Part 7
In an ordinary way you cannot tell the _real_ brightness of a light merely by looking at it. If it appears dim, that may mean either real faintness or great distance. At night time on the sea you observe many lights whose distance and real brightness you cannot estimate; your judgement of the real brightness may be wrong by a factor of a quintillion if you happen to mistake Arcturus for a ship’s light. But among them you may notice a light which goes through a regular series of changes in a certain number of seconds; that tells you that it is such-and-such a lighthouse, known to project a light of so many thousand candlepower. You may now estimate with certainty how far off it is--provided, of course, that there is no fog intervening.
So, too, when we look up at the sky, most of the lights that we see might be at any distance and have any real brightness. Even the most refined measurements of parallax only succeed in locating a few of the nearer lights. But if we see a light winking in the Cepheid manner with a period of 5⅓ days, we know that it is a replica of δ Cephei and is a light of 700 sun-power. Or if the period is any other number of days we can assign the proper sun-power for that period. From this we can judge the distance. The apparent brightness, which is a combination of distance and true brightness, is measured; then it is a simple calculation to answer the question, At what distance must a light of 700 sun-power be placed in order to give the apparent brightness observed? How about interference by fog? Careful discussions have been made, and it appears that notwithstanding the cosmical cloud in interstellar space there is ordinarily no appreciable absorption or scattering of the starlight on its way to us.
With the Cepheids serving as standard candles distances in the stellar universe have been surveyed far exceeding those reached by previous methods. If the distances were merely those of the Cepheid variables themselves that would not be so important, but much more information is yielded.
Fig. 11[26] shows a famous star-cluster called ω Centauri. Amongst the thousands of stars in the cluster no less than 76 Cepheid variables have been discovered. Each is a standard candle serving to measure the distance primarily of itself but also incidentally of the great cluster in which it lies. The 76 gauges agree wonderfully among themselves, the average deviation being less than 5 per cent. By this means Shapley found the distance of the cluster to be 20,000 light years. The light messages which we receive to-day were sent from the cluster 20,000 years ago.[27]
The astronomer, more than other devotees of science, learns to appreciate the advantage of not being too near the objects he is studying. The nearer stars are all right in their way, but it is a great nuisance being in the very midst of them. For each star has to be treated singly and located at its proper distance by elaborate measurements; progress is very laborious. But when we determine the distance of this remote cluster, we secure at one scoop the distances of many thousands of stars. The distance being known, the apparent magnitudes can be turned into true magnitudes, and statistics and correlations of absolute brightness and colour can be ascertained. Even before the distance is discovered we can learn a great deal from the stars in clusters which it is impracticable to find out from less remote stars. We can see that the Cepheids are much above the average brightness and are surpassed by relatively few stars. We can ascertain that the brighter the Cepheid the longer is its period. We discover that the brightest stars of all are red.[28] And so on. There is a reverse side to the picture; the tiny points of light in the distant cluster are not the most satisfactory objects to measure and analyse, and we could ill spare the nearer stars; but the fact remains that there are certain lines of stellar investigation in which remoteness proves to be an actual advantage, and we turn from the nearer stars to objects fifty thousand light years away.
About 80 globular clusters are known with distances ranging from 20,000 to 200,000 light years. Is there anything yet more remote? It has long been suspected that the spiral nebulae,[29] which seem to be exceedingly numerous, are outside our stellar system and form ‘island universes’. The evidence for this has become gradually stronger, and now is believed to be decisively confirmed. In 1924 Hubble discovered a number of Cepheid variables in the great Andromeda nebula which is the largest and presumably one of the nearest of the spirals. As soon as their periods had been determined they were available as standard candles to gauge the distance of the nebula. Their apparent magnitude was much fainter than that of the corresponding Cepheids in globular clusters, showing that they must be even more remote. Hubble has since found the distance of one or two other spirals in the same way.
With the naked eye you can see the Andromeda nebula as a faint patch of light. When you look at it you are looking back 900,000 years into the past.
_The Contraction Hypothesis_
The problem of providing sufficient supplies of energy to maintain the sun’s output of light and heat has often been debated by astronomers and others. In the last century it was shown by Helmholtz and Kelvin that the sun could maintain its heat for a very long time by continually shrinking. Contraction involves an approach or fall of the matter towards the centre; gravitational potential energy is thus converted and made available as heat. It was assumed that this was the sole resource since no other supply capable of yielding anything like so large an amount was known. But the supply is not unlimited, and on this hypothesis the birth of the sun must be dated not more than 20,000,000 years ago. Even at the time of which I am speaking the time-limit was found to be cramping; but Kelvin assured the geologists and biologists that they must confine their outlines of terrestrial history within this period.
