How does Nature keep count of the 0’s? It seems clear that there must be something inside the star itself which keeps check and, so to speak, makes a warning protest as soon as the right amount of material has been gathered together. We think we know how it is done. You remember the ether waves inside the star. These are trying to escape outwards and they exert a pressure on the matter which is caging them in. This outward force, if it is sufficiently powerful to be worth considering in comparison with other forces, must be taken into account in any study of the equilibrium or stability of the star. Now in all small globes this force is quite trivial; but its importance increases with the mass of the globe, and it is calculated that at just about the above mass it reaches equal status with the other forces governing the equilibrium of the star. If we had never seen the stars and were simply considering as a curious problem how big a globe of matter could possibly hold together, we could calculate that there would be no difficulty up to about two thousand quadrillion tons; but beyond that the conditions are entirely altered and this new force begins to take control of the situation. Here, I am afraid, strict calculation stops, and no one has yet been able to calculate what the new force will do with the star when it does take control. But it can scarcely be an accident that the stars are all so near to this critical mass; and so I venture to conjecture the rest of the story. The new force does not prohibit larger mass, but it makes it risky. It may help a moderate rotation about the axis to break up the star. Consequently larger masses will survive only rarely; for the most part stars will be kept down to the mass at which the new force first becomes a serious menace. The force of gravitation collects together nebulous and chaotic material; the force of radiation pressure chops it off into suitably sized lumps.
This force of radiation pressure is better known to many people under the name ‘pressure of light’. The term ‘radiation’ comprises all kinds of ether-waves including light, so that the meaning is the same. It was first shown theoretically and afterwards verified experimentally that light exerts a minute pressure on any object on which it falls. Theoretically it would be possible to knock a man over by turning a searchlight on him—only the searchlight would have to be excessively intense, and the man would probably be vaporized first. Pressure of light probably plays a great part in many celestial phenomena. One of the earliest suggestions was that the minute particles forming the tail of a comet are driven outwards by the pressure of sunlight, thus accounting for the fact that a comet’s tail points away from the sun. But that particular application must be considered doubtful. Inside the star the intense stream of light (or rather X-rays) is like a wind rushing outwards and distending the star.
[The Interior of a Star]
We can now form some kind of a picture of the inside of a star—a hurly-burly of atoms, electrons, and ether-waves. Dishevelled atoms tear along at 100 miles a second, their normal array of electrons being torn from them in the scrimmage. The lost electrons are speeding 100 times faster to find new resting places. Let us follow the progress of one of them. There is almost a collision as an electron approaches an atomic nucleus, but putting on speed it sweeps round in a sharp curve. Sometimes there is a side-slip at the curve, but the electron goes on with increased or reduced energy. After a thousand narrow shaves, all happening within a thousand millionth of a second, the hectic career is ended by a worse side-slip than usual. The electron is fairly caught, and attached to an atom. But scarcely has it taken up its place when an X-ray bursts into the atom. Sucking up the energy of the ray the electron darts off again on its next adventure.
I am afraid the knockabout comedy of modern atomic physics is not very tender towards our aesthetic ideals. The stately drama of stellar evolution turns out to be more like the hair-breadth escapades on the films. The music of the spheres has almost a suggestion of—jazz.
And what is the result of all this bustle? Very little. The atoms and electrons for all their hurry never get anywhere; they only change places. The ether-waves are the only part of the population which accomplish anything permanent. Although apparently darting in all directions indiscriminately, they do on the average make a slow progress outwards. There is no outward progress of the atoms and electrons; gravitation sees to that. But slowly the encaged ether-waves leak outwards as through a sieve. An ether-wave hurries from one atom to another, forwards, backwards, now absorbed, now flung out again in a new direction, losing its identity, but living again in its successor. With any luck it will in no unduly long time (ten thousand to ten million years according to the mass of the star) find itself near the boundary. It changes at the lower temperature from X-rays to light-rays, being altered a little at each re-birth. At last it is so near the boundary that it can dart outside and travel forward in peace for a few hundred years. Perhaps it may in the end reach some distant world where an astronomer lies in wait to trap it in his telescope and extort from it the secrets of its birth-place.
It is the leakage that we particularly want to determine; and that is why we have to study patiently what is going on in the turbulent crowd. To put the problem in another form; the waves are urged to flow out by the temperature gradient in the star, but are hindered and turned back by their adventures with the atoms and electrons. It is the task of mathematics, aided by the laws and theories developed from a study of these same processes in the laboratory, to calculate the two factors—the factor urging and the factor hindering the outward flow—and hence to find the leakage. This calculated leakage should, of course, agree with astronomical measurements of the energy of heat and light pouring out of the star. And so finally we arrive at an observational test of the theories.
[Opacity of Stellar Matter]
Let us consider the factor which hinders the leakage—the turning back of the ether-waves by their encounters with atoms and electrons. If we were dealing with light waves we should call this obstruction to their passage ‘opacity’, and we may conveniently use the same term for obstruction to X-rays.
We soon realize that the material of the star must be decidedly opaque. The quantity of radiation in the interior is so great that unless it were very severely confined the leakage would be much greater than the amount which we observe coming out of the stars. The following is an illustration of the typical degree of opacity required to agree with the observed leakage. Let us enter the star Capella and find a region where the density is the same as that of the atmosphere around us;[5] a slab of the material only two inches thick would form a screen so opaque that only one-third of the ether-waves falling on one side would get through to the other side, the rest being absorbed in the screen. A foot or two of the material would be practically a perfect screen. If we are thinking of light-waves this seems an astonishing opacity for material as tenuous as air; but we have to remember that it is an opacity to X-rays, and the practical physicist knows well the difficulty of getting the softer kinds of X-rays to pass through even a few millimetres of air.