(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

    [Please excuse the recitation of dry facts, but to explain how all this was 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.) Still heavier nuclei are not found naturally on Earth.

    [Why are helium nuclei especially stable? Some time ago I received e-mail from a teacher asking for suggestions of ways of demonstrating fusion to her students, "e.g. using M&Ms." One can do so (although tennis balls are better, being visible even from the last row of the classroom!) by showing how 4 balls (or candy pieces) can be stacked in a pyramid, each touching the other 3. Considering that the nuclear forces has a short range, this "close packing" gives the tightest binding. Maybe that is why helium (4 nucleons) is such a stable combination, as shown by its peak on the curve of binding energy above. No larger number can be stacked with every single ball touching all the others!]

The Sun's Energy Source

    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

    Stars several times the size of our Sun have enough gravity to crush together not just atoms but even nuclei, compressing all their matter to a sphere perhaps 15 kilometers across. After their collapse they become "neutron stars" consisting only of neutrons (the protons all switching form), giant nuclei as dense as the ones in atoms. A huge amount of energy is liberated in that final collapse which is quite rapid, blowing off the top layers of the collapsing star and also producing elements heavier than iron.

    [You may wonder why that collapse is so rapid, considering that Helmholtz and Kelvin--cited at the start of this section--found the gravitational energy of the Sun was sufficient to keep it hot for tens of millions of years. The answer was given by George Gamov and the Brazilian physicist Mario Schenberg in 1941: enormous energy is indeed generated, but the extreme temperature produces nuclear processes which generate neutrinos and these remove energy very, very quickly. The neutrino is an almost massless uncharged particle with very weak interactions, able to move unimpeded through thick layers of material--even the entire solid Earth, even the Sun. Neutrinos escaping through the outer layers of the supernova carry away its energy, in what Gamov facetiously named "the Urca process," comparing it to the rapid way in which a gambler's money disappeared at the roulette tables of the Casino da Urca in Rio de Janeiro. The process was dramatically confirmed by the supernova of 1987 (picture above shows it some years later; a larger picture, with added links, here) whose observation coincided with a burst of 11 neutrinos, detected by the sensitive Kamiokande underground observatory in Japan, and by 8 registered independently on a detector in Ohio]

    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. By the way, the Crab Nebula is still expanding; see here for a comparison of two images, taken 30 years apart. Another image of the nebula, highly detailed, is given here.

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 the image of a supernova remnant in Centaurus, as seen by Chandra, 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. For some time now it was believed that very massive black hole existed at the center of our galaxy, and if so, probably also at the centers of other galaxies, helping hold them together. We now have some pretty definite proof, and also a good estimate of what the mass of that monstrous object may be. The story of that discovery is given in the following section, "The black hole at the center of our galaxy".

Another take on Edna St. Vincent Millay's rhyme:

My ice cream cone drips at both ends
I eat it in great haste
But ah, my foes, and oh, my friends
It has a lovely taste!