But this necessitates an entire rearrangement of the scheme of evolution, because the order according to density is by no means the same as the order according to surface temperature. On the former view all the cool red stars were old and dying. But a large number of them are now found to be extremely diffuse—stars like Betelgeuse, for instance. These must be set down as the very youngest of the stars; after all it is not unnatural that a star just beginning to condense out of nebulous material should start at the lowest stage of temperature. Not all the red stars are diffuse; there are many like Krueger 60 which have high density, and these we leave undisturbed as representing the last stage of evolution. Both the first and last periods of a star’s life are characterized by low temperature; in between whiles the temperature must have risen to a maximum and fallen again.
The ‘giant and dwarf theory’ proposed by Hertzsprung and Russell brought these conclusions into excellent order. It recognized a series of giant stars, comparatively diffuse stars with temperature rising, and a series of dwarf or dense stars with temperature falling. The two series merged at the highest temperatures. An individual star during its lifetime went up the giant series to its highest temperature and then down the dwarf series. The brightness remained fairly steady throughout the giant stage because the continually increasing temperature counterbalanced the reduction of the surface area of the star; in the dwarf stage the decreasing temperature and the contraction of the surface caused a rapid decrease of brightness as the star progressed down the series. This was in accordance with observation. The theory has dominated most recent astrophysical research and has been instrumental in bringing to light many important facts. One example must suffice. Although we may have a giant and a dwarf star with the same surface temperature, and therefore showing very similar spectra, nevertheless a close examination of the spectrum reveals tell-tale differences; and it is now quite easy to ascertain from the spectrum whether the star is a diffuse giant or a dense dwarf.
The attractive feature of the giant and dwarf theory was the simple explanation given for the up-and-down progress of the temperature. The passing over from the giant to the dwarf series was supposed to occur when the density had reached such a value (about one-quarter the density of water) that the deviation of the material from a perfect gas began to be serious. It was shown by Lane fifty years ago that a globe of perfect gas must rise in temperature as it contracts, his method of finding the internal temperature being that considered on [p. 12]; thus the rising temperature in the giant stage is predicted. But the rise depends essentially on the easy compressibility of the gas; and when the compressibility is lost at high density the rising temperature may be expected to give place to falling temperature so that the star cools as a solid or liquid would do. That was believed to account for the dwarf stage.
I have been trying to recall ideas of twenty and ten years ago, and you must not suppose that from the standpoint of present-day knowledge I can endorse everything here stated. I have intentionally been vague as to whether by the hotness of a star I mean the internal or the surface temperature since ideas were formerly very loose on this point; I have made no reference to white dwarfs, which are now thought to be the densest and presumably the oldest stars of all. But it is the last paragraph especially which conflicts with our latest conclusions, for we no longer admit that stellar material will cease to behave as a perfect gas at one-quarter the density of water. Our result that the material in the dense dwarf stars is still perfect gas ([p. 38]) strikes a fatal blow at this part of the giant and dwarf theory.
It would be difficult to say what is the accepted theory of stellar evolution to-day. The theory is in the melting-pot and we are still waiting for something satisfactory to emerge. The whole subject is in doubt and we are prepared to reconsider almost anything. Provisionally, however, I shall assume that the former theory was right in assuming that the sequence of evolution is from the most diffuse to the densest stars. Although I make this assumption I do not feel sure that it is allowable. The former theory had strong reasons for making it which no longer apply. So long as contraction was supposed to be the source of a star’s heat, contraction and increasing density were essential throughout its whole career; with the acceptance of subatomic energy contraction ceases to play this fundamental role.
I propose to confine attention to the dwarf stars[35] because it is among them that the upset has occurred. They form a well-defined series stretching from high surface-temperature to low surface-temperature, high luminosity to low luminosity, and the density increases steadily along the series. We now call this the Main Series. It comprises the great majority of the stars. To fix ideas let us take three typical stars along the series—Algol near the top, the Sun near the middle, and Krueger 60 near the bottom. The relevant information about them is summarized below:
| Star. | Mass (Sun = 1). | Mean density (Water =1) | Central temperature (million deg.). | Surface temperature (deg.). | Colour. | Luminosity (Sun = 1). |
|---|---|---|---|---|---|---|
| Algol | 4·3 | 0·15 | 40 | 12,000 | white | 150 |
| Sun | 1 | 1·4 | 40 | 6,000 | yellow | 1 |
| Krueger 60 | 0·27 | 9·1 | 35 | 3,000 | red | 0·01 |
The idea of evolution is that these represent the stages passed through in the life-history of an individual star.[36] The increasing density in the third column should be noticed; according to our accepted criterion it indicates that the order of development is Algol→Sun→Krueger 60. A confusion between internal temperature and surface temperature is responsible for some of the mistakes of the older theories. To outward view the star cools from 12,000° to 3,000° in passing down the series, but there is no such change in its internal heat. The central temperature remains surprisingly steady. (No special reliance can be placed on the slight falling off apparently shown by Krueger 60.) It is very remarkable that all stars of the main series have a central temperature of about 40 million degrees as nearly as we can calculate. It is difficult to resist the impression that there is some unusual property associated with this temperature, although all our physical instincts warn us that the idea is absurd.
But the vital point is the decrease of mass shown in the second column. If an individual star is to progress any part of the way down the main series it must lose mass. We can put the same inference in a more general way. Now that it has been found that luminosity depends mainly on mass, there can be no important evolution of faint stars from bright stars unless the stars lose a considerable part of their mass.
It is this result which has caused the hypothesis of annihilation of matter to be seriously discussed. All progress in the theory of stellar evolution is held up pending a decision on this hypothesis. If it is accepted it provides an easy key to these changes. The star may (after passing through the giant stage) reach the stage of Algol, and then by the gradual annihilation of the matter in it pass down the main series until when only one-sixteenth of the original mass remains it will be a faint red star like Krueger 60. But if there is no annihilation of matter, the star when once it has reached the dwarf stage seems to be immovable; it has to stay at the point of the series corresponding to its constant mass.