IX. HELIUM STARS WITH BRIGHT LINES
Temporary stars, and a few stars variable in short periods, belong, properly speaking, to this class; but for the sake of clearness and convenience, they are reserved for separate treatment. The question of light-change will demand later on our undivided attention; it bristles with difficulties, which we are not at present prepared to encounter.
Alcyone, the chief Pleiad, long passed for an ordinary Orion star. Dark lines of hydrogen and helium were prominent in its spectrum; there seemed no reason to suspect the slightest deviation from normality. Nevertheless, Campbell perceived in 1893[423] the red radiance of C set off by a narrow dark line on its more refrangible side; and this state of incipient emission appears to be permanent.[424] Alcyone might then be counted a linking instance between Classes i. and vii. The discovery was startling that a single substance could show certain of its rays bright, the remainder dark, in one and the same star. But the fact, although highly perplexing,[425] has become so common to experience as to have ceased to be surprising. Examples of its occurrence have been registered by the score as regards both hydrogen and helium. They are all found in Classes vii. and viii. (bright-line helium and Wolf-Rayet stars); Mira-variables seem never to have their hydrogen spectrum thus conditioned. Professor Campbell[426] noticed it as an invariable rule that the bright lines in Orion stars “are those of greater wave-length,” while “the dark lines are those of shorter wave-length.”[427] This applies also to helium, but in a qualified sense. If all the lines in its spectrum are taken indiscriminately, the bright and the dark appear to succeed each other without method; but their consideration by series makes it at once evident that, within the limits of each set of vibrations, the bright members are invariably fundamental. This is important, not only for the better ordering of stellar phenomena, but as regards the theory of spectral series in general.
In Alcyone, then, emission is at a minimum; it could scarcely diminish and remain existent. And it is quite possible that it may be on the wane; after the lapse of some hundreds, or thousands of years, the chief Atlantid will perhaps have lost the distinctive note of its spectrum, and will have sunk to the level of unrelieved absorption. One of its companions at present stands out from the crowd in the same way, but more decidedly. Pleione shows three hydrogen lines pretty strongly bright, and they are inevitably C, F, and Hγ. Centrally superposed upon wide dark bands,[428] they assert by this fact alone the non-correspondence in position of their originating stratum with the glowing hydrogen in stars like Mira. And this teaches us the important lesson that there is no stereotyped recipe for the production of stellar bright lines, but that they may originate diversely in the various spectral classes.
The Pleiades are nebulous collectively, and in many cases individually as well; but they are less closely folded in nebular swaddling-bands than the group of stars forming the nucleus of the great Orion nebula. It consists of four leaders, of about the fourth, fifth, sixth, and seventh magnitudes respectively, two of which have faint companions; and, scattered promiscuously, there are to be found besides four minute stellar points, detected at Lick by Professor Barnard and Mr. Alvan G. Clark. For spectroscopic purposes the “trapezium,” or quartette of bright stars, may be treated as one, since they shine with sensibly the same quality of light, while their scarcely visible associates give radiations negligible in amount. Most difficult questions arise in attempting to decide upon the true nature of the trapezium-spectrum. The prevalent view at first was that the stars were of the ordinary dark-line helium type, bright lines coming in here and there simply as projections from the enormous volume of gaseous stuff interposed between the eye and the stellar nucleus of the formation. But the opinion was grounded on superficial evidence, and has not held its ground. Some lines, bright in the nebula, refuse to cross the thin strip of continuous light due to the star; they stop short on one side of it, and reform on the other,[429] the two sections being divided by a narrow gap of absorption. This proves that the nebular rays do not in all cases show bright against the background of continuous stellar light. The very strongest may do so; but it is just possible that in them the appearance is illusory, and due to a kind of irradiation.
There can, on the other hand, be no reasonable doubt that the trapezium-stars have bright lines of their own. But they are peculiar, and peculiarly conditioned. A spectrograph taken by Sir William and Lady Huggins, 5th February 1888,[430] proved to be crossed in the ultra-violet by at least four groups of fine, faint, bright lines, derived primarily from two stars of the trapezium, but extending, through their influence, as it were, some little way into the adjacent nebula. Their origin is problematical; they have not been recorded elsewhere;[431] they have been only partially verified on later Tulse Hill plates. Yet the original negative survives, and its examination has convinced several experts of the reality of the curious script read from it. Conviction, however, on such a point is apt to share the dim character of gloaming phenomena—phenomena on the border between the seen and the not seen.
But there is more. With refined apparatus the same observers succeeded, in 1894 and subsequently,[432] in separately photographing three of these remarkable spectra, and they were now perceived to be rich throughout in bright and dark lines, “with the special character strongly marked of bright bands associated with corresponding dark absorption lines.” Most singular of all, the relative positions of these bright and dark lines were found subject to change. Hydrogen radiations, for instance, which in 1894 lay on the blue sides of the absorption stripes, lay in 1897 on their redward margins. This might be explained on the hypothesis of orbital movement by supposing each star of the trapezium composed of a dark-line and a bright-line member, the spectra of which are periodically shifted through the alternations of their velocities in the line of sight. It remains to be seen, however, whether or not the shiftings are periodical; for by this one condition the explanation stands or falls.
So far as their absorption-elements are concerned, the stars of the trapezium belong to the earliest variety of the Orion type. All the lines are wide and diffuse, and the strongest are members of the Pickering series of hydrogen. Rydberg’s series—if we may call it so under reserve—is represented by the prominent reversal of its solitary ray at λ 4689. Mr. McClean recognised oxygen absorption in these stars; Sir William and Lady Huggins identified nitrogen, silicium, and titanium, and the calcium K shows both bright and dark. Few sidereal objects combine so many points of interest as the multiple star at the heart of the great nebula. The origin and meaning of the throngs of delicate rays, here just tantalising vision, pressingly invite research; nor less the manner of relative displacement exhibited by the bright and dark coupled lines. Do they betray a circulatory period? And if so, is it the same for each member of the group? Or do they rather form independent systems, in subordination to a higher scheme, completing itself in the long leisure of many millenniums? Other problems suggest themselves in immediate connection with these stars; nor is it impossible that they may be proposed over again, perhaps in a modified form, by the multiple stellar nucleus of the Trifid Nebula in Sagittarius. But instruments of no insignificant light-power will be needed for the satisfactory examination of its spectrum.
In one other star besides θ Orionis, the shifting of bright hydrogen lines occurs irrespectively, to all appearance, of binary revolution. Spectroscopic duplicity was at first naturally attributed to 11 Monocerotis when its peculiar character disclosed itself on the Harvard plates. Thus in the years 1888–90 the dark F of hydrogen had an illuminated border lying redward; it was on the blue side in 1891–92.[433] We are not informed whether it has since changed its position; but any attempt to impose a period upon alterations so spasmodical would evidently be hopeless. Like θ Orionis, 11 Monocerotis ( = Σ 919) is compound. It consists of three stars of about fifth and sixth magnitudes, which have maintained a strict relative immobility since Herschel divided them in 1781. Their spectra, photographed as one by Pickering, were separately examined by Campbell in 1894.[434] He found two of them to include the brilliant red ray of hydrogen, while it was absent from the third. Presumably, then, only two of the trio are bright-line stars, and it may be that in these two, significant differences in the mode of emission will be brought to light by detailed and systematic investigation.
The swing of the bright lines observed in θ Orionis and 11 Monocerotis is extremely uncommon. In general, a fixed arrangement prevails, and it is of two alternative varieties. Either the bright lines centrally divide broader dark bands, as in γ Cassiopeiæ, or the bright and dark lines are bracketed in pairs, the bright below, the dark above, as in P Cygni.
Father Secchi’s notice of γ Cassiopeiæ as a gaseous star goes back to 1866. He noticed the vividness in its spectrum of C, F, and D_{3}, but the helium line has not since held its own with the others. It is subject to prolonged extinctions; nor is it certain that even the hydrogen rays always keep up the same standard of brightness. The variability of the spectrum will, however, be discussed later in connection with other similar instances; here we have to do with its fundamental characteristics. The hydrogen lines in γ Cassiopeiæ are doubly reversed.[435] Wide absorption bands are divided by narrower emission bands, and these again by hair-lines of darkness. Their structure is analogous to that of H and K in the solar spectrum. The radiations fall off in intensity—as Campbell’s rule prescribes—with diminishing wave-length, while the absorptions gain in the same proportion. F is “superlatively bright”;[436] Hε is neutral; no bright lines have been photographed in the ultra-violet. The helium lines are dark, with occasional exceptions; but the green and blue magnesium lines shine by direct emission, and Father Sidgreaves recognises as a probable vanadium line a strong dark-blue ray (λ 4586), which seems to fluctuate in brightness. Another remarkable circumstance relating to this star is the recent effacement from its spectrum of the signs of sodium absorption formerly visible in it. They have, at any rate, escaped notice since Von Konkoly’s record of 15th September 1884.[437] But the immense vogue and value of spectrography have tended to reduce to a minimum the attention bestowed upon the lower spectral sections, and thus unduly to incline the balance of observation. The study of γ Cassiopeiæ might alone furnish a not inadequate task for a well-equipped observer. Only individual enthusiasm is likely to deal successfully with the baffling problems it presents. Spectral variability is, in its case, accentuated by perfect photometric constancy. The star is steadily of 2·3 magnitude. It is purely white in colour, lies immersed in the Milky Way, and has no measurable parallax. Its real size and splendour are then inestimably great.
The spectrum of P Cygni is not known to vary, although the star itself was reckoned a “Nova” on its discovery by Janson in 1600, and by its capricious emergences earned from Huygens, half a century later, the title of the “revenante of the Swan.”[438] Finally, it settled down to fifth-magnitude brightness, which it seems disposed indefinitely to retain. Its spectrum shows an approximately complete set of bright and dark hydrogen and helium rays; but in their arrangement into couples juxtaposition replaces superposition—that is to say, the bright lines are in their normal places,[439] while the corresponding dark ones are shifted upward, as if by rapid motion, towards the eye. But there can be no real question of motion, since the relation persists without change year after year. Nor can it be explained on the pressure-principle of altered refrangibility. The action, if exerted at all, would be of the opposite kind to that observed. The displacements in the spectrum of P Cygni are towards the blue; if due to pressure, they should be towards the red. The phenomenon of the relative displacement of bright and dark lines in the same spectrum is one of the most interesting in stellar physics, and has received, up to the present, no adequate explanation.
The absorption lines in P Cygni are much sharper and narrower than in γ Cassiopeiæ. Those of calcium, magnesium, and sodium are at once apparent, and Bélopolsky ascribes many of the remainder to nitrogen.
The spectrum of the great southern variable, η Carinæ, resembles that of P Cygni by its inclusion of many bright lines shadowed by dark ones on their blue sides. It has been photographically studied by Sir David Gill, Mr. McClean, and Miss A. J. Cannon.[440]
Among stars nearly related to γ Cassiopeiæ may be mentioned φ Persei (4·2 magnitude), υ Cygni (4·4 magnitude), α Columbæ (2·7 magnitude), δ and μ Centauri (2·8 and 3·4 magnitude). Bright F was detected by Mr. Espin[441] in the spectrum of the star in Perseus, and was found by Campbell[442] to be accompanied by a much brighter C. The total absence of K is surprising, but may not be permanent if the spectral variability suspected at Potsdam[443] be substantiated. In υ Cygni there appear to be double reversals of helium as well as of hydrogen.[444] Of α Columbæ it is only known that F is a broad dark line bisected by a narrow bright one. The spectra of the two stars in Centaur are thought to be almost identical.[445] Hydrogen emissions in them are strong and numerous, but none others have been recognised. The helium lines are all dark; metallic lines are inconspicuous.
Bright hydrogen and helium lines seem like relics of past conflagrations. In a few cases we know them to be such, and it is possible that in all they have the same implications. For any of these stars may have undergone prehistoric vicissitudes of lustre, after which they would have settled down into stability; although the recurrence of such incidents in the future can alone afford secure grounds for inferring that they diversified stellar biographies in earlier times. Bright-line helium stars are for the most part situated in the Milky Way. They are subject to the influences exercised by that strange aggregation.
X. WOLF-RAYET STARS
A very remarkable star was described by Professor Pickering in 1896.[446] Through the measurement of its absorption lines a companion hydrogen series to that already known was, for the first time, recognised; while both the Wolf-Rayet bands in the azure showed in it by direct emission. Only the presence of a dark K obliges us to separate ζ Puppis from Wolf-Rayet stars proper, and to consider it as a linking instance between them and helium stars of the earliest variety. Just this trace of calcium-absorption differentiates the hybrid spectrum of the star in the Poop from spectra of Class viii., which include no legible metallic impressions. Their absence is of especial importance as extending to nebulæ. Nebular chemistry is entirely non-metallic.
The Pickering series in Wolf-Rayet stars is not infrequently bright in its lower members, submerged by absorption higher up. The bands in the blue, on the other hand, are always bright. They form a multiple group, the mutual relations of which await more complete disentanglement. The lowest member is, or may be, the “fundamental” of Rydberg’s hydrogen series at λ 469. Yet the circumstance that it is not really solitary tends to discountenance this identification.[447] The “lazulite” ray at λ 465 is never entirely effaced, and Campbell has provided it with several associates of still shorter wave-lengths.[448] Some of these fall suspiciously near nitrogen lines. The possibility is not then excluded that all these enigmatical blue effluences may be the joint products of glowing hydrogen and nitrogen, although this view, like every other that can be proposed, is beset by serious difficulties. Among the less refrangible of the Wolf-Rayet bright lines there are two (at about λ 569 and 559) which appear to coincide with rays photographed by Professor Hale in carbon stars. Neither has been chemically interpreted. One of them, the greenish or “citron” line (λ 569), seems in some way correlated with the blue band at λ 465. A more definite connection can be traced between the latter and the yellow line at λ 581. They are emphasised in the same stars, while the brilliancy of the Rydberg beam at λ 469 is accompanied by a special vivifying of the green Pickering line at λ 541. This rule is quasi-universal; it may stand, at least temporarily, as a useful principle of order amid half-intelligible phenomena.
Hydrogen is most diversely imprinted on the Wolf-Rayet spectra. Its lines, according to Professor Campbell, “have nearly every known character. In many of the stars they are dark. Again, they are dark with bright borders, and suggest strongly that they are doubly reversed. The bright hydrogen lines vary from faint to very bright, from monochromatic lines to very broad bands, and from those clearly single to those apparently multiple.” This splitting-up of widened lines is evidently analogous to the tripling of the brilliant hydrogen rays observed in Mira, and once more recalls the possibility that certain peculiar stellar spectra may be produced in powerful magnetic fields. Helium is not very prominent in spectra of this type. It frequently shows by emission in D_{3}, and occasionally, even in the same star, by absorption at λ 4472; but its display is subordinate to that of other known and unknown elements.
The grand exemplar of the Wolf-Rayet class is γ Argûs (alias γ Velorum), a star of 2·4 magnitude, giving a resplendent spectrum ablaze with yellow and blue lines. It was first effectively studied by Professor Campbell in 1893–94,[449] although at the Lick Observatory the star barely attains an altitude of six degrees, and can be observed for only a few minutes on any one night. The main facts that struck him were the brilliancy of C, the transitional character of F, and the unmitigated darkness of all the upper hydrogen lines. Similarly, the initial term of the Pickering series at λ 541 shows by emission, the rest by absorption, while a bright D_{3} contrasts with a number of more refrangible dark associates. As usual, both blue bands are visible, but the weight of radiation falls upon that of shorter wave-length, the Rydberg line being comparatively inconspicuous. Miss Cannon found several of the hydrogen lines in both series to be dark with illuminated borders, an arrangement, as she remarked, the inverse of that prevailing in γ Cassiopeiæ and its allies.[450] Mr. McClean recognised oxygen absorption in this star,[451] and the feature is not unlikely to prove, on fuller inquiry, common to all the members of its class. The absence of H and K is more than probable, and suggests comparisons and reflections.
A 7·5 magnitude star in Cygnus (D.M. + 43° 3571) shows, like γ Argûs, a mixed succession of hydrogen lines, but modified, perhaps, by double reversals.[452] With the Lick thirty-six inch Professor Keeler perceived its spectrum as “an extremely complicated range of absorption bands and faint bright lines,”[453] the unusual width of which struck both him and Professor Campbell. Thus the azure bands actually overlap, forming a single indistinct glow one hundred tenth-metres broad. A spectrograph of this object, taken by Mr. Ellerman with the forty-inch Yerkes refractor, is described[454] as totally unlike any spectrum of the fourth type. Whether the dissimilarity is of a nature to be generalised so as to exclude all idea of kinship between these stellar families is more than we can tell at present.
A star of about the same brightness, distinguished as “Argelander-Oeltzen, 17,681,” was swept up in Sagittarius by Pickering in 1881. In its spectrum the golden ray at λ 581 and the lazulite beam at λ 465 predominate almost exclusively. Vogel could see no others with the great Vienna refractor in 1883;[455] nevertheless, Campbell succeeded, ten years later, in measuring twenty bright lines in this wonderful spectrum.[456] Only one among them, and that of secondary importance, can be attributed to helium; but many due to that substance may be included in the unexplored absorption spectrum of “A.O. 17,681.”
A star of 6·4 magnitude in Canis Major, catalogued as “Lalande 13,412,” shows, instead of the unknown blue and yellow rays at λ 465 and λ 581, the “new” hydrogen lines at λ 469 and λ 541.[457] The spectrum includes, besides, a more refrangible blue band, centred about λ 461, but diffuse and divided. These multiple azure effulgences in the Wolf-Rayet stars offer a problem of singular interest. They possess none of the structure of genuine flutings; they seem apt to spread unsymmetrically. Is this an effect of pressure on the emitting vapour? Or does it arise from some property inherent in it, or some mode of action exerted upon it? The answers may be long postponed, but cannot fail to prove interesting.
A unique specimen of this class was photographically detected in Cygnus in the course of the “Draper Memorial” surveys.[458] It is extremely faint—below the ninth magnitude—and was enrolled in the Bonn Durchmusterung as D.M. + 30° 3639. Nevertheless, its spectrum offers more than common facilities for exact observation, owing to the sharpness of its component rays. Thirty were measured by Campbell in 1893,[459] and they include, with many common to the type, several that appear to be individual to the star. The two brightest lines, however, are F and λ 569, the “citron” line strong in γ Argûs. The Pickering and Rydberg series are faint, while the alternative blue band at λ 465 glows intensely. But the distinctive feature of the star is that it is spectroscopically nebulous. Observed on the F-line like a solar prominence, Professor Campbell found it to present a very appreciable disc,[460] which, on narrowing the slit, became reduced to a line, as shown in Figure 20. The length of this line is about 5″ of arc, and it measures the apparent diameter of the incandescent envelope of hydrogen which surrounds the body of the star. Only the hydrogen lines behave thus exceptionally; all the other spectral rays show as mere bright points upon the continuous background, which they do not transcend by a hair’s-breadth. That is to say, hydrogen is the sole glowing constituent of the enormous appendage revealed by the powerful appliances available at the Lick Observatory. It has been seen nowhere else, but Runge[461] and Keeler[462] separately verified its existence.
There are a few circumstances worth noting in connection with this extraordinary appearance. First, the vast spread of incandescent hydrogen round the star has no effect in thickening the representative lines of that substance in the star’s spectrum. They are, on the contrary, particularly fine and narrow. The envelope, we can hence infer, is not an atmosphere; there is no appreciable downward pressure of its strata. Again, it must be—in the ordinary sense—hotter than the photosphere it surrounds; for the bright lines emanating from it are not reversed where they cross the prismatic thread due to the nucleus, as they should be if the nucleus were at a higher temperature than its envelope. Finally, it may be possible, by researches into the parallax and proper motion of this star, to form some estimate of its actual distance, and consequently of the real extent of its gaseous surroundings. Thus might be opened a novel line of inquiry destined to lead future students of the skies far afield.
The chemistry of the Wolf-Rayet stars—judging from partial interpretations of the disclosing script—is of the simplest. They have as unfailing constituents hydrogen and helium; oxygen is at least occasionally present, and the detection of nitrogen may be expected with some confidence. Sir William and Lady Huggins showed in 1890[463] the inadmissibility of a carbon origin for any of the blue bands, and defined their positions by exact measurements. Professor Campbell’s observations, visual and photographic, of thirty-two members of the class contributed materially to promote acquaintance with their peculiarities; yet they stimulated, rather than satisfied curiosity.
The distribution of these objects is strongly selective. They are virtually confined to the Milky Way. The rule is emphasised by its apparent exceptions, for the single specimen of the type deviating considerably in position from the galactic plane has proved, on closer inquiry, to be situated in a galactic offset; while the twenty-two grouped in the Magellanic Clouds belong to aggregations of the galactic order, and subject presumably to galactic conditions. The Milky Way, then, and the Nubeculæ afford analogous and exclusive facilities for the development of such bodies. They seem, moreover, to be provided more freely in some regions than in others, since the objects in question tend to collect into knots or groups, the finding of one Wolf-Rayet star being generally the prelude to additional detections in the same neighbourhood. Yet they rarely or never form binary combinations. They are loosely associated without any suggestion of mutual circulation. Nor has any of them, so far, given signs of spectroscopic duplicity. They are singularly steady light-givers. No Wolf-Rayet star is under the slightest suspicion of variability. Atmospheric incandescence on the largest scale is compatible in them with the perfectly uniform working of arrangements for the transference of heated matter from the interior to the surface of the radiating bodies. Considering the frequent and extreme instability of many bright-line stars of other varieties, this fact can hardly be too strenuously insisted upon.
