Chapter XVII: Spectroscopic Binaries

Between the old and the new astronomy lies a region claimed by both, yet belonging by exclusive right to neither. This is the department of spectroscopically determined, or radial movements. Now the distinction between radial and transversal movement is purely artificial; it is made in the interests of our imperfect faculties; nature ignores it. Motion, although by a geometrical fiction resolvable _ad infinitum_, is essentially simple. At any given instant it takes place in one direction only. But if that direction be oblique to our view, we see the line of travel foreshortened; nor can we tell by direct vision how much foreshortened. That is to say, the eye perceives one component of velocity—the tangential component, the component lying square before it—while of the other component along the visual ray it takes no heed. Here the spectroscope comes to the rescue. Helpless to deal with tangential speed, it can measure radial speed by its effects upon the refrangibility of light. The first method gives one side of the parallelogram of velocities, the second, the other; combining their results, we get the diagonal actually traversed by the observed luminous body. Data obtained by visual means formed the sole materials of the elder gravitational science; none others were indeed available at the period of its growth and elaboration; nor, even if they had been, would they have been of essential service in constructing planetary theories. In sidereal astronomy they occupy quite a different position. Without them its progress is crippled, and the possibility of procuring them fortunately developed just when they began to be urgently needed.

As grist for the mathematical mill, motions determined spectroscopically serve equally well with motions determined telescopically. The calculus deals indifferently with either kind. The calculus, however, is an instrument of precision, and demands minute accuracy in the materials operated upon. And it is just the effort to satisfy this demand which has broken down the barrier between celestial mechanics and celestial physics. For radial velocities cannot be unadvisedly accepted; the line-displacements significant of them may be otherwise occasioned. Cases have to be discriminated; conditions scrutinised; recondite problems attacked. The information within reach is, nevertheless, too important to be neglected; at any cost of pains it must be extricated from uncertainty and used for all that it is worth; and so it has come about that traditional astronomers of the most abstract type find themselves involved in experimental difficulties, and confronted by questions answerable only in the laboratory.

Astrophysicists, on their side, have no choice but to cultivate the spectroscopic branch of dynamical astronomy. Not merely because it springs from the stem of physical principles and physical experience, but because the study of its subject-matter is essential to the furtherance of knowledge respecting stellar constitution and development. Thus sidereal physics merges into sidereal mechanics; yet somewhere between them a line of demarcation must, for the purposes of the present book, be drawn. Arbitrarily drawn in many places it will be; but there are cases in which it is better to lack logic than limit; and this is one of them. We shall then regard spectroscopic but not telescopic binaries as making part of our subject, although fully aware that the two classes are fundamentally one. Stellar and nebular proper motions, transversal or radial, must also as such be excluded. Only when they give evidence, by periodic variability, of the progress of orbital revolutions, do they fall within our scope. Uniform velocities in space, in whatever direction, or however determined, do not concern us. Foreign to our theme as well, is the grand topic of sidereal construction, prescribed as it is and conditioned by the flittings of the stars. Something, however, will be said about the physical peculiarities of the Milky Way, since apart from them the spectroscopic relations of the various families of stars and nebulæ would remain imperfectly intelligible.

Spectroscopic binaries are stars telescopically single, but inferred to be compound from the evidence of a regular flow of spectral change. The change is of a perfectly definite nature. It consists in the swinging of all the bright or dark lines to and fro in a fixed period across their average positions. These, indeed, are not precisely their normal terrestrial places. They are affected by the motion of the system, as a whole, towards or from the eye. This constant element of shifting is, however, easily eliminated, and the circulating pair can then be studied as if their centre of gravity were at rest relatively to the sun. Ascribing to them, to begin with, a circular orbit, it is easy to see that, at two diametrically opposite points—the extremities of the line of conjunction—radial motion vanishes, the entire measurable velocity being across the direction of view; while at the corresponding points of greatest elongation, the radial component represents full speed. In an elliptic orbit these four points of zero and maximum line-of-sight movement may be slightly displaced according to the situation of the major axis; they can, however, be located with the help of exact observational data, and their positions then serve as an index to the shape and orientation of the ellipse. One of its elements, nevertheless, remains incalculable. Unless the revolving stars eclipse one another, there is no means of determining its plane. It cannot be perpendicular to the line of sight, for in that case all the motion would be tangential; no part of it could be spectroscopically apparent. But it may be inclined at any angle short of a right angle; and the larger the angle, the smaller the proportion of the orbital velocity directed along the visual ray. In other words, the measured rates are the true rates multiplied by the cosine of an unknown angle. They are, accordingly, minimum values; the actual speed indefinitely exceeds them. Nevertheless, it can rarely be more than double the seeming amount, since the chances of discovery manifestly fall off for systems with highly inclined planes. Thus the scale of orbits computed from spectroscopic data is indeterminate; but the uncertainty does not extend to their form, which is as strictly derivable as that of the paths of visible binary stars.[540] The mass of the revolving bodies, however, escapes us. It depends upon the compass of their rounds; we can only assign to it a value less than which it cannot be, although it may be considerably greater.

