colleague, concluded with disappointment that synthesis in the big bang was “incapable of explaining the way in which the elements have been formed.”
Fermi’s conclusion that carbon and heavier elements could not be produced in the big bang combined with Bethe’s assertion that these elements could not be produced in stars such as the Sun created a perplexing mystery: Where and how were the heavy elements synthesized? This was the point at which Fred Hoyle entered the picture.
And God Said: “Let There Be Hoyle”
In the late fall of 1944, Hoyle’s wartime activities in naval radar took him to the United States, where he used the opportunity to meet with one of the most influential astronomers of the time, Walter Baade, at the Mount Wilson Observatory in California. At the time, this observatory contained the largest telescope in the world. From Baade, Hoyle learned how enormously dense and hot the cores of massive stars can become during the late stages in their lives. Examining those extreme conditions, he realized that at temperatures approaching a billion degrees, protons and helium nuclei could easily penetrate the Coulomb barriers of other nuclei, resulting in such a high frequency of nuclear reactions and back-and-forth exchanges that the entire ensemble of particles could reach a state known as statistical equilibrium.