Stars and Atoms

Lecture Iii. the Age of the Stars 85

Pulsating Stars 85

The Cepheid as a ‘Standard Candle’ 90

The Contraction Hypothesis 94

Subatomic Energy 99

Evolution of the Stars 106

Radiation of Mass 113

APPENDIX

Further Remarks on the Companion of Sirius 122

LIST OF ILLUSTRATIONS

FIG.

1. The Sun. Hydrogen Spectroheliogram. (J. Evershed)

2. Solar Vortices. Hydrogen Spectroheliogram. (Mount Wilson Observatory)

3. Tracks of Alpha Particles (helium atoms). (C. T. R. Wilson)

4. Tracks of Beta Particles (electrons). (C. T. R. Wilson)

5. Ionization by X-rays. (C. T. R. Wilson)

6. Ions produced by Collision of a Beta particle. (C. T. R. Wilson)

7. The Mass-luminosity Curve.

8. The Ring Nebula in Lyra. Slitless Spectrogram. (W. H. Wright)

9. Flash Spectrum of Chromosphere showing Head of the Balmer Series. (British Eclipse Expedition, 14 Jan. 1926)

10. Solar Prominence. (British Eclipse Expedition, 29 May 1919)

11. Star Cluster ω Centauri. (Cape Observatory)

Lecture I

THE INTERIOR OF A STAR

THE sun belongs to a system containing some 3,000 million stars. The stars are globes comparable in size with the sun, that is to say, of the order of a million miles in diameter. The space for their accommodation is on the most lavish scale. Imagine thirty cricket balls roaming the whole interior of the earth; the stars roaming the heavens are just as little crowded and run as little risk of collision as the cricket balls. We marvel at the grandeur of the stellar system. But this probably is not the limit. Evidence is growing that the spiral nebulae are ‘island universes’ outside our own stellar system. It may well be that our survey covers only one unit of a vaster organization.

A drop of water contains several thousand million million million atoms. Each atom is about one hundred-millionth of an inch in diameter. Here we marvel at the minute delicacy of the workmanship. But this is not the limit. Within the atom are the much smaller electrons pursuing orbits, like planets round the sun, in a space which relatively to their size is no less roomy than the solar system.

Nearly midway in scale between the atom and the star there is another structure no less marvellous--the human body. Man is slightly nearer to the atom than to the star. About 10^{27} atoms build his body; about 10^{28} human bodies constitute enough material to build a star.

From his central position man can survey the grandest works of Nature with the astronomer, or the minutest works with the physicist. To-night I ask you to look both ways. For the road to a knowledge of the stars leads through the atom; and important knowledge of the atom has been reached through the stars.

* * * * *

The star most familiar to us is the sun. Astronomically speaking, it is close at hand. We can measure its size, weigh it, take its temperature, and so on, more easily than the other stars. We can take photographs of its surface, whereas the other stars are so distant that the largest telescope in the world does not magnify them into anything more than points of light. Figs. 1 and 2 show recent pictures of the sun’s surface. No doubt the stars in general would show similar features if they were near enough to be examined.

I must first explain that these are not the ordinary photographs. Simple photographs show very well the dark blotches called sunspots, but otherwise they are rather flat and uninteresting. The pictures here shown were taken with a spectroheliograph, an instrument which looks out for light of just one variety (wave-length) and ignores all the rest. The ultimate effect of this selection is that the instrument sorts out the different levels in the sun’s atmosphere and shows what is going on at one level, instead of giving a single blurred impression of all levels superposed. Fig. 2, which refers to a high level, gives a wonderful picture of whirlwinds and commotion. I think that the solar meteorologists would be likely to describe these vortices in terms not unfamiliar to us--‘A deep depression with secondaries is approaching, and a renewal of unsettled conditions is probable.’ However that may be, there is always one safe weather forecast on the sun; cyclone or anticyclone, the temperature will be very warm--about 6,000° in fact.

