# Popular Science Monthly/Volume 69/August 1906/The Study of the Variable Stars

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* THE STUDY OF THE VARIABLE STARS
By Professor SOLON I. BAILEY,
HARVARD COLLEGE OBSERVATORY
THE ancient philosophers taught that the celestial bodies were 'incorruptible and eternal,' not subject to change, as are all terrestrial objects. In more recent times the stars were regarded merely as convenient points of reference for the determination of the motions of the planets. In this way they became known as the fixed stars. Relatively, they are indeed fixed; absolutely, all are in motion. Their light remains constant, also, for the most part, so that, if Hipparchus or Ptolemy should come back to earth after 2,000 years, he would probably notice few changes in the positions or brightness of the stars.
Any one who observes the sky carefully, through a period of years, is sure to be deeply impressed with the absence of change. Nevertheless, there are many stars which undergo more or less regular changes in brightness, and such objects are known as variable stars. In some cases the whole cycle of change takes place within a few hours, while in other cases it consumes months, or even years. The amount of the variation, also, varies enormously, ranging all the way from zero to many magnitudes, how many is not known. It is possible, even probable, that at minimum the light of some variable may, for us at least, be entirely extinguished. Mr. J. A. Parkhurst found that the variable V Delphini was invisible at its minimum of 1,900 in the forty-inch refractor of the Yerkes Observatory. This, it is estimated, would make it fainter than the seventeenth magnitude. Since its light at maximum is of about the seventh magnitude, this implies a range of at least ten magnitudes. Other stars vary as much or more. A change of ten magnitudes means that at maximum its light is 10,000 times as great as that at minimum. To illustrate this we may imagine a room illuminated by 1,000 ten-candle power electric lamps, and that these are replaced by the light of a single candle. To reduce the light of our sun by ten magnitudes would be equivalent to increasing its distance 100 times, or to more than 9,000,000,000 miles. At such a distance its apparent size would be less than the present mean size of Jupiter or Venus. Fortunately our sun, if a variable star as seems probable, has a small range of variation.
The general problem of variable stars may be divided into three parts—the discovery of the variables, the observation of all the phenomena involved, and the search for the causes. The present ​generation, thanks to the powerful aid of photographic methods, may hope to bring near completion the first part of the problem, and to make good progress on the two remaining portions.
The existence of a variable star was probably first recognized by Holwarda of Franeeker, in 1639. The number was slowly increased, and some knowledge of their nature learned during the next two centuries. Their observation was placed on a scientific basis through the labors of various astronomers, especially Argelander and Schönfeld. The latter astronomer issued, in 1865, a catalogue of 113 variables, and later, one of 165 variables, which included all stars then known to be variable. The list was enlarged, in 1883, at the Harvard Observatory by the addition of forty-eight variables. In 1888 Dr. S. C. Chandler published his first catalogue of variable stars, 225 in number, which had been discovered by some thirty different observers in various countries, by visual methods. Many of these observers have continued their investigations till the present time—the most successful in the line of discovery being Dr. T. D. Anderson, of Edinburgh, who by visual means alone has found forty new variables, a result truly remarkable.
About the year 1889, however, began a rapid increase in the number of variables through the introduction of photographic methods. The first notable addition was made by Mrs. Fleming, through the examination of the photographic spectra of the stars, while engaged in the work of the Henry Draper Memorial, a research carried on at the Harvard Observatory under the direction of Professor E. C. Pickering. By means of an objective prism, placed in front of the lens of a photographic telescope of large aperture and short focal length, photographs ​were obtained which showed well the characteristics of scores of spectra on a single plate. Variable stars of long period were found to have spectra in which the hydrogen lines were bright, when the variables were near maximum. By taking advantage of this spectral peculiarity Mrs. Fleming has been able to 'pick up' as a by-product of other investigations concerning stellar spectra, some 200 variables of long period.
In 1895, the writer, while engaged in photographic work at the Arequipa Station of the Harvard Observatory, began an examination of photographs of the globular clusters of stars. By the use of improved devices for controlling the motion of the telescope, satisfactory photographs were obtained of the dense globular clusters. An examination
of these led to striking results. It was found that while certain clusters contained few or no variable stars, other similar clusters were closely packed with them. Messier 3, a faint group, barely visible as a hazy star to the naked eye, was found to contain 137 variables out of 900 stars examined, or about one in every seven stars. This is by far the greatest proportion of variables yet found anywhere in the sky. Over 500 variable stars have been found so far in dense globular clusters, and, undoubtedly, these do not entirely exhaust the number.