About the beginning of the present century the contraction theory was in the curious position of being generally accepted and generally ignored. Whilst few ventured to dispute the hypothesis, no one seems to have had any hesitation, if it suited him, in carrying back the history of the earth or moon to a time long before the supposed era of the formation of the solar system. Lord Kelvin’s date of the creation was treated with no more respect than Archbishop Ussher’s.
The serious consequences of the hypothesis become particularly prominent when we consider the diffuse stars of high luminosity; these are prodigal of their energy and squander it a hundred or a thousand times faster than the sun. The economical sun could have subsisted on its contraction energy for 20,000,000 years, but for the high luminosity stars the limit is cut down to 100,000 years. This includes most of the naked-eye stars. Dare we believe that they were formed within the last 100,000 years? Is the antiquity of man greater than that of the stars now shining? Do stars in the Andromeda nebula run their course in less time than their light takes to reach us?
It is one thing to feel a limitation of time-scale irksome, ruling out ideas and explanations which are otherwise plausible and attractive; it is another thing to produce definite evidence against the time-scale. I do not think that astronomers had _in their own territory_ any weapon for a direct attack on the Helmholtz-Kelvin hypothesis until the Cepheid variables supplied one. To come to figures: δ Cephei emits more than 700 times as much heat as the sun. We know its mass and radius, and we can calculate without difficulty how fast the radius must contract in order to provide this heat. The required rate is one part in 40,000 per annum. Now δ Cephei was first observed carefully in 1785, so that in the time it has been under observation the radius must have changed by one part in 300 if the contraction hypothesis is right. You remember that we have in δ Cephei a very sensitive indicator of any changes occurring in it, viz. the period of pulsation; clearly changes of the above magnitude could not occur without disturbing this indicator. Does the period show any change? It is doubtful; there is perhaps sufficient evidence for a slight change, but it is not more than ¹⁄₂₀₀th of the change demanded by the contraction hypothesis.
Accepting the pulsation theory, the period should diminish 17 seconds every year--a quantity easily detectable. The actual change is not more than one-tenth of a second per year. At least during the Cepheid stage the stars are drawing on some source of energy other than that provided by contraction.
On such an important question we should not like to put implicit trust in one argument alone, and we turn to the sister sciences for other and perhaps more conclusive evidence. Physical and geological investigations seem to decide definitely that the age of the earth--reckoned from an epoch which by no means goes back to its beginnings as a planet--is far greater than the Helmholtz-Kelvin estimate of the age of the solar system. It is usual to lay most stress on a determination of the age of the rocks from the uranium-lead ratio of their contents. Uranium disintegrates into lead and helium at a known rate. Since lead is unlike uranium in chemical properties the two elements would not naturally be deposited together; so that the lead found with uranium has presumably been formed by its decomposition.[30] By measuring how much lead occurs with the uranium we can determine how long ago the uranium was deposited. The age of the older rocks is found to be about 1,200 million years; lower estimates have been urged by some authorities, but none low enough to save the contraction hypothesis. The sun, of course, must be very much older than the earth and its rocks.
We seem to require a time-scale which will allow at least 10,000,000,000 years for the age of the sun; certainly we cannot abate our demands below 1,000,000,000 years. It is necessary to look for a more prolific source of energy to maintain the heat of the sun and stars through this extended period. We can at once narrow down the field of search. No source of energy is of any avail unless it liberates heat in the deep interior of the star. The crux of the problem is not merely the provision for radiation but the maintenance of the internal heat which keeps the gravitating mass from collapsing. You will remember how in the first lecture we had to assign a certain amount of heat at each point in the stellar interior in order to keep the star in balance. But the internal heat is continually running away towards the cooler outside and then escaping into space as the star’s radiation. This, or its equivalent, must be put back if the star is to be kept steady--if it is not to contract and evolve at the rate of the Kelvin time-scale. And it is no use to put it back at the surface of the star--by bombarding the star with meteors, for example. It could not flow up the temperature-gradient, and so it would simply take the first opportunity of escaping as additional radiation. You cannot maintain a temperature-gradient by supplying heat at the bottom end. Heat must be poured in at the top end, i. e. in the deep interior of the star.