But just now I do not wish to linger over the surface layers or atmosphere of the sun. A great many new and interesting discoveries have recently been made in this region, and much of the new knowledge is very germane to my subject of ‘Stars and Atoms’. But personally I am more at home underneath the surface, and I am in a hurry to dive below. Therefore with this brief glance at the scenery that we pass we shall plunge into the deep interior--where the eye cannot penetrate, but where it is yet possible by scientific reasoning to learn a great deal about the conditions.

Temperature in the Interior

By mathematical methods it is possible to work out how fast the pressure increases as we go down into the sun, and how fast the temperature must increase to withstand the pressure. The architect can work out the stresses inside the piers of his building; he does not need to bore holes in them. Likewise the astronomer can work out the stress or pressure at points inside the sun without boring a hole. Perhaps it is more surprising that the temperature can be found by pure calculation. It is natural that you should feel rather sceptical about our claim that we know how hot it is in the very middle of a star--and you may be still more sceptical when I divulge the actual figures! Therefore I had better describe the method as far as I can. I shall not attempt to go into detail, but I hope to show you that there is a clue which might be followed up by appropriate mathematical methods.

I must premise that the heat of a gas is chiefly the energy of motion of its particles hastening in all directions and tending to scatter apart. It is this which gives a gas its elasticity or expansive force; the elasticity of a gas is well known to every one through its practical application in a pneumatic tyre. Now imagine yourself at some point deep down in the star where you can look upwards towards the surface or downwards towards the centre. Wherever you are, a certain condition of balance must be reached; on the one hand there is the weight of all the layers above you pressing downwards and trying to squeeze closer the gas beneath; on the other hand there is the elasticity of the gas below you trying to expand and force the superincumbent layers outwards. Since neither one thing nor the other happens and the star remains practically unchanged for hundreds of years, we must infer that the two tendencies just balance. At each point the elasticity of the gas must be just enough to balance the weight of the layers above; and since it is the heat which furnishes the elasticity, this requirement settles how much heat the gas must have. And so we find the degree of heat or temperature at each point.

The same thing can be expressed a little differently. As before, fix attention on a certain point in a star and consider how the matter above it is supported. If it were not supported it would fall to the centre under the attractive force of gravitation. The support is given by a succession of minute blows delivered by the particles underneath; we have seen that their heat energy causes them to move in all directions, and they keep on striking the matter above. Each blow gives a slight boost upwards, and the whole succession of blows supports the upper material in shuttlecock fashion. (This process is not confined to the stars; for instance, it is in this way that a motor car is supported by its tyres.) An increase of temperature would mean an increase of activity of the particles, and therefore an increase in the rapidity and strength of the blows. Evidently we have to assign a temperature such that the sum total of the blows is neither too great nor too small to keep the upper material steadily supported. That in principle is our method of calculating the temperature.

One obvious difficulty arises, The whole supporting force will depend not only on the activity of the particles (temperature) but also on the number of them (density). Initially we do not know the density of the matter at an arbitrary point deep within the sun. It is in this connexion that the ingenuity of the mathematician is required. He has a definite amount of matter to play with, viz. the known mass of the sun; so the more he uses in one part of the globe the less he will have to spare for other parts. He might say to himself, ‘I do not want to exaggerate the temperature, so I will see if I can manage without going beyond 10,000,000°.’ That sets a limit to the activity to be ascribed to each particle; therefore when the mathematician reaches a great depth in the sun and accordingly has a heavy weight of upper material to sustain, his only resource is to use large numbers of particles to give the required total impulse. He will then find that he has used up all his particles too fast, and has nothing left to fill up the centre. Of course his structure, supported on nothing, would come tumbling down into the hollow. In that way we can prove that it is impossible to build up a permanent star of the dimensions of the sun without introducing an activity or temperature exceeding 10,000,000°. The mathematician can go a step beyond this; instead of merely finding a lower limit, he can ascertain what must be nearly the true temperature distribution by taking into account the fact that the temperature must not be ‘patchy’. Heat flows from one place to another, and any patchiness would soon be evened out in an actual star. I will leave the mathematician to deal more thoroughly with these considerations, which belong to the following up of the clue; I am content if I have shown you that there is an opening for an attack on the problem.

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