XI. THE GENERAL QUESTION OF BRIGHT LINES IN STELLAR SPECTRA
The more closely we study the phenomena of bright lines in stellar spectra, the more fully convinced we become that no single or simple principle avails to explain them. They are evidently produced under varied circumstances, at different elevations above the stellar photospheres, and in manifold forms of connection with the adjacent absorbent layers. Reviewing rapidly the chief types of emissive spectra, we can, to some extent, gather their implications.
The sine quâ non for the display of bright lines is the presence of a stratum in the star’s atmosphere outshining the photosphere. The difficulty is indeed very great of attributing this superiority in brightness to a superiority in temperature; but it can be evaded by the use of Wiedemann’s convenient term “luminescence,” signifying a state of glow unconditioned in the strict sense by heat. The rationale of “luminescence” is still uncertain, but the introduction of the new idea it represents marks an important departure from the old groove of thought. Now we can trace two modes of emission in the sun, faintly indicated, it is true, but instructive as being within reach of comparatively immediate study. In the first place, some of the Fraunhofer lines seem to be relieved against vague effusions of light,[464] originating, almost certainly, beneath the reversing layer, among the interstices of the photospheric clouds. In the second place, the violet calcium lines, and occasionally one or two lines of hydrogen, are doubly reversed in the chromosphere. Both kinds of effect are reproduced in stellar spectra.
Carbon stars show bright lines, which may be described as chromospheric; the gases emitting them surmount the vapours generating the noted dark bands. Moreover, these rays appear to be simple and uncompounded of bright and dark elements; they are not perceptibly affected by reversals or absorptions. The same may be said of the bright lines in Mira-variables. Yet the locality of their origin is widely different. They are essentially photospheric and deep-seated, shining from beneath the dusky flutings they diversify. The leading characteristic of bright-line helium stars is the duplication of their spectra. The vivid rays have dark companions. And this, not through the optical conjunction of two distinct bodies, but as the result of physical conditions prevailing in a single globe. In such stars, then, there are complex stratifications of emitting and reversing vapours diversely affected, we cannot tell how, by heat, pressure, magnetism, or electricity. The gradual penetration into the secrets of nature that must accompany their study offers an enticing, and a far from hopeless prospect to the rising generation of astrophysicists. But it will involve an indefinite expenditure of time and labour. The conditions of bright-line production in Wolf-Rayet stars are extremely hard to define. They probably vary greatly in individual specimens. The state of some probably resembles that of helium stars showing analogous symptoms of gaseous incandescence. The corresponding reversals, however, are less emphatic, and have indeed been rather suspected than perceived. Other members of the Wolf-Rayet class (for Campbell’s star presumably has fellows) possess vast gaseous envelopes, uniformly glowing, and scarcely arresting light.
As to the theory of bright lines in stellar spectra, it is only certain that they testify to a real excess of incandescence in certain layers of the stellar atmospheres. They are not optically created by the concentration, through distance, of far-reaching, cool, gaseous appurtenances. This is proved by the example of the sun, by the study of Campbell’s star in Cygnus, in which not a cool, but a strongly glowing appurtenance is actually visible, and by the phenomena of spectral variability, totally inexplicable on the view that mere extent of gaseous surroundings is competent to produce bright lines. It is much easier, however, to deny than to affirm—to perceive incongruities with fact than to trace the lines of a true hypothesis. This cannot be done off-hand; much preliminary toil must be undertaken. Of prime necessity is the continuous study of the sun’s facular rays, of their originating conditions, their displacements, their periodical changes. Laboratory inquiries will proceed simultaneously—inquiries into the nature of “luminescence,” into the temperature of radiating gases, into the spectral effects of varied modes of electrical illumination, all which topics may demand subterfuges of treatment not yet easily imaginable. But need will stimulate invention, and knowledge will advance along the arduous ways by which alone future progress is possible.
XII. ANOMALOUS AND VARIABLE SPECTRA
A small proportion of stellar spectra show marked individualities; they differ notably from the recognised types, and may help, by their very diversity, to elucidate them. Some belong to stars variable in light; most are probably inconstant in their peculiarities; none have as yet received the persistent attention that they deserve.
The “comet variable,” R Geminorum, was last observed by Vogel in 1874,[465] and then not to the best advantage. A maximum, at which the star rose somewhat above the seventh magnitude, occurred 7th April, and during a month previously dark and bright bands were distinguishable in its spectrum. Repeated measurements proved the latter to coincide in position with the dusky colonnade in fourth-type stars. They were due, quite unmistakably, to the direct radiations of carbon. The variable, in other words, glowed with a light fundamentally the same in quality as that of a comet approaching perihelion. No hydrogen or helium lines seem to have been present; but the strong yellow ray located at λ 581 must be identified with the Wolf-Rayet line,[466] specially associated, as we have seen, with the lazulite band at λ 465. It will be interesting to learn whether the same connection subsists in the variable; but some years must elapse before any kind of new information regarding it can be obtained. Just at present the star, in its bright phases, is too near the sun for purposes of useful research, and its period of 370 days differs so little from a year that the conjunction passes off with extreme slowness. The minima of this curious variable carry it to the very verge of extinction, below the range of ordinary telescopes. The attempt has not yet been made to keep it in view with those of large aperture.
A star capriciously variable both in the kind and in the quantity of its light was discovered by Pigott in 1795. Usually almost constant at the sixth magnitude, R Coronæ is liable, at intervals counted by years, to lapses into obscurity,[467] varied by spasmodic efforts towards recovery, each crisis of instability lasting many months. The spectral fluctuations of the star seem unrelated to its changes of brightness. They were first noticed by Mr. Espin in 1890, but so far have not been very clearly defined. Migrations from type to type are somewhat vaguely indicated; their reality would involve so much that is novel and surprising that it can only be admitted on irrefragable evidence. On 14th September 1890[468] the spectrum appeared of Type iv.; it was interrupted by obscure bands held to be those of carbon absorption. In April 1893[469] bright lines and nondescript dark bands alternately stood out to view and became effaced; and on 4th May 1899[470] a spectrum resembling that of the sun had established itself. Mr. Espin is convinced that a double light-source is in question, and that the observed changes are explicable by the conjunctions and elongations of revolving stars, giving contrasted spectra; but unless they can be brought into conformity with some time-regimen, such an hypothesis is evidently inapplicable.
The spectrum of a star in the Shield of Sobieski is probably analogous to that of R Coronæ, but the suspected variation is not from the fourth, but from the third to the second type. In August 1890 Mr. Espin derived from R Scuti a set of faint bands, modelled to all appearance on those of Mira or α Herculis;[471] a glimmer of bright lines in the blue and violet, however, betrayed unusual characteristics, completely drowned, like the concomitant absorption, in the flood of continuous light accompanying and occasioning the maximum in October. Less than two years later, 25th June 1892, Dr. Krüger found the spectrum definitely solar, the b-group of magnesium being particularly distinct.[472] R Scuti never sinks below the ninth magnitude. It is then at all times fairly accessible to exact investigations, which should serve, without much difficulty, to fix the true nature of this still enigmatical object. The mode of spectral variability which it exemplifies is not generally accounted as possible by those who undertake to discuss the intricate subject of stellar development; this could hardly, indeed, be dealt with on the old lines if the suspected phenomenon proved to be an unquestionable fact.
Spectral and luminous variability are, in certain stars, inseparably connected. With increasing light the hydrogen lines brighten; with ebbing light they fade. A common cause evidently governs the two kinds of change. This close correspondence is observed only in periodical objects of the Mira-class. Variables of a less regular type, such as R Coronæ, fluctuate spectrally in apparent disregard of their light-vicissitudes; while yet a third description of spectroscopic variables are exempt from the least suspicion of instability in brightness. A conspicuous example of the last kind is γ Cassiopeiæ.
Normally, the red hydrogen line is the brightest in its spectrum; yet it seemed extinct when looked for by Dr. Vogel, 18th June 1872.[473] To the Dunecht observers, however, it showed “superbly” bright 20th December 1879,[474] then lapsed into invisibility, until rekindled under the eyes of Von Gothard at Herény, 13th August 1883.[475] Since then it has not been missed, but has rarely been sought; for it can scarcely be called accessible to spectrographic observation, and direct inspection of stellar spectra has unfortunately fallen out of vogue. On 13th September 1885 Dr. Copeland found C very bright in γ Cassiopeiæ, F just measurable;[476] on fifty-two plates taken at Stonyhurst during the years 1891–99[477] F was “superlatively bright,” C being of course below their range. No evidence was elicited from them of alteration in the hydrogen spectrum, but they gave strong grounds for suspicion of change in lines due to other substances, notably in a strong ray at λ 4586, doubtfully associated with vanadium. Suspicion might have been raised to certainty if the yellow helium line had fallen within the scope of inquiry, for the variability of D_{3} in this star may safely be taken as proved. Although observed as bright by Secchi in 1867,[478] measured by Von Gothard 20th August 1883,[479] and just recognised at the O Gyalla Observatory in 1891, and at South Kensington late in 1889 and 1894,[480] the line is commonly invisible under the most favourable conditions. Keeler could not find it with the great Lick refractor in the summer of 1889;[481] three spectrograms, taken on orthochromatic plates with the Pulkowa thirty-inch by Bélopolsky in 1892, bore no trace of it;[482] its emergences, in brief, are so transient and uncertain as to be altogether exceptional. They seem quite casual—that is to say, their law of causation is to us inscrutable. The remaining chief lines of helium in γ Cassiopeiæ are dark, with indications of fine bright reversals at their centres.[483]
The metallic spectrum, too, is unmistakably variable. Von Konkoly noted sodium absorption at D, 15th September 1884.[484] Yet Keeler’s examination, five years later, showed the spectrum in that vicinity to be absolutely continuous. No subsequent record of dark D has probably been made. The magnesium group b, on the other hand, seen dark by Keeler, appeared bright on the Stonyhurst photographs, and it was accompanied by the blue emission from “high temperature” magnesium at λ 4482. No iron lines are brightened in this spectrum. A clue to its intricacies may be found by the employment of combined visual and photographic methods. Neither by itself is altogether satisfactory. Changes in one part of the spectrum lose half their significance unless correlated with changes in the remaining parts. The assurance of their reality, besides, would be immensely strengthened by the demonstration of their not being isolated. Sympathetic variations, independently recorded, could hardly be the creation of instrumental or other extraneous causes.
The chromospheric instability of γ Cassiopeiæ is shared by a good many other stars. Among them is J Velorum (A.G.C. 14,145), spectrographically registered at various dates in the course of the Harvard College southern surveys of the heavens. Miss A. J. Cannon’s examination[485] showed that on the plate taken 2nd June 1893 the green and blue hydrogen lines (Hβ and Hγ) were bright, superposed upon broad absorption bands. Nevertheless on 19th April 1895 and 19th March 1896 they were simply dark, with no trace of vivid reversals. And so they remained in 1899. Whether the red line, usually in such stars the most brilliant of the series, responded to the chromospheric extinction attested by its more refrangible associates, can never now be known; but something may, in the future, be discovered about its behaviour should the spectrum of J Velorum ever be rekindled. The star, which is of the fifth magnitude, does not vary appreciably in lustre.
An inverse change to that observed in J Velorum was detected by similar means in a seventh-magnitude star in the southern constellation Chamæleon (A.G.C. 14,686). On 20th May 1892 it appeared to be of the Sirian type; hydrogen showed only by absorption; but on 3rd April 1895 Hβ was bright, eighteen days later Hγ had followed suit, and fringes of light seemed attached to the lower edges of two of the ultra-violet hydrogen lines.[486] The progressive incandescence, betokened by the creeping upward of the illumination, was a complete novelty; its probable initial symptom in the blaze of C necessarily remained unnoticed. It is earnestly to be hoped that this unique object may not slip out of view amid so many conflicting claims for attention advanced by the denizens of the southern heavens.
A star in Canis Major (A.G.C. 9181)[487] is distinguished by frequent fluctuations from brilliancy to obscurity of the green and blue hydrogen lines. Miss Cannon has traced their spectrographic history since 1892. The more refrangible members of the series are present—it can be inferred—as absorption lines, and C is explicitly stated by Campbell to have been glowing in 1894.[488] Variations of its green companion (Hβ), analogous to those just described, have recently been detected in the spectra of η Centauri and κ^2 Apodis.[489]
The percentage of abnormal stars found on the Draper Memorial plates is exceedingly small; yet they sum up to a not insignificant total. A few may be named as worthy of sustained attention. A sixth-magnitude star in Libra (A.G.C. 20,937) was announced in 1895[490] to show a spectrum resembling that of the great Looped Nebula (30 Doradûs), which differs in light-quality from other gaseous nebulæ; and a stellar apparition in the Centaur, then visible, was added to the spectral group. “Nova Centauri” promptly disappeared, but the star in Libra is permanently present, and available year by year for prismatic comparisons. The peculiarities of the following objects have not been expressly defined:—
1. S.B.D. −22° 1070; R.A. 5^h 14·5^m; Dec. −22° 19′. Mag. 8·7. Photographed at Arequipa.[491]
2. Z.C. 17^h 734; R.A. 17^h 13·2^m; Dec. −66° 15′. Mag. 8·5. Photographed at Arequipa.
3. S.D.M. −8° 1467; R.A. 6^h 28·1^m; Dec. −8° 48′. Mag. 8·5, but slightly variable.[492]
4. S.D.M. −11° 1941; R.A. 7^h 22·4^m; Dec. −11° 31′. Mag. 8·9 variable. Banded spectrum of uncertain type.
5. S.D.M. −10° 5057; R.A. 19^h 7·7^m; Dec. −10° 54′. Mag. 7. Unique spectrum of bands.[493]
Possibly the original records secured of these stars may never be duplicated, since they are not unlikely to be spectrally variable as well as peculiar. In any case their characteristics, which are precisely of the kind to prove specially instructive, need to be more fully ascertained.
The spectra of φ and ψ Persei—both bright-line helium stars—have been suspected of fluctuations; but those of the first may depend upon varying radial velocity,[494] while those of the second, although slight in amount, are of a particularly interesting description. They consist in the occasional shifting of the brilliant narrow F of hydrogen to one or other side of the absorption-band upon which, in general, it is centrally placed.[495] These displacements are probably of the same nature as the alternate marginal illuminations of Hβ in θ Orionis and 11 Monocerotis; they are certainly unconnected with revolving movements in a system of bodies. Many more instances might be given of stellar spectra apparently abnormal, and at least ostensibly variable, but the above may suffice as specimens.
XIII. COLOUR VARIABILITY
Colour variation in stars is a somewhat elusive phenomenon. It cannot be measured; no “colorimeter” yet constructed has given satisfactory results. Then it is subject to adventitious modifications depending upon the state of the atmosphere, the fluctuating sensitiveness of the retina, the nature and aperture of the telescope employed. The same observer after a prolonged vigil will often receive quite different chromatic impressions from those derived with unfatigued sight; nay, his right and left eyes may sometimes pronounce incongruous judgments upon a colour-harmony or a colour-contrast. Such counterfeit changes, however, are slight and evanescent; with due care they can always be separated from intrinsic variations. The endless individualities of colour-vision have, indeed, also to be taken into account. There is no branch in which personal equation tells so heavily, yet so intangibly. Hence casual anomalies of description hardly raise a presumption of actual change. Evidence that it has occurred can only be admitted with extreme caution. The difficulty is to disengage what really deserves consideration from the multitude of floating statements tending only to bewilderment.
Three kinds of colour-variation may be discriminated. They severally affect periodical stars, red stars fairly constant in light, and tinted star couples.
(1) Stars with a light-cycle of less than a hundred days are usually of an unchanging yellowish hue; but “long-period” variables are characteristically red, and redness in stars appears to be rarely a fixed or stable property. It might be compared to an external covering capable of alteration in opacity, or even of entire removal, and connected in its effective action with complex, more or less unsettled conditions. Very commonly, the rises and descents in magnitude of such stars are associated with fadings and flushings of colour, a deeper tint generally accompanying a low light-phase. For this there is a double cause, in the diminution of brightness, and in the increase of absorption. The first acts physiologically. A faint ray strikes the eye as redder than one more brilliant, although both be of the same refrangibility. The second works objectively. Absorption in stellar atmospheres tells mainly on the blue end of the spectrum. Hence, as darkening closes in upon the shorter wave-lengths, the stars redden more and more. Mira, which is not properly a colour-variable, shows this effect markedly. Certain objects of the same class, however, change more radically, and less consistently. Their fluctuations in hue correspond very partially to their fluctuations in light. Colour-change seems to progress independently, and from a superficial point of view quite capriciously.
At Sir Cuthbert Peek’s observatory near Lyme Regis, a score of variable stars have been kept under watch since 1887. The data regarding them collected by Mr. Grover are remarkable and suggestive in several particulars, especially as regards the correlation of colour with magnitude. An important example is afforded by S Herculis, a star varying from the seventh to the thirteenth magnitude in about ten months. It is strongly red with a fine fluted spectrum, yet has, at sundry times, been seen completely blanched. We extract from the Rousdon Observations some notes of its colour, with the corresponding dates and magnitudes.
S Herculis ┌──────────────┬──────────┬──────────────────────────────┐ │ Date. │Magnitude.│ Remarks. │ ├──────────────┼──────────┼──────────────────────────────┤ │1886, Nov. 12 │ 9·4│White, sharp, and distinct. │ │ „ Nov. 29 │ 8·5│Decided red. │ │1887, May 16 │ 10·9│White; little, if any, colour.│ │ „ Dec. 20 │ 7·3│Deep ruddy. │ │1888, Oct. 15 │ 6·5│Fiery red. │ │1889, June 29 │ 9·0│Dull greyish. │ │ „ Sept. 30│ 8·3│Deep coppery red. │ │ „ Oct. 22 │ 9·1│Blood red, well defined. │ │1890, May 23 │ 9·1│Grey or ashen colour. │ │1891, May 12 │ 6·8│Brilliant scarlet. │ │1893, Aug. 17 │ 9·3│Dull white, well defined. │ │1894, Sept. 8 │ 7·5│Nearly white, sharp. │ └──────────────┴──────────┴──────────────────────────────┘
No trace of regularity is perceptible in these changes. The mean magnitude of the star when white was 9·0, when at its reddest, 8·5. They are then obviously unrelated to its light-phases.
An analogous object is T Ursæ Majoris, which alternates between deep red and “creamy,” or pure white, though with a decided tendency to assume paler tints as brightness increases. A typical pair of observations were made on 5th and 14th February 1893. On the first evening T Ursæ was estimated as of 10·1 magnitude, and of a “deep, dull, ruddy hue”; on the second, it had risen to 9·3 magnitude, and become a “dull leaden colour,” showing “no trace of orange or red—a very curious change,” and one altogether unaccountable. Spectroscopic information, simultaneously procured, would have been likely to prove instructive, but none, unfortunately, is available.
A counter-example to T Ursæ is S Cephei, which, observed under the same conditions, and undergoing similar variations of brightness, was nevertheless recorded as at all times conspicuously red. On the other hand, χ Cygni, a flagrantly red variable of the Mira type, occasionally divests itself of colour as it brightens, although “scarlet” maxima are more common than “white.” Espin’s observations confirm the striking variability in hue of χ Cygni. On the whole, it cannot be doubted that temporary whiteness is a frequent feature of this class of ruddy stars, and the fact implies a great deal.
(2) In the second class of colour variables, light-change supervenes incidentally or not at all. It includes two historic examples—Sirius and Algol, both exceedingly unlikely, yet both attested on good authority to have been red within the scientific memory of man. The Sirian question has been exhaustively discussed by Dr. See[496] and by M. Schiaparelli;[497] their arguments are of most curious interest, but we can here only attempt to give what appears, on a fair view, to be their upshot. Two facts are incontestable; Seneca compared the colours of Mars and Sirius, and pronounced the star to be more intensely red than the planet, and Ptolemy applied to it his current epithet for “glowing ruddy” objects (ὑπόκιρρος), a piece of evidence vainly sought to be explained away as a transcriber’s error. Many other ancient authors imply, or are held to imply, what Seneca and Ptolemy definitely state; but even apart from these confirmatory hints, the simplest and perhaps the safest course appears to be to accept such definite statements. Their improbability does not in itself warrant their rejection. It has been suggested that the rapid scintillation of the Dog-star may have lent to it a fictitious redness, but it does not do so now. “Sirius is glancing blue-bright like a spirit,” Carlyle wrote from Templands in April 1842. And certainly the atmospheric disguise of colour cannot have been less effective in Dumfriesshire than at Rome or Alexandria. In the Iliad, a fiery nature and aspect are ascribed to Sirius; but Homeric indications are often loose or figurative. They, however, lend in this case countenance to the plausible surmise that the redness of the star was of antique standing. As to the date of its vanishing, nothing positive can be asserted; but the negative testimony of Al-Sûfi places it almost conclusively before the tenth century.