Spectroscopic binaries are broadly divisible into three classes: those that are constant in brightness, those that vary in light through eclipses, and those that vary in light otherwise than by eclipse. In the present chapter we shall confine our attention to the first category. And here again we have to distinguish between stars with bright, and stars with dark companions. In the spectra of bright pairs the lines split into doublets twice in the course of each revolution; in those of bright and dark pairs they execute a complete vibration simultaneously with the description of a circuit, but remain always single. But these different conditions are not sharply separated. As usual, the rule of continuity is observed. Satellites are met with in all gradations of luminosity. Some shine no less brilliantly than their primaries, in which case the duplicated lines are exact pairs; others are large but dim, and show very faint rays periodically appended to the comparatively intense ones of the greater orb; while the majority, remarkably enough, are quite obscure, so far at least as spectral indications enable us to judge.

These marvellous systems have, one and all, been discovered by spectrographic means. The required consistency and certainty of measurement are unattainable visually. They have been realised only by the employment of chemical impressions comparable night by night and year after year. The first result of the kind was achieved at Harvard University by the detection as a close double of ζ Ursæ Majoris, the middle star in the Plough handle. The components are Sirian suns of the same stamp, and of nearly equal brightness; but they may be to some extent relatively variable.[541] The nature of their movements was long an enigma. The period of 104 days at first assigned to them implied duplication of the spectral lines once in 52 days. Yet this consequence did not ensue in fact with the inevitableness exacted by theory. Grave discrepancies became manifest; the anticipated separation of the two spectra, often non-apparent, was always curtailed in duration, and repeated attempts were baffled to get rid of these anomalies by adding a third body to the system, by heightening the eccentricity of the ellipse traversed, or by shortening the period of its description.[542] At last, in 1901,[543] by a discussion of a fresh series of Potsdam spectrographs, Dr. Vogel reached a satisfactory conclusion. He now assigned to the revolving couple a period of only 20 days 14 hours; the eccentricity of their orbit came out = 0·5, so that their periastron-approach is one-half their mean distance; while their least possible mass proved to be four times that of the sun. Up to the present they seem inclined to conform to these rules of the road.

The parallax of 0·045″ found by Klinkerfues for Mizar (to give ζ Ursæ its Arabic name) is likely to be largely erroneous, but erroneous by excess rather than by defect. If it be correct, the star sends abroad thirty-eight times more light than our sun. If it be too large, the star is proportionately brighter; and, judging by Höffler’s estimate[544]—certainly a most precarious one—it is greatly too large. Since the components are spectroscopically unlike the sun, the ratio of the quantity of light they emit to the quantity of matter they contain must be widely different. Were it the same, a 38-fold brilliancy would imply their possession of about 160 times the solar mass; whereas Vogel’s data almost enforce the belief that this value at least decuples the truth. This may serve to exemplify the difficulty of deducing massiveness from luminosity. Only in exceptional cases can any fixed proportionality be safely assumed as the basis of calculation.

Mizar is attended visibly as well as invisibly. A star of the fourth magnitude circulates round it at a distance of 14″ with an almost imperceptible progression. Unless it mends its pace, 10,000 years will have elapsed before a revolution is completed. It may be worth recalling that on 18th April 1841, Mädler was unable to find this object, ordinarily plain to be seen; and the failure seemed so strange that he endeavoured to account for it by supposing the star subject to sudden obscurations like those of Algol.[545] No second disappearance is on record; but phases of the kind are extremely evasive when no time-bill of their recurrences is at hand. The connection into one system of two close pairs is not in itself improbable, although no such arrangement has yet been anywhere verified.

