Part 10

A careful examination of these variations shows us a very remarkable feature. On a preliminary study, the period will seem to be six and one-half days. But, comparing the alternate minima, we shall find them unequal. Hence the actual period is thirteen days. In this period there are two unequal minima, separated by equal maxima. That is to say, the partial eclipses at intervals of six and one-half days are not equal. At the alternate minima the star is half as bright again as at the intermediate minima.

It is impossible to explain such a change as this merely by the interposition of a dark body, and this for two reasons. Instead of remaining invariable between the minima, the variation is continuous during the whole period, like the rising and falling of a tide. Moreever, the inequality of the alternating minima is against the theory.

Pickering, however, found from the doubling of the spectral lines that there were two stars revolving round each other. Then Prof. G. W. Myers, of Indiana, worked out a very elaborate mathematical theory to explain the variations, which is not less remarkable for its ingenuity than for the curious nature of the system it brings to light. His conclusions are these:

Beta Lyræ consists of two bodies, gaseous in their nature, which revolve round each other, so near as to be almost touching. They are of unequal size. Both are self-luminous. By their mutual attraction they are drawn out into ellipsoids. The smaller body is somewhat darker than the other. When we see the two bodies laterally, they are at their brightest. As they revolve, however, we see them more and more end on, and thus the light diminishes. At a certain point one begins to cover the other and hide its light. Thus the combined light continues to diminish until the two bodies move across our line of sight. Then we have a minimum. At one minimum, however, the smaller and darker of the two bodies is projected upon the brighter one, and thus diminishes its light. At the other minimum, it is hiding behind the other, and therefore we see the light of the larger one alone.

This theory receives additional confirmation from the fact, shown by the spectroscope, that these stars are either wholly gaseous, or at least have self-luminous atmospheres. Some of Professor Myers’s conclusions respecting the magnitudes are summarized as follows:

The larger body is about 0.4 as bright as the smaller.

The flattening of the ellipsoidal masses is about 0.17.

The distance of centers is about 1-7/8 the semi-major axis of the larger star, or about 50,000,000 kilometers (say 30,000,000 miles).

The mass of the larger body is about twice that of the smaller, and 9½ times the mass of the sun.

The mean density of the system is a little less than that of air.[F]

[F] ‘Astrophysical Journal’, Vol. VII, January, 1898.

It should be remarked that these numbers rest on spectroscopic results, which need further confirmation. They are, therefore, liable to be changed by subsequent investigation. What is most remarkable is that we have here to deal with a case to which we have no analogy in our solar system, and which we should never have suspected, had it not been for observations of this star.

The gap between the variable stars of the Algol type and those of the Beta Lyræ type is, at the present time, being filled by new discoveries in such a way as to make a sharp distinction of the two classes difficult. It is characteristic of the Algol type proper that the partial eclipses are due to the interposition of a dark planet revolving round the bright star. But suppose that we have two nearly equal stars, _A_ and _B_, revolving round their common center of gravity in a plane passing near our system. Then, _A_ will eclipse _B_, and, half a revolution later, _B_ will eclipse _A_, and so on in alternation. But, when the stars are equal, we may have no way of deciding which is being eclipsed, and thus we shall have a star of the Algol type, so far as the law of variation is concerned, yet, as a matter of fact, belonging rather to the Beta Lyræ type. If the velocity in the line of sight could be measured, the question would be settled at once. But only the brightest stars can, so far, be thus measured, so that the spectroscope cannot help us in the majority of cases.

The most interesting case of this kind yet brought to light is that of Tau Cygni. The variability of this star, ordinarily of the fourth magnitude, was discovered by Chandler in December, 1886. The minima occurred at intervals of three days. But in the following summer he found an apparent period of 1 d. 12 h., the alternate minima being invisible because they occurred during daylight, or when the star was below the horizon. With this period the times of minima during the summer of 1888 were predicted.

It was then found that the times of the alternate minima, which, as we have just said, were the only ones visible during any one season, did not correspond to the prediction. The period seemed to have greatly changed. Afterward, it seemed to return to its old value. After puzzling changes of this sort, the tangle was at length unraveled by Dunér, of Lund, who showed that the alternate periods were unequal. The intervals between minima were one day nine hours, one day fifteen hours, one day nine hours, one day fifteen hours, and so on, indefinitely. This law once established, the cause of the anomaly became evident. Two bright stars revolve round their common center of gravity in a period of nearly three days. Each eclipses the other in alternation. The orbit is eccentric, and, in consequence, one-half of it is described in a less time than the other half. If we could distinguish the two stars by telescopic vision, and note their relative positions at the four cardinal points of their orbit, we should see the pair alternately single and double, as shown in the following diagrams:

A B Position (1), stars at pericenter * * Interval, 16 hours.

