The proton-proton reaction was insufficiently energetic, however, to account for the much higher luminosities of stars much larger than the sun—stars like the blue supergiants of the Pleiades, which occupy the higher reaches of the Hertzsprung-Russell diagram. This Bethe was to remedy before the year was out.
In April 1938, Bethe attended a conference organized by Gamow and Teller at the Carnegie Institution in Washington to bring astronomers and physicists together to work on the question of stellar energy generation. “At this conference the astrophysicists told us physicists what they knew about the internal constitution of the stars,” Bethe recalled. “This was quite a lot [although] all their results had been derived without knowledge of the specific source of energy.”6 Back at Cornell, Bethe attacked the problem with such alacrity that Gamow would later joke that he had calculated the answer before the train that carried him home arrived at the Ithaca station. Bethe wasn’t that quick, but within only a matter of weeks he had succeeded in identifying the carbon cycle, the critical fusion reaction that powers stars more than one and a half times as massive as the sun.
Publication of the paper, however, was delayed. Bethe finished it that summer and sent it to the Physical Review, but then was informed by a graduate student, Robert Marshak, that the New York Academy of Sciences offered a five-hundred-dollar prize for the best unpublished paper on energy production in stars. Bethe, who had need of the money, coolly asked that the paper be sent back, entered it in the competition, and won. “I used part of the prize to help my mother emigrate,” he told the American physicist Jeremy Bernstein. “The Nazis were quite willing to let my mother out, but they wanted two hundred and fifty dollars, in dollars, to release her furniture. Part of the prize money went to liberate my mother’s furniture.”7 Only then did Bethe permit publication of the paper that was to win him a Nobel Prize. He had, for a time, been the sole human being who knew why the stars shine.
Curiously stutter-stepped were the fusion reactions Bethe perceived. The proton-proton reaction begins with the collision, deep inside the sun, of two protons that have sufficient velocity and good fortune to penetrate the Coulomb barrier. If the collision succeeds in transforming one of the protons into a neutron—another rather unlikely event, involving a weak-force interaction called beta decay—the result is a nucleus of heavy hydrogen. The interaction releases a neutrino, which flies out of the sun, and a positron, which plows into the surrounding gas and thus helps heat the sun. The average proton at the center of the sun finds it necessary to wait more than thirty million years before chancing to experience this brief fling.
The next step, however, comes quickly. Within a few seconds, the heavy hydrogen nucleus snaps up another proton, transforming itself into helium-3 and releasing a photon that carries off further energy into the surrounding gas. Nuclei of helium-3 are rare, and so most are obliged to wait another few million years before encountering a second helium-3 nucleus. Then the two nuclei can fuse, forming a stable helium nucleus and releasing two protons, which are free to join the dance in their turn. The result has been to release energy: The helium end-product weighs sixth tenths of 1 percent less than did the particles that went into the reaction. This mass has been converted into energy, in the form of quanta that slowly make their way to the surface, blundering into atoms and being absorbed and reemitted as they go, until, centuries later, they at last break into the clear and are released into space as sunlight.
The proton-proton reaction has ramifications that are not completely understood—measurements of the neutrino flux on earth have to date yielded only a third as many neutrinos as the theory says should be released—and the carbon cycle is more complicated still. Nonetheless, enough is now known about solar fusion for us humans to begin to appreciate the elegance of the workings of our mother star. We have learned, for one thing, that the sun is not a bomb, although nuclear fusion is the same mechanism that functions in a thermonuclear weapon. When a chain reaction occurs in one tiny area in the center of the sun, it does not normally touch off other reactions in the surrounding gas; instead, the additional heat expands the gas slightly, lowering its density and so decreasing the probability of further proton-proton collisions for the moment. Owing to the operation of this self-regulating process, as averaged out for countless interactions, the entire star equilibrates, expanding to damp the rate of thermonuclear processes when they can attain a runaway rate, then contracting and heating to increase the rate when the center begins to cool. Although only one five-billionth of the sun’s light strikes the earth, that has been sufficient to endow the earth with warmth, and life, and with bipeds clever enough to decipher the particulars of their debt to Sol.
