The majority of points fall into a definite sequence—the "main series"—ranging from bright, hot, white stars like those in Orion's Belt, through those of moderate brightness like the sun, to faint, cool, red ones like Barnard's star of large proper motion, as is indicated by the points 1, 3, 4, 5 in fig. i. There are also many bright red and yellow "giant" stars like Antares, Arcturus or Capella (6, 7 and 8), and probably many more faint white dwarfs like the Companion of Sirius (9), which fall quite outside the main series.
The Main Series.—Since most of the known stars belong to the main series, we may begin by trying to account for this. Accord ing to Eddington's calculations the central temperatures of the stars along this series are nearly the same, and not far from 40,000,000°C. Suppose now that there is a process of liberation of sub-atomic energy within the stars, such that its rate is low at temperatures of a few millions of degrees, increases steadily, and, for a central temperature of 40,000,000°, becomes equal to the rate of loss for a star of corresponding mass. If now we have a star of great mass and low density it will be bright, red, and of large diameter, and represented by a point such as in fig. 2. Its central temperature will be low, it will contract, drawing on its gravitational energy, and the point on the diagram will move to A, and A,. But as it approaches the dotted line corresponding to the central temperature 40,000,000°, heat from sub-atomic sources will be turned on—so to speak—and the star will come into a steady state at and remain at it, drawing on sub-atomic energy, for a very long time. Similarly, stars of smaller mass and low initial density will pass through the stages represented by B,–B,B. and If we imagine a star of mod erate mass and very high density at the start, it would have too great an income of sub-atomic energy and expand through the stages D,, and come to rest on the same line. If no other sub-atomic process were at work within the stars it is clear that, however they were started, they would all be found, of ter a few millions of years, along the main series B., The strong, actual concentration of stars along this series suggests that some such process of energy liberation may actually take place. The points actually lie not in a line, but along a strip of some width; but this is easily explained. If the percentage of active material in a star were lower than that at first considered the central temperature would have to be higher to cause income and outgo to balance, and we should have points along a line like A'C'. It is freely admitted that no theoretical reason can be given, in our present ignorance of the laws governing the structure of atomic nuclei, and still more those which determine the existence of protons and electrons, why liberation of energy should occur at this particular temperature, and be so adjusted as to be much more rapid in the more massive stars, where the central density is relatively low, than in those of small mass, where it is high. But no conclusive reasons against it can be given either,
and the facts speak for themselves.
Giants and White Dwarfs.—This temperature does not account for the existence of the red giants, or the white dwarfs. They appear to demand the assumption of a second process, independ ent of the first, which liberates energy at a rate also increasing with the temperature, but very much greater when the density is low than when it is high, so that, for stars of different mass, it would make income equal to outgo for points along such a line as shown in fig. 3.
If this process alone were in operation, stars of various masses would follow courses represented by etc., and concentration would ensue along a sequence including the red giants and the white dwarfs. With both processes at work at once the result is shown in fig. 4. A star of large mass, as it contracts, will turn on the second process first, and settle down as a red giant, at If, however, the material thus transform able were absent, or soon exhausted, it would proceed farther to the left and become a white giant at Ao. Less massive stars would settle down at and the latter drawing on both sub atomic processes at once. Still smaller masses would be sta bilized as yellow dwarfs at and red dwarfs at E., unless ma terial of the first sort were absent, when the latter would become a white dwarf at Star Clusters.—Suppose now that a great quantity of matter were broken up into masses of various sizes which started in dependent careers as stars. After a few millions, or tens of millions, of years, the points representing them would be found along the broken line (fig. 4)—all stages from red giants to red dwarfs being represented among stars of the same age in years. With the lapse of time the bright giant stars, which expend energy very rapidly, might exhaust the material of the second kind, and move over to the line or near it, while the relatively sluggish dwarf stars changed very little. This distribution of color and brightness would result at once if material of the second kind were absent. Now precisely these two situations are found among star clusters. (See R. J. Trump ler, Publications of the Astronomical Society of the Pacific, vol. xxxvii. pp. 307-318, 1925.) In some there is a group of bright red stars, near and others on the main series, while in others the branch A0' is represented.