Position (2), A eclipses B * Interval, 20 hours.

B A Position (3), stars at apocenter * * Interval, 20 hours.

Position (4), B eclipses * Interval, 16 hours.

Position (1) is repeated * *

_U_ Pegasi is a star which proved as perplexing as Tau Cygni. It was first supposed to be of the Algol type, with a period of about two days. Then it was found that a number of minima occurred during this period, and that the actual interval between them was only a few hours. The great difficulty in the case arises from the minuteness of the variation, which is but little more than half a magnitude between the extremes. The observations of Wendell, at the Harvard Observatory, with the polarizing photometer, enabled Pickering to reach a conclusion which, though it may still be open to some doubt, seems to be the most likely yet attainable. The star is of the Beta Lyræ type; its complete period is 8 hours 59 minutes 41 seconds, or 19 seconds less than nine hours; during this period it passes through two equal maxima, each of magnitude 9.3, and two unequal minima 9.76 and 9.9, alternately.

The difference of these minima, 0m. 14, is less than the errors which really ordinarily affect measures of a star’s magnitude with the best photometers. Some skepticism has, therefore, been felt as to the reality of the difference which, if it does not exist, would reduce the periodic time below four and one-half hours, the shortest yet known. But Pickering maintains that, in observations of this kind upon a single star, the precision is such that the reality of the difference, small though it be, is beyond reasonable doubt.

Taking Pickering’s law of change as a basis, Myers has represented the light-curve of _U_ Pegasi on a theory similar to that which he constructed for Beta Lyræ. His conclusion is that, in the present case, the two bodies which form the visible star are in actual contact. A remarkable historic feature of the case is that Poincaré has recently investigated, by purely mathematical methods, the possible forms of revolving fluid masses in a condition of equilibrium, bringing out a number of such forms previously unknown. One of these, which he calls the apiodal form, consists of two bodies joined into one, and it is this which Myers finds for _U_ Pegasi.

Quite similar to these two cases is that of Zeta Herculis. This star, ordinarily of the seventh magnitude, was found, at Potsdam, in 1894, to diminish by about one magnitude. Repeated observations elsewhere indicate a period of very nearly four days. Actually it is now found to be only ten minutes less than four days. The result was that during any one season of observation the minima occur at nearly the same hour every night or day. To an observer situated in such longitude that they occur during the day, they would, of course, be invisible.

Continued observations then showed a secondary minimum, occurring about half-way between the principal minima hitherto observed. It was then found that these secondary minima really occur between one and two hours earlier than the mid-moment, so that the one interval would be between forty-six and forty-seven hours and the other between forty-nine and fifty. The time which it takes the star to lose its light and regain it again is about ten hours. More recent observations, however, do not show this inequality, so that there is probably a rapid motion of the pericenter of the orbit.

It will be seen that this star combines the Algol and Beta Lyræ types. It is an Algol star in that its light remains constant between the eclipses. It is of the Beta Lyræ type in the alternate minima being unequal.

From a careful study, Seliger and Hartwig derived the following particulars respecting this system:

Diameter of principal star, 15,000,000 kilometers. Diameter of smaller star, 12,000,000 kilometers. Mass of the larger star, 172 times sun’s mass. Mass of the smaller star, 94 times sun’s mass. Distance of centers, 45,000,000 kilometers. Time of revolution, 3d. 23h. 49m. 32.7s.

It must be added that the data for these extraordinary numbers are rather slender and partly hypothetical.

Beta Lyræ is always of the same brightness at the same hour of its period, and Algol has always the same magnitude at minimum. It is true that the length of the period varies slowly in the case of these stars. But this may arise from the action of other invisible bodies revolving around the visible stars. This general uniformity is in accord with the theory which attributes the apparent variations to the various aspects in which we see one and the same system of revolving stars.

Another variable star showing some unique features is Eta Aquilæ. What gives it special interest is that spectroscopic observations of its radial motion show it to have a dark body revolving round it in a very eccentric orbit, and in the same time as the period of variation. It might therefore be supposed that we have here a star of the Algol or Beta Lyræ type. But such is not the case. There is nothing in the law of variation to suggest an eclipsing of the bright star, nor does it seem that the variations can readily be represented by the varying aspects of any revolving system.

