(S-7) The Energy of the Sun

The Sun is the source of most of the energy on Earth--the power source for plants, the cause of flows of atmosphere and of water, the source of the warmth which makes life possible. None would exist without it. At the Earth's orbit, neglecting absorption by the atmosphere, each square meter of area facing the Sun receives about 1380 joules per second (nearly 2 horsepower). That quantity is known as the solar constant and sensors aboard NASA's satellites over the 1979-99 interval suggest it varied by only about 0.2% (see graphs in Nature, vol 401, p. 841, 28 October 1999) .

But what powers the Sun itself? How much longer will it shine, before its fuel runs out? For how long has it given out its energy?

The first to consider these questions seriously was the great German physicist Hermann von Helmholtz, who noted in 1854 that the Sun's own gravity could supply an appreciable amount of energy. If the Sun were gradually shrinking--if all its matter was gradually falling towards its center--enough energy could be released to keep it radiating for a fairly long time. He calculated that this source could provide the Sun's energy for times of the order of up to 20 million years.

Then radioactivity was discovered, the decay of heavy elements into lighter ones through the emission of fast particles, containing a great deal of energy. As it turned out, it was this energy, from radioactive elements in rocks, that provided the internal heat of the Earth. Radioactivity also allowed new estimates of the age of the Earth, since the amount of accumulated decay products in ores indicated how long the process had been going on. This suggested the Earth was much older than Helmholtz'es estimate, perhaps billions of years old. Could perhaps the new source of internal energy also supply the Sun's needs for such a long time?

Nuclear Physics

[Sorry for just reciting the dry facts--to explain how they were established would be asking too much from such a brief review. A few of the benchmarks in the discovery of atoms and nuclei are listed here.]

Electrons and nuclei were kept together by electric attraction (negative attracts positive). Furthermore, electrons were sometimes shared by neighboring atoms or transferred to them (by processes of quantum physics), and this link between atoms gave our world its many chemical compounds.

But something else was needed to hold nuclei together, since all protons carried positive charges and repelled each other. Electric forces are definitely not the glue that holds nuclei together, they act in the wrong direction! Besides, binding neutrons to nuclei clearly requires a non-electrical attraction.

All that suggested a different kind of force, a nuclear force, was holding nuclei together. That force had to be stronger than the electric repulsion at short distances, but weaker far away, or else different nuclei might have tended to clump together, too. In other words, it had to be a short-range force, like the force between two small magnets--very hard to separate when stuck together, but once pulled a short distance apart, the force between them drops almost to zero (please do not take this analogy too literally!).

Actually two kinds of force are active in the nucleus, known simply as the "strong force" and the "weak force," or more commonly the "strong interaction" and the "weak interaction" (because their main effect is in converting and creating particles). The weak interaction also affects electrons and other particles, but in the nucleus its main role is to maintain a balance between protons and neutrons, which except for their electric charge are very similar particles (diferent kinds of "nucleons"). Nuclear structure (in light nuclei, at least) favors nuclei containing equal numbers of protons and neutrons, and although moderate inequalities can also exist (in "isotopes"), when they get too big, the weak interaction can convert nucleons of one kind to the other, emitting an electron (or a positron, its positive counterpart) in the process. That is known as beta radioactivity and will not be discussed any further.

The strong nuclear force (the only nuclear force considered from here on) can bind protons and neutrons into bigger nuclei. Being positively charged, all these nuclei repel each other, and therefore, except in the presence of extreme temperatures and pressures--such as exist in the core of the Sun--two different nuclei are not likely to combine into one. Their electric repulsion does not allow them to get close enough for the nuclear force to take over.

The Binding Energy of Nuclei

As we go on to elements heavier than oxygen, the energy which can be gained by assembling them from lighter elements decreases, up to iron. For nuclei heavier than iron, one actually gains energy by breaking them up into 2 fragments. That, of course, is how energy is extracted by breaking up uranium nuclei in nuclear power reactors.

The reason the trend reverses after iron is the growing positive charge of the nuclei. The electric force may be weaker than the nuclear force, but its range is greater: in an iron nucleus, each proton repels 25 other nuclei, while (one may argue) the nuclear force only binds close neighbors.

As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time uranium is reached (92 protons), nuclei can no longer accomodate their large positive charge, but emit their excess protons in the process of alpha radioactivity--the emission of helium nuclei, each containing two protons and two neutrons. (Helium nuclei are an especially stable combination, as evidenced by the peak they form on the curve of binding energy above!) Still heavier nuclei are not found naturally on Earth.

The Sun's Energy Source

Heat is the motion of atoms and molecules: the higher the temperature, the greater is their velocity and the more violent are their collisions. When the temperature at the center of the newly-formed Sun became great enough for collisions between nuclei to overcome their electric repulsion, nuclei began to stick together and protons were combined into helium, with some protons changing in the process to neutrons (plus positrons, positive electrons, which combine with electrons and are destroyed). This released nuclear energy and kept up the high temperature of the Sun's core, and the heat also kept the gas pressure high, keeping the Sun puffed up and stopping gravity from pulling it together any more.

