The Story of Algol
This is a detective story, which we might call ‘The Missing Word and the False Clue’.
In astronomy, unlike many sciences, we cannot handle and probe the objects of our study; we have to wait passively and receive and decode the messages that they send to us. The whole of our information about the stars comes to us along rays of light; we watch and try to understand their signals. There are some stars which seem to be sending us a regular series of dots and dashes—like the intermittent light from a lighthouse. We cannot translate this as a morse code; nevertheless, by careful measurement we disentangle a great deal of information from the messages. The star Algol is the most famous of these ‘variable stars’. We learn from the signals that it is really two stars revolving round each other. Sometimes the brighter of the two stars is hidden, giving a deep eclipse or ‘dash’; sometimes the faint star is hidden, giving a ‘dot’. This recurs in a period of 2 days 21 hours—the period of revolution of the two stars.
There was a great deal more information in the message, but it was rather tantalizing. There was, so to speak, just one word missing. If we could supply that word the message would give full and accurate particulars as to the size of the system—the diameters and masses of the two components, their absolute brightness, the distance between them, their distance from the sun. Lacking the word the message told us nothing really definite about any of these things.
In these circumstances astronomers would scarcely have been human if they had not tried to guess the missing word. The word should have told us how much bigger the bright star was than the fainter, that is to say, the ratio of the masses of the two stars. Some of the less famous variable stars give us complete messages. (These could accordingly be used for testing the relation of mass and absolute brightness, and are represented by triangles in Fig. 7.) The difficulty about Algol arose from the excessive brightness of the bright component which swamped and made illegible the more delicate signals from the faint component. From the other systems we could find the most usual value of the mass ratio, and base on that a guess as to its probable value for Algol. Different authorities preferred slightly different estimates, but the general judgement was that in systems like Algol the bright component is twice as massive as the faint component. And so the missing word was assumed to be ‘two’; on this assumption the various dimensions of the system were worked out and came to be generally accepted as near the truth. That was sixteen years ago.9
In this way the sense of the message was made out to be that the brighter star had a radius of 1,100,000 kilometres (one and a half times the sun’s radius), that it had half the mass of the sun, and thirty times the sun’s light-power, &c. It will be seen at once that this will not fit our curve in Fig. 7; a star of half the sun’s mass ought to be very much fainter than the sun. It was rather disconcerting to find so famous a star protesting against the theory; but after all the theory is to be tested by comparison with facts and not with guesses, and the theory might well have a sounder basis than the conjecture as to the missing word. Moreover, the spectral type of Algol is one that is not usually associated with low mass, and this cast some suspicion on the accepted results.
If we are willing to trust the theory given in the last lecture we can do without the missing word. Or, to put it another way, we can try in succession various guesses instead of ‘two’ until we reach one that gives the bright component a mass and luminosity agreeing with the curve in Fig. 7. The guess ‘two’ gives, as we have seen, a point which falls a long way from the curve. Alter the guess to ‘three’ and recalculate the mass and brightness on this assumption; the corresponding point is now somewhat nearer to the curve. Continue with ‘four’, ‘five’, &c.; if the point crosses the curve we know that we have gone too far and must take an intermediate value in order to reach the desired agreement. This was done in November 1925, and it appeared that the missing word must be ‘five’, not ‘two’—a rather startling change. And now the message ran—
Radius of bright component = 2,140,000 kilometres.
Mass of bright component = 4·3 x sun’s mass.
If you compare these with the original figures you will see that there is a great alteration. The star is now assigned a large mass much more appropriate to a B-type star. It also turns out that Algol is more than a hundred times as bright as the sun; and its parallax is 0·028”—twice the distance previously supposed.
At the time there seemed little likelihood that these conclusions could be tested. Possibly the prediction as to the parallax might be proved or disproved by a trigonometrical determination; but it is so small as to be almost out of range of reasonably accurate measurement. We could only adopt a ‘take it or leave it’ attitude—‘If you accept the theory, this is what Algol is like; if you distrust the theory, these results are of no interest to you.’
But meanwhile two astronomers at Ann Arbor Observatory had been making a search for the missing word by a remarkable new method. They had in fact found the word and published it a year before, but it had not become widely known. If a star is rotating, one edge or ‘limb’ is coming towards us and the other going away from us. We can measure speeds towards us or away from us by means of the Doppler effect on the spectrum, obtaining a definite result in miles per second. Thus we can and do measure the equatorial speed of rotation of the sun by observing first the east limb then the west limb and taking the difference of velocity shown. That is all very well on the sun, where you can cover up the disk except the special part that you want to observe; but how can you cover up part of a star when a star is a mere point of light? You cannot; but in Algol the covering up is done for you. The faint component is your screen. As it passes in front of the bright star there is a moment when it leaves a thin crescent showing on the east and another moment when a thin crescent on the west is uncovered. Of course, the star is too far away for you actually to see the crescent shape, but at these moments you receive light from the crescents only, the rest of the disk being hidden. By seizing these moments you can make the measurements just as though you had manipulated the screen yourself. Fortunately the speed of rotation of Algol is large and so can be measured with relatively small error. Now multiply the equatorial velocity by the period of rotation;10 that will give you the circumference of Algol. Divide by 6·28, and you have the radius.
That was the method developed by Rossiter and McLaughlin. The latter who applied it to Algol found the radius of the bright component to be
2,180,000 kilometres.
So far as can be judged his result has considerable accuracy; indeed it is probable that the radius is now better known than that of any other star except the sun. If you will now turn back to p. 44 and compare it with the value found from the theory you will see that there is cause for satisfaction. McLaughlin evaluated the other constants and dimensions of the system; these agree equally well, but that follows automatically because there was only one missing word to be supplied. In both determinations the missing word or mass ratio turned out to be 5·0.
This is not quite the end of the story. Why had the first guess at the mass ratio gone so badly wrong? We understand by now that a disparity in mass is closely associated with a disparity in brightness of the two stars. The disparity in brightness was given in Algol’s original message; it informed us that the faint component gives about one-thirteenth of the light of the bright one. (At least that was how we interpreted it.) According to our curve this corresponds to a mass ratio 2½, which is not much improvement on the original guess 2. For a mass ratio 5 the companion ought to have been much fainter—in fact its light should have been undetectable. Although considerations like these could not have had much influence on the original guess, they seemed at first to reassure us that there was not very much wrong with it.
Let us call the bright component Algol A and the faint component Algol B. Some years ago a new discovery was made, namely Algol C. It was found that Algol A and B together travel in an orbit round a third star in a period of just under two years—at least they are travelling round in this period, and we must suppose that there is something present for them to revolve around. Hitherto we had believed that when Algol A was nearly hidden at the time of deepest eclipse all the remaining light must come from Algol B; but now it is clear that it belongs to Algol C, which is always shining without interference. Consequently the mass ratio 2½ is that of Algol A to Algol C. The light from Algol B is inappreciable as it should be for a mass ratio 5.[11]
The message from Algol A and B was confused, not only on account of the missing word, but because a word or two of another message from Algol C had got mixed up with it; so that even when the missing word was found to be ‘five’ and confirmed in two ways, the message was not quite coherent. In another place the message seemed to waver and read ‘two-and-a-half’. The finishing step is the discovery that ‘two-and-a-half’ belongs to a different message from a previously unsuspected star, Algol C. And so it all ends happily.
The best detective is not infallible. In this story our astronomical detective made a reasonable but unsuccessful guess near the beginning of the case. He might have seen his error earlier, only there was a false clue dropped by a third party who happened to be present at the crime, which seemed to confirm the guess. This was very unlucky. But it makes all the better detective story of it.