Chapter XXI: The Problem of Beta Lyræ

FIG. 29.—Light-Curve of β Lyræ (Argelander). ]

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.

FIG. 30.—System of β Lyræ (Myers).
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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.

PLATE XVI.

THE ALTERNATING SPECTRUM OF NOVA PERSEI STONYHURST COLLEGE
OBSERVATORY.

1. Hζ Line in Spectrum of β Lyræ at Secondary Minimum.
1a. Hζ Line in Spectrum of β Lyræ at Second Maximum.
2. D-Lines in β Lyræ (Keeler).
3. D-Lines in Nova Persei (Hale).
4. Spectra of Nova Sagittarii.
5. Alternating Spectrum of Nova Persei (Sidgreaves).
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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.