That, in greatly simplified terms, is the "nuclear fusion" process which still takes place inside the Sun. Different nuclear reactions may predominate at different stages of the Sun's existence, including the proton-proton reaction and the carbon-nitrogen cycle which involves heavier nuclei, but whose final product is still the combination of protons to form helium. A more detailed qualitative account, by astrophysicists of the University of California at Berkeley, can be reached here.

A branch of physics, the study of "controlled nuclear fusion," has tried since the 1950s to derive useful power from "nuclear fusion" reactions which combine small nuclei into bigger ones--power to heat boilers, whose steam could turn turbines and produce electricity. Unfortunately, no earthly laboratory can match one feature of the solar powerhouse--the great mass of the Sun, whose weight keeps the hot plasma compressed and confines the "nuclear furnace" to the Sun's core. Instead, physicists use strong magnetic fields to confine the plasma, and for fuel they use heavy forms of hydrogen, which "burn" more easily. Still, magnetic traps can be rather unstable, and any plasma hot enough and dense enough to undergo nuclear fusion tends to slip out of them after a short time. Even with ingenious tricks, the confinement in most cases lasts only a small fraction of a second.

The Sun today still consists mostly of hydrogen. The fuel supply which has seen it through its first 5 billion years should be good for about as long in the future.

The Evolution of Stars

The Earth keeps its size because its gravity is not strong enough to crush the minerals of which it consists. Not so with a star massive enough to sustain nuclear burning. A small star may crush all its atoms together, creating a "white dwarf"--e.g. of half the mass of the Sun, but only as big as the Earth. Some energy release continues (hence "white") but ultimately, the star probably becomes a dark cinder.

This may be the fate of our Sun, too. In the final transition strange changes occur--the star becomes a "red giant," diffuse and enormously large, and later much of the material is blown to space where it forms a "planetary" nebula, but there is no explosion. See "The Complexity of Stellar Death" by Yervant Terzian, "Science" vol. 256 p. 425-6, 15 October 1999.

Supernovas

That catastrophic event is known as a supernova explosion (technically, a "type 2 supernova"). Tycho Brahe was fortunate to have seen one that occured in our galaxy, outshining Venus and visible even in the daytime. The Chinese observed one in the year 1054, in the Crab constellation of the zodiac, and still another occured in Kepler's lifetime. Since then, however, none seemed to have occured close to Earth. The most notable event of this type was observed (quite extensively) in 1987 in the Large Magellanic Cloud, a small galaxy neighboring ours (see image above; the inner cloud is the one produced in the explosion, the rings seem older). For more about supernovas, see here

The material blown off by a supernova explosion ultimately scatters throughout space, and some of it is incorporated in clouds of dust and gas which later form new suns and planets. All elements on Earth heavier than helium (except, possibly, a small amount of lithium) must have arrived that way: products of nuclear burning in some pre-solar star, released or created in the explosion accompanying its final collapse. Our bodies are made of star stuff--carbon, oxygen, nitrogen and the rest have all been produced by nuclear fusion.

As for the "supernova remnant" left over from the collapse, its fate depends on its mass. If the star was not too massive, the remnant (as explained) is a neutron star. It that star originally rotated around its axis, that rotation is enormously speeded up; the remnant of the supernova of the year 1054 (its ejected cloud, the "Crab Nebula," is shown on the left) is spinning at about 30 revolutions per second! Any magnetic field of the original star is also enormously amplified, and associated phenomena can make it beam radio waves. Pulsars, pulsed radio sources with remarkably stable pulsation periods, are produced that way.

Added 20 October 1999: The new Chandra orbiting X-ray telescope has taken a high-resolution picture in X-rays of the central region of the Crab nebula. Before this, astrophysicists guessed the remnant star might be surrounded by orbiting debris, with high-energy particles shooting out along its magnetic axis, the one direction in which magnetic field lines do not confine them. The picture on the right suggests something like that might indeed be happening. For more about this image, see here.

Theory suggests that a star much more massive than the Sun will collapse even further and become a black hole. What happens then can only be guessed and calculated, not observed, for the star's gravity in the collapsed state is so strong that no light and no information can return from it to the outside world. One therefore expects such objects to be completely black; they are called "black holes" because the general theory of relativity suggests that the matter in such a star keeps falling indefinitely, as the star contracts to a point. Thus in theory such stars are like the proverbial bottomless pit, although no observation could ever confirm it.

Although astronomers cannot see such objects, they have considerable evidence that they exist, at least in a number of locations. A very massive black hole may exist at the center of our galaxy, and if so, probably also at the centers of other galaxies, helping hold them together.

This concludes our discussion of the Sun. "From Stargazers to Starships" continues with sections dealing with spaceflight and spacecraft, starting with The Principle of the Rocket

However... you may want to extend what you have learned
about the atomic nucleus to find out how nuclear power is
comercially obtained. If so, go next to (S-8) Nuclear Energy.