Since we cannot well imagine an extraneous source of heat able to release itself at the centre of a star, the idea of a star picking up energy as it goes along seems to be definitely ruled out. _It follows that the star contains hidden within it the energy which has to last the rest of its life_.
Energy has mass. Many people would prefer to say--energy _is_ mass; but it is not necessary for us to discuss that. The essential fact is that an erg of energy in any form has a mass of 1·1. 10^-21 grammes. The erg is the usual scientific unit of energy; but we can measure energy also by the gramme or the ton as we measure anything else which possesses mass. There is no real reason why you should not buy a pound of light from an electric light company--except that it is a larger quantity than you are likely to need and at current rates would cost you something over £100,000,000. If you could keep all this light (ether-waves) travelling to and fro between mirrors forming a closed vessel, and then weigh the vessel, the observed weight would be the ordinary weight of the vessel plus 1 lb. representing the weight of the light. It is evident that an object weighing a ton cannot contain more than a ton of energy; and the sun with a mass of 2.000 quadrillion tons (p. 24) cannot contain more than 2.000 quadrillion tons of energy at the most.
Energy of 1·8. 10^{54} ergs has a mass 2. 10^{33} grammes which is the mass of the sun; consequently that is the sum total of the energy which the sun contains--the energy which has to last it all the rest of its life.[31] We do not know how much of this is capable of being converted into heat and radiation; if it is all convertible there is enough to maintain the sun’s radiation at the present rate for 15 billion years. To put the argument in another form, the heat emitted by the sun each year has a mass of 120 billion tons; and if this loss of mass continued there would be no mass left at the end of 15 billion years.
_Subatomic Energy_
This store of energy is, with insignificant exception, energy of constitution of atoms and electrons; that is to say, subatomic energy. Most of it is inherent in the constitution of the electrons and protons--the elementary negative and positive electric charges--out of which matter is built; so that it cannot be set free unless these are destroyed. The main store of energy in a star cannot be used for radiation unless the matter composing the star is being annihilated.
It is possible that the star may have a long enough life without raiding the main energy store. A small part of the store can be released by a process less drastic than annihilation of matter, and this might be sufficient to keep the sun burning for 10,000,000,000 years or so, which is perhaps as long as we can reasonably require. The less drastic process is transmutation of the elements. Thus we have reached a point where a choice lies open before us; we can either pin our faith to transmutation of the elements, contenting ourselves with a rather cramped time-scale, or we can assume the annihilation of matter, which gives a very ample time-scale. But at present I can see no possibility of a third choice. Let me run over the argument again. First we found that energy of contraction was hopelessly inadequate; then we found that the energy must be released in the interior of the star, so that it comes from an internal, not an external, source; now we take stock of the whole internal store of energy. No supply of any importance is found until we come to consider the electrons and atomic nuclei; here a reasonable amount can be released by regrouping the protons and electrons in the atomic nuclei (transmutation of elements), and a much greater amount by annihilating them.
Transmutation of the elements--so long the dream of the alchemist--is realized in the transformation of radio-active substances. Uranium turns slowly into a mixture of lead and helium. But none of the known radio-active processes liberate anything like enough energy to maintain the sun’s heat. The only important release of energy by transmutation occurs at the very beginning of the evolution of the elements.
We must start with hydrogen. The hydrogen atom consists simply of a positive and negative charge, a proton for the nucleus plus a planet electron. Let us call its mass 1. Four hydrogen atoms will make a helium atom. If the mass of the helium atom were exactly 4, that would show that all the energy of the hydrogen atoms remained in the helium atom. But actually the mass is 3·97; so that energy of mass a 0·03 must have escaped during the formation of helium from hydrogen. By annihilating 4 grammes of hydrogen we should have released 4 grammes of energy, but by transmuting it into helium we release 0·03 grammes of energy. Either process might be used to furnish the sun’s heat though, as we have already stated, the second gives a much smaller supply.
The release of energy occurs because in the helium atom only two of the four electrons remain as planet electrons, the other two being cemented with the four protons close together in the helium nucleus. In bringing positive and negative charges close together you cause a change of the energy of the electric field, and release electrical energy which spreads away as ether-waves. That is where the 0·03 grammes of energy has gone. The star can absorb these ether-waves and utilize them as heat.