The detection of a second spectroscopic binary followed immediately upon that of the first. Miss Maury announced late in 1889, as a result of her scrutiny of the Harvard plates, that the absorption lines in the spectrum of β Aurigæ appear alternately single and double once in forty-eight hours. Hence the period of revolution is four days, while the relative velocity of the components, given by the extent to which their spectral rays separate, is 150 miles a second. Their joint orbit has been computed by Rambaut,[546] Lehmann-Filhés,[547] and Schwarzschild[548] so accordantly as to leave little room for improvement. They find its eccentricity to be somewhat less than that of the orbit of Mercury; the major axis makes an angle of 32° with the line of sight, and the periastron is at the end farthest from the earth. The plane being unknown, its dimensions, as already explained, cannot be ascertained. If indeed the observed velocity were the true velocity,—that is, if it lay in a level passing through the eye—the corresponding orbital radius would be 7,500,000 miles, and the mass of the system would rather exceed that of 4½ suns;[549] but these are only the least possible values; they may be greatly surpassed. The components of β Aurigæ shine with the Sirian quality of light; they are almost perfectly matched, reciprocal variability, according to Miss Maury,[550] causing each in turn to appear the brighter. A parallax of 0·062″ was photographically determined for them by Professor Pritchard. At the distance indicated, the sun would seem twenty-eight times less bright; it would sink to the paltry status of a 5·6 magnitude star. If β Aurigæ were a single globe, constituted like the sun, and giving out a twenty-eight-fold supply of light, it should be of 147-fold mass. Neither of these conditions is fulfilled; and allowance for their realisation might possibly bring into fair agreement calculations of mass from gravitational and from photometric data. In which case the plane of revolution would deviate but slightly from that traversed by the line of sight.

The preceding star of two named μ Scorpii was disclosed as compound in 1896 by Professor Bailey’s notice of the doubling of its spectral lines on many of the Draper Memorial negatives.[551] The period is only 34 hours 42 minutes; the velocity is correspondingly high. By their wide separation the lines tell of relative movement at the rate of 286 miles a second, this being the sum of the opposite velocities of the conjoined bodies. Their orbit, apart from the foreshortening effect of its inclination, has a radius of nearly 6,000,000 miles, and they possess at least fifteen times the gravitating power of the sun. They show a helium spectrum; and one member of the pair is not only fainter than the other, but fainter, apparently, in a variable degree.

The spectrographic method employed at Harvard supplies evidence of line-duplications, but none of the shiftings of solitary lines. This is easily understood. The dispersing apparatus is placed in front of the object glass; the stellar images formed at its focus are then ready-made spectra. Hence no slit is required, and without a slit no comparison-spectrum can be availed of. Displacements therefore betray themselves only when the rays furnish standards of mutual reference by splitting into pairs. The binary nature of stars both bright is, accordingly, discoverable in this way, but not the association of a bright with a dark body.

The spectroscopic discovery of these remarkable combinations was initiated at Potsdam. Dr. Vogel[552] in 1890 found the brilliant Spica (α Virginis) to have its spectrum shifted to and fro once in four days, the revolutions thereby intimated proceeding at the rate—apart from perspective abridgment—of fifty-seven English miles a second. This implies, if the components be of equal mass, a distance for each from their common centre of gravity of 3,100,000 miles, and a joint mass 2·6 times that of the sun. The spectrum is of the helium type. Sir David Gill obtained a null result for the parallax of the star, which must accordingly be of amazing actual splendour. The attendant of Spica is not wholly obscure. Traces of its spectrum can be perceived, although too faintly for purposes of exact measurement. The couple might then be termed a linking instance between systems composed of twin suns, and those consisting of a luminous and a non-luminous member. The conditions of observation are not only more arduous in the latter case, but the data within reach prove less adequate. They are one-sided; they relate exclusively to the bright star. All that can be learned about its dark companion is that it describes, in the same period, a similar orbit. The size of the orbit is left vague. It is large if the mass of the body traversing it is small, and _vice versâ_; and the mass of the primary is involved in the same uncertainty.

