Thermonuclear Fusion
Over a century ago astronomers understood that the energy already radiated by the Sun could never have been supplied by ordinary combustion (for example, by the burning of wood or coal). Another way of producing energy known to astronomers was by the conversion of gravitational potential energy into heat during contraction. In fact, in the nineteenth century, this was thought to be the only source for the Sun's energy. We now know that contraction is a vital source of energy on which a star can draw at various stages in its life. But at its current luminosity, our Sun could not have survived on gravitational potential energy alone for more than about 15 million years.
For stars like the Sun, a source of energy must keep the luminosity approximately constant for billions (not just millions) of years. The question plaguing astronomers in the early part of this century was what that source is. The answer is the fusion of small-mass nuclei to form more massive nuclei. Sir Arthur Eddington (1882-1944) suggested in 1920 that fusion of hydrogen could form helium and that this could be the long-sought fuel. After it was found that stars have vast quantities of hydrogen, the physicist Hans Bethe (b. 1906) proposed in 1938 a way in which four hydrogen nuclei (four protons) could be converted into a helium nucleus, releasing energy. If many hydrogen nuclei are converted, they will release sufficient energy through this process (known as thermonuclear fusion) to keep stars shining for billions of years.
What determines whether hydrogen can be fused to form helium? The answer is the temperature and density of a gas; the higher the temperature and density, the more readily the process will proceed. Thermonuclear reactions will therefore be most numerous in a star's central region, where the temperature and density are highest. The reactions will gradually decline to zero somewhere out from the center, where temperature and density are too low to sustain them. This distance from the center, then, defines the energy-generating core of a star, such as the Sun.
The p-p Chain and CNO Cycle
Hydrogen burning proceeds by two principal schemes: the proton-proton chain (p-p chain) and the carbon-nitrogen-oxygen cycle (CNO cycle). In each process, four protons are fused into one helium nucleus with a slight loss in mass, which is converted into energy. Which thermonuclear process produces more energy depends on the temperature. Up to about 16 million K the p-p chain dominates. Beyond that temperature, however, the CNO cycle takes over as the most important thermonuclear process. The average rate of energy generation for the entire Sun, which depends primarily on the p-p chain, is about 2 erg/g/s. For a star of 10Msun, the average rate of energy generation, supplied principally by the CNO cycle, is about 1000 times greater than that of the Sun.
The mass of the end product of hydrogen burning, He4, is 0.71 percent less than the combined masses of four reacting protons (4H1). What has happened to the rest of the mass? Early in this century Einstein pointed out that there is an equivalence between mass and energy. Mass is just one more manifestation of energy, and what is conserved in any type of interaction between particles of matter is the total energy, including the energy equivalent of the mass. The equivalence is symbolized in Einstein's equation E = mc2, where E is the energy, m is the mass, and c is the velocity of light.
In hydrogen burning 1 gram of hydrogen is converted into 0.9929 grams of helium plus 6.4 x 1018 erg of energy--exactly 0.71 percent of the original 1 gram of hydrogen times c2. In what form does the energy appear? In the various steps, several gamma-ray photons are created and degraded by absorption and reemission into many photons having the same total energy. Also, some of the material particles created have large kinetic energies, which they will soon redistribute to other particles by collisions. Thus both radiant energy and heat energy come from the mass that is lost in these thermonuclear fusion processes.
Translated into practical units, every second the Sun converts 600 million metric tons of hydrogen into 596 million metric tons of helium and 4 million metric tons of mass into energy. This energy will diffuse to the surface, where it will supply the 3.83 x 1033 erg of energy radiated away into space each second. In its core the Sun has enough hydrogen to keep it shining for about 10 billion years. In 4.6 billion years the Sun has existed so far, it has used up about half its core's hydrogen supply and lost about 0.043 percent of its mass.
Steps in Hydrogen Burning
Step 1 in the p-p chain (see table below) is fusion of two colliding protons (H1) to form a deuteron (H2), which is the nucleus of the hydrogen isotope deuterium, resulting in the emission of a positron (e+) and a neutrino ( ). This reaction happens, on average, once every 14 billion years for each isolated pair of protons. The time for the entire thermonuclear process is determined by this first step, and it is only the enormous quantity of hydrogen in the cores of stars that makes this process a significant source of energy.
The positron is a positively charged particle with the mass and other characteristics of an electron; it is the antiparticle for the electron. The collision of a positron with an electron destroys them as matter and creates two gamma-ray photons. The neutrino, however, is a massless, chargeless particle that moves at the speed of light. Since the neutrino has a low probability of interacting with matter, it immediately escapes from the star, carrying away about 2 percent of the energy released in the p-p chain of reactions.
Step 2 in the p-p chain is the collision within a few seconds of another proton with the deuteron to fuse and form the light isotope of helium (He3), resulting in the emission of a gamma-ray photon. Finally, in step 3, two He3 nuclei collide every few million years and fuse to form the heavy isotope of helium (He4), accompanied by the return of two protons. (We should point out that there are other branches of these reactions leading to the same end.)
All told, six protons have taken part in producing two He3 nuclei, from which one He4 nucleus is produced and two protons are returned to the reservoir of fusionable matter.
The other hydrogen-burning reaction, the CNO cycle, has six steps occurring at rates between 80 seconds and 300 million years but leading to the same result as the p-p chain; that is, the conversion of four protons to produce one helium nucleus and to liberate energy. The cycle begins with C12 and closes with the return of C12, so that carbon is thus only a catalyst that makes the reaction go.