The same Persian astronomer supplies the only extant notice of Algol’s early redness. Perhaps a merely temporary phase, it seems nevertheless to have recurred after nine centuries. This was in 1841, when Schmidt at Athens perceived the star as yellowish red,[498] although its subsequent whiteness was patent to him as to all other observers. Was Schmidt deluded? It is very difficult to determine. Only the star itself can authenticate, by renewing, its evanescent glows of colour.
The pronounced redness of a seventh-magnitude star, No. 8 in Schjellerup’s “Red” Catalogue,[499] was recorded by Oeltzen during his revision of Argelander’s northern zones. Copeland, nevertheless, found it white, 1st January 1876; Espin, yellow, with a continuous spectrum, 14th November 1887; while Krüger registered on 6th October 1891 well-developed bands of the third type corresponding to an orange tint. Again, a ninth-magnitude star in Taurus[500] appeared to Hind “very red,” 3rd September 1848, but “bluish” 14th November 1850. Lost sight of for a quarter of a century, it was next observed by Copeland in January and February 1876 as pale yellow, and by Doberck, three years later, as reddish orange. Finally, on 10th January 1888, Espin saw it white, with a seemingly continuous spectrum; since when no attention—that the present writer is aware of—has been paid to it. A much brighter star in Aquila[501] (seventh magnitude) showed red to Schjellerup in 1863, but to Birmingham colourless in 1872 and 1874, and blue 18th May and 20th July 1873. These changes were in a manner verified by subsequent spectroscopic observations; for the object, which had then recovered a ruddy tinge, was classed by Espin as of the fluted type, 20th September 1889, but by Krüger, 25th June 1892, as a solar star with a pale yellow cast. The colour-phases of an eighth-magnitude star, “63 Schjellerup,”[502] are attested by the best authorities; it is impossible to doubt their reality. Picked out for its redness at Copenhagen in 1863, the object, after numerous alternations, was described by Franks in 1885 as white. No later observations appear to be extant.
The following short list of the best-authenticated colour-variables may be useful to observers:—
┌───────────────────┬──────────┬──────────────────────────────────────┐ │ Designation. │Magnitude.│ Remarks. │ ├───────────────────┼──────────┼──────────────────────────────────────┤ │ 5 Schjellerup │ 7·0 │“Full garnet,” J. Herschel; red, │ │ = Krüger 75 │variable? │ Schjellerup, 1863; white, Dreyer, │ │ │ │ 1876. │ │ 8 Schjellerup │ 7·0 │Deep red about 1850; white, 1st │ │ = Krüger 102 │ │ January 1876. │ │ 63 Schjellerup │ 7·8 │Rubra, Schjellerup, 1863; blue, │ │ = Krüger 504 │ │ Birmingham frequently in 1873; │ │ │ │ decided red, Gould; colourless, │ │ │ │ Dreyer, 1880. │ │ 90 Schjellerup │ 7·7 │Rubra, Struve; bluish white, │ │ = Krüger 687 │ │ Birmingham, 1874; orange, Dreyer, │ │ │ │ 1879; white, Espin, 1888. │ │ 93 Schjellerup │ 9·0 │Blood red, Schjellerup, 1863; orange, │ │ = Krüger 698 │ │ Copeland, February 1876; colourless,│ │ │ │ Espin, 10th February 1888. │ │ γ Circini[503] │ 3·4–5·2 │Very red, Gould, about 1875; white, │ │ │ │ Stanley Williams, 1886. │ │64 b Schjellerup │ 8·8 │Very red, Hind, 1848; bluish white, │ │ = Krüger 513 │ │ Hind, 1850; red, Dreyer, 1879; │ │ │ │ white, Espin, 1888. │ │ 148 Schjellerup │ 8·5–9·5 │Scarlet, Rosse, 1861; dark red, │ │ = Krüger 983 │ │ d’Arrest, 1866; colourless, │ │ │ │ Birmingham, 1874; red, intense │ │ │ │ bands, Dunér, 1878. │ │ 214 Schjellerup │ 7·0 │Red, Schjellerup, 1863; not red, │ │ = Krüger 1436 │ │ Birmingham, 1872, 1874; blue, │ │ │ │ Birmingham, 1873; orange, fluted │ │ │ │ spectrum, Espin, 1889; yellowish, │ │ │ │ solar spectrum, Krüger, 1892. │ │ r Velorum │ 5·0 │Red, Gould, 1870·73; leaden white, │ │ │ │ 1888, A. M. Clerke; slight red │ │ │ │ tinge, Tebbutt, 1891. │ │222 b Schjellerup│ 7·8 │Red, Lamont; yellow, Dreyer, 21st July│ │ = Krüger 1512 │ │ 1875; white, Dreyer, 18th August │ │ │ │ 1875; yellow, Espin, 1889; white, │ │ │ │ Krüger, 1891. │ └───────────────────┴──────────┴──────────────────────────────────────┘
Two stars[504] have been mentioned in an earlier chapter as anomalously white, considering that their spectra are of the fourth type. The possibility should not be overlooked that their paleness is only temporary. They are perhaps colour-variables, and will, at some future time, show the ruddy hue appropriate to the quality of their light.
(3) The colour changes of double stars are a peculiarly baffling subject of inquiry. Many have been recorded that can safely be dismissed as illusory; some that are unquestionably real. Yet in most cases there is a large element of doubt. Personal idiosyncrasies come strongly into play; meteorological influences, instrumental diversities, and all the chances and changes of existence swell the reckoning of uncertainty. To say nothing of the indeterminateness of language. Star tints are often so delicate as to defy verbal definition. Distinctions between rose-pink and amethyst, sea-green and apple-green, ashen, lilac, and grey, have only a nominal meaning. These tender shades, moreover, while escaping some eyes altogether, are enhanced by others into vivid contrasts; and hence observers, expecting to see star-couples glowing like fruits of the Hesperides, are apt to carry away the impression that the subtle coloration actually presented to them implies a marked change. To separate the kernel of fact from the husk of opinion or illusion is then no easy matter. Yet an inadequate attempt to banish confusion is almost always better than none, and may here be worth making.
The more closely the chromatics of double stars are studied, the more clearly emerges an irreducible minimum of change. A satisfactory example is afforded by one of the most carefully watched binaries in the heavens. The primary in 70 Ophiuchi is of 4·5, the satellite of 6·5 magnitude, and it is unquestionably the satellite which conspicuously varies in hue. Sir William Herschel in 1779 perceived in it a very slight reddish suffusion, and J. Herschel and South described the pair in 1824 as “white and livid.” Yet the elder Struve, an incomparable authority, considered their “yellow and purple” tints remarkable enough to warrant their inclusion in a restricted list of objects showing colores insignes,[505] and they were still “topaz and violet” when observed successively by Smyth and Webb.[506] “Gold and purple” again they appeared in July 1883 to Perrotin at Nice, although less than a month previously he had noted them “greenish yellow and reddish yellow,” while a year later he recorded them as “golden and orange.”[507] This vesture they continue to wear. They are ordinary yellowish stars with an ordinary solar spectrum. Sooner or later, however, the companion may be expected to put off its crocus-veil and shine Tyrian-hued.
The stars of γ Delphini are now finely contrasted in orange and green. They appeared, nevertheless, white to the elder Herschel in 1779; white and yellowish to Herschel and South in 1824; “reddish yellow and greyish lilac” to Gore in 1874;[508] pale rose and light green to Dembowski in 1876–77; orange and green to Flammarion in 1877. Moreover, the companion showed “light emerald” during the years 1831–39, but “flushed grey” in 1850. Doberck found it bluish in 1882, and the primary yellow;[509] Vogel in 1883 recorded both stars as creamy white; while in 1895—according to Mr. Franks—the colours were “very pronounced, the chief star being a strong yellow and the companion greenish.”[510] They are of fourth and fifth magnitudes respectively, and a sky-gap of 11″ divides them. Their mutual revolutions have made little sensible progress during a century and a quarter, but their common drift through space certifies their systematic connection.
The case of 95 Herculis is somewhat perplexing.[511] This is an equal pair of fifth-magnitude stars, rigidly fixed during the last twelve decades at an apparent distance of 6″. Their “magnificent tints of orange and green” excited Father Secchi’s admiration in 1855; and Piazzi Smyth was accustomed to see them “apple green and cherry red” until 29th July 1856, when he perceived with stupefaction, from his point of vantage on the Peak of Teneriffe, that both were of the undistinguished white attributed to them by Herschel in 1780. Fitful and partial displays of their original chromatic brilliancy appear to be vouched for by Dunér’s and Flammarion’s[512] observations of the stars as “bright green and yellow,” and “gold and azure”; but their pale primrose is now unrelieved by a shade of difference. There is no good reason to doubt that, in the earlier part of the century, they were marked by vivid complementary colours. Obvious to Webb, they were remarked by Admiral Smyth as an unusual instance of diversity in tint “between components so nearly equal in brightness.”
Instances are not infrequent of the small star in pairs of disparate brightness varying in colour; but the relation is never inverted; no primary is exclusively subject to change of tint. The satellite of δ Herculis, a greenish star of the fourth magnitude, appeared to Struve alternately grape red and ashen white; to Dembowski, blue; to Knott, bluish green in 1850, ruddy purple in 1871; to Fletcher, in 1851, red; to Flammarion, violet. The conjunction of these stars is thought to be merely fortuitous. They are moving along divergent straight lines, and hence seem destined to definitive separation. Yet colour-changes of the kind affecting the satellite do not occur in isolated objects, and would rather imply a physical connection with a dominating orb. It will then be of particular interest to determine quite certainly whether δ Herculis is a truly gravitational, or simply an optical couple.
The companion of δ Cygni shows analogous variations. “Ashen grey” to Struve’s perception during the years 1826–33, it surprised him with a strong red glow in 1836; three years later, Dawes found it blue; Secchi, by turns red, blue, and violet in 1856–57; Dembowski, grey in 1862–63; Engelmann, red in 1865. Of late its blue aspect has predominated; yet Perrotin recorded it as yellow or orange with the great Nice refractor both in 1883 and in 1886. These stars make a very much closer pair than δ Herculis, and are in slow orbital movement.
Two at least of the four stars grouped in σ Orionis may be admitted to fluctuate in hue.[513] One of 7·5 magnitude appeared ashen grey in 1837, ruddy in 1851 and 1869, bluish in 1883. A more distant, somewhat brighter component, usually dust-coloured, was marked “grape red” by Smyth in 1832. Even the chief star is not of the perennial whiteness that should match its helium spectrum. Webb found it yellow in 1851, and Gould entered it as “red” in the Argentine Uranometry. It was divided by Burnham in 1888 into an excessively close pair (fourth and sixth magnitudes at 0·26″), which, already in 1891, gave indications of circulatory movement.[514]
The following is an enumeration of some double stars reputed, on good grounds, to be colour-variables:—
┌────────────┬───────────┬─────────┬──────────────────────────────────┐ │Designation.│Magnitudes.│Distance.│ Remarks. │ ├────────────┼───────────┼─────────┼──────────────────────────────────┤ │70 Ophiuchi │ 4·5, 6·5 │ 1·6″ │Primary white or yellow, satellite│ │ = Σ 2272 │ │ │ alternately purple, rosy, and │ │ │ │ │ yellow. Spectrum, solar. │ │ γ Delphini │ 4, 5 │ 11″ │Primary cowslip to orange; │ │ = Σ 2727 │ │ │ companion emerald to blue, │ │ │ │ │ lilac, and topaz. Spectra, solar│ │ │ │ │ and Sirian. │ │95 Herculis │ 5·3, 5·3 │ 6″ │Contrasted green and red to │ │ = Σ 2264 │ │ │ uniform yellow. Spectra, solar │ │ │ │ │ and Sirian. │ │ δ Herculis │ 4·0, 8·5 │ 26″ │Companion by turns ashen, red, │ │ = Σ 3127 │ │ │ violet. Chief star gives a │ │ │ │ │ helium spectrum. │ │δ Cygni = Σ │ 3, 8 │ 1·5″ │Satellite grey to red, blue, or │ │ 2579 │ │ │ green. Slow binary. Large star │ │ │ │ │ gives a Sirian spectrum. │ │ σ Orionis │ 4·1, 7·5, │13″, 41″ │Chief star white to reddish; │ │ = Σ 762 │ 7·0 │ │ helium spectrum. Companions grey│ │ │ │ │ to ruddy. Fixed. │ │38 Geminorum│ 5·5, 8·0 │ 6·8″ │Companion varies in magnitude, 7·5│ │ = Σ 982 │ │ │ to 10; in colour, from bluish │ │ │ │ │ (1829) to red (1856, 1863), and │ │ │ │ │ azure (1872). │ │ γ Leporis │ 4·0, 6·5 │ 93″ │Companion pale green, 1832; │ │ │ │ │ garnet, 1851 and 1874 (Webb). │ │ │ │ │ Chief star gives a solar │ │ │ │ │ spectrum. │ │γ Serpentis │ 4·5, 9·0 │ 51″ │Small star lilac, 1832; “native │ │ │ │ │ copper,” 1851 (Webb). │ └────────────┴───────────┴─────────┴──────────────────────────────────┘
Colour-variability has hitherto been only observed, as it were, in passing. And the casual study of a subject is seldom effectual. Here much more is required if any progress is to be made towards discovering the laws and cause of the phenomenon. What is essential to ascertain is the nature of the spectroscopic response to colour-change. On this side the problem can be attacked with some hope of getting nearer to a solution. If visual alterations of hue can satisfactorily be brought to the test of prismatic analysis, the way will be thrown open for an important gain of knowledge; while it is hard to see by what other means ignorance on the curious topic we have been discussing can be dissipated. It is not, indeed, always easy to combine work in different branches; yet the correlation of results is a vital need of astronomy, and scarcely ever fails to prove especially and widely illuminative.
XIV. THE SPECTRA OF DOUBLE STARS
The spectra of double stars stand in the closest relations to their colours. This, indeed, is almost a truism, since spectra merely show in detail what is summarised in mixed tints. Yet the two forms of statement are not tautological. The result of prismatic analysis cannot be wholly anticipated from the visual impression. The eye makes no attempt to reduce its sensations to their elements. Totally different rays may be blended and balanced so as to produce an identical sum-total to the perception of the optic nerve. Nor would it be in all cases easy to pronounce upon the colour of a star from the simple inspection of its spectrum. One cannot tell beforehand, so to speak, how the eye will take things. Some scarcely measurable reinforcement of selective stoppage, a few rays of absorption added or removed, may make the difference between rosy and golden, or purple and pink. Thus neither direct nor prismatic observations are superfluous; but the latter, as affording scientifically accurate and—through photographic means—permanent records, are by far the more important.
The spectra of double stars unlike in colour are usually of different types; and here a remarkable rule applies. Contrasted pairs are, with few and doubtful exceptions, notably unequal in brightness, and the warmer tint invariably belongs to the larger component. Blue, green, or violet stars are always the satellites of red or yellow primaries; and, in accordance with these indications, they give first-type spectra, while their brighter and more ruddy neighbours show Antarian flutings or solar lines. We are thus led to the unexpected conclusion that, of two globes simultaneously contracting, the larger, which should naturally cool more gradually, and therefore run through its evolutionary stages at a more leisurely pace, attains solar standing while its companion still remains a “white star.” This relation is the very crux of cosmic growth-theories; something more will be said about it in the next chapter.
The separate spectral examination of coupled stars is far from easy, and has indeed rarely been attempted. Only by Sir William and Lady Huggins has the subject been prosecuted systematically and with success. Their application to it of photography, rendered possible by the completion, in 1897, of an ingeniously devised reflecting slit, constituted in itself an immense advance. Previously, only the superposed spectra of double stars had been chemically recorded, and these, for discriminatory purposes, were of no more than provisional use. One coloured pair, however, presents less difficulty in this respect than the rest. The components of β Cygni lie far enough apart to give distinct spectrographic images, formed by an objective prism, on the Draper Memorial plates.[515] Specially inviting as well to direct scrutiny, they were among the earliest objects subjected to Sir William Huggins’s light-analysis.
The pair consists of a third-magnitude “topaz” star and a fifth-magnitude “sapphire” at 34″. The unaltered value of this interval since Bradley’s measurement of it in 1755 almost assures us that they drift together through space under the stress of a physical bond. For their proper motion, though very small, would have sufficed, in the course of a century and a half, to produce unmistakable relative displacement. Blue stars, besides, are never solitary; and the companionship upon which their uncommon hue depends must evidently be real, not simply optical. Plate IX. Fig. iv. shows the spectra of these stars as photographed by Sir William and Lady Huggins.
Their complete diversity is apparent at a glance.[516] The hydrogen series is writ large and strong on that of the minor luminary; helium absorption is not apparent; the Sirian type is pronounced. Of solar quality, no less decidedly, is the golden light of the primary. Yet it cannot escape notice that the photographed spectra do not explain the vivid colouring of β Cygni; they might have been taken (speaking broadly) from any two stars of the types represented. This, indeed, was just what should have been expected, since the special absorption differentiating them from the common run of stars was known to lie outside the range of sensitiveness of ordinary plates. As regards the blue member of the pair, at any rate, there could be no doubt of the fact. A set of dark bands, cutting out a goodly proportion of its yellow and orange rays, were observed by Sir William Huggins in 1864,[517] and again by Dr. Vogel in 1872,[518] and they correspond with, and fully explain, its chromatic peculiarity. The topaz hue of the primary cannot be so directly associated with the subtraction of particular qualities of light; it is more probably due to an enhancement of that veiling of the higher spectral reaches to which sunshine owes its primrose tinge. Further investigation is, however, desirable; above all, the photographic registration on isochromatic plates of the unfamiliar absorption-bands from which the companion of β Cygni derives its distinction as an azure star.
The theory of “composite stellar spectra” was proposed by Professor Pickering in 1891.[519] Spectrographic impressions showing a mixture of types should, he explained, result from the superposition of dissimilar spectra derived from close or telescopically indivisible stars. The forecast was verified by Miss Maury’s detection of eighteen self-imprinted images of the compound sort.[520] “In spectra of this class,” she writes, “the K-line appears either unduly narrow or overspread with a peculiar haziness. This appears to be due to the presence of an additional star, having a spectrum which belongs to some group earlier in the series. It is also significant that in such spectra the first-type characteristics predominate in the ultra-violet, the second or third-type features in the green and blue.” These duplex effects demonstrably own, in certain of the instances enumerated, a duplex cause; for they include γ Andromedæ, ε Boötis, and α Piscium, all three remarkable pairs. The presumption is accordingly strong that spectra appearing hybrid in small-scale delineations really emanate from a double source, although visual evidence of duplicity be wanting. Indeed, several of Miss Maury’s crypto-doubles, ο Leonis, ο Andromedæ, and α Equulei among the number, have been spectroscopically resolved by Professor Campbell into unlike pairs. And even should the motion-test fail, it need not be inferred that the star recalcitrant to it is single; for a negative result may signify merely that the method is inapplicable owing to the high inclination of the plane in which coupled stars revolve.
One of the show-objects of the heavens is γ Andromedæ, composed of a chrome-yellow star of 2·2 magnitude, and a sea-green fifth-magnitude attendant at 11″. The attendant itself can be divided with a good telescope into a blue and a green star, considerably advanced along an elliptic track since their first observation by Otto Struve in 1842; while the wide pair, discovered by Christian Mayer in 1777, remains relatively fixed, although their systematic union is attested by an identical secular progress of about 7″. Their spectra, photographed at Tulse Hill, closely resemble those of the components of β Cygni, the different patterns of absorption stamped on them forming almost as striking a contrast in the negatives as the colours of the original objects do in the sky. A similar combination is offered by ε Boötis, but on a reduced scale. The ultramarine satellite is here poised at a distance of only 3″ from its golden primary. Their spectra have, indeed, been no more than inferentially distinguished. Miss Maury’s scrutiny of the joint impression left by them upon the Harvard plates made it, however, fairly certain that, as usual, the blue star is of Sirian, the yellow star of solar quality; so that a relation of development is again indicated just the converse of that held, on à priori grounds, to be probable.
The theoretical incongruity is, in some cases, heightened by the substitution for the sun-like primary of a red star giving a fluted spectrum. Such a pair is α Herculis. An “emerald” star of the sixth magnitude, at a distance of 5″ from its glowing leader-orb, yielded to Sir William Huggins’s early examination a spectrum of precisely the same character as that of the satellite to β Cygni. Antares, too, is quite similarly coupled with a green star, the spectrum of which, judging by the duplex impressions obtained at Harvard College, resembles that of Sirius, with, it may be, some approximation to that of Procyon.[521]
Mr. Burnham performed in 1881 the unprecedented feat of dividing a third-type star into a very close pair. He detected a satellite of the ninth magnitude situated within just one second of arc of η Geminorum, a fine red star, variable in a period of 229 days, although its maxima are unmarked by any signs of gaseous emission, doubtless because of the comparatively slight extent of the light-change. The spectrum of the small star cannot, of course, be directly observed, but its nature may be indicated by colour-observations. Should a glint of blue or green be caught under favourable circumstances, the inference that it proceeds from a source of the Sirian quality can be unhesitatingly drawn. A particular interest attaches to η Geminorum as the only Antarian star with a companion likely to prove sensibly mobile within a reasonable lapse of time.
