Chapter 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.

FIG. 25.—Curves representing the Variations (A) in Light, (B) in
Radial Velocity of ζ Geminorum (Campbell).
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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.

FIG. 26.—Orbit of ζ Geminorum (Campbell).
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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.

FIG. 27.—Photometric Curve of U Pegasi (Pickering).
]

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.

FIG. 28.—Light-Curves of Cluster-Variables (Bailey).
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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.