Madame L. Ceraski, wife of the director of the astronomical observatory of Moscow, has found a large number of variables by an examination of photographs made by M. Blajko, of the same ​observatory. Madame Ceraski has been especially successful in finding variables of the interesting Algol type. Of sixty-seven variable stars discovered by her, no less than ten are of this class. This is remarkable when we take into consideration that of over 3,000 variables now known only thirty-eight are of the Algol type.
Through her generous gifts in aid of astronomical research, the late Miss Catherine W. Bruce, of New York, made her name widely known in astronomical circles. Dr. Max Wolf, director of the Astrophysical Observatory at Heidelberg, was presented by her with a photographic telescope, which has enabled him not only to find some seventy new asteroids, but also to increase materially the number of known
variables. Dr. Wolf, recently assisted by Frau G. Wolf, has discovered about 200 new variable stars.
Nowhere else, however, has so large a collection of celestial photographs been made, covering so long a period of time, as at the Harvard Observatory. In 1903, Professor Pickering instituted, among other pieces of work, an examination of the Magellanic Clouds. This work was assigned to Miss H. S. Leavitt, who has shown rare talent for this line of investigation. The regions selected were very fortunate, also, since, aside from the dense globular clusters, no other region has been found as rich in variables as the Small Cloud, although the Large Cloud also promises to yield nearly as many. It should be noted that the Magellanic Clouds are by no means merely irregular extensions of the Milky Way. They appear to be as unique in structure as in position. ​Altogether Miss Leavitt has added 1,500 new variables to the already rapidly growing list.
It may be asked, why it is necessary, or even desirable, to go on indefinitely with the discovery of new variables. The answer is that, aside from the value of adding any new fact about the universe to the sum of human knowledge, the problem is now so well advanced that it seems unwise not to render the search complete for the whole sky. A serious international attempt is about to be made, for the first time, to investigate systematically all the leading problems concerned in the construction of the universe, so that a scientific cosmogony may be possible. It will be of value in this greatest of all problems to find
the discussion of the variable stars reasonably complete for the whole sky. At the Harvard Observatory, where variable stars have been given serious attention during more than twenty years, a new catalogue, compiled by Miss Cannon, is in course of publication, which contains reference to about 1,850 variables. This does not include the variable stars in the Magellanic Clouds. Also, a committee of the Astronomische-Gesellschaft. consisting of the well-known astronomers, Dunér, Müller, Oudermans and Hartwig, have in hand the preparation of a catalogue, which will be an extension of the former catalogues of Chandler.
The work of discovery, however arduous, is but a small part of the whole problem of the variable stars. Long series of observations are necessary, in order to learn the amount, duration and rapidity of the light-changes, or, in other words, to determine the light-curve.
​Recent advances in methods of research have also made possible the study of various other phenomena, in addition to the variability in brightness. All available information will be needed to assist us in finding the true explanation of the changes. Especially must we study the spectra of these stars, and the changes in the spectra at different phases of the light-curve, as well as the motions of the stars in the line of sight. For a long time it has been known that the radial motion of any bright body may be studied from the shifting positions of the spectral lines. This principle is proving of great importance in different branches of astronomy. Only recently, however, and in few cases has this crucial method been applied to the problem of variable stars; yet it appears that the true solution of the difficulties must await, in many cases, the application of this method of research.
The determination of these different phenomena—the light-curve, the velocity-curve and the spectrum—is often carried on without special reference to the physical causes which produce them. But it
will be convenient in what follows to refer to the phenomena and the probable causes together. No final classification of variable stars is possible at the present time, since such a classification would doubtless be based on the physical causes which underly the phenomena, and these are known in comparatively few cases. The division proposed by Professor Pickering, in 1881, is as convenient as any for our purposes. He placed them all in the following classes:
I. New stars. II. Long-period variables, undergoing great variations in light. III. Stars undergoing slight changes, according to laws as yet little understood. IV. Short-period variables of the β Lyræ type. V. Algol stars.
​Reference will be made in what follows only to classes II., IV. and V. New stars may well be considered as a class apart. There is, possibly, no sufficient reason for including them among variable stars, technically so-called. The stars of class III. are few, doubtful, not well understood, and relatively unimportant.
II. Variable stars of long period and large variation in light are perhaps the easiest to observe and the most difficult to interpret of all. Many of them are bright enough to be observed, near maximum at least, by the naked eye. and the variations are so great that observations of the highest precision are not essential for the determination of the light-curves. The length of period ranges in general from 100
days to 400 days. Some of these stars have been observed by different astronomers during the last two centuries, and elaborate investigations concerning them have been made by Argelander, Schönfeld, Chandler, Pickering, and others. Omicron Ceti, or Mira, The Wonderful, has been studied more carefully than any other. Even here, however, much remains to be learned. The light-curve of Mira is shown in Fig. 1, and is fairly typical of the group. The variations in brightness are irregular and a single light-curve can only represent mean results. Irregularity characterizes all the phases; the exact time of any return of maximum is uncertain, and the brightness at different maxima, and at different minima, varies greatly.