The spectra of double stars that are unstable in colour have an importance both evidential and explanatory. They illustrate and tend to expound chromatic phenomena. The diversity in light-quality of 95 Herculis is then of extreme significance. These stars, as our readers will remember, are now perfectly matched. They are of equal brightness, and of the same yellow shade. But half a century ago they displayed brilliant complementary radiance in red and green. And their spectra correspond, not to their present uniformity, but to their historic contrast. Vogel in 1899 recorded for one component—presumably the star formerly green—a Sirian, for its twin a solar spectrum. Additional weight is thus lent to the old observations; and a hint, not to be neglected, is given as to the probability of future change.
It is less surprising to meet with spectral dissimilarity in the components of γ Delphini. For they differ in magnitude, and very markedly in colour, notwithstanding past intervals of agreement. And it was just during one of their periods of agreement, in 1883, that Vogel found the larger star to be of solar type, while its companion, now green, but then colourless, gave a Sirian spectrum. Here again, as in 95 Herculis, spectral distinctions seem to persist while chromatic distinctions are alternately effaced and restored.
A good many yellow stars have purplish attendants of dubious spectroscopic standing. Their quality remains untried, and is difficult to conjecture. One of the best examples is η Cassiopeiæ, a revolving pair consisting of a 3·5 and a 7·5 star 5″ apart. The primary emits golden light marked with the solar stamp of absorption; its satellite has been variously described as violet, rosy, and garnet. These notes of colour, indeed, supply no hint as to the nature of the corresponding spectrum; but some indication that it is more “advanced” than that of the large star may be gathered from the mass-relations of the pair. Their gravitational disparity, as determined by Otto Struve, is 3·7 to 1, while their light disparity is 40 to 1. In other words, the satellite is nearly seventeen times less luminous than it would be if of the same mean density with its primary, and of equal areal lustre. In reality it is probably both more compressed and less brilliant. But these properties belong to a comparatively late stage of growth, and should be associated with a strongly absorptive atmosphere. The precise type of absorption characterising dependent stars of a violet hue it would be rash to predict, but it is very desirable to ascertain.
A pair closely resembling η Cassiopeiæ is ξ Boötis. Again in this case a yellow primary of solar type has a rose-purple attendant actively circulating round it. With it may be classed a couple in Pisces (Σ 3036), coloured “very little yellow and dusky red,”[522] and probably β Cephei, composed of a sulphur-tinted helium star of 3·4 magnitude,[523] and an eighth-magnitude violet attendant at 14″.
The great majority of double stars present, however, the same or similar tints; they are white and creamy, or sulphur-coloured and golden, and the spectra derived from them accord entirely with these indications. They are almost always variants of one type. But the rule observed in contrasted pairs that the smaller is the earlier star is here inverted. The subordinate members of systems undistinguished for colour often show signs of having progressed further on the road towards extinction than the larger orbs. This principle is finely illustrated by the grand southern binary, α Centauri. Now these stars are almost exactly equal in mass, yet one gives only a quarter of the other’s light. It is also more deeply tinted with yellow; we may, indeed, safely infer that it is dimmer mainly because of the additional absorption to which its colour testifies. The spectra of the pair, splendidly delineated in Sir David Gill’s photographs, are both of the solar class, but with a difference.
That of the brilliant component is an exact copy of the Fraunhofer spectrum (see Plate X. Fig. 2), while that of the inferior star might be called post-Arcturian, manifesting traces of affinity with the fluted type of Betelgeux.[524] The spectral relations of α Centauri doubtless prevail in many other systems, but they do not arise inevitably, even under quite similar conditions. Thus the unequal stars of γ Leonis give virtually identical spectra of the Arcturian or post-Arcturian species;[525] and the equal stars of γ Virginis, though of Sirian type, are unmarked by the smallest difference in the mode of absorption. It would then appear that, while two globes cast, as it were, in the same mould, like those united in α Centauri and γ Virginis, frequently proceed pari passu along the life-course of suns, one may outrun the other under the influence of unknown circumstances. Couples unassorted in size comport themselves differently; but here, too, allowance has to be made for original diversities of constitution, or supervening incidents of development.
To resume. The colours of double stars afford preliminary indications as to the nature of their spectra, but cannot, in all cases, be interpreted with much confidence. Blue and green stars are, as a nearly invariable rule, the satellites of red or yellow primaries. They belong to the Sirian type, modified, probably, by special absorption serving to lend predominance to the more refrangible rays, and so produce their unusual tints. “Purple” attendant stars have also been observed; the quality of light, however, corresponding to this designation remains unknown. It may prove to be stamped with strong absorption, such as would be symptomatic of advanced condensation; and if so, purplish or violet satellites are a radically distinct class of bodies from azure stars; for they might be inferred to be proportionately more massive and less luminous than their primaries, while the inverse relation doubtless holds good in gold and green as well as in topaz and turquoise combinations. Stellar pairs of equal magnitudes are, with the rarest exceptions, alike in colour and spectrum. They are primrose-tinted—scarcely ever pure white—and of solar or Sirian type.
The spectra of couples no more than two seconds apart can be separately photographed with the Tulse Hill apparatus; and indications of duplicity are often obtained from the composite nature of the spectral impressions given by apparently single stars. Only dissimilar components, however, are capable of being thus distinguished; superposed spectra disclose themselves as such by their differences, among which opposite motion-displacements are occasionally met with. The discrimination of mixed qualities of light in single spectrographic records is a branch of research promising further developments.
XV. THE EVOLUTION OF THE STARS
The suns of space are subject to the sic transit of mortality. The time has been when they were not, and in the time to come they will surely cease to be. The “incorruptibility of the heavens” is no longer a postulate of science; it has been in a measure superseded by the still more antique notion of the “perpetual flux” of things. Creation is a process; it has a history; and the records of its history are not wholly illegible to science.
Those inscribed in the heavens more particularly invite attempts at decipherment. Inquiries into the physical constitution of the stars inevitably lead to them, nay, insensibly merge into them. In the celestial regions, more than elsewhere, we are impelled to read the past and future between the lines of the present. There, by a wonderful course of development, the designs of the Maker are being unfolded, but with such majestic leisureliness that each step represents the lapse of millions of years. To trace even its broad features is, then, a task to be undertaken only with extreme diffidence; yet some few safe principles are available, guided by which we hope not to wander far from the truth.
Long ago it became evident to observation that nebulæ were the matrices of stars. Stars visibly nebulous are then in the earliest stage of growth. So much, at any rate, may be assumed without sensible risk of error. Again, radiating globes necessarily condense with the efflux of time. As heat, the source of their expansive vigour, is dissipated, their particles succumb to gravity, which suffers no waste. They contract; the same quantity of matter occupies in them a continually diminishing space, and acquires a proportionately more substantial consistence.
The application of these tests gives a concordant result. Both point to helium stars as being at the start of the cosmical procession. They have often nebulous appurtenances; they congregate in nebulous regions; they show with nebulæ spectral relationships of a subordinate, but significant kind. Their mean density, moreover, is known to be extremely small. The conditions of their eclipses, where they form occulting couples, gives the means of assigning to it a fairly definite value; and it appears to be about one-seventh that of the sun. This result is, of course, only preliminary, and cannot legitimately be generalised. It serves, however, to confirm what evidence of a different kind more vaguely indicates.
Helium stars are, then, the most primitive class of suns; and the point of outset being once established, the advance takes a prescribed and inevitable line. We have seen that helium stars pass by the finest gradations into Sirian, Sirian into solar stars, and these again into stars giving fluted spectra. So far there is no breach of continuity. Individual varieties must unquestionably arise, varieties due to minor diversities of chemical constitution, to systemic conditions, to physical influences exerted, possibly, in certain tracts of space; but the great wave of change sweeps on independently of these ripples on its surface.
The order of succession of the four chief stellar families leaves, accordingly, little room for doubt. Our next inquiry relates to the causes of their progressive transformation. We know of two which must be operative—dissipation of heat and augmentation of gravity. The function of a sun is to dispense energy; its distinctive organ, the photosphere, is precisely an apparatus for discharging this function rapidly and effectively; every year of a star’s radiation involves, then, a corresponding subtraction from its not unlimited thermal store. Yet this is not necessarily accompanied by a fall in temperature. Gaseous bodies, on the contrary, grow hotter as they cool. This seeming paradox was enunciated by Homer Lane of Washington in 1870. It is now a universally admitted principle of science. What is signified by it is that the contraction of masses in the gaseous state more than supplies their loss of heat by radiation. It ceases to apply when liquefaction sets in, but we are entirely unable to fix the stage of evolution at which this point is reached. We are only certain that the youngest stars, being unquestionably gaseous to the core, are rising in temperature; their acme is still to come.
But average temperature is not the same thing as surface temperature. The former, in two radiating globes, may be the same, while the latter is very different. For it depends essentially upon the rapidity with which heat can be conveyed outward and upward, and this again is prescribed by interior conditions varying with mass, density, and radiative facilities. Now Lane’s law has to do only with average temperature, while spectral indications relate to purely superficial heat-conditions. If we can learn something definite even as to these it will be much; but at present the utmost uncertainty prevails as to how the recorded facts should be interpreted. It seems indeed pretty clear, from the frequent occurrence of “enhanced” lines in the spectra of white stars, both of the Orion and the Sirian kinds, that the state of things in their reversing strata approximates to that in the electric spark, while vapours glowing in the arc represent better the layers absorbing sunbeams and the rays of Antarian stars. But in regard to the essential nature of the difference, authorities are not unanimous. According to Sir Norman Lockyer, Dr. Scheiner, and others, temperature alone is concerned; the spark is hotter than the arc. Intense molecular excitement, due to the disruptive discharge, gives rise to altered modes of vibration, betrayed by substitutions of new spectral lines for those previously visible; and these substitutions, reiterated in the stars, tell emphatically of their enormous temperatures. On the other hand, Sir William and Lady Huggins relegate temperature to a position of secondary importance, and count density the main factor in spectral change, their contention being supported by impressive experimental arguments. Their photographs, too, show some unexpected signs of superior strength of ultra-violet radiation in solar as compared with white stars; and this, if substantiated, would assuredly imply their higher temperature. For the radiative centre of gravity shifts upward with increase of heat, a relation familiarly illustrated by the whitening of red-hot iron before the melting-point is reached.
All of which is exceedingly perplexing; and there is more behind. Gravity is of potent influence in determining temperature. The physical condition of bodies cannot be compared without reference to the scale of their construction, and their spectra vary to correspond. A score of years ago Ritter enunciated the theorem that “the surface temperatures of two stars of equal densities are to each other nearly as the square roots of their masses.”[526] And Professor Perry reached quite lately the analogous conclusion that the temperature of a star varies as the product of its age and mass so long as it behaves after the manner of a body gaseous throughout.[527] Further, the superficial heat of stars obviously depends upon the activity of convection-currents in their interiors, and these of course slacken as viscosity increases. This adds greatly to the complexity of the problem, since the transcendental temperature and pressure reigning in the depth of stellar globes must affect in unforeseen ways the viscosity of the materials placed under circumstances outside experience.
Clearly, then, the stars can be arranged in order of temperature only with hesitation and tentatively. If we might accept Ritter’s inference that the sun’s radiating layer was never in the past, and can never be in the future, at a much higher temperature than that now belonging to it, some difficulties would be removed. For it involves the consequences that the solar type of spectrum marks the culminating point of superficial heat, and that no star can be hotter than the sun unless it contains a larger quantity of matter; and these, if valid, would provide solid ground for classification. But they are highly disputable, and we can only conclude that it is safest not to dogmatise about relative stellar temperatures.
Sir William and Lady Huggins regard as of primary importance in the development of stars the gain of surface-gravity which inevitably accompanies their contraction. They are unquestionably right. Atmospheric pressure varies with gravity, and the spectral characteristics of incandescent vapours are affected to an incalculable degree by their density. Every addition to gravitational power, moreover, serves to quicken atmospheric circulation. The tendency to sorting out by the formation of concentric shells of substances differing in atomic weight, is overborne by the uprushing of convection-currents. The strata become mixed, and the heat-gradient becomes steep. These atmospheric modifications are reasonably numbered among the concurrent causes of development from the Sirian to the solar spectral type. They must, at any rate, be concomitants of stellar condensation, unless the path of progress is deflected by unknown agencies. It is well to remember that electro-magnetic forces play a part in cosmical evolution—a part deprived of none of its importance by our inability to define its nature. We can only see that they may not be excluded, and await patiently the outcome of future research.
All this refers to the individual history of cooling globes. How, we may ask, does it apply to the relative histories of various globes differing very greatly in mass? The customary answer is that massiveness retards development. That it retards cooling is quite certain, since the larger of two unequal spheres has, relatively, the smaller radiating surface. Hence the old view that change of temperature and spectrum proceeds evenly together had as a corollary that the quicker pace belonged to the lesser star. Spectra of the Orion and Sirian patterns should, accordingly, distinguish orbs on the whole of far more imposing proportions than those giving light of the solar and Antarian qualities. Just the reverse, however, appears to be the case. All practicable modes of comparison agree to indicate that the “mean” solar star sends out a larger sum-total of light from a considerably smaller luminous surface than the “mean” Sirian star.[528] The solar star is, moreover, the denser body, and therefore the more massive in a ratio very much beyond that of its superiority in luminous power.
But the most cogent proof that giant suns develop quickly is derived from the spectra of double stars. The members of binary systems may fairly be regarded as contemporaneous. Their origin was in common; their destinies are indissoluble; they are identically circumstanced; they must be similarly composed. They should then be exceptionally trustworthy guides to the unravelment of evolutionary time-relations. Now they inform us, in distinct terms, that in contrasted pairs the earlier type of spectrum characterises the minor body. The primary being solar or Antarian, the satellite is of the Sirian class. Further, the inequality of mass in such cases is certainly greater than the inequality of light. The small blue star is more tenuous than the reddish luminary it attends. These phenomena enforce the conclusion—the inverse of Ritter’s—that stars of the first type are greatly less massive than coeval stars of the second.
Here resides the crux of the evolutionary problem. We have no choice but to believe that the four ages of stellar life succeed each other with relative promptitude in globes built on a great scale. But what looks like an insurmountable difficulty may, on closer inspection, prove a most valuable help towards the establishment of sound doctrine. Sir William and Lady Huggins threw out the suggestion in 1897[529] that “the effect of great mass on surface density, together with the working of Lane’s law, will favour the coming in of a solar type of spectrum at a somewhat earlier relative time.” They indeed finally rejected the idea;[530] yet it is strongly confirmatory of their own views as to the importance of the gravitational factor in the unfolding of stellar life-history. Rapid atmospheric circulation, indispensable, as they hold, to the production of a solar spectrum, would be set up earlier in heavy than in light globes; and the requisite adjustment between temperature and pressure should be similarly anticipated. That this is what really happens, we are assured by the prismatic observation of jewel-tinted star couples.
It does not, however, follow that large stars are short-lived. The explanation of the facts just offered involves no such paradox. For it is amply possible that the lesser order of stars may not survive to reach the Antarian stage. They may perish on the way. Extinction perhaps overtakes them while still in mid-career. They may lapse into the ranks of “dark stars” before time has been allowed them to put on any recognisable badge of decadence. If this be so, stars with fluted spectra are the outcome of a kind of natural selection. They are bodies endowed with sufficient heat to keep them luminous to the end, while others, having squandered less ample supplies by quicker cooling, sink prematurely into invisibility. This is no idle speculation. The sidereal system is known to include countless non-luminous globes, the origin of which is largely enigmatical. Their obscurity, most likely, dates from various epochs in stellar life. And the smallest masses should, under similar circumstances, cease first from sun-like existence.
So far, account has been taken of only four stellar families, selected as the basis of the evolutionary argument because their mutual relations seem unmistakable. Helium stars are the direct progeny of nebulæ. The formation of a photosphere definitely marks the transition. By the gradual effacement of “Orion” lines they merge into hydrogen suns, these, through the creeping into prominence of innumerable metallic absorption rays, into solar orbs, which finally pass, by successive minute changes, into the fluted stage. But what, we cannot refrain from asking ourselves, lies beyond? Through what phases of decline do great red stars of the Antarian order subside into extinction? No confident pronouncement on the subject is possible, but the conjecture may be hazarded that a stadium of variability precedes the end. Periodic light-spasms perhaps indicate failing vitality. They may eventually die out, and be succeeded by a permanent minimum. Already one such example seems to be afforded by T Ophiuchi, which has for some time ceased from its annual brightenings. Recurrent maxima may, after all, be only flickerings in the socket. This possibility lends a particular interest to research into the causes of these extraordinary outbursts.
Now about the same proportion of carbon stars as of Antarians are markedly variable. Hence, if radiative instability betoken decrepitude in one class, it must do so in the other. It would, indeed, on many grounds, be unreasonable to set the two families far apart in the chronology of the heavens. Professor Vogel regards them as collaterals. They represent, in his scheme, alternative lines of descent towards the final quenching, there being a total absence of evidence that either has sprung from the other. The pedigree of carbon stars is, in truth, highly obscure. Besides them only one celestial body shows recognisable traces of carbon absorption, and that body is our sun. As effete suns, accordingly, Sir Norman Lockyer ranks these remarkable objects. But the transitional spectra we should expect to meet with, if this were the case, are missing. Solar stars with incipient carbon flutings are unknown. No road runs between the designated stations. A line of communication is wanting. Nor is the development of Antarian into carbon stars easy to admit. A few instances of nondescript banded spectra have, to be sure, been recorded, and might conceivably serve to bridge the gap; nothing, however, resembling an intermediary series can be made out. Now stars without obvious relationships presumably developed quickly under abnormal conditions. And carbon stars seem to be in this case. They must indeed have had progenitors, although none openly claim them. With three stocks, nevertheless, they show distant affinities, and from one or other they must have sprung. Their banded spectrum can be traced in embryo in the sun; their dark-line spectrum is analogous to that associated with Antarian flutings; their bright-line spectrum partially matches Wolf-Rayet emissions. But these are no more than hints towards a genealogy, of which nature still keeps the secret.
There can be no hesitation in placing the Wolf-Rayet and the bright-line helium groups at an early stage of cosmic growth. The Pickering and Rydberg hydrogen lines, which commonly go together, are, for some unknown reason, characteristic of a primitive condition, and they are essential elements of the Wolf-Rayet spectrum. The absence from it of metallic rays is an indication of the same purport; for they are similarly suppressed in nebulæ, while gaining strength and depth in the successive stellar generations. Yet Wolf-Rayet stars are not visibly nebulous. Must we then suppose that they have sprung from stars that are? This is scarcely possible, in view of the peculiarities just adverted to; nor is the admission necessary. Small, compact nebulæ, without hazy appendages, are quite likely, by their condensation, to have given rise to this class of stars. If so, their telescopic sharpness is a necessary consequence of their mode of origin. But the connecting links have still to be detected. Until they are, the suggested parentage remains an unverified conjecture.
Nebulous attachments, on the other hand, plainly seen or photographed, not unfrequently declare the affinities of bright-line helium stars. They are accordingly at the outset of their careers as suns—that is to say, they have given since the time when they were first formed into powerfully radiating globes the same kind of spectrum now exhibited by them. It will, however, eventually become modified; and the most probable modification to which, so far as our limited view extends, it can be subject, is by the disappearance of its specific rays of emission. Their progressive effacement might plausibly be represented by a series of objects, in which linear radiation grows less and less, from γ Cassiopeiæ, with its full complement of bright lines, down to Alcyone, showing a solitary C. Yet this would not compel the admission that every dark-line helium star has traversed a bright-line phase. Such an episode, on the contrary, can be inferred from many indications to occur by exception in stellar history as a consequence, perhaps of peculiarities of internal constitution, perhaps of unusual influences exerted from without, possibly of the mutually reactive effects of both classes of cause.
We must be prepared to meet with side-tracks in evolution. Nature does not run in a groove. Her operations are free and various; they defy the restrictions of feasibility which a rigid methodism of thought would seek to impose. The order of the universe has a wider scope than is imaginable by us. Creative Wisdom disposes of superabundant resources, and, if we may dare say so, takes delight in bringing them into play. Our best attitude of mind, then, in attempting to speculate on the course of things, is that of the utmost possible flexibility to the teaching of well-ascertained facts.
