Coming of Age in the Milky Way (39 page)

The Hertzsprung-Russell diagram plots the spectral classes (or colors) of stars against their brightnesses. This version of the diagram is thought to represent the general stellar population of our galaxy.

What happens when protons collide? Well, we know that they can stick together—“fuse”—because they are found, stuck together, in the nuclei of all the heavier elements. Might the fusion of protons release energy? A strong hint that this is so lay in the fact that the heavier nuclei weigh a little less that the sum of their parts. There was some confusion about this point, but the basic idea was correct—that energy is released in stars when the nuclei of the light atoms fuse to make those of heavy atoms. Rutherford already had been performing experiments in what he called “the newer alchemy,” bombarding nuclei with protons and changing them into the nuclei of different elements, and, as Eddington wryly noted, “what is possible in the Cavendish Laboratory may not be too difficult in the sun.”
⁵

So far, so good; science was close to identifying thermonuclear
fusion as the secret of solar power. But it was here that the Coulomb barrier intervened. Protons are positively charged; particles of like charge repel one another; and this obstacle seemed too strong to be overcome, even at the high velocity of protons flying about in the intense heat at the center of a star. Seldom, according to classical physics, could two protons in a star get going fast enough to breach the walls of their electromagnetic force fields and merge into a single nucleus. The calculations said that the proton collision rate could not possibly suffice to sustain fusion reactions. Yet there stood the sun, its beaming face laughing at the equations that said it could not shine.

There was nothing wrong with the argument, so far as it went: Were classical physics declared the sole law of nature, the stars would indeed wink out. Fortunately, nature on the nuclear scale does not function according to the proscriptions of classical physics, which works fine for big objects like pebbles and planets but breaks down in the realm of the very small. On the nuclear scale, the rules of quantum indeterminacy apply.

In classical mechanics, subatomic particles like protons were viewed as analogous to macroscopic objects like grains of sand or cannonballs. Viewed by these lights, a proton hurled against the Coulomb barrier of another proton had no more chance of penetrating it than a cannonball has of penetrating a ten-foot-thick fortress wall. Introduce quantum indeterminacy, however, and the picture changes dramatically. Quantum mechanics demonstrates that the proton’s future can be predicted only in terms of probabilities: Most of the time the proton will, indeed, bounce off the Coulomb barrier, but from time to time it will pass right through it, as if a cannonball were to fly untouched through a fortress wall.
^*

This is “quantum tunneling,” and it licenses the stars to shine. George Gamow, eager to exploit connections between astronomy and the exotic new physics at which he was adept, applied quantum probabilities to the question of nuclear fusion in stars and found that protons could surmount the Coulomb barrier—almost. Quantum tunneling took the calculations from the dismal, classical prediction,
which had protons fusing at only one one-thousandth of the rate required to account for the energy released by the sun, up to fully one tenth of the necessary rate. It then took less than a year for the remaining deficit to be accounted for: The solution was completed in 1929, when Robert Atkinson and Fritz Houtermans combined Gamow’s findings with what is called the Maxwellian velocity distribution theory. In a Maxwellian distribution there are always a few particles moving much faster than average; Atkinson and Houtermans found that these fleet few were sufficient to make up the difference. Now at last it was clear how the Coulomb barrier could be breached often enough for nuclear fusion to function in stars.

But how, exactly, do the stars do it? Within another decade, two likely fusion processes were identified—the proton-proton chain reaction and the carbon cycle.

The key figure in both developments was Hans Bethe, a refugee from Nazi Germany who had studied with Fermi in Rome and gone on to teach at Cornell. Like his friend Gamow, the young Bethe was an effervescent, nimble thinker, so gifted that he made his work look like play. Though untrained in astronomy, Bethe was a legendarily quick study. In 1938 he helped Gamow’s and Edward Teller’s student C. L. Critchfield calculate that a reaction beginning with the collision of two protons could indeed generate approximately the energy—some 3.86 × 10
³³
ergs per second—radiated by the sun.
^*
And so, in the span of less than forty years, humankind had progressed from ignorance of the very existence of atoms to an understanding of the primary thermonuclear fusion process that powers the sun.

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 × 10
³³
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 split 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).