The spectrum of stars of this class is in general of Seechi's third type, with heavy banded lines and flutings. A short time before maximum the bright lines of hydrogen appear, and persist till the star has grown somewhat faint again. At least, this is true of Mira, and of ​some others, and is perhaps true for all. These bright lines, clue to incandescent hydrogen, undergo various modifications during the time in which they are present. The relative intensity of different lines varies greatly in different stars, and also in the same star at different phases. Mrs. Fleming has been able to arrange them in a series having ten subdivisions, with R Lyncis at one end, with the H β and H γ lines prominent and H δ wanting, and R Leonis at the other end with H β wanting, H γ faint, and H δ prominent. There are also corresponding changes in the distribution of the remaining light of the spectrum, a peculiarity which is shared by stars of the same type which are not variable. These characteristics are well shown in Fig. 7.
Their great range of variation makes many of these stars invisible when near minimum in telescopes of ordinary size. This may account for the custom which has been followed by many observers of measuring the light only when the star is near maximum. This is unfortunate, since the determination of the length of the period is not sufficient in itself for the solution of the problems involved. On this account special efforts have been made at the Harvard Observatory, where the observations are carried on by Miss A. J. Cannon and Mr. Leon Campbell, to get measures of the variables at all the different phases. Even thus it is doubtful if the secrets of the changes can be found, until the research is made to include a more detailed spectroscopic study than has yet been made. A systematic study of a large number of wellselected stars is much needed. This could probably be done best by a photographic reflector of the largest size. Such a scheme of work has been proposed by Professor W. W. Campbell, director of the Lick Observatory, and from it we may expect results of the highest value. It may be well, also, to study the radial motions of these variables, but it is more than doubtful if their variability is in any way associated with orbital motion, such as would be found in binary systems. The irregularity in the recurrence of the phenomena seems to preclude the possibility of such an explanation. The stars of this class probably contain within themselves the causes of their changes. They are, perhaps, at that critical stage of development where occasional internal disturbances cause tremendous outbursts, especially of incandescent hydrogen, resulting in an enormous increase of light. The commotion slowly dies down only to return again with more or less of regularity. For the details of these disturbances we must await further study.
IV. Of the 3,000 variables known at present probably the vast majority have short periods, that is, periods of a few days, or a few hours. The periods, also, are uniform; or, at least, if apparent irregularity exists at times, this is capable of being expressed by rigorous mathematical formulæ, η Aquilæ and β Lyræ are well-known examples of this class. Recent investigations have shown that such stars are binary systems, and that in some way the light phenomena are ​associated with orbital revolution. Belopolsky, and later Campbell and Wright have investigated the velocity-curve of η Aquilæ. From their investigations it appears that this variable is a binary, whose period of revolution is of the same duration as the period of the light-changes. The determination of the velocity-curve is accomplished by the use of a slit-spectroscope, which gives a comparison spectrum of some known clement, which is also present in the spectrum of the star. Since the velocity-curve and light-curve are synchronous it might be suspected that the light variation was caused by an eclipse of the star by a relatively dark companion. This can not be true, however, in the case of η Aquilæ, for various reasons. In the first place, the light-curve is not that of an eclipsing star. An eclipse must occur when two stars are both in the line of sight, at which time the apparent motion would be small or zero. As a fact, the minimum of the star does not occur at such a time. The light maximum occurs noticeably later, and the minimum noticeably earlier than the periastron of the star. These facts seem not inconsistent with the theory that the variations in lights are caused by the close approach of the components of a double star moving in elliptical orbits, the outburst of light resulting from some tidal disturbance incited by the enormously increased mutual attractions of the two bodies. An objection to this explanation is that under these circumstances the outburst would probably manifest itself by the presence of bright lines in the spectrum at maximum, as is the case with long-period variables. Small evidence exists that this is true. Another difficulty is found by a comparison of the curves of velocity and light, as determined by Wright and Schur. The former is a smooth curve, while the latter has a secondary maximum. That this may be due in part to an error in the form of the light-curve as given by Schur, seems not impossible, if we compare it with the light-curve of the same star as determined by Pickering with a polarizing photometer. The latter curve shows merely an indication of a secondary maximum. It may be true, of course, that the secondary maximum is sometimes present, at other times absent. That the relation between the curves of motion and light may be most intimate, in some cases at least, is beautifully shown by the variable ω Sagittarii. The velocity-curve of this star was determined by Dr. Curtiss, of the Lick Observatory. As pointed out by him, the velocity-curve, and the light-curve determined by Professor Pickering, show a close resemblance even in the details, which proves conclusively that both phenomena are associated with the same underlying causes. Incidentally, a striking proof is furnished of the accuracy of these two widely separated investigations, thus critically compared. These curves are shown in Fig. 5.