XVI. ROTATION OF THE STARS
Sir William Abney adverted, in 1877,[531] to the theoretical effects of rotation on stellar spectra. Quite obviously, they must tend to make the component lines wide and diffuse. For each line integrates the displacements and counter-displacements occasioned by the opposite radial movements of the limbs; while the central and polar sections of the disc, having their velocities directed across the line of sight, send out rays in their normal positions, fringed on either side through the juxtaposition of the shifted rays. The amount of broadening in each particular star depends, first, upon the linear speed of rotation, secondly, upon the position of its axis. If this be erect as viewed from the earth, the motion-shifts will tell to their full extent in spreading the bright or dark spectral lines; they will become less and less effective as the axis is less inclined, and will disappear wholly on its coincidence with the visual ray. Now there can be no doubt that every star has a movement of gyration as well as a movement of translation; and it is no less certain that stellar spectra are modified in accordance with its rapidity and direction. Only the question of degree has to be considered. Are the effects produced likely to be appreciable? And if so, have they been perceived?
The spectrum of α Aquilæ (Altair), noticed for some time back as peculiar, has sometimes been thought to intimate a composite origin. It is of the Sirian type, but with a reinforced contingent of metallic lines; and these run together into hazy bands, the general aspect of which was imitated at Potsdam in 1895 in spectrographs of the sun taken out of focus.[532] The defective nature of the agreement, however, discredited the hypothesis of a double spectrum, marked by diffuse hydrogen absorption proceeding from one source, and by metallic lines fused into bands, proceeding from another. Yet M. Deslandres considered that his measures of the star’s radial motion lent it support. They seemed to indicate velocity variable in a period of forty-two days, with minor fluctuations superadded.[533] But the supposed multiple system is, according to Dr. Vogel, a mere creation of accidental errors,[534] and α Aquilæ must for the present, at any rate, be counted a solitary star.
Its spectrum was, in 1893, commented upon by Professor Pickering.[535] He had recourse, for the explanation of its ill-defined character, to the rotational principle, adding a caveat based on the improbable greatness of the required velocity of about 100 miles per second. Adopted, nevertheless, five years later by Dr. Vogel, it was rendered more plausible by his reduction to 27 kilometres (16·8 miles) of the equatorial speed needed to widen the lines to the observed extent. This rate of movement, which is just double that of a point on Jupiter’s equator, might reasonably be admitted as subsisting in a star. But the view encounters other, and more fundamental objections. If it were true, all the lines in the affected spectrum should be similarly diffuse. Movement acts indiscriminately. Every ray emanating from the advancing or receding surface is, in due measure, displaced. None can be exempt from change of refrangibility. The occurrence, then, of a single sharp line in a stellar spectrum suffices to show that the haziness of its associates must be due to some other cause than rotation. And there are many sharp lines in the spectrum of α Aquilæ. They are faintly discernible, as Sir Norman Lockyer pointed out in 1894,[536] on the South Kensington plates, and are unmistakably apparent in Sir William and Lady Huggins’s spectrographs.[537] Those taken at Potsdam are so limited in range of wave-length that negative conclusions cannot safely be founded on them. The hypothesis of rotation must, accordingly, be regarded as inapplicable to the case of α Aquilæ.
Now α Aquilæ is not without analogues. It belongs to a pretty numerous stellar group, differing in chemical constitution, but agreeing in the diffuseness of the absorption traits significant of it. They form one of Miss Maury’s three collateral series—her “Division b.” It embraces no “advanced” stars; only those of the helium and hydrogen types, with a few verging towards the intermediate stage of Procyon, are represented in it. Hazy spectra are thus a sign of cosmic youth. They characterise, without exception, the stars of Miss Maury’s “Group i.,” in which the Pickering series of hydrogen is prominent; they cease to appear, or appear by imperfect indications, soon after the Sirian stage is passed. Their explanation by opposite displacements through axial movement would then involve the consequence that stars, as they develop, lose much of their rotational speed. There is, however, but one recognised agency by which it can be retarded—the agency of tidal friction; and it acts sensibly only on bodies attended by closely-revolving satellites of considerable relative mass. Solitary suns like our own can have spent but little of their energy of rotation. Actual velocity in spinning becomes, in fact, accelerated as contraction proceeds, so that ageing stars should have their spectral lines more broadened by motion than those in a primitive condition. And since the effect is imperceptible in the former, we may feel assured that it has not been observed in the latter.
Confirmatory evidence is not wanting. There is a certain class of stars which, we have the strongest reason to believe, rotate in very short periods, and on axes almost perpendicular to the line of sight. They combine, accordingly, both the conditions needed for the display of spectra rendered diffuse by motion-shifts. These are occulting variables like Algol. Since they revolve in planes passing very nearly through the earth, and their equators cannot deviate materially from the same level, it is certain that virtually the whole speed of their advancing and receding limbs is radially directed; no considerable part of it is spectroscopically ineffective. Further, although they may rotate faster, they cannot rotate more slowly than they revolve, and their orbital periods are extraordinarily short. The system of Algol, which is by no means one of the quickest eclipsing pairs, circulates in sixty-nine hours. Its equatorial rate of rotation, by a minimum estimate, is thirteen miles a second, or just eleven times the solar. The absorption rays in the light from one limb are accordingly displaced towards the blue, and those from the opposite limb towards the red, eleven times more than the Fraunhofer lines measured by Young and Dunér; and their compounded effect in the stellar spectrum is to widen the lines by an amount corresponding to a speed of twenty-six miles. In other words, each should spread over nearly one quarter the interval between the D-lines in the sun. The alteration is, nevertheless, inconspicuous. The spectrum of Algol does not strike the eye as hazy. The hydrogen series shows the distension proper to the type, no more; the rays of helium, magnesium, and calcium are of the average sharpness. Now some eclipsing stars must rotate much more rapidly than Algol. U Ophiuchi, for instance, has a period of only twenty hours. Yet in none of them have blurred spectra been noticed. Enormous velocities—velocities most probably non-existent—would evidently be indispensable for their production.
Such spectra as that of α Aquilæ must then be accounted for otherwise than by rotation. For the suggested geometrical cause, which proves inadequate, a physical cause has to be substituted. One may be found in excessive pressure. The diffuse lines possibly originate at unusual depths in the stellar atmospheres. Sir William and Lady Huggins advert[538] to the probability of great differences in this respect between various stellar classes. In early stars they say—and none of the members of “Division b” are mature—“we may see deep down into the star, and the continuous spectrum may come from a thick region of dense gas, throughout which little, or possibly no condensation to the liquid or the solid state takes place. Under these conditions, the absorbing gases in front of it will not be, as in the sun, of very limited thickness, but will occupy a region of vast extent.”
The solar H and K illustrate the character of lines generated in dense vapours at a high temperature; their “wings,” as we may remind our readers, being added in the immediate vicinity of the photosphere to the comparatively definite lines produced in the upper reversing strata. Now it is a curious fact that distended lines, such as H and K, are apt to be doubly reversed. Dr. Scheiner has noticed symptoms of incipient illumination at the centres of the broad hydrogen bands distinctive of first-type stars, and they are similarly manifest in Wolf-Rayet stars showing mixed series of emission and absorption. Hence the particular significance of M. Deslandres’ detection in α Aquilæ of fine “chromospheric” lines of hydrogen, and occasionally of calcium and iron,[539] superposed upon the dim, dusky bands indicative of the state of those substances in the reversing layer. Diffuse spectra may thus, with some probability, be assigned to abortive bright-line stars. Or they perhaps mark objects just losing the faculty of specific emission. If so, the mode of its departure is different from that exemplified by Alcyone, in which the dark lines have their normal aspect, while one red ray survives as the sole remnant of what was perhaps once a blazing spectrum. The future course of stars resembling α Aquilæ can be traced only by conjecture. But what hints are at hand lead to the supposition that they will proceed by insensible gradations to the solar stage, their absorption rays becoming narrower, more numerous, and better defined with the slow advance of condensation.
The upshot of our inquiry is to bring the conviction that no approach has yet been made towards determining the rotation of any star. Spectra are not rare composed mainly of blurred lines, and so suggesting at first sight diffusion on the principle of movement; the intermixture of sharp lines, visible on closer scrutiny, nevertheless peremptorily negatives the suggestion. Again, rotational velocity in the line of sight should be at a maximum in Algol variables; yet they do not possess specially diffuse spectra. Theory, however, need not be at fault because it fails to be verified by observation. The failure merely informs us that its consequences, by their smallness, elude our means of discovery.
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.
XVIII. ECLIPSING STARS
Stellar eclipses are necessarily included among the phenomena of spectroscopic binaries. For the planes of a proportion of these systems must pass through the earth, with the result that the circulating bodies occult one another when they cross the line of conjunction. The circumstance is particularly valuable as supplying a datum unattainable with the spectroscope for star couples differently conditioned. The rapid loss and recovery of light which tell us that one body is passing in front of the other, tell us, at the same time, that they revolve in an orbit seen edge on—that is to say, making an angle of 90° with the “tangent plane” of the sphere. Radial velocities are, accordingly, measured in their true proportions, and the masses of stars giving double spectra become strictly determinable. The duration of eclipse, moreover, indicates the density of the obscured and obscuring globes; and where the dimensions of even one of their orbits is known, it supplies a measure for their actual diameters. Thus precise evaluations of the light-changes and radial velocities of these singular objects go hand in hand; both kinds of research are equally necessary to the advancement of knowledge concerning systems which are peculiarly interesting because they are, more than any others in the sidereal world, accessible to investigation.
The circumstances of stellar eclipses are endlessly varied, and their differences are full of meaning. They are central when the orbit is directed straight towards us; they are partial when it deviates from coincidence with the line of vision. Then the interposing body may be dark or bright; it may be larger or smaller than the globe behind it. Supposing it to be sensibly obscure and the transit central, the eclipse will be either total or annular. The first case is not known, although quite likely to occur; no complete periodical disappearances have been witnessed. The second has not been definitely attested. Its inevitable indication would obviously be a stationary minimum. While the two discs are superposed, the light must remain steadily at its lowest level; and if the eclipse be annular, the discs are, ipso facto, superposed during an appreciable interval, the length of which bears an inverse ratio to the depth of the obscuration.
While a bright and dark pair can undergo but one eclipse in each revolution, two are the portion of a couple radiant in both its members. If they are alike in size and brilliancy and pass one another centrally, the eclipses will be equal and the loss of light one-half. And it is noteworthy that in nature this seems to be a somewhat prevalent arrangement. Several systems are known in which it may subsist; spectroscopic observations can peremptorily decide whether it does, in fact, subsist or not. The principle of their decision lies on the surface. Eclipses necessarily take place at points of the orbit where radial motion approximates to zero. If they are duplicated in each period, the cessation of movement marks at one, the transition from speed of approach to speed of recession; at the next, the turning-point where speed of recession changes to speed of approach. A minimum of light, that is to say, precedes each reversal of movement. If, on the other hand, the eclipses are single, occurring only once in a revolution, the cycle of motion to and from the eye is completed in the interval between them. The criterion is thus absolute and unmistakable; only the faintness of the stars impedes its general application. Where unequal eclipses alternate, however, the spectroscope is not needed to inform us that they take place two and two in each circuit. They are then evidently due to the mutual occultations of disparate stars; and the species of combination they indicate is frequently met with. It is varied to the utmost, as might be expected, by gradations of disparity, in the production of which deficient luminosity may concur with inferiority of size, or be partially neutralised by its superiority. Thus as each globe in its turn comes in front of the other, there results a double series of eclipses, the odd ones (dating from a fixed epoch) being perfectly similar each to each, but differing in depth and duration from those of the even or intermediate series.
Further diversities arise through slight tilting of the orbits. The corresponding eclipses are partial, even to the limit of evanescence, when the star discs just escape contact. And it may be noted that the second eclipse in each revolution, properly belonging to a luminous pair, may be suppressed where the path traversed is at the same time sensibly inclined and considerably eccentric. Partial eclipses are doubtless the rule, central ones the exception; but their discrimination is often a matter of some delicacy. Indeed, the photometric study of such phases is an art in itself, the practice of which demands skill, vigilance, and patience beyond the common. The aid of photography, lately enlisted for it, is likely to enhance its security and precision.
Eclipsing stars, once more, are close binaries circulating nearly in the line of sight. Not any intrinsic peculiarity, but our situation in space, determines their special character. Relatively to us, they are periodically variable, as Spica or Castor would become were our place suitably shifted. Their changes are of a distinctive kind; they are short, sharp, and decisive. When well developed, that is to say; for photographic photometry may ere long afford the means of detecting occultations barely adumbrated by a drop not perhaps exceeding one-tenth of a magnitude. All members of the class so far have been recognised by their variation in brightness; their accompanying circulatory motion, inferred in all cases, has been verified in only a few. The following list gives the designations, periods, and phases of the eclipsing stars with which astronomers had made acquaintance down to the end of 1902. They are enumerated in the order of their discovery.
┌──────────┬─────────────────┬───────────┬─────────────┬─────────┐ │Chandler’s│ Name. │ Period. │Light Range. │Duration │ │ No. │ │ │ │of Phase.│ ├──────────┼─────────────────┼───────────┼─────────────┼─────────┤ │ │ │d. h. m. s.│ m. m.│ h. m.│ │ 1090│ Algol │ 2 20 48 55│ 2·3 to 3·4│ 9 20│ │ 3109│ S Cancri │ 9 11 37 45│ 8·2 „ 9·8│ 21 30│ │ 1411│ λ Tauri │ 3 22 52 12│ 3·4 „ 4·2│ 10 0│ │ 5374│ δ Libræ │ 2 7 51 23│ 5·0 „ 6·2│ 12 0│ │ 5484│ U Coronæ │ 3 10 51 12│ 7·5 „ 8·9│ 9 42│ │ 6546│ RS Sagittarii │ 2 9 58 36│ 6·4 „ 7·6│ 10 40│ │ 320│ U Cephei │ 2 11 49 38│ 7·1 „ 9·4│ 11 0│ │ 6189│ U Ophiuchi │ 0 20 7 43│ 6·0 „ 6·7│ 5 20│ │ 7488│ Y Cygni │ 1 11 57 26│ 7·1 „ 7·9│ 9 0│ │ 2610│ R Canis Majoris│ 1 3 15 46│ 5·9 „ 6·7│ 5 0│ │ 5949│ R Aræ │ 4 10 12 42│ 6·9 „ 8·0│ 9 30│ │ 3055│ X Carinæ │ 0 12 59 30│ 7·9 „ 8·6│ 6 39│ │ 5144│ Y Boötis │ 2 14 24 0│ 8·0 „ 8·6│ 4 0│ │ 3416│ S Velorum │ 5 22 24 35│ 7·8 „ 9·3│ 15 11│ │ 6442│ Z Herculis │ 3 23 50 0│ 6·9 „ 8·0│ 6 36│ │ 7399│ W Delphini │ 4 19 21 12│ 9·3 „ 12·1│ 14 0│ │ 6636a│ RX Herculis │ 0 21 20 33│ 7·0 „ 7·8│ 4 8│ │ 2781│R^2 Puppis │ 6 10 19 36│ 9·1 „ 10·8│ 17 0│ │ │U^3 Cygni │ 4 13 45 2│ 8·7 „ 11·4│ 13 0│ │ │V^2 Cygni │ 6 0 8 48│10·8 „ 12·8│ │ │ 3707│R^2 Velorum │ 1 20 30 2│10·0 „ 10·9│ 3 20│ │ 6773│ U Scuti │ 0 22 54 0│ 9·1 „ 9·6│ 5 0│ │ 7318│ UW Cygni │ 3 10 49 12│10·5 „ 12·0│ 8 30│ │ 6927│ U Sagittæ │ 3 9 19 12│ 6·5 „ 9·1│ 12 0│ │ 7891│ UZ Cygni │31 7 17 46│ 8·9 „ 11·85│ 48 0│ │ │ RV Lyræ │ 3 14 22 23│11·0 „ 12·8│ │ │ │14, 1902 Persei │ 3 1 21 32│ 9·4 „ 12·0│ │ └──────────┴─────────────────┴───────────┴─────────────┴─────────┘
Algol (β Persei) is the model eclipsing star. Goodricke’s sagacious conjecture that such was its nature, adopted and developed by Pickering, obtained experimental confirmation after a lapse of 107 years. Vogel’s spectrographs showed in 1889 that, previously to each obscuration, the star was swiftly receding from the earth, while recovered brightness was attended by a somewhat greater velocity of approach. The excess is simply due to the fact that the system is travelling towards the sun at the leisurely pace of 2⅓ miles a second. The true orbital speed is sensibly uniform; accelerations, pointing to ellipticity in the track pursued, have not been detected. One eclipse takes place in each revolution; the eclipsing body is to all intents and purposes a gigantic planet; it gives no perceptible light. The sun round which it circulates is, on the contrary, peculiarly brilliant for its size, partly because its absorption, being of the helium type, produces little or no mellowing effect upon its keen white rays.
Much has been learned about the system formed by these contrasted globes. Its visible member travels at the rate of 26⅓ miles a second; and since the period of revolution comprises 247,735 seconds, the distance of its centre from the centre of gravity slightly exceeds 1,000,000 miles. The length of the eclipse, moreover, gives the actual size of the star. It has a diameter of slightly more than 1,000,000 miles, or about five-fourths that of the sun. The dimensions of the satellite, too, are approximately known. From the loss of light through its interposition, Professor Pickering in 1880[564] calculated the ratio of its diameter to that of its primary to be as 764 to 1000. The ratio should be increased if the transit were not central, which it does not appear to be. For the eclipse is not annular, since there is no pause at minimum; the flow of change is continuous; the turning of the luminous tide is not appreciably delayed; decline is immediately succeeded by restoration. The orbit is not then level with the eye; and Mr. Yendell considers that an inclination of 7° would agree best with the light-curve.[565] In Vogel’s opinion it is such as to imply for the dark body a diameter of 830,000 miles, an estimate which can hardly be far from the truth.[566] Admitting with him that the two stars are of equal density—possibly a hazardous assumption—we can infer their masses, knowing their respective volumes, and the circulatory speed of one of them. They are in the proportion of two to one, and both spheres together contain two-thirds as much matter as our sun. They are, accordingly, at least four times more tenuous; but the consequence cannot be said to discredit the postulate in view of the extreme rarefaction characterising white stars in general and helium stars in particular. The distance of Algol from its satellite (always on Vogel’s hypothesis of equal densities) is 3,230,000 miles, leaving an interval between their surfaces of scarcely more than 2,250,000 miles. But we shall find that even closer degrees of contiguity are compatible with stability in the mechanism of the stellar heavens.
The period of Algol has long been known to vary minutely but continuously. But as to the nature, law, or cause of these inequalities nothing had been ascertained, and little had even been surmised, prior to Dr. Chandler’s discussion of them in 1888.[567] He proved them to be slowly compensatory, not indefinitely progressive. Consistently in advance of their due time down to about the year 1804, the obscurations of the star then began to fall behind it, and the delay had in 1843 accumulated to 156 minutes. A gradual process of restoration thereupon set in, and the normal epoch was reached near the beginning of 1873. It was, however, quickly transcended, for acceleration was still going forward, and may not attain its term for some years yet to come.[568] These irregularities are evidently comprised in a cycle of considerably more than a century; they can scarcely, for that very reason, be accounted for on gravitational principles; since a third body, revolving in so long a period, would be too distant to perturb markedly the movements of the close pair traversing an inner circuit. Dr. Chandler hence resorted to another mode of explanation.[569] He proposed to account for the alternate anticipations and retardations of Algol’s eclipses on the principle of the equation of light. They might result, he pointed out, from the description, by the occulting pair, of an orbit so wide that the transmission of light across it takes close upon 300 minutes. The star’s phases would then be observed too soon or too late according as they occurred on the hither or the farther side of the great ellipse. They would be shifted by turns backward and forward in time just as are the eclipses of Jupiter’s satellites while the earth performs its annual circuits. The system of Algol is, on this view, triple. Two dark masses and a vividly shining one unite to form it. The revolutions of the eclipsing pair round the common centre of gravity, which is at a distance from it just equal to that of Uranus from the sun, are accomplished in about 130 years, at the rate of 2·7 miles a second. Its members are at present nearer to us than their mean place, and their occultations consequently forerun the mean times; this will continue until towards the year 1934, when, on the passage of the ascending node, a coincidence of epochs should be observed. Two other criteria are applicable to Chandler’s theory. If it be true, Algol’s approaching systemic movement of 2·3 miles a second should disappear within the next decade, neutralised by orbital velocity at that time directed away from the sun. Again, the wide circuits performed in a plane supposed to make an angle of 20° with the line of sight, might be directly traceable as undulations impressed upon the straight track of the star’s proper motion. Minute fluctuations of position simulating the looked-for effects have indeed been observed; but whether they are merely casual, or represent an actual, though almost evanescent phenomenon, is too delicate a question to be decided off-hand.[570] Twenty years hence the waves of disturbance may have defined themselves;[571] scarcely sooner.