The orbit of this star has been exhaustively investigated by Wright from Campbell’s observations of the radial motion. The laws of change in the system are shown by the curves below, which are reproduced, in great part, from Wright’s paper in the ‘Astrophysical Journal.’

The lower curve is the light-curve of the star during a period of 7.167 days. Starting from a maximum of 3.5 mag., it sinks, in the course of 5 days, to a minimum of 4.7m. It was found by Schwab that the diminution is not progressive, but that a secondary maximum of 3.8m. is reached at the end of the second day. After reaching the principal minimum it rises rapidly to the principal maximum in 2¼ days.

The upper curve shows the radial velocity of the star during the period of variation. It will be seen that the epoch of greatest negative velocity, which referred to the center of mass of the system, is 16.2 km. per second, occurs at the time of maximum brightness. The greatest positive velocity, 23.9 km., occurs during the sixth day of the period just after the time of minimum brightness.

Finally, the moments of inferior and superior conjunction of the dark body with the bright one are neither of them an epoch of minimum brightness, which takes place half-way between the two.

The most plausible conclusion we can draw is that the light of the star is affected by the action of the dark body during its revolution. But how the change may be produced we cannot yet say.

CLASSIFICATION OF VARIABLE STARS.

A classification of variable stars, based on the period of variation and the law of change, was proposed by Pickering. It does not, however, seem that a hard and fast line can yet be drawn between different types and classes of these bodies, one type running into another, as we have found in the case of the Algol and Beta Lyræ types. Yet the discovery of the cause of the variation in these types makes it likely that a division into two great classes, dependent on the cause of variation, is possible. We should then have:

(1) Stars, or systems, constituting to vision a single star, of which the apparent variability arises from the rotation of the system as a whole, or from the revolution of its components around each other.

(2) Stars of which the changes arise from other and as yet unknown causes.

The main feature of the stars of the first class is that we are under no necessity of supposing any actual change in the amount of light which they emit. Their apparent variations are purely the effect of perspective, arising from the various aspects which they present to us during their revolution round each other. If we could change our point of view so that the plane of the orbit of Algol’s planet no longer passed near our system, Algol would no longer be a variable star. Under the same circumstances the apparent variations in a star of the Beta Lyræ type would cease to be noticeable, if they did not disappear entirely.

The stars of this class are also distinguished by the uniformity and regularity with which they go through their cycle of change.

The stars of the other class, which we may call the Omicron Ceti type, are different not only in respect to the length of the period, but in the character of the variation. There are certain general laws of variation and irregularities of brightness which stars of this class go through. Starting from the time of the minimum, the increase of light is at first very slow. It grows more and more rapid as the maximum is approached, in which time there may be as great an increase in two or three days as there formerly was in a month. The diminution of light is generally slower than the increase. The magnitude at corresponding times in different periods may be very different. Thus, as we have already remarked, Omicron Ceti is ten times as bright at some maxima as it is at others. The periods also, so far as they have been made out, vary more widely than those of stars of the other type.

The idea has sometimes been entertained that these variations of light are due to a revolution of the star on its axis. A very little consideration will, however, show that this explanation cannot be valid. However bright a star might be on one side, or however dark on the other, any one region of its surface would be visible to us half the time and a change of brightness from different degrees of brilliancy on different sides would be gradual and regular.

It is not impossible that the variability may be in some way connected with the action of a body revolving round the star. This seems to be the case with Eta Aquilæ. The radial motion of this object shows the existence of a dark body revolving round it in the same period as that of the star’s variation.

From what has been said, it will be seen that, although a sharp line cannot be drawn, there seems to be some distinction between the stars of short and long periods. The number of stars which have been known to belong to the first class is quite small, only about fifteen, all told. On the other hand, there are still left some stars having a period less than ten days, which are otherwise not distinguishable from the Omicron Ceti type. It seems quite likely that the variations in the periods of these stars are, in some way, connected with the revolution of bright or dark bodies round them.

They also vary more widely than those of stars of the other two types. This might easily happen in the case of stars really variable through a cycle of changes going on in consequence of the action of interior causes.

The periodic stars of short period, which have not been recognized as of the Algol or Beta Lyræ type, form an interesting subject of study. Although the separation between them and the stars of long period is not sharp, it seems likely to have some element of reality in it. But no conclusions on the subject can be reached until the light-curves of a large number of them are carefully drawn; and this requires an amount of patient and accurate observation which cannot be carried out for years to come.

SUSPECTED VARIATIONS IN THE COLOR OF STARS.