With the basic physics of solar fusion now in hand, it became possible to rework Kelvin’s estimates of the age of the sun. The sun’s mass can be determined, and very accurately so, from Newton’s laws and the orbital velocity of the planets. The result is 1.989 × 1033 grams, the equivalent of three hundred thousand Earths. The sun’s composition, at the surface at least, is revealed by the spectrograph to be principally hydrogen and helium. Knowing, then, the mass, volume, and approximate composition of the sun, one can ascertain the conditions that pertain at its center, where the thermonuclear processes take place. One can, for instance, calculate that the temperature at the core is about 15 million degrees, that the density is about twelve times that of lead (though the heat keeps the dense material in a gaseous and not a solid state), and that the fusion reaction rate is such that some 4.5 million tons of hydrogen are fused into helium inside the sun every second. Since the sun contains a finite amount of hydrogen, it must eventually run low on fuel, at which time its nuclear furnaces will falter. The total hydrogen-burning “lifetime” for the sun can thus be calculated. It turns out to be about ten billion years. Since radiometric dating of the asteroids and the earth yields an age for the solar system of a little less than five billion years old, we conclude that the sun now is in its middle age, and has another five billion years of hydrogen-burning ahead of it. And so the investigation of stellar energy sources, which had been driven in part by the demands of the geologists and biologists for a time scale longer than the old ideas permitted, opened up immensities of astronomical history even longer than the Darwinians had required.
The lifetimes of other stars can be calculated similarly. The fusion rate increases by the fourth power of the mass; consequently, dwarf stars last much longer than giants. The least massive stars have about 1 percent of the mass of the sun. (Much less and they would fail to generate sufficient interior heat for fusion to take place, and would instead be planets.) These little dwarfs, residents of the lower tiers of the Hertzsprung-Russell diagram, burn their hydrogen fuel so prudently that they can last for a trillion years or more. At the other end of the scale, toward the top of the diagram, stand giant stars with up to sixty times the mass of the sun. (If much larger, they would blow themselves apart as soon as they got fired up.) These huge stars squander their fuel profligately, and run out of hydrogen almost immediately; a star ten times as massive as the sun lasts less than one hundred million years.
These considerations greatly enriched and enlivened human appreciation of what might be called the ecology of the Milky Way. They revealed that the most spectacular stars in the galaxy, the giant, blue-white O and B stars, are also the stars that have the least time to live: Giants typically burn for only ten million to one hundred million years, and some may last no longer than a million years. This means that the brilliant giants that trace out the spiral arms are, by galactic standards, flowers that bloom for but a day. Indeed, that is why they trace out the arms. Stars of various masses condense along the arms, but while more modest stars last long enough to drift off into the surrounding disk, the brilliant superstars die before they ever get far from their birthplaces, which, consequently, they demark.
How do stars die? This, too, depends principally on their mass. When an ordinary star like the sun runs low on fuel it takes on a sp
lit personality: Its core contracts, no longer propped up by the radiation of energy from thermonuclear processes at the center, while its outer portion—its “atmosphere,” so to speak—expands and cools. The star’s color changes from a yellow-white to a deepening red: It has become a “red giant.” Ultimately the stellar atmosphere boils away into space, leaving behind the naked core, a massive, dense sphere only about the size of the earth—a “white dwarf” star.
Such a prognosis, plotted on the Hertzsprung-Russell diagram, serves to animate the tree of stars. When an average star like the sun exhausts its hydrogen fuel, it leaves the main sequence and moves upward—since the growing size of its outer atmosphere briefly makes it brighter—and to the right, since it is getting redder. Many stars during this phase may become unstable, staggering back and forth from right to left on the diagram. When the star sheds its atmosphere, it drops down the diagram and skids to the left, settling finally into the zone of the white dwarfs. Giant stars follow an approximately similar course, but start higher on the main sequence (since they are brighter) and leave it sooner (since they run out of fuel more rapidly).