An alternative hypothesis to Chandler’s was put forward by M. Tisserand early in 1895.[572] Rejected by the former investigator as insufficient, it assumed in the hands of the latter an extremely plausible form. No third body is demanded by it; a slight flattening of the globe of Algol, together with a moderate degree of ellipticity in the orbit of its satellite, meet the needs of explanation. The combined effect would be to produce a slow revolution of the orbital major axis, occasioning just such an inequality in the times of conjunction as that discussed by Dr. Chandler; and the fundamental postulated cause is likely to be present. Algol must have a rapid rotation; otherwise its system could not long subsist. That is to say, the maximum length of its axial period is 2^d 21^h, the period of its revolution. This implies an equatorial speed of 13½ miles a second, and a consequent equatorial bulging of very considerable amount. One of the conditions stipulated by Tisserand may then be granted, and the second can scarcely be absent, since the eccentricity of stellar orbits rarely falls short of the degree required. Verification may be procured by the spectroscopic detection of variations of velocity in different sections of Algol’s path. But the crucial test of the theory is of the photometric kind. At intervals of 120 years, if it correspond with fact, the shortest and longest radii of the ellipse traversed would, owing to the progression of the apsides, alternately point towards the earth. In the first case, the eclipses would be abbreviated by periastral acceleration; in the second, they would be long, because the movement at apastron should be slow. Their duration at present approaches to being the longest possible; if they shorten notably from 1910 onward, Tisserand’s hypothesis will be amply confirmed, while their failure to do so will compel its final rejection. Chandler’s, on the other hand, will remain in possession of the field should the alleged periodical disturbance of Algol’s proper motion be definitively established. Thus the rival theories alike wait on the future, and invite the award of events.
As the upshot of a careful series of measurements with the Yale heliometer, Dr. Chase[573] ascribes to Algol a parallax of 0·035″, equivalent to a light-journey of ninety-three years. If actually so remote, it gives just eighty times as much light as the sun from a surface not very greatly larger, but fifty-two times more brilliant—an inference surprising indeed, but not incredible.
A second Algol-variable was recognised by Hind in 1848.[574] Usually of 8·2 magnitude, S Cancri loses and regains more than three-fourths of its light in 21½ hours, divided between 8½ of decline and thirteen of restoration. The dissymmetry of the phases is increased by a remarkable pause in the brightening after minimum, as if a secondary cause of obscuration had supervened. Nor should it be forgotten that Schmidt observed on 14th April 1882 an excessive darkening of the star, which remained for a whole hour sunk nearly to the twelfth magnitude. The period which, until lately, was the longest ascertained for any member of its class, is subject to a cyclical disturbance embracing at least 300 light-cycles.[575] The deviations of the computed minima sometimes run up to forty minutes. It will be of great interest to determine whether they imply the presence of a third attractive body, or whether spheroidal deformation will suffice to account for them. The dimness of S Cancri places it for the present beyond the reach of useful spectrographic research. Its density has, however, been calculated by Mr. H. N. Russell of Princeton University,[576] from the ratio between its period of revolution and the duration of the eclipses suffered by it, with the result of showing that the star is composed of materials forty times more attenuated than those of the sun! And this is an upper limit.
Shortly after Hind’s detection of S Cancri, Baxendell found that its peculiarities were shared by λ Tauri, a radiantly white star of 3·4 magnitude. Its eclipses, as in several other cases, deepen more quickly than they lighten. They occur at intervals of 3^d 23^h, and last ten hours. They do not, indeed, come off quite punctually. An oscillatory disturbance of unknown law affects them, which occasions “errors” from the computed epochs, amounting at times to three hours.[577] Plassmann regards λ Tauri as continuously variable.[578] He noticed in 1891 a secondary dip in brightness fifty hours after the chief minimum, besides two intermediate maxima; and the Pulkowa photographs lent in 1897[579] some partial countenance to his views. They showed the spectrum to be occasionally and unequally double, the fainter rays, by their relatively large displacements, betraying their origin from a mass greatly inferior to that of the star characterised by the less mobile, and more intense absorption-lines they accompany. Thus M. Plassmann’s second eclipse[580] is real, though inconspicuous. No orbital elements have yet been assigned to this star. M. Bélopolsky regarded his materials as inadequate for purposes of computation; and indeed the movements derived from his plates were of a somewhat problematic nature. They greatly need elucidation, which it ought not to be very difficult to supply. The spectrum of λ Tauri is of pure helium type. The calculated density of the pair is about one-tenth that of the sun.
The fourth Algol variable is an all but perfect timekeeper. The phases of δ Libræ have been watched since 1858 without the detection of any assured irregularity. They last twelve hours, of which 5½ are spent in a decline from 5·0 to 6·2 magnitude, and 6½ in the reversal of the process. The eclipsing body appears to be wholly obscure, but the spectrographic method has not been applied to the system. The limit of density found for it by Mr. H. N. Russell is one-twenty-fifth that of the sun.
The phases of U Coronæ are very similar to those of Algol, but the intervening time is longer—eighty-three in lieu of sixty-nine hours. Each pair, too, is similarly composed of a bright and dark member, and their mean density comes out nearly the same. The analogy is completed by the presence of a variation in the period, evidently akin to the disturbances of Algol,[581] and explicable, doubtless, on an identical principle. U Coronæ, however, is a comparatively faint object; at high light it is of only 7·5 magnitude, and consequently offers scant facilities for research.
The eclipsing system designated RS Sagittarii, discovered by Gould in 1874, was subjected in 1896 to exact inquiries by Alexander W. Roberts of Lovedale, South Africa.[582] From them it appears that the coupled stars are alike in size, but so unlike in lustre that one gives more than twice as much light as the other. There result two unequal minima in each revolution; at the first, the combined magnitude of 6·6 drops to 7·6, at the second, to 6·9. The former has, besides, a duration of 10^h 40^m, the latter of only seven hours; whence the orbit is found to have an eccentricity of 0·25, the long, deep eclipse occurring at apastron, the slighter phase coinciding with the rapid sweep through periastron. The intervals of time from each to the next are of 2^d 10^h very nearly; and their equality implies that the major axis of the path pursued is directed towards the earth. The plane of the ellipse, however, must be somewhat inclined, since the mutual transits of the globes circulating in it are not central; and the amount of its inclination may be determined when the course of light-change is more accurately known. The gravitational period (as it may be called) is, of course, double the eclipse-period, or 4^d 20^h; but the mass of the system can be ascertained only by spectroscopic means. Its brighter member proves to be of about one-sixth, the dim component of one-fifth, the solar density.[583] All these particulars have been gathered from the photometric relations of these intimately conjoined bodies. From their dynamical relations, truths no less remarkable will perhaps before long be elicited.
At Moscow, in 1880, U Cephei was added by Ceraski to the Algol family. This object is distinguished by the abruptness and extent of its changes. In four and a half hours it descends from 7·1 to 9·4 magnitude, this profound obscuration lasting for about two hours, after which brightness returns, almost, if not quite as quickly as it departed. The light-curve, determined photometrically by Professor Pickering, is shown in Fig. 21.
He explains its singularities on the hypothesis of a total eclipse by a large semi-obscure body,[584] and alleges confirmatory evidence in a barely perceptible secondary minimum corresponding to the transit of the brilliant over the dusky globe. Chandler and Yendell, nevertheless, deny the reality of the minor eclipse;[585] and Wilsing vainly endeavoured in 1890[586] to bring the observed phases of U Cephei into harmony with any conceivable form of the occultation-theory. And the star, by its faintness, evades spectrographic tests for motion. Some increase of blue absorption is, however, stated to occur at its minima; and this is noteworthy as an instance, unique among Algol variables, of alteration in the quality of their diminished rays. Irregularities of the same type as those of Algol affect the period of U Cephei. If dependent on the light-equation principle, they signify the description, by the eclipsing couple, of an orbit larger than the Saturnian, in a period of between thirty and forty years.[587] Changes in radial motion, due to deflection in this wide path, would, if measurable, lend authenticity to an ingenious speculation, which may otherwise be superseded by Tisserand’s hypothesis[588] of a revolving major axis. Mr. Russell finds U Cephei to be a considerably more tenuous body than Algol.
The exceedingly short period of U Ophiuchi—20^h 8^m—and the halving of its light at minimum, suggest that it is composed of twin suns, alternately occulting one another. The period of revolution would, in that case, be twice the period of variation, and the globes would have more room to circulate than if one of them were dark. For then the brief intervals between the eclipses would represent each a complete round of the orbit, and the duration of the phases would imply such close proximity of the bright and the dark stars that the gap dividing their surfaces would scarcely exceed three-tenths of their joint radii. Such an arrangement is possible; a single spectrographic impression, taken five hours before or after a minimum, would show whether it actually subsists. If it do, the spectral lines will be single, though shifted; if not, they should appear incipiently double, and the movements indicated might unhesitatingly be taken to be included in a cycle twice the length of the eclipse-interval.
Discovered by Sawyer in 1881, U Ophiuchi showed to Chandler’s patient scrutiny individualities that should not be passed over.[589] Thus the return of light after minimum is interrupted by a pause similar to that observed in S Cancri, but which tends to become obliterated in a “mean curve.” Its reality has not been established photometrically (see Fig. 21), but may emerge with the application of finer methods. The circumstance, too, is worth remark that—again like S Cancri—U Ophiuchi was once caught sight of during an abnormally obscure phase.[590] An inequality of its period, comprised within thirty-seven to forty years, further noticed by Chandler, is perhaps visibly reflected in the disturbance of the star’s proper motion.
A still more curiously interesting object of the same class is met with in Y Cygni. Here, at least, as M. Dunér virtually demonstrated in 1892,[591] eclipses are duplicated; two occur in the course of each revolution. Its phases, first recognised by Chandler, 9th December 1886, range from 7·1 to 7·9 magnitude, and are completed in nine hours. But they were soon perceived to recur with conspicuous irregularity.[592] Towards the middle of 1888 they were no less than seven hours behind their calculated times, which shortly afterwards began to be largely anticipated. Perturbations on such a scale had never previously been betrayed by the occultations of a binary; and the task of accounting for them by inequalities of light-transmission was evidently a formidable one. The problem they offer was, however, destined to receive a different, and, we may add, a definitive solution.
When Dunér came to discuss the results of his own observations at Upsala in 1891–92, and to compare them with those made elsewhere, he was at once struck with a persistent discrepancy between the odd and the even sets of minima. The first, third, fifth, and so on, from an assigned epoch, obeyed a law of recurrence quite distinct from that conformed to by the intervening obscurations. Thus in November 1891, the intervals from an even to an odd minimum, and from an odd to an even minimum, differed by no less than nine hours, forty-three minutes. Clearly, the constant sum of these discrepant periods gives the true time-measure of systemic circulation. Two bright bodies, then, eclipse each other, and they seem to be matched “to a hair”; their eclipses, moreover, must be central, since the loss of light amounts to just one-half. The disparity of their intervals depends primarily upon the eccentricity of the orbit; secondarily, upon the situation of the line of apsides. It vanishes when the line in question points directly towards the earth; it attains a maximum when it is viewed at right angles, for then the right and left sections of the eclipse being traversed respectively with the least and greatest possible velocities, the succession of alternate occultations reaches the limit of time-inequality. Dunér’s final conclusions regarding the system were expressed as follows:—[593]
“The variable star Y Cygni consists of two stars of equal size and equal brightness, which move about their common centre of gravity in an elliptical orbit whose major axis is eight times the radius of the stars. The period of an anomalistic revolution[594] is 2·996933 days, and the eccentricity is 0·145. A minimum occurred while the stars were at periastron, on 8th December 1885. The line of apsides of the orbit, which then coincided with the line of sight, completes one revolution in the plane of the orbit in 41·1 tropical years.”
The next coincidence of the kind, if the above elements are correct, should take place in 1906. The compelling cause of the orbit’s gyration remains to be investigated. It may be found in disturbance exercised by an unseen, exteriorly revolving mass upon the conjoined suns; or their own spheroidal shape may be solely concerned in producing it; the question has an important bearing upon the construction of all such systems. The linear dimensions of the orbit of Y Cygni will unquestionably be determined ere long with the spectroscope, whence the mass of the bodies travelling in it will at once follow. A mean density less than one-sixth the solar is ascribed to them with some confidence.[595]
The variations of R Canis Majoris, detected by Sawyer in 1887, have been traced, as it were, only in outline. Their period is 28^h 16^m, five hours of which are occupied by the phases, and since the star fades to half its normal lustre, they are likely to be conditioned much as are those of Y Cygni. Two similar globes presumably undergo them in turn, mutually revolving in double the period of their occultations.
The character of R Aræ was noticed by Mr. A. W. Roberts in 1891.[596] He considers the eclipses, which recur once in 4^d 10^h, to be not always of the same depth; but this symptom of intrinsic variability in one or both of the transiting stars needs to be verified. The curve at minimum is symmetrical.
The nature of X Carinæ—another southern variable discovered by Roberts in 1892—is still dubious. It changes from 7·9 to 8·6 magnitude in 6^h 39^m, and remains constant only during 6^h 20^m. So that the phases extend over more than half the period of variation, which must evidently be doubled to give the period of revolution, since no eclipse can possibly have a duration of more than one-half the occulted body’s orbital circuit. The alternate minima of X Carinæ are thought by Roberts[597] to be, to a very small extent, unequal, and to succeed each other at slightly different intervals. If this be so, the system is composed of two stars, one a little brighter than the other, pursuing a nearly circular track in a period of twenty-six hours, and in such close contiguity that the times during which their discs overlap are longer than the intervals of their apparent separation. The actual subsistence, however, of this, or some analogous arrangement has yet to be proved.
The variations of Y Boötis are also more or less enigmatical.[598] They are limited to six-tenths of a magnitude, and have a period rather shorter than that of Algol. The eclipsing character of this eighth-magnitude star, suggested by Parkhurst in 1893,[599] was confirmed, on the strength of a year’s observations, by Yendell. Chandler, nevertheless, expresses doubts as to its genuineness, which is compromised by extraordinary anomalies, hardly amenable to explanatory efforts. The predicted minima do not always occur, and their failures seem capricious and inconsequential. But if they depended, as Parkhurst thinks they must,[600] upon a certain critical inclination of the orbit, causing transits to be occasionally missed, a law of periodicity should be traceable in the lapsed phenomena.
The obscurations of S Velorum recorded themselves on the plates of the Cape “Durchmusterung,” and the record was duly interpreted by Mr. Ray Woods in 1894.[601] They are marked by the same peculiarities as those of U Cephei, and probably indicate total effacements of a radiant sun by the prolonged transits across it of a voluminous, but dimly shining companion sphere, the diameter of which, according to Roberts,[602] cannot fall short of half the distance between the revolving bodies. Their respective densities, as estimated by him, are 0·61 and 0·03 that of the sun,[603] the dusky mass proving, on the assumed data, to be twenty times more rarefied than the brilliant one. A disparity so extreme cannot readily be admitted as real. If only the star could be elevated on the photometric scale,[604] the taking of a few spectrographs would at once acquaint us with the true plan of its system; but its faintness—7·8 magnitude—must long continue to baffle experiments of this kind.
A modified specimen of the Y Cygni sub-class is met with in Z Herculis. Its eclipsing character was announced by Chandler in 1894;[605] about a month later, Hartwig and Dunér independently detected in it a double sequence of disparate minima, with periods respectively of forty-seven and forty-nine hours. Hence the revolution of a pair of unequally bright stars in a period of just four days was inferred with virtual certainty.[606] In M. Dunér’s words, “Z Herculis consists of two stars of equal size, one of which is twice as bright as the other. These stars revolve round their common centre of gravity in an elliptical orbit, the semi-axis major of which is six times the diameter of the stars. The plane of the orbit passes through the sun, the eccentricity is 0·2475, and the line of apsides is inclined at an angle of 4° to the line of sight.” The chief minimum lasts 6·6 hours, and occurs not far from apastron. The secondary phase is hurried through in four hours, when the stars are moving with nearly their greatest speed. It is, however, unlikely that this relation will continue unchanged;[607] since it may be taken almost as an axiom that orbits so conditioned pivot round in space, turning their longest axes successively in every direction.
The first Algol variable photographically discovered was W Delphini. On 18th July 1895, Miss Louisa D. Wells missed a 9·3 magnitude star from a Harvard plate exposed 26th September 1891,[608] while upon seventy-one earlier and subsequent ones it was normally imprinted. The one tell-tale photograph had been taken during eclipse, when it sinks to 12·1 magnitude—that is to say, eleven-twelfths of its light are cut off by the interposing body. Pickering[609] believes the latter to be partially luminous and very large, affording prolonged totalities, but the photometric curve (see Figure 21) hardly warrants this assumption. It is fairly sharp at minimum, not flat, like that of U Cephei, and corresponds better with a partial occultation by a wholly dark satellite than with the central transit of one dimly radiative. The period is not constant.[610] Deviations from regularity amounting to one hour had become manifest early in 1898.
The phases of a seventh-magnitude star (DM + 12° 3557) named RX Herculis were discovered by Sawyer in 1898.[611] They range over eight-tenths of a magnitude, and recur at intervals of 21^h 21^m. Like those of U Ophiuchi, they probably indicate the revolution, in double that period, of two equal stars; and since the minimum brightness is just one-half the maximum, their mutual occultations may be total.
The variability of R^2 Puppis (CPD − 41° 1681), noticed by Professor Kapteyn during his inspection of the Cape Durchmusterung negatives, was verified and defined by Mr. Innes in 1899.[612] The period at first assigned of nearly thirteen days was abridged to one-half that length by Mr. Roberts’s investigations.[613] The light fades at minimum to one-third its full amount, through the intervention of a dimly luminous mass.
U^3 Cygni and V^2 Cygni were both detected by Madame Ceraski in studying photographs of the sky taken at Moscow.[614] They undergo analogous changes, investigated at Harvard College in 1899–1900.[615] Those of U^3 Cygni are remarkable for their extent, the greatest known in an eclipsing star, unless (which is doubtful) W Delphini should be bracketed with it. V^2 Cygni, at full brightness, ranks little higher than the eleventh magnitude, and descends, once in six days, nearly to the thirteenth. It is thus an object at the limit of detailed observation. Innumerable systems of the same kind must lie beyond that limit. The twenty-first star on our list—R^2 Velorum—suspected as an Algol variable by Innes in 1901, was verified and investigated by Roberts.[616] Of the remaining six objects enumerated, U Sagittæ was found by M. Schwab of Ilmenau to vary after the manner of U Cephei;[617] and UZ Cygni, detected by Mrs. Fleming in 1902, is remarkable for a period more than thrice as long as that of S Cancri. UW Cygni, RV Lyræ, and the still unnamed star in Perseus have been recently discovered by Mr. Stanley Williams.
Algol variables, without any recognised exception, show first-type spectra. They are either helium or Sirian stars. This specialty is unaccountable, and may perhaps vanish with the widening of experience; for many close binaries exempt from eclipses belong to the solar class, and no reason is apparent why those happening to revolve in planes coincident with the visual ray should differ in quality of light from those revolving in orbits variously inclined to it. Nor is it yet quite certain that the eclipse-theory accounts for certain minor phenomena in the stars to which it applies. Thus some of their light-curves, as drawn visually, are marked by peculiarities incapable of being explained as the outcome of purely dynamical relations. They may, however, turn out to be illusory or subjective; their reality is not incontrovertible. Again, the exceptionally low minima recorded for S Cancri and U Ophiuchi need confirmation. The possibility of mistake is not excluded so long as each remains an isolated event.
Three varieties of eclipsing stars may be distinguished. The first includes bright and dark pairs, like Algol and its companion, revolving in slightly oblique orbits. One partial occultation takes place in each revolution. The intimate association which they present of bodies at opposite extremes of luminosity is not a little remarkable. In the second variety, exemplified by U Cephei, a brilliant star circulates round a larger, but far less lustrous globe. One prolonged totality marks the orbital period. The secondary minima, theoretically inevitable in such cases, have not been certainly observed. Vanishing stars, could they be discovered, would appropriately illustrate this mode of construction where the contrast in light-power had reached its limit. Finally, the third species of occulting systems consists of stars undergoing nearly equal double eclipses, the period of revolution comprising two periods of variation. Y Cygni is a typical example. If the loss of light amount to one-half, or eight-tenths of a magnitude, and the alternate minima be of the same intensity, the eclipses are total; for two similar stars, one is temporarily substituted. If, owing to the inclination of their path, they only partially conceal one another, the phases will be slighter, yet still equal. Their disparity, in odd and even series, shows at once that the balance of luminosity is tilted; and indications are not wanting that its level is disturbed rather by inequalities of intrinsic lustre than of shining area.
The time-keeping of eclipse-stars is a subject demanding profound and persistent study. The minutest irregularities traceable in it may be of far-reaching significance.[618] On what principle they should be explained, is still largely an open question. Possibly several forms of action conspire, even in the same system, to produce the sum-total of their deviations. In no case has the presence of a third body been proved; in no case have perturbations of the ordinary gravitational type been suspected. On the other hand, the occulting and the occulted globes must be deformed through rotation; hence one true cause for the observed inequalities falls within our ken; whether it is a sufficient cause alone remains doubtful. Essentially, however, increase of knowledge regarding these marvellous combinations depends upon the development of spectrographic methods. Surely, although perhaps in slow succession, they will yield the secrets of their construction to a mode of inquiry that continually gains power and accuracy, and is capable of dealing directly with the most recondite springs of celestial mechanics.