The question whether certain stars vary in color without materially changing their brightness has sometimes been raised. This was at one time supposed to be the case with one of the stars of Ursa Major. This suspected variation has not, however, been confirmed, and it does not seem likely that any such changes take place in the color of stars not otherwise variable.

POSSIBLE SECULAR VARIATIONS IN THE BRILLIANCY OF STARS.

All the variations we have hitherto considered take place with such rapidity that they can be observed by comparisons embracing but a short interval of time--a few days or months at the outside. A somewhat different question of great importance is still left open. May not individual stars be subject to a secular variation of brilliancy, meaning by this term a change which would not be sensible in the course of only one generation of men, but admitting of being brought out by a comparison of the brightness of the stars at widely distant epochs? Is it certain that, in the case of stars which we do not recognize as variable, no change has taken place since the time of Hipparchus and Ptolemy? This question has been investigated by C. S. Pierce and others. The conclusion reached is that no real evidence of any change can be gathered. The discrepancies are no greater than might arise from errors of estimates.

There is, however, an analogous question which is of great interest and has been much discussed in recent times. In several ancient writings the color of Sirius is described as red. This fact would, at first sight, appear to afford very strong evidence that, within historic times, the color of the brightest star in the heavens has actually changed from red to a bluish white.

Two recent writers have examined the evidence on this subject most exhaustively and reached opposite conclusions. The first of these was Dr. T. J. J. See, who collated a great number of cases in which Sirius was mentioned by ancient writers as red or fiery, and thus concluded that the evidence was in favor of a red color in former times. Shortly afterwards, Schiaparelli examined the evidence with equal care and thoroughness and reached an opposite conclusion, showing that the terms used by the ancient authors, which might have indicated redness of color, were susceptible of other interpretations; they might mean fiery, blazing, etc., as well as red in color, and were therefore probably suggested by the extraordinary brightness of Sirius and the strangeness with which it twinkled when near the horizon. In this position a star not only twinkles, but changes its color rapidly. This change is not sensible in the case of a faint star, but if one watches Sirius when on the horizon, it will be seen that it not only changes in appearance, but seems to blaze forth in different colors.

It seems to the writer that this conclusion of Schiaparelli is the more likely of the two. From what we know of the constitution of the stars, a change in the color of one of these bodies in so short a period of time as that embraced by history is so improbable as to require much stronger proofs than any that can be adduced from ancient writers. In addition to the possible vagueness or errors of the original writers, we have to bear in mind the possible mistakes or misinterpretations of the copyists who reproduced the manuscripts.

THE PARALLAXES OF THE STARS.

It needs only the most elementary conceptions of space, direction and motion to see that, as the earth makes its vast swing from one extremity of its orbit to the other, the stars, being fixed, must have an apparent swing in the opposite direction. The seeming absence of such a swing was in all ages before our own one of the great stumbling blocks of astronomy. It was the base on which Ptolemy erected his proof that the earth was immovable in the center of the celestial sphere. It was felt by Copernicus to be a great difficulty in the reception of his system. It led Tycho Brahe to suggest a grotesque combination of the Ptolemaic and Copernican systems, in which the earth was the center of motion, round which the sun revolved, carrying the planets with it.

With every improvement in their instruments, astronomers sought to detect the annual swing of the stars. Each time that increased accuracy in observations failed to show it, the difficulty in the way of the Copernican system was heightened. How deep the feeling on the subject is shown by the enthusiastic title, _Copernicus Triumphans_, given by Horrebow to the paper in which, from observations by Roemer, he claimed to have detected the swing. But, alas, critical examination showed that the supposed inequality was produced by the varying effect of the warmth of the day and the cold of the night upon the rate of the clock used by the observer, and not by the motion of the earth.

Hooke, a contemporary of Newton, published an attempt to determine the parallax of the stars, under the title of “An Attempt to Prove the Motion of the Earth,” but his work was as great a failure as that of his predecessors. Had it not been that the proofs of the Copernican system had accumulated until they became irresistible, these repeated attempts might have led men to think that perhaps, after all, Ptolemy and the ancients were somehow in the right.

The difficulty was magnified by the philosophic views of the period. It was supposed that Nature must economize in the use of space as a farmer would in the use of valuable land. The ancient astronomers correctly placed the sphere of the stars outside that of the planets, but did not suppose it far outside. That Nature would squander her resources by leaving a vacant space hundreds of thousands of times the extent of the solar system was supposed contrary to all probability. The actual infinity of space; the consideration that one had only to enlarge his conceptions a little to see spaces a thousand times the size of the solar system look as insignificant as the region of a few yards round a grain of sand, does not seem to have occurred to anyone.