A peculiarly interesting bright and dark couple was brought to notice in 1896 through M. Bélopolsky’s work with the thirty-inch Pulkowa refractor.[553] Castor, the lucida of the constellation Gemini, was the object of his researches; and it dominates a system no less wonderful than that of ζ Ursæ Majoris. Two lustrous Sirian stars, of second and third magnitudes respectively, wheel slowly at an interval of 6″. Although they have been wards of science since Bradley’s measure of them in 1719, their orbit is not yet, in any strict sense, calculable. It is, however, certainly very eccentric, and takes many centuries to describe. A small, distant star shares the proper motion of this majestic pair, and is hence known to form with them a ternary combination, which the spectroscope has rendered quaternary by assigning an invisible satellite to the minor component of the original binary. Its revolutions are rapid; they have a period of not quite three days, and its gravitative power suffices to impart a radial velocity of 22 miles a second to the luminous orb in its vicinity. The corresponding distance from the centre is 1,800,000 miles; but this, as in all such cases, is a minimum value. The ellipse traversed is slightly more eccentric than the path of Mercury round the sun. And here arose a curious complication.[554] Obviously, the interval between two periastron passages should, if the major axis remained fixed in space, be identical with the time occupied in making the circuit from node to node. It proved, nevertheless, to be notably longer, and the hypothesis was, so to speak, compulsorily adopted that the major axis shifts forward as the stars revolve. The period of the inequality, as determined by Bélopolsky in 1899, is 2100 days. In four years and forty days the orbital axis makes a complete gyration, and is once more directed as at first. The cause assigned for the disturbance is the spheroidal form impressed upon the conjoined bodies by their reciprocal tide-raising power. A flattening of one-seventh would suffice to produce the observed effect, admitting that the system has the same dimensions as that of Algol. This special kind of perturbation, long theoretically recognised, has been found practically operative only within the narrow precincts of close stellar systems. Its continued study in them may lead to important developments.

The disclosure of a duplex character in Capella was eminently unexpected. Its reputation as an exemplary solar star, irreproachably regular in its movements, had been established at Potsdam, where the spectrographic investigation of radial velocities was set on foot in 1888.[555] But the instrumental resources then at Professor Vogel’s command were inadequate to bring out certain deviations from the Fraunhofer pattern lately noticed. The spectrum is indeed both oscillatory and compound; but a powerful and perfect apparatus is required for the manifestation of these singularities. The discovery was, nevertheless, made in duplicate by Professor Campbell at Lick,[556] and by Mr. Newall at Cambridge.[557] It is of unique interest.

Capella is one of the very few spectroscopic binaries at a determined distance from the earth. The carefully revised parallax of 0·081″, implying a light-journey of forty years, assigned to it by Dr. Elkin in 1897, has every mark of authenticity. Located thus remotely, our sun would appear as a star below the fifth magnitude; 102 orbs like it should be combined to give the light of Capella. Hence the joint volume of the components, assuming them to be equal globes of solar intrinsic brilliancy, must be just 730 times that of the sun. And their joint mass should be even proportionately greater, unless the tremendous force of internal compression proper to bodies so gigantic were counterbalanced by exorbitant heat. There is strong, if not convincing evidence that this is actually the case.

The members of the Capellan system are unequally luminous, and differ in their absorptive qualities. One is spectroscopically indistinguishable from the sun, the other, of about half its brightness, is more akin to Procyon. It has, accordingly, been found possible to measure separately the swing of each set of lines, and they have proved to be of much the same amplitude. This means that the two bodies are animated by equivalent movements, and are hence nearly equal in mass. Their revolutions proceed in a slightly eccentric orbit, the mean radius of which, if seen edgewise, would measure 52,000,000 miles. It is not, however, seen edgewise; very far from it. Capella possibly makes an exception to the rule that the circulatory plane of non-eclipsing spectroscopic pairs is unascertainable; and for this reason, that it may be, to some extent, a visual pair as well. Mr. Newall adverted to the probability, based upon the star’s parallax and conditions of movement, that the distance between its components would subtend from the earth an angle of nearly one-tenth of a second. Telescopic observations might then have a successful issue; and the opportunity for testing the powers of great instruments was, at any rate, too tempting to be neglected. Those of the Lick refractor, strange to say, though employed with all Professor Hussey’s skill, failed to answer the demand made upon them. The star was seen persistently round.[558] Yet Messrs. Dyson and Lewis were persuaded of its genuine elongation with the Greenwich twenty-eight-inch equatorial. The components were never seen clearly divided; no thread of dark space was perceptible between them; but they formed together an oval image, and the direction of lengthening changed consistently with the period of their mutual circulation.[559] The visual data thus procured even served for the calculation of a provisional orbit, and the missing element of its inclination proved to have a value of 30°. The stars, if this be so, travel in a plane making an angle of 60° with the line of sight, and the actual radius of their path is double that derived from spectroscopic velocities. It measures 104,000,000 miles; these immense bodies are not much farther apart than the earth is from the sun. Their mass can hence be arrived at; together they contain somewhat more matter than seventeen suns. This result, though in many ways plausible, is extraordinarily discrepant from what we may call the light-value of the same element. If they gravitated in the proportion of their luminosity, these orbs, as we have seen, should outweigh the sun 730 times; in point of fact, they seem to possess no more than seventeen times the solar mass. Even apart from the Greenwich results, we seem here to find evidence that stars differing enormously in density may show spectra of the same stamp, and that large bodies traverse the various stages of development more rapidly than small. The members of the Capellan pair, admitting the alleged facts, are some forty times more rarefied than the sun; liquid hydrogen is a heavy substance compared with them. They are, accordingly, at an early epoch of their career as radiant globes, while their spectra indicate full maturity. Confirmation is thus afforded to the inference, already drawn from the spectral diversities of double stars, that mass accelerates evolution.

