Chapter XXII: Stars Variable in Long Periods

FIG. 31.—Distribution of the Periods of 208 Variable Stars. ]

“Long periods” of variability range from 120 to 610 days. None more protracted have been definitely ascertained, and those that are shorter belong, with rare exceptions, to stars differently characterised. The distribution of the periods we are at present concerned with is exhibited graphically in Fig. 31. They number 208, and are taken from Chandler’s _Third Catalogue_, only three, which exceed 500 days, being for convenience omitted. Periods of several years have besides been ascribed to a few stars, but on insufficient grounds. No true conformity to them is maintained. Phases that are unusually slow are also extremely uncertain in development. So far, the 610-day cycle of S Cassiopeiæ is the longest that can be depended upon to recur. A cursory reference to our diagram will show how largely, among long periods, those between 280 and 300 days preponderate. Accidents of discovery connected with the length of the year cannot well have produced this preference, which seems to be genuine, and not merely apparent. On the other hand, the indentations of the curve are assuredly casual, and will be smoothed down with the multiplication of objects.

The typical long-period variable is Mira Ceti. It was the first detected; it rises to the brightest maxima; it presents the most vivid and distinctive spectrum. More than 300 of its cycles have been watched, more or less attentively; yet familiarity has not diminished wonder at the “Wonderful” star.[673] Its modes of procedure are as much an enigma to the spectroscopists of Lick and Potsdam as they were to Fabricius and Holwarda. An instructive comment upon them is the omission, from Chandler’s _Third Catalogue_, of the modifying terms appended to the mean period of 332 days in his _Second_. It amounts to an abandonment of the attempt to predict, with even approximate accuracy, the capricious changes of the Frisian pastor’s _Stella insolita_. Argelander’s laborious efforts for their regulation have thus proved futile. He considered an oscillation extending over 80 years, and comprising 88 periods, to be fairly well established, and found indications of another of 160 years;[674] but their supposed effects have ceased to be apparent. Guthnick’s “long inequality,” covering 200 cycles, will doubtless prove equally illusory. No method is indeed securely traceable in the accelerations or retardations of the maxima, and they digress to the extent of fully two months. Long and short periods can neither be perceived to alternate nor to occur in series; still opposite deviations balance each other; there is no progressive alteration in the length of the cycle.

The highest maximum and the lowest minimum recorded for Mira were both observed by Sir William Herschel. He found the variable nearly equal to Aldebaran on 6th November 1779,[675] while four years later it was invisible with a telescope showing stars of the tenth magnitude. Of late it has not been known to descend below 9·5, and it sometimes stops short at 8·0 magnitude. Its greatest brightness is even more inconstant. No more than 5·6 magnitude was attained in November 1868,[676] or one-fortieth the lustre of the phase viewed by the Bath organist, and maxima higher than the third magnitude are uncommon. The course of change likewise fluctuates, but in general the rise is considerably more rapid than the decline, and the high-level status is maintained for about two months, the low-level for at least three, without striking alterations. Yet change is always in progress. The light-curve has no flat stretches.[677] No connection is apparent between the acuteness of the light crises in this star and the times of their occurrence.[678] They do not tend to become abortive when hurried, nor is delay accompanied by intensification. Argelander entirely failed to correlate irregularities of period with discrepancies in the amplitude of change. As the fruit of tercentennial experience it has, however, been learned that long-period variables are no transitory phenomena. Mira, at any rate, exhibits no symptoms of decadence since the maximum which surprised Fabricius in August 1596.

Its spectrum gives evidence of powerful disturbance, but none of duplicity. Motion-shifts depending upon orbital revolution are imperceptible. The periodicity of the star must be explained otherwise than by attributing to it a binary character. The task of doing so is indeed most arduous. Once in eleven months the brightness augments some hundreds of times, and concomitant spectral modifications afford assurance that these annual outbursts are accompanied by atmospheric ignition. What occasions them? We are ignorant; yet the issue may be narrowed by the following consideration. If external action of any kind were concerned in their production we should expect the incandescence to be coronal or chromospheric—to affect primarily the outer layers of the gaseous envelope. But in fact the innermost strata are those set aglow, while the overlying vapours remain comparatively cool. The masking of a bright hydrogen line by calcium absorption places the subsistence of this relation beyond question. So far, then, the evidence favours the view that variability of the Mira type arises spontaneously, rather than through outside influence.

On the 13th of December 1885 Mr. J. E. Gore was struck with an unfamiliar reddish star of the sixth magnitude in the Club of Orion. No map included it, and until it reappeared a year later after an interval of quasi-extinction, there was no telling whether it should be reckoned as a Nova or a variable. Dr. Copeland recorded for it “a very beautiful banded spectrum of the third type, seven dark bands being readily distinguished with the prism.” The intervening spaces appeared “full of bright lines, especially in the green and blue.” Two of these were certainly emitted by hydrogen, and others probably by helium, since a vivid D_{3} was observed by Von Konkoly ten days later, the adjacent sodium pair being, as usual, dark. Fig. 32 exhibits the light-curve of U Orionis during the maximum half of its period, as delineated by M. Porro at Turin 1889–90. Its form is by no means invariable. In general, the brightest phase is reached much more abruptly than it was in 1890. The main rise, however, is always prompt, and the decline gradual, although the minima appear to be well defined. They have not, indeed, owing to their faintness, been much observed. The widest amplitude of the star’s change is from 5·3 to about 12·5 magnitude; but these limits are seldom attained. Nor is the assigned period of 375 