β Lyræ represents a somewhat different variety of the short-period variable. This star has been studied for more than a century and still remains something of a mystery. The spectrum is complex, the lines ​showing displacement, apparently due to the motions of the bright components of a close binary. These displacements were explained in 1891 by Pickering as the result of the revolution of the unlike components of a binary system, having a relative velocity of 300 miles per second, and a radius of 50,000,000 miles. Belopolsky has also investigated this object, obtaining results which differ somewhat from those given above. Professor G. W. Myers has made a mathematical discussion of the problem, reaching the conclusion that the phenomena can be explained on the theory of a binary system, composed of two gaseous, scarcely separated, components of different masses, mutually eclipsing each other during their revolutions. Indeed the two components may not have separated, but exist still as a single body of unusual form, such as Poincaré's, or Darwin's figures of equilibrium. The problem is extremely complicated, and well illustrates the almost infinite diversity which is met with in the various problems about variable stars. The binary character of this type of variables seems sure in many cases, while in others even three bodies appear to be present; but the details involved are still in doubt.
The variable stars found in clusters have periods ranging for the most part from ten to fourteen hours. The elements of about 300 of them have been determined by the writer. The uniformity of the periods found in the same cluster is remarkable, pointing unmistakably to a common cause. What that cause is has not yet been found. The form of light-curve is shown in Figs. 3 and 4. Owing to the faintness of these stars, which generally vary between the twelfth and fifteenth magnitudes, it has not yet been possible to determine either the nature of the spectrum or the radial motion. The light-curve shows no indication of eclipsing phenomena. The uniformity in the period, traced in many cases through more than 5,000 returns of maximum, points to axial rotation or orbital revolution. Variability might result, undoubtedly, from the rotation of an elliptical, or unevenly luminous body; but the light-curves of cluster variables are difficult of explanation on this theory. They may be binaries with small, elliptical orbits, but even this is hardly consistent with the form of light-curve. The rejection of these hypotheses, nevertheless, seems to leave the phenomena without plausible explanation. A few cluster variables have been found where the maxima succeed each other at intervals of about six hours, one half the usual period. This indicates pretty clearly a double variable with alternating maxima, both components having the same period. These apparently accidental cases of duplicity may throw some light on the physical condition of all these stars.
V. Of the Algol variables Algol itself is a good example. Its light usually remains at a uniform brightness of the second magnitude, but once in a little less than three days it falls to the third magnitude, where it remains for some twenty minutes before beginning to regain ​its brightness. The whole time for the decrease and the restoration of light is about ten hours. The form of this light-curve points unmistakably to the eclipse of a bright star by a relatively dark companion. This explanation, first proposed by Goodricke, was developed by Pickering, and proved spectroscopically by Vogel. Dr. Alexander W. Roberts, of Lovedale, South Africa, has recently developed a method for determining the absolute dimensions of an Algol binary. The theory which underlies the determination is that light takes an appreciable interval of time to traverse the orbit of a binary system. For an accurate solution observations of the highest precision are essential. Precise photometric observations of such objects have been made by Professor O. C. Wendell, of the Harvard Observatory. The cause of variation is in general the same for all the Algol variables, though there are minor differences of importance. As might be expected, they show great regularity. Nevertheless, there are certain secular variations from causes not well understood. The period of Algol is believed to vary slightly, and Dr. Chandler explains this as due to the presence of a third body. M. Tisserand, however, has advanced a different theory. He assumes a slight flattening of the globe of Algol, and an elliptical orbit for the companion. These rival theories can be settled only by elaborate determinations of the light-curve during many years. According to Dr. Chase, Algol is at a distance of ninety-three light-years. Vogel finds the diameter of each of the components to be nearly a million miles, and the distance between them little more than three million miles. There are doubtless thousands of binary systems in the heavens, one component of which is more or less obscure. Such a system, and it holds true even if the components are equally luminous, becomes for us an Algol variable when the plane of revolution passes through or near the earth. Such systems are comparatively rare. At the present time only thirty-eight are known. The largest variation yet found is that of Fleming's Algol, R. W. Tauri, whose light at minimum is only one twenty-sixth as great as its usual amount. It would be possible for a dark companion of the same size as the bright component to completely eclipse it. In the case of ν Cephei, indeed, this probably takes place, so that the light while the eclipse lasts comes entirely from the dark companion. The companion is only relatively dark, however, so that its light alone is about one eighth as great as the combined light of both components. If the companion, in such a case, were completely obscure, there would be a total eclipse of the star's light, but no such case has yet been found.