Late in 1896 Professor Campbell undertook at the Lick Observatory a comprehensive investigation of stellar radial motion. The adjustment of the fine apparatus known as the “Mills spectrograph” to the great refractor made this feasible; and among its “bye-products,” the analysis of visually single stars into revolving pairs is particularly important, first, because of the individual interest of the facts collected, next, on account of their significance in the scheme of the Cosmos. The abundance with which such systems occur is quite unexpected, and very remarkable. Professor Campbell finds that, of 285 stars observed by him, more than one in nine is a spectroscopic binary.[560] And this excludes several objects suspected, but not demonstrated to belong to the same class, and makes no allowance for those cases in which the orbital plane is so nearly vertical that movement in it makes no appreciable spectroscopic effect. He has then good reason for holding it probable “that at least one star in five or six will be found to be a spectroscopic binary,” and he is quite prepared “to see a still larger ratio established. The proven existence,” he adds, “of so large a number of stellar systems differing widely in structure from the solar system gives rise to a suspicion, at least, that our system is not of the prevailing type of stellar systems. The new field of astronomical research thus opened up is of great richness, and may well occupy the attention, for an indefinite period, of the large number of observers and institutions now engaging in its development. It is perhaps unnecessary to say that the measure of success attainable is dependent upon the degree of accuracy realised in the observed velocities.”

The Lick results in this branch are in several respects noteworthy.[561] They show the wide diffusion of arrangements strange to experience, if admissible in speculation. They serve, by the variety of periods which they indicate, to narrow the lacuna between stars directly seen, and stars inferred from Doppler’s principle to be revolving. They have rendered it obvious that no generic distinction separates the two classes. A pair revolving in 2½ years, like η Pegasi, cannot be set apart fundamentally from δ Equudei, with its period of 5·7 years. It is, indeed, clear that spectroscopic and telescopic binaries differ only in the mode of their observation; not what they are in themselves, but the aspect under which we regard them, has caused them to be artificially disconnected. Already, however, a tentative beginning has been made with Capella in the telescopic observation of spectroscopic couples; and spectroscopic determinations of orbital speed, long a desideratum for visual pairs, have been tried with good promise of success. Individually, too, the detections announced from Mount Hamilton are frequently curious and suggestive. Thus Polaris claims the attendance of two dark companions; while the bluer component of κ Pegasi, besides circulating visibly in a period of 11·4 years, circulates invisibly in six days. Again, the primary of the classic pair, ξ Ursæ Majoris, proves to have a variable radial movement, the conditions of which invite investigation. The duplicity of υ Sagittarii is significant for a different reason. The spectrum of this star includes bright hydrogen lines; it was noted by Miss Maury[562] as compound, and perhaps mutable. Motion-displacements, giving a velocity-range of about twenty-five miles a second, were measured in it by Professor Campbell in 1899; but their period remains undetermined, as well as the extent to which they are shared by the responsive lines of the companion-spectrum.[563] For in this case both the stars are luminous, and both show absorption of the helium type. The exceptional constitution of υ Sagittarii, indicated by its emissive symptoms, accentuates the interest of its systemic relations. It should accordingly be an object of particular and persevering attention. Indeed, each of these wonderful pairs may be expected to develop peculiarities of its own, demanding study by varied, and perhaps recondite methods.