We can go on from helium to higher elements, but we do not obtain much more release of energy. For example, an oxygen atom can be made from 16 hydrogen atoms or 4 helium atoms; but as nearly as we can tell it has just the weight of the 4 helium atoms, so that the release of energy is not appreciably greater when the hydrogen is transmuted into oxygen than when it is transmuted into helium.[32] This becomes clearer if we take the mass of a hydrogen atom to be 1·008, so that the mass of helium is exactly 4 and of oxygen 16; then it is known from Dr. Aston’s researches with the mass-spectrograph that the atoms of other elements have masses which are very closely whole numbers. The loss of 0·008 per hydrogen atom applies approximately whatever the element that is formed.
The view that the energy of a star is derived by the building up of other elements from hydrogen has the great advantage that there is no doubt about the possibility of the process; whereas we have no evidence that the annihilation of matter can occur in Nature. I am not referring to the alleged transmutation of hydrogen into helium in the laboratory; those whose authority I accept are not convinced by these experiments. To my mind the existence of helium is the best evidence we could desire of the possibility of the _formation_ of helium. The four protons and two electrons constituting its nucleus must have been assembled at some time and place; and why not in the stars? When they were assembled the surplus energy must have been released, providing a prolific supply of heat. Prima facie this suggests the interior of a star as a likely locality, since undoubtedly a prolific source of heat is there in operation. I am aware that many critics consider the conditions in the stars not sufficiently extreme to bring about the transmutation--the stars are not hot enough. The critics lay themselves open to an obvious retort; we tell them to go and find a _hotter place_.
But here the advantage seems to end. There are many astronomical indications that the hypothesis attributing the energy of the stars to the transmutation of hydrogen is unsatisfactory. It may perhaps be responsible for the rapid liberation of energy in the earliest (giant) stages when the star is a large diffuse body radiating heat abundantly; but the energy in later life seems to come from a source subject to different laws of emission. There is considerable evidence that as a star grows older it gets rid of a large fraction of the matter which originally constituted it, and apparently this can only be contrived by the annihilation of the matter. The evidence, however, is not very coherent, and I do not think we are in a position to come to a definite decision. On the whole the hypothesis of annihilation of matter seems the more promising; and I shall prefer it in the brief discussion of stellar evolution which I propose to give.
The phrase ‘annihilation of matter’ sounds like something supernatural. We do not yet know whether it can occur naturally or not, but there is no obvious obstacle. The ultimate constituents of matter are minute positive charges and negative charges which we may picture as centres of opposite kinds of strain in the ether. If these could be persuaded to run together they would cancel out, leaving nothing except a splash in the ether which spreads out as an electromagnetic wave carrying off the energy released by the undoing of the strain. The amount of this energy is amazingly large; by annihilating a single drop of water we should be supplied with 200 horsepower for a year. We turn covetous eyes on this store without, however, entertaining much hope of ever discovering the secret of releasing it. If it should prove that the stars have discovered the secret and are using this store to maintain their heat, our prospect of ultimate success would seem distinctly nearer.
I suppose that many physicists will regard the subject of subatomic energy as a field of airy speculation. That is not the way in which it presents itself to an astronomer. If it is granted that the stars evolve much more slowly than on the contraction-hypothesis, the measurement of the output of subatomic energy is one of the commonest astronomical measurements--the measurement of the heat or light of the stars.[33] The collection of observational data as to the activity of liberation of subatomic energy is part of the routine of practical astronomy; and we have to pursue the usual course of arranging the measurements into some kind of coherence, so as to find out how the output is related to the temperature, density, or age of the material supplying it--in short, to discover the laws of emission. From this point onwards the discussion may be more or less hypothetical according to the temperament of the investigator; and indeed it is likely that in this as in other branches of knowledge advances may come by a proper use of the scientific imagination. Vain speculation is to be condemned in this as in any other subject, and there is no need for it; the problem is one of induction from observation with due regard to our theoretical knowledge of the possibilities inherent in atomic structure.
I cannot pass from this subject without mentioning the penetrating radiation long known to exist in our atmosphere, which according to the researches of Kohlhörster and Millikan comes from outer space. Penetrating power is a sign of short wave-length and intense concentration of energy. Hitherto the greatest penetrating power has been displayed by Gamma rays originated by subatomic processes occurring in radio-active substances. The cosmic radiation is still more penetrating, and it seems reasonable to refer it to more energetic processes in the atom such as those suggested for the source of stellar energy. Careful measurements have been made by Millikan, and he concludes that the properties accord with those which should be possessed by radiation liberated in the transmutation of hydrogen; it is not penetrating enough to be attributed to a process so energetic as the annihilation of protons and electrons.