XIX. SHORT-PERIOD VARIABLES
The limit of length for “short periods” of stellar variation is conventionally fixed at thirty days; but it is seldom reached by objects of typical character. Rapid fluctuations are almost always accomplished with extreme exactitude both as to time and amount. To this rule there are very few exceptions, and a reason for it is not difficult to find. Variability of the kind in question is precise because it originates extrinsically. It might be called a “forced vibration” of change. Its course is, in some way, prescribed by the revolutions of a satellite. No more curious spectroscopic discovery has been made than that of the binary nature of short-period variables. By it a breach has been made in the wall of mystery surrounding stellar light-change. The breach has not yet been mounted, nor is it quite practicable; but by persevering efforts it can be gradually widened and levelled.
In dealing with variable stars we must proceed tentatively. The subject is so complex that no intelligible view of it can be gained all at once. A unifying principle is still lacking. We can only take things as they present themselves, noting differences, tracing partial analogies, and arranging into some fashion of order a multitude of heterogeneous examples. Thus stars fluctuating in short periods may be separated into three families. The first has δ Cephei, the second ζ Geminorum for its head, and their members may conveniently be designated Cepheid and Geminid variables. The third is represented profusely, but almost exclusively, in globular clusters. To begin with the Cepheids.
They are numerous and well known. Their changes are continuous and of moderate amplitude, but proceed unsymmetrically as regards time. The rise to maximum occupies on an average about a third of the period, or half the time allowed for the decline from it to minimum. This retardation is accompanied by an inherent tendency to a second maximum, sometimes barely indicated as a pause in descent, but in several cases giving rise to a pronounced “hump” on the downward slope of the light-curve. The variations of δ Cephei range from 3·7 to 4·9 magnitude in 5^d 8^h 47^m 39^s, of which 1^d 14^h 36^m suffice for the phases of increase. The spectrum is of the solar type, and does not change with the brightness. Oscillatory movements, however, of its constituent lines, detected by Bélopolsky in 1894,[619] betray the presence of an obscure companion revolving in the light-period. The ellipse described is so eccentric that the companion-bodies when at apastron are three times further apart than at their nearest approach; and its major axis deviates only by two degrees from a vertical plane passing through the earth. There is nothing indeed to show that it may not be highly inclined to the corresponding horizontal plane. The orbital level is undetermined, being evidently such as to exclude eclipses. This was unexpected, but it is certain. The criterion is simple. Radial velocity should vanish at minima if a transiting globe were concerned in their production; in point of fact, the epochs of least brightness precede the epochs of conjunction by a full day. The system of δ Cephei is not then an eclipsing system. The star’s variability must be otherwise accounted for. Nor would it be easy, without abusing the licence of hypothesis, to expound it as the result of occultations. The inducement to make the attempt is, at any rate, removed by the ascertainment of their non-occurrence. Nevertheless, the coincidence of periods assures us that orbital revolution, in one mode or another, prescribes the flow of change. But the ideas so far entertained on the subject scarcely bear examination. Obviously untenable, for instance, is Mr. Roberts’s view that the companion of δ Cephei is raised, by the heat received at periastron, from sensible obscurity to a nearly equal grade of lustre with its primary.[620] If this were so a double spectrum should be observed at quadratures. Again, the maximum should, on the hypothesis, fall short of twice the minimum brightness; actually, it exceeds it three times. Mr. Roberts himself adverts to these objections, but holds them not insuperable. Mr. Eddie’s suggestion[621] of luminous increase through intensified tidal action at periastral approach, is more plausible. Bodily strain due to mutual gravitation would, in so eccentric an orbit, gain twenty-seven-fold efficacy as the bodies moving in it come together from its farthest point; and the processes of internal circulation might possibly be sufficiently quickened by the disturbance to yield a largely augmented output of light. But commotions of the requisite violence could not subside with perfect regularity every five days, and they should inevitably be accompanied by gaseous outbursts spectroscopically evident. That they do not occur may be securely inferred from the one circumstance that no trace of emissive symptoms is met with in the light of this star. As to the scale of its system we are, moreover, completely ignorant, and are hence unable to estimate the absolute power over its members of tidal influences. The line-displacements of the bright star acquaint us merely with its rate of motion as projected upon the visual plane; they correspond to a mean orbital radius of 620,000 miles, the real path being perhaps six or eight times wider than that spectroscopically indicated, while the companion-ellipse traversed by the dark satellite may be of any imaginable size. A sapphire-blue star of the sixth magnitude forms with δ Cephei, which has a golden sheen, a combination resembling that so beautifully exhibited in β Cygni.
The variations of η Aquilæ are, in every respect, analogous to those of δ Cephei. They have the same range of 1·2 magnitudes, and a somewhat longer period of 7^d 4^h 14^m, which they divide, in about the same proportions, between a rapid increase and a leisurely decay of brightness. The abortive secondary maximum of δ Cephei, however, develops in η Aquilæ into a pronounced recovery of lustre. The light-curve shown in Fig. 22, from Dr. Schur’s delineation, renders the duplex phase conspicuous. The binary character of the star was detected by Bélopolsky in 1895,[622] and he computed its orbit from improved spectrographic data in 1897.[623] It proved to be of nearly the same apparent size as that of δ Cephei, and the conditions of revolution were, in this case again, manifestly inconsistent with the occurrence of eclipses. An interval of two days was found to separate each minimum from the ensuing conjunction of the bright and dark spheres. Their conjunctions, accordingly, are not transits, since they are unaccompanied by any diminution of light. “Very remarkably,” Bélopolsky writes, “the same state of things is present in the variable star δ Cephei. Hence some other cause must be sought by which the variations in lustre and the spectral displacements of these two stars may be brought into harmony.”
Mr. W. H. Wright of the Lick Observatory renewed in 1899,[624] and substantially confirmed the Pulkowa investigations. His orbit, however, came out considerably more eccentric than that computed by his predecessor, and he located its major axis somewhat differently. But on the essential point for the theory of the star’s variability—the impossibility of eclipses—they agreed. Fig. 23 reproduces Mr. Wright’s drawing of the ellipse described by η Aquilæ round its invisible companion, supposed immovable at the focus (O). Its situation at minimum epochs (marked Min. in the figure) obviously corresponds to nearly the highest rate of speed in the line of sight, and to a comparatively wide visual separation of the coupled bodies. The periastron is at P; the points where the secondary phases take place are indicated respectively as _Min.__{2} and _Max.__{2}. They are unaccompanied by irregularities of movement. In fact, neither in this object nor in the analogous one decorating the crown of Cepheus is there any traceable connection, except their significant agreement in period, between the flow of spectroscopic velocity and the rise and fall of brightness. The spectra of these two variables are quite similar, only the lines of η Aquilæ are more diffuse. Both, too, are approaching the sun at uniform rates of about fourteen and nine miles a second respectively. Finally, both are subject to some slight disturbances in time.[625] Those of η Aquilæ, discussed by Dr. Lockyer,[626] have an amplitude of five hours, and are self-compensatory in a cycle of 400 light periods.
The generalisation is a tolerably safe one that all Cepheid stars are binaries; but its establishment must be a work of time. Those of the shortest periods are the most promising for purposes of spectrographic inquiry, since they are likely to be in swift circulation, and hence to show conspicuous line-displacements. Negative results, however, as already said, may simply imply an unfavourable situation of the orbits; they do not necessarily indicate the solitary condition of the stars. A few examples of Cepheid variables are given below in the order of increasing length of period. Some brief description of the peculiarities of each follows.
┌──────────────┬──────────────────┬───────────┐ │ Name. │Limits of Change. │ Period. │ ├──────────────┼──────────────────┼───────────┤ │ │ │ d. h. m.│ │ R Muscæ │6·6 to 7·4 mag. │ 0 21 10│ │ R Trianguli │6·6 „ 8·0 „ │ 3 9 20│ │ Australis │ │ │ │ST Cygni │6·6 „ 7·4 „ │ 3 20 10│ │ T Vulpeculæ │5·5 „ 6·5 „ │ 4 10 28│ │ Y Sagittarii │5·8 „ 6·6 „ │ 5 18 33│ │ U Sagittarii │7·0 „ 8·3 „ │ 6 17 46│ │ X Sagittarii │4·0 „ 6·0 „ │ 7 2 50│ │ W Sagittarii │4·8 „ 5·8 „ │ 7 14 16│ │ S Sagittæ │5·6 „ 6·4 „ │ 8 9 7│ │ X Cygni │6·4 „ 7·7 „ │ 16 9 15│ │ W Virginis │8·7 „ 10·4 „ │ 17 6 30│ │ T Monocerotis│5·8 „ 8·2 „ │ 27 0 18│ └──────────────┴──────────────────┴───────────┘
R Muscæ, being circumpolar at the Cape, can be observed to advantage only in southern latitudes. Once in twenty-one hours it doubles its light, and so emerges into naked-eye visibility, then sinks back again out of sight. The rise occupies just seven hours, or one-third of the period—the normal proportion for stars of this class. Evidence of rapid circulatory motion is pretty sure to be elicited by spectrographic means.
The phases of R Trianguli Australis were noticed by Gould in 1871, and have of late engaged the attention of Roberts. They show the peculiarity, surprising in a Cepheid star, of being uncertain in extent. The full measure of change is from 6·6 to 8·0 magnitude, but at certain maxima it mounts no higher than 6·8; at certain minima it descends no lower than 7·5 magnitude. It would be of interest to learn whether these oppositely incomplete phases occur together or disconnectedly. No methodical account of them has, we believe, been published. The increase of brightness in R Trianguli occupies little more than one quarter of the period.
The light-curve of ST Cygni is “humped” like that of δ Cephei. About forty-six hours after maximum the decline is stayed, then, a brief pause ended, resumes its course. The interval from minimum to maximum is 21½ hours, that from maximum to minimum seventy.[627] The variability of this star[628] was detected at Potsdam in 1896 by G. Müller and P. Kempf.
The spectrum of T Vulpeculæ is similar to that of δ Cephei.[629] Its changes, discovered by Sawyer in 1885, consist in a rise of one magnitude in 1^d 7^h, followed by subsidence in 4^d 3^h. The comparative brightness of the star brings its movements well within range of spectroscopic investigation.
The four stars in Sagittarius, which come next on our list, form a singular group, discovered by Schmidt in 1866.[630] They are included in a space of about ninety square degrees, and all vary after the fashion of δ Cephei in periods comprised between 5·8 and 7·6 days. Among them X Sagittarii, which attains once a week fourth-magnitude rank, is the most conspicuous. Its spectrum is of the solar type. One of its associates, U Sagittarii, distinguished by a strong orange tint, is the centre of a little cluster. Its fluctuations, upward in 2½, downward in 4¼ days, proceed with the regularity of clockwork.
S Sagittæ shows the retarded decrease and inflected curve distinctive of its class.[631] Yendell considered the maximum to be double (see Fig. 24). The change at minimum is unusually slow. In quality of light the star was found by Sir Norman Lockyer to be an exact match for δ Cephei.
X Cygni was discovered by Chandler in 1886. It rises without fail in 6^d 19^h to 6·4 magnitude, but shows an inconstant minimum brightness, sometimes descending to 7·7, at others stopping short at 7·2 magnitude. The period of 16^d 9¼^h is not known to vary. The star is quite colourless; information as to the character of its spectrum is not at present forthcoming.
W Virginis is uncertain both at maximum and minimum. Its highest rise is to 8·7, its lowest descent to 10·4 magnitude. But these limits are far from being always reached; phases deficient by quite half a magnitude either way are often observed, and seem to intervene casually. The period, on the other hand, of 17^d 6½^h is strictly conformed to. The time of increase, 8^d 5^h, is proportionately long for a Cepheid variable.
That of T Monocerotis is, on the contrary, relatively short, although the entire cycle of twenty-seven days is the most protracted yet ascertained for a star of its class. And here again the amplitude of change is inconstant. Maxima occur as high as 5·8, as low as 6·4 magnitude, while the minimum brightness ranges between 7·4 and 8·3 magnitude. There are then spring and neap tides of stellar fluctuation; yet no clue can be found to the cause of their difference. The four Cepheid variables in which they appear—namely, R Trianguli, X Cygni, W Virginis, and T Monocerotis—have no other features visibly in common. Perhaps the spectroscope may reveal unlooked-for analogies connecting their physical qualities or their systematic relations; but its dicta have still to be pronounced.
About three dozen stars had been registered at the close of last century as variable on the model of δ Cephei. Most generalisations regarding them are liable to lose validity by future experience; but there are two properties in the absence of which they should be otherwise classified. In all, light-change progresses unceasingly; in all, it advances more rapidly in the direction of increase than of decrease. An inclination, more or less accentuated, to pause in descent is probably connected with this kind of dissymmetry. Among their other distinctive qualities the following may be provisionally enumerated:—(1) Their spectra are of the solar type. (2) They are binaries revolving in the periods of variation. (3) They are not eclipsing pairs; their orbits may be inclined at any angles to the visual plane. (4) Their fluctuations in lustre are unaccompanied by spectral change. (5) Being nearly devoid of proper motion, they are presumably at vast distances from the earth. They are then giant suns.
Future research will decide whether Cepheid stars are marked off from ordinary spectroscopic binaries by any peculiarities in their manner of circulation. Are their orbits, for instance, in all cases highly eccentric? Is there a fixed relation between the situation of the periastron and the point of lowest brightness? Do the major axes revolve? Above all, what differentiates short-period variables from revolving pairs constant in light? Why do δ Cephei and η Aquilæ show an incessantly changing lustre, while Polaris and Θ Ursæ shine steadily? The four appear to be of analogous constitution, and to suffer no diminution by eclipse. What form of influence, then, is it which acts so strikingly upon the two former objects, while leaving the two latter unaffected? Undoubtedly the close attendance of a satellite is instrumental to the production of the observed changes of luminosity; but other conditions also come into play—conditions that are absent in Polaris, in β Aurigæ, in α Virginis, in Θ Ursæ, in Θ Draconis. What is their nature? Here is the main issue as regards short-period variability.
XX. SHORT-PERIOD VARIABLES—Continued
The second family of short-period variables resemble the first in the continuous nature of their fluctuations. They are distinguished from them by the symmetrical apportionment in time of those fluctuations. The intervals from minimum to maximum, and from maximum to minimum, are almost exactly equal. Not very many such stars are known. First singled out as rarities by Dr. Chandler in 1896,[632] they have for their exemplar ζ Geminorum.
The variations of this star, discovered by Schmidt in 1847, carry it from 4·5 to 3·7 magnitude in five days and twenty-two minutes, and back again to its former level in a space of time just three hours longer. The difference may be called negligible. Fig. 25, A, shows the representative light-curve. Its undulations at present succeed each other without sensible alteration; but observers of an earlier generation regarded them as subject to disturbance. Their period, according to Argelander, was ten minutes longer in 1869 than it had been in 1847;[633] and Schmidt pronounced the fluctuations in brightness to be nearly suppressed in 1868, and irregular in 1881.[634] Fresh interest was imparted to the history of the star by Bélopolsky’s detection, early in 1898, of its composite nature;[635] and the discovery, which had not been published, was repeated a year later by Campbell at Lick. He remarked besides unaccountable deviations from the even pace of elliptical progression, established as genuine by critical test-observations. Their nature will be seen at a glance by a reference to Fig. 25; the lower curve in which (B) represents the radial velocities of ζ Geminorum. The unit of time is one day, the unit of speed five kilometers per second. A comparison with the upper curve (A) shows that the period of motion agrees with the period of light, but that its rate varies oppositely to the brightness—that is to say, the star is moving rapidly in the line of sight just when its minima take place. They are, accordingly, not due to eclipses, which should coincide absolutely, or very approximately with zero radial velocity. The relations of the pair are made still clearer by Professor Campbell’s drawing of the orbit deduced from the velocity-curve (see Fig. 26). It represents that of the bright component round the centre of gravity, while the similarly shaped path followed by the dark star must be larger or smaller in the inverse ratio of its mass. The ellipse depicted in Fig. 26 has an eccentricity of 0·22; PA is the line of apsides, OE the line of sight. Minima occur 1^d 7^h after periastron at the point Min.; and since the companion is then situated somewhere in the direction Om, its interposition is evidently out of the question. Recurring now to Fig. 25, B, we perceive that the heavy black line connecting the points determined by actual measurement, pursues an undulating course. In Professor Campbell’s words, “The observed velocity-curve is alternately above and below the elliptic curve, and the intersections of the two occur at approximately equal intervals of time. There are six of these intersections, corresponding to three complete periods or cycles in one period of the light-curve.” The oscillations showed no signs of intermission during fifteen months, and assuredly indicate an inherent peculiarity of the system. They might be formally explained by assuming it to be triple, the bright star revolving in 3^d 9¼^h round one invisible attractive mass, and the two together in 10^d 3½^h round another more distant. But the arrangement, as Professor Campbell points out,[636] could scarcely be stable, owing to the commensurability of periods, and the consequent subversive piling-up of disturbances. Nor is it easy to accept the idea that the digressions of ζ Geminorum from a mean rate of travel are “minor tidal effects.” Prolonged and diversified researches are, in fact, needed before any promising theory of them can be formed.
The star is of a golden yellow colour. Its spectrum is a replica of that of δ Cephei. An annual proper motion is attributed to it of 0·0165″, but the value is too small to be altogether reliable. The remoteness of this problematic system is hence unimaginably great.
The following brief list of Geminid variables, with some ensuing comments, will serve to widen the reader’s acquaintance with the characteristics of the species.
┌─────────────┬──────────────────┬────────┐ │ Name. │Limits of Change. │Period. │ ├─────────────┼──────────────────┼────────┤ │ │ │d. h. m.│ │R^2 Centauri │ 7·4 to 7·8 mag.│ 0 7 16│ │ S Antliæ │ 6·7 „ 7·3 „ │ 0 7 47│ │ U Pegasi │ 9·3 „ 9·9 „ │ 0 9 0│ │ 24 Centauri │13·4 „ 14·0 „ │ 0 11 5│ │ ω │ │ │ │ V Puppis │ 4·1 „ 4·9 „ │ 0 17 27│ │ U Vulpeculæ│ 6·9 „ 7·6 „ │ 8 0 4│ │d Serpentis│ 5·0 „ 5·7 „ │ 8 17 17│ │ β Lyræ │ 3·4 „ 4·5 „ │12 21 47│ └─────────────┴──────────────────┴────────┘
The variability of R^2 Centauri, discovered by Mr. A. W. Roberts in 1896,[637] is slight but sure, and proceeds by evenly measured steps of increase and decrease. The period is the shortest found for any star outside the precincts of a cluster. With its companion, should it prove to be spectroscopically double, R^2 Centauri must form an exceedingly close, or an enormously massive pair.
S Antliæ bore for eight years the reputation of being an Algol variable.[638] The shortness of the period and the flatness of the curve, conveying the impression of a stationary maximum, produced a deception removed in 1896 by the Harvard photometric results. They showed the light-change to advance continuously along a smooth curve, unbroken by the sudden drop indicative of an eclipse. It is, however, marked by the “interesting feature” (in Professor Pickering’s words[639]) “that the time of increase occupies 0·62 of the entire time of variation.” Here then is an ostensible case of dissymmetry opposite to the usual kind. But the relation was stated by Mr. Sperra of Randolph, Ohio, to be inconstant, and he deduced from his observations an average equality of the intervals between opposite phases.[640] This is perhaps the essential fact. S Antliæ is a white star with a transition-spectrum[641] resembling that of Procyon. The lines are never seen double, so that two bright components cannot be present unless they revolve in a plane nearly at right angles to the visual ray. But line-displacements due to motion round an obscure body, may possibly be detected by the application to this curious object of a slit-spectroscope.
A small star in Pegasus was noticed by Dr. Chandler in 1894 as apparently subject to eclipses; but its waxings and wanings proved, on fuller inquiry, to be without pause. A controversy as to their nature[642] was practically terminated by Mr. Wendell’s measures with the polarising photometer at Harvard College in December 1897.[643] Their upshot is graphically exhibited in Fig. 27. Each of the closely set dots through which the curve was drawn represented eighty settings made on eight nights, none being rejected for discordance. The crosses, each of which gives the average of sixteen settings, embody single nights’ results. The divisions in time (abscissæ) represent intervals of thirty minutes; the divisions in brightness (ordinates), tenths of a magnitude. The complete period of the star is nine hours less nine seconds, but it is nearly cut in two by a secondary decline falling short of full minimum by only 0·15 of a magnitude. The reality of this trifling difference, contested by Chandler, appears to be substantiated by the Harvard data, and stamps U Pegasi as of the kindred of ß Lyræ, the premier short-period variable. A mathematical discussion of the conditions of U Pegasi, based upon the eclipse-theory, was published in 1898 by Mr. G. W. Myers of the Yerkes Observatory.[644] It is valuable as an authoritative proposal of the terms demanded by that theory under the given circumstances. They are not wholly unacceptable. They involve, at least, no contradiction of any known law of nature; yet they are difficult to imagine realised. The system must obviously be composed, if its luminous variations be geometrically explicable, of two bright bodies revolving almost in contact. Indeed, they are probably more than in contact, if the assumed data are correct; they interpenetrate and together form an “apioid,” which, according to Poincaré, is a figure of equilibrium for rotating masses. One of the conjoined globes proved, moreover, to have a radius about four-fifths that of its primary, and to be less intrinsically brilliant in sensibly the same proportion. Their revolutions in a period of nine hours afford eclipses, alternately total and partial, at intervals of four and a half hours, the orbit being viewed by us edgewise. Now such an arrangement as that indicated for U Pegasi might conceivably prevail in an embryonic binary system. It would, in fact, accord well with Dr. See’s views as to the evolution of double stars; but evidence of its actual existence is still a desideratum. Until affirmed by the spectroscope, it must be treated as only a speculative possibility; and the example of ζ Geminorum is not encouraging to the occultation-rationale of continuous variability. The time, however, is not far distant when the decisive motion-test will be applied, if not to this faint object, at any rate to others that are analogous and more accessible.
