The theory of a steady star, which was described in the first lecture, can be extended to pulsating stars; and we can calculate the free period of pulsation for a star of assigned mass and density. You will remember that we have already calculated the heat emission or brightness and compared it with observation, obtaining one satisfactory test of the truth of the theory; now we can calculate the period of pulsation and by comparing it with observation obtain another test. Owing to lack of information as to a certain constant of stellar material there is an uncertainty in the calculation represented by a factor of about 2; that is to say, we calculate two periods, one double the other, between which with any reasonable luck the true period ought to lie. The observational confirmation is very good. There are sixteen Cepheid variables on which the test can be made; their periods range from 13 hours to 35 days, and they all agree with the calculated values to within the limits of accuracy expected. In a more indirect way the same confirmation is shown in [Fig. 7] by the close agreement of the squares, representing Cepheid variables, with the theoretical curve.
[The Cepheid as a ‘Standard Candle’]
Cepheid variables of the same period are closely similar to one another. A Cepheid of period 5⅓ days found in any part of the universe will be practically a replica of δ Cephei; in particular it will be a star of the same absolute brightness. This is a fact discovered by observation, and is not predicted by any part of the theory yet explored. The brightness, as we have seen, depends mainly on the mass; the period, on the other hand, depends mainly on the density; so that the observed relation between brightness and period involves a relation between mass and density. Presumably this relation signifies that for a given mass there is just one special density—one stage in the course of condensation of the star—at which pulsations are liable to occur; at other densities the star can only burn steadily.
This property renders the Cepheid extremely useful to astronomers. It serves as a standard candle—a source of known light-power.
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.