The main-sequence lifetimes of stars are determined principally by their masses: Massive stars exhaust their fuel much more rapidly than do low-mass stars.
The destinies of stars once they leave the main sequence also differ greatly, according to their masses. When the sun runs low on fuel it will exit the main sequence toward the right, becoming a red giant. After another billion years or so it will eject its outer atmosphere, skidding from right to left across the diagram as it does so, then plunge down into the graveyard of the white dwarfs. A star with five times the mass of the sun remains on the main sequence for less than a tenth as long, then begins oscillating back and forth near the top of the diagram as an unstable giant. For stars of ten solar masses or more, such instabilities may culminate in the explosion of the star as a supernova.
The ages of star clusters may be inferred from their Hertzsprung-Russell diagrams. In a young cluster like the Pleiades, nearly all the visible stars lie on the main sequence: There are few red giants or white dwarfs to be found, because the cluster is not yet old enough for many of its stars to have run out of hydrogen fuel and departed from the main sequence.
The Hertzsprung-Russell diagram for any given population of stars—a star cluster, say—therefore provides evidence of its age. When the cluster is in its infancy, virtually all its stars lie on the main sequence, contentedly burning hydrogen. Soon the giant stars—those at the upper-left extremity of the main sequence—run out of fuel and balloon into red giants; each, as it does so, leaves the main sequence and moves to the right. As more time goes by, the same fate afflicts stars of ever less mass. The result, on the diagram, is a “cutoff point,” a place along the main sequence where the tree branches off to the right. The diagram is only a snapshot of a moment amid billions of years of stellar history, but the location of the cutoff point tells us how long the cluster has been there: The farther down the trunk the cutoff point falls, the older the tree.
The Hertzsprung-Russell diagram of the Pleiades cluster, for example, shows almost entirely main sequence stars. This tells us that the Pleiades is a young cluster, in which not enough time has passed for even the giant stars to burn down to the red giant stage. (The stars of the Pleiades are estimated to be less than one hundred million years old.) The diagram of the globular cluster M3, however, looks dramatically different. Here the great majority of stars are either in the red giant phase or are on their way to becoming dwarfs. (We don’t see the dwarfs themselves because they are too dim; M3 is an ample thirty thousand light-years away.) The cutoff branch points like the hand of a clock at the age of the cluster: For M3, the age reads out to some fourteen billion years, making it one of the oldest ever dated.
To envision the pace of stellar evolution more directly, imagine that the sun was a star in a young star cluster and that we were present on the earth right from the outset, when our planet had just cooled sufficiently for its crust to have solidified. Imagine, further, that we could speed up the passage of time, so that ten billion years would pass in a single night. As the sun sets, at time zero, we find the sky studded with main-sequence stars. There are as yet no red giants and no dwarfs. A few bright giants stand out, as well as a number of stars about as luminous as the sun, but the great majority of stars are dimmer and less bright than the sun.
Almost immediately, the giant stars exhaust their fuel, become unstable and explode as Supernovae, flooding the landscape with scalding white light. On our compressed time scale, where each hour equals a billion years, all these spectacular stars die within the first few minutes. Conceivably their explosions may shock any remaining gas in the cluster into collapsing to form new stars, but any giant stars produced in this fashion will also consume themselves quickly, so that the fireworks are over by the time we’ve settled down to watch the show.
In the hours that follow, successively less massive stars in turn leave the main sequence; we watch them swell into red giants, shed shells of multicolored gas, and reduce themselves to dim dwarf stars. These events are rare enough to hold our attention, however, because relatively few stars in the cluster are more massive than the sun. By dawn some ten billion years have gone by. Now it is the sun’s turn to die. There is a sudden, shuddering contraction of the sun’s core, and the solar atmosphere balloons into an aethereal red cloud that expands and swallows up the planets Mercury and Venus, and then Earth. Backing away to a prudent distance, we watch the cloud disperse and see the naked, helium-rich core of the sun exposed as a dim, dense dwarf.