Some few of the variable stars in clusters belong to the Geminid class. An example is afforded by No. 24 in the great southern star globe ω Centauri. One of five or six thousand silvery specks crowded together into the “span of a man’s hand,” it yet preserves individuality. Once in 11^h 5^m it gains twofold brightness, then fades even more rapidly than it increased.[645] The changes are said to resemble those of S Antliæ. If occasioned by the uninterrupted mutual eclipses of equally luminous bodies, a mean density would be implied for them of one-fifth the solar. And this irrespectively of their mass. In a system composed of a pair of globes revolving just in contact, density depends solely upon period.[646] The reason is easily seen. With a constant period the mass of a system varies as the cube of the distance, and in the same proportion the component spheres must, if they remain contiguous, vary in bulk. Thus, since volume and mass preserve under these circumstances a fixed ratio, density is the same for any assignable value of their absolute amounts.
A variable star, more than commonly enigmatical in its procedure, comes next on our list. Discovered by Mr. Stanley Williams in 1886,[647] V Puppis fluctuates between 4·1 and 4·9 magnitude in a period fixed by Mr. Roberts, with vigilant care, at 17^h 27^m 13^s. The alternate minima are slightly unequal, and he assumes them to correspond to a trifling disparity in brightness between the members of a mutually occulting “dumb-bell” combination revolving in double the light-period, or 1^d 10^h 54½^m.[648] But here the spectroscope intervenes. From an examination of spectrographs taken by Bailey at Arequipa, Professor Pickering inferred in 1896[649] the binary character of the star. During thirty-seven hours at a stretch it shows double absorption lines, which then close up, and after a brief interval open out again, this time with the fainter component in the reversed position. These shiftings to and fro take place in a cycle of 3^d 2^h 46^m, and indicate a relative velocity of 385 miles a second, giving a minimum value for the radius of the orbit of 16,500,000 miles, and a combined mass seventy-seven times that of the sun. Have we then, in V Puppis, a genuine instance of discrepancy between the motion and light-periods? Or is their eventual reconcilement probable? Mr. Roberts has spoken his last word on the subject, and the spectrographic data seem sure. Yet if any compromise were possible, it should be, one would suppose, by subdividing the longer period, not by extending the shorter one. The anomaly of their discordance is too flagrant to be admitted without cogent proof.[650]
The variations of U Vulpeculæ proceed equably, according to their discoverers, MM. Müller and Kempf,[651] in a period of eight days. M. Luizet of Lyons agrees, and regards them as strictly conformable to those of ζ Geminorum.[652] The Harvard measures, nevertheless, indicated an accelerated increase.[653] If it be substantiated, the star should rank as intermediate between the Cepheid and the Geminid families.
The instability of d Serpentis, suspected at Potsdam in 1891, was verified by Yendell in 1894.[654] Its phases, as determined by him, resemble those of β Lyræ. They include a secondary minimum, symmetrically placed between two equal maxima. The spectroscopic investigation of this star, which never descends so low as the sixth magnitude, should present few difficulties, and will be of special interest from the side-lights it may throw on the problem of the Lyre variable. This latter subject is so complex as to demand treatment in a separate chapter.
Another inviting object to the possessors of spectrographic apparatus is the southern variable κ Pavonis. It ranges from 3·8 to 5·2 magnitude in a period of nine days two hours, but by gradations lacking distinctive character. Their correlation with spectral line-shiftings might serve more clearly to define their nature. Physically, the star belongs to the solar family.
One of the many singularities connected with stellar variation is that it takes a special form in condensed clusters.[655] Even in them this form does not prevail universally; sporadic cases of many kinds are met with; but in general the light change of aggregated stars has the following characteristics. The periods are extremely short. They average half a day in “Messier 5,” and 90 out of 132 determined for the components of ω Centauri fall below twenty-four hours.[656] The rise to maximum is wonderfully swift. One-tenth part of the cycle is about the proportion claimed by it, and No. 45 ω Centauri increases by two magnitudes in the space of one hour. The minima are prolonged dead-level tracts. In other words, the variation is discontinuous. It might be described as a sudden leap upward into comparative brightness from a habitually low state. The maxima are episodes, foreign, as it were, to the internal economy of the stars. They recur, nevertheless, with the utmost precision. Hundreds, nay, thousands of successive periods have been watched without the detection of the smallest irregularity. The light-curves of two stars in Messier 5 are given in Fig. 28 from Professor Bailey’s drawings. Each has a range exceeding one magnitude, and a period of approximately twelve hours.
The discovery of “cluster variables” as a class apart was made by Professor S. I. Bailey in the course of his photographic work at the equatorial station of Harvard College. They literally swarm in certain groups, while in others they occur scantily or not at all. An isolated southern star, S Aræ, the character of which was detected by Innes, and has been investigated by Roberts,[657] appears to be of their type. Ordinarily hibernating near the eleventh, it springs up to 9·5 magnitude, at the rate of a magnitude in twenty minutes, once in eleven hours. U Leporis, over which Mr. Innes has kept watch, approximates to the same type. This mode of variation is peculiarly difficult to explain. Eclipses will not here serve our turn; however modified, they evidently fail to meet the requirements of the situation.[658] The phenomena, indeed, to a certain extent, invert those with which eclipses are associated. Instead of an abrupt failure, a sudden access of light has to be accounted for. The question whether such stars are binaries is of great interest. Cluster-components, which are rarely brighter than the thirteenth magnitude, can indeed scarcely be expected to furnish a reply to it; but something definite on the point may be learned by a spectrographic appeal to S Aræ. The direction that should be given to further inquiries will then become apparent.
XXI. THE PROBLEM OF BETA LYRÆ
On the 10th of September 1784, John Goodricke of York, a deaf-mute scarcely twenty years of age, perceived the second brightest star in the Lyre to be variable. He ascertained, further, the main features of its light-change. They are very peculiar.[659] Four phases of approximately equal duration are comprised in a period of twelve days and nearly twenty-two hours. They are portrayed in the symmetrical curve drawn from Argelander’s observations in Fig. 29. The twin maxima, situated midway between the principal and secondary minima, are of absolutely constant brilliancy. Constant, too, is the chief phase of obscurity, so that the compass of variation, from 3·4 to 4·4 magnitude, is a fixed quantity. The intermediate minimum, however, is not so immutable. Defect and excess are occasionally observed in it. But the flow of change is always smooth and uninterrupted. Nor is there any pause in a slow lengthening of the period, which has progressed, during the last hundred years, at the average rate of about one-third of a second at each recurrence. That the disturbance will prove compensatory can scarcely be doubted; but the law of restoration is not yet apparent.
The spectrum of β Lyræ is dominated by helium. It includes members of all the six series emanating from that substance, and they are mostly composite aggregations of bright and dark rays.[660] The Huggins series of hydrogen is similarly represented; among metals, calcium and magnesium are prominent, and ten dark oxygen lines in the ultra-violet were photographed at Tulse Hill in 1899.[661] But the special characteristic of this spectrum is its variability. The coupled lines are neither fixed in position nor constant in structure. They shift, they split, they flash and fade; they spread into diffuse bands or contract to definite filaments; and this in obvious, though disturbed, subordination to the light-period of the star. The two kinds of variation are, to some extent, mutually dependent; yet they are far from showing a strict concurrence. The loose and indeterminate nature of their relations places formidable obstacles in the way of investigating either.
Already, in 1866, Father Secchi noticed bright lines in the dispersed light of β Lyræ, and Von Gothard was struck in 1883 with their unaccountable fluctuations of visibility.[662] But the complexities they presented wholly baffled direct observation; their unravelment only began to be possible when spectrographic methods became fully developed. Through Mrs. Fleming’s examination of the Harvard plates, it was made evident in 1891 that the emission-rays had dark companions, and were not stationary with regard to them; and Professor Pickering[663] gathered from their displacements the probability that the two sets belonged severally to the unlike components of a close binary, revolving synchronously with the ebb and flow of total brightness. He estimated their relative velocity at 300 miles a second in a circular orbit, with a radius of 50,000,000 miles. This hypothesis is beyond question founded in fact. The star is composite, and the emissive and absorptive elements of its spectrum shift, on the whole, oppositely; each battalion, as Mr. McClean has indicated, moves as a unit, and in a contrary sense to the other. To distinguish them ought then to be a simple matter. The differently affected lines ought of themselves, one might expect, to declare their separate origin. Difficulties well-nigh insuperable, nevertheless, beset the interpretation of this spectrum. Their main source is this. The constituent lines do indeed oscillate through motion, but they are subject to further influences of a more complex kind, and of a barely conjecturable manner of working. The various species of change are hence entangled and disguised to a bewildering extent; and totally divergent views have been expressed as to the proper apportionment of the spectrum between the bodies jointly originating it. Sir Norman Lockyer attributes the absorption lines to a pair of “Orion” stars, unequally advanced in development,[664] with a relative velocity of 156 miles a second; and the addition of a bright-line companion is an implied necessity of his scheme. Mr. McClean[665] demands a dark-line and a bright-line component, mutually circling at a speed of 400 miles a second. Miss Maury considers that three stars must be engaged.[666] Dr. Vogel[667] and Father Sidgreaves,[668] although they have investigated the spectrum in detail, make no attempts at its analysis. M. Bélopolsky, by minimising the scope of attack, made a substantial advance towards the solution of the problem.[669] He dealt with only two lines—the absorption ray of magnesium at λ 4482 and the brilliant F of hydrogen; but succeeded in establishing, it might be said, incontrovertibly, their separate production from conjoined bodies dissimilarly constituted. The magnesium line is better adapted for measurement than most of the spectral elements of β Lyræ; it is subject to only moderate alterations in width and definition, and determinations of its motion-shifts afford, accordingly, consistent results. From them Bélopolsky has calculated the orbit of the originating globe, which may be identified with Lockyer’s Rigel star. He found it to be but slightly eccentric (e = 0·04); the mean radius (supposing the plane to coincide with the line of sight) is 15,000,000 miles; the system is advancing towards the sun at the rate of seven miles a second, and the times of zero radial velocity agree so nearly with the epochs of minimum as to lend countenance to the eclipse-rationale of light-failure. A second orbit was then computed—though far less securely—for the component showing bright F, each being described round the common centre of gravity. It proved to be about half the size of the former, which implied that the body travelling in it (designated A) was twice as massive as the companion (B). It possesses, in fact, the gravitating power of eighteen, the latter of nine suns. Nevertheless, the principal minimum corresponds to the obscuration of the minor globe, while at the secondary phase, the primary star is the one partially occulted. The bright-line star, A, must then be much less luminous in proportion to the quantity of matter it contains than the dark-line star, B. This does not appear probable, but it cannot be pronounced impossible.
On the whole, Bélopolsky’s results are plausible, and the basis they rest upon is solid, if narrow. Yet the development of their consequences leads to a network of perplexities. The star A, characterised by hydrogen-emission, can be no other than Lockyer’s second dark-line star—that resembling Bellatrix; but if so, “the bright bands,” as Miss Maury says, “have a residual motion of their own, which places them sometimes towards the red, and sometimes towards the violet end of their own system of dark lines, and at other times upon the lines of one, or both spectra.” Yet the suggested triple combination is inadmissible. The presence of a third body would require the introduction of a second period, and of this no trace is discernible. The spectral phenomena are in many ways abnormal and unaccountable, but in the long run they conform to the single and nearly uniform time-measure of the system, and preserve a modified fidelity to the course of its light-change. Gravitational disturbances, too, might be expected to betray the influence of an extra member, and none have been detected; for the slight retardation now going forward is otherwise explicable. We seem prohibited from carrying the subdivision of β Lyræ any further than into a pair of globes, exemplifying distinct varieties of the Orion spectral pattern, one or both vivified by a range of bright lines.
An effort was made by Mr. G. W. Myers in 1897[670] to bring this star’s variations within the explanatory scope of the “satellite-theory.” By suitably combining effects of occultation with effects of tidal deformation, he showed that the observed periodicity could be represented with the satisfactory exactitude conveyed in the upper section of Fig. 30, the lower section of which exhibits his plan of the supposed orbit and its egg-shaped occupants. Evidently, when they are seen broadside on there is full light, while a minimum attends an end-on view of them. And this altogether apart from possible eclipses. If these occur as well, the effects reinforce each other; while those due to the gradual turning of the discs soften off the abruptness of occultation-phases, and thus serve to give the light-curve its smooth character. The mutually eclipsing spheroids must, however, be extremely close together, if they do not actually coalesce. Combining, on the questionable assumption of their congruity, the displacements of F measured by Bélopolsky with those attributed by Lockyer to three dark lines, Mr. Myers found the masses of his two stars to be respectively twenty-one and ten (nearly) in terms of that of the sun, and determined the radius of their joint orbit at 31,000,000 miles. Their mean density proved to be lower than that of air at sea-level, and suggested a “nebulous condition.” Indications were even discerned of a process of separation between the components, scarcely yet, or just recently accomplished. “In either case,” Mr. Myers adds, “we seem to have here the first concrete example of a world in the act of being born.” And it cannot but be noted with profound interest that “an attempt at a formal representation of the condition of things prevailing in the system of β Lyræ leads to the assumption of a single body, such as Poincaré’s or Darwin’s figures of equilibrium.”
Yet the “formal representation” in question is difficult to accept as a physical actuality. The extreme tenuity attributed by it to a star shining with vivid lustre almost defies credence, yet is an inevitable consequence of the satellite-hypothesis of variability. Where there is no halt in change, there can be only a transient cessation of eclipse, and the revolving globes must be virtually in contact. But under these circumstances, their density, as we have seen, is a function of the period alone; and thirteen days is long compared with the nine hours of U Pegasi, for which star the upshot of a similar experimental investigation has been recorded. This theory, moreover, takes account only of the optical changes in β Lyræ. Occultation-effects, distortion-effects, and motion-displacements of spectral lines are of this kind. They imply no intrinsic alteration. They are compatible with an absolute constancy in the state of the system; they depend merely upon the visual relations to ourselves of the bodies forming it. They are accordingly calculable and measurable. Exactly what sort and amount of fluctuations they are capable of producing, can be ascertained from given data. But with the physical influences of close duplicity upon radiation we have only a speculative acquaintance. And in the present case, those that might be due to unequal tidal disturbances are excluded by the circular shape necessarily ascribed to the path of a star noted for the equal duration of all its phases. Intrinsic variations in its spectrum are, nevertheless, glaringly apparent, and they tend to recur cyclically in just thirteen days. We spare our readers the bewilderment of their minute description, asking them instead to fix their attention on a few salient points.
Let us consider, for instance, the spectral symptoms at the critical epoch of chief minimum. Almost as a matter of course, the continuous radiance has faded; sixty per cent of it is intercepted or otherwise suppressed. This is, in fact, the essential cause of the falling-off in brightness. What is distinctive is that the emission-lines have become narrower, sharper, and fainter than usual; they are considerably shifted towards the red, and strongly developed dark companions, in their normal places, are attached to their more refrangible sides. Now the downward shove of the whole range of bright lines is either due to motion, or it is not. If it is, the emitting body is travelling rapidly away from the earth at the time of the supposed eclipse, which must accordingly be dismissed as fictitious. If, on the other hand, the alteration of wave-length denotes physical action of some kind in the atmosphere of the star, then inferences as to its orbital revolution, since they have only a spectroscopic warrant, are highly precarious. The possibility, to be sure, may be admitted that the dark lines shift optically, the bright lines physically and optically; but the distinction has an air of arbitrariness which does not recommend its confident adoption.
Another significant circumstance is that the spectral appearances at the secondary minimum and at the ensuing maximum are much alike. The most characteristic among them is the projection of a black line centrally upon a wide bright band. Dr. Vogel’s drawings of the first ultra-violet hydrogen line (Η ζ) at these successive phases are reproduced in Plate XVI., Figs. 1 and 1a. Here, at any rate, a single light-source is concerned. A moment’s consideration suffices to show that a dark line in the spectrum of one star cannot cut a slice out of a brilliant band proceeding from another. Absorption implies real superposition of the arresting and absorbing layers. The effect observed is then one of reversal. It arises through the stoppage by a cooler stratum of hydrogen of the emissions from a denser and hotter underlying stratum in the same stellar atmosphere. Fig. 2 in the same Plate represents, from a drawing by Professor Keeler, the “D lines” in β Lyræ at principal minimum. It was made with the great Lick refractor, 14th and 15th November 1889, and shows the sodium pair to the right merged into a dark, hazy band, with above it D_{3} brilliant and unsymmetrically reversed. Moreover, the thin dark line constituting the reversal seemed to be nearly, or exactly in its proper place;[671] the obvious relative shift measured the lessened refrangibility of the emissive beam. In the gaseous envelope, then, of one and the same star we find a helium line originating at a low level moved towards the red, while its repetition by absorption higher up preserves its wave-length unchanged. The indicated difference in conditions can here scarcely be anything else than a decrease of pressure upward from the photospheric surface. The significance of such an inference hardly needs to be pointed out, and it seems impossible to avoid drawing it.
The red ray of hydrogen is particularly brilliant in β Lyræ; but since it lies beyond the ordinary spectrographic range it has of late received little attention. Yet the history of the modifications which it assuredly undergoes, and of the modes of their correlation with those of its associates in the spectrum, must be learned, unless knowledge of this wonderful star is to remain essentially incomplete.
We may now endeavour to sum up our conclusions regarding its nature, tentative and fragmentary though they be. A finished theory on the subject cannot at present be formulated; but the ground may be prepared for it by the removal of inadmissible hypotheses and by the clarification of thought.
(1) The system of β Lyræ is binary. Two stars, and no more, are concerned in producing the observed changes in the quantity and quality of its light. Both show strong hydrogen and helium absorption; one is distinguished besides by oxygen absorption, and it is this latter which, in all probability, emits the more conspicuous set of bright lines. There are indications, too, that a second set is occasionally sub-apparent, and that the spectrum really consists of two separate ranges of dark, and two accompanying ranges of vivid rays.
(2) The dark lines are in their normal positions at minima; they are shifted from them at maxima, when some of their number open out into doublets. The conjunctions at times of least light, and elongations at intervening epochs, of two bodies giving absorption spectra are thus presumably signified.
(3) At chief minimum, the more prominent bright lines are shifted towards the red, so as to lie beside the corresponding dark lines. The spectrum has then the coupled aspect distinctive of “Novæ” and of certain other emission-stars. The change of refrangibility during this phase cannot be due to motion; it may be due to pressure.
(4) During the second half of the period, reversals are a leading feature of the spectrum, which thus affords evidence, not only of orbital revolution, but also of a course of physical vicissitudes comprised in the same cycle.
(5) Finally, the cause of variability has to be considered. Is it to be found in mutual occultations? The geometrical conditions are such as to admit of an affirmative reply; the physical conditions are adverse. They involve a rarefaction of the circling bodies so extreme as to repel assent unless under the stress of rigid demonstration. And that is by no means at hand. Evidence on the subject could perhaps more easily be collected from objects with analogous light-curves, than from β Lyræ itself. The endless complications which embarrass research in the “problem star” would not, for instance, be likely to present themselves in d Serpentis. Another variable, highly desirable to be included in such a comparative study, is R Sagittæ. This remarkable object has a period of seventy days, symmetrically divided by two unequal minima, and two slightly disparate maxima. The light-curve, however, underwent a curious change in 1874. A reversal of the minima was perceived.[672] Equalisation first took place. Then the secondary minimum gradually gained emphasis at the expense of the primary; and the exchange of relative values was not redressed until 1883, when the pristine state was restored. An arrested tendency towards such a transformation is sometimes shown by β Lyræ in the fluctuating accentuation of its subordinate phase, but it has never reached so far as a bisection of the period. A suggestion is, nevertheless, irresistibly conveyed that the two stars form similarly constructed systems. When the spectra of R Sagittæ, d Serpentis, and U Pegasi have been examined, and their changes tabulated and collated, we shall be in a better position to interpret those manifest in the Lyre variable.