An old star cluster like the globular cluster M3 displays a strikingly different Hertzsprung-Russell diagram. Here, the more massive stars have had ample time to burn up their fuel and become red giants, moving up and toward the right on the diagram, and then to slide down and to the left as some evolve into dwarfs. The result is a dramatic “cutoff point” at which the main sequence is interrupted. All else being equal, the lower the cutoff point, the older the cluster.
The night is over, but the story has hardly begun. Most of the cluster stars, less massive than the sun, continue to burn steadily, with an unexceptional, candle-yellow glow. These members of the silent majority have long lives ahead of them on the main sequence; they will still be shining aeons after the evacuated atmosphere of the sun has been gathered up to make new stars and planets. The study of stellar evolution teaches us that the meek shall inherit the galaxy.
Once it had been established that stars shine by means of nuclear fusion, it became apparent that they must also be in the business of building light elements into heavy elements. They could hardly do otherwise, inasmuch as nuclear fusion involves the fusing of the nuclei of light atoms to make the nuclei of heavier atoms. Through a variety of fusion processes, stars build hydrogen into helium; helium into carbon; carbon into oxygen and magnesium, and so forth. Indeed, given that the energy released amounts to but a tiny fraction of the mass being shuffled about, we could say that element-making is the primary business of stars, and that their light and heat, though subjectively important to creatures like ourselves who owe their lives to it, is but a by-product of that process, as incidental as the heat ventilated out of the smokestack of a tool and die works. If, as the textbooks like to say, atoms are the building blocks of matter, stars are the place where the building blocks are built. As Eddington wrote presciently in 1920, “The stars are the crucibles in which the lighter atoms which abound in the nebulae are compounded into more complex elements.”8
Two essential questions remained.
One was just how stars make the heavy elements. Bethe’s proton-proton reaction yields nothing heavier than helium, which is the second lightest element. If stars build heavier atoms, they must do so by means of other fusion processes. The carbon cycle won’t do the trick; it employs carbon, nitrogen, and oxygen merely as catalysts, leaving no new elements behind. Clearly, it would take some fancy nuclear physics to bet
ter reconstruct the full complexity of stellar fusion.
The other question, closely related to the first, was whether stars are the sole, or even the primary, source of the elements. There was a competing hypothesis. It held that most of the elements were fused, not in stars, but in the big bang.
For fusion to have taken place in the big bang, the universe at the very onset of its expansion would have had to be hot. The hypothesis that this was the case came in part from the basic laws of thermodynamics, which show that any given volume of material will become hotter if it is compressed. Suppose, for instance, that the Milky Way galaxy were to be enclosed in a gigantic hydraulic press, like the ones used to crush the hulks of old cars into cubes of scrap metal, and were squeezed down into a volume of, say, only one cubic foot. (This is thought to have been its state when the universe was but a fraction of a second old.) While the compression process was taking place, the stars and planets would be melded together, then the molecules would break down, and finally, when the temperature exceeded that of a stellar interior, even the nuclear structures of the matter in the galaxy would begin to decompose, reducing everything to a hot, dense gas made of subatomic particles—what physicists call a plasma. Release the press, and the plasma would expand and cool, recombining into atoms and molecules in the process. This, then, is a small-scale model of what is thought to have happened in the big bang, with the universe evolving from a high-density plasma into the structures—nuclear, atomic, molecular, stellar, and planetary—that we see around us today.
If astronomers at first regarded the hot big bang idea with reservation, the nuclear physicists were more open to it. They were growing accustomed to envisioning conditions of high temperatures and high densities, if only because of their work on chain reactions in nuclear bombs. Gamow in particular was interested in the question of whether the chemical elements that compose the universe today could have been forged in the fires of the big bang. It was a reasonable supposition—the heavier the element, the more energy was required to build it, and where was there more energy than in the big bang?—and Gamow went to work painting in the details with the broad brush and vivid colors that characterized his approach to physics.
Coming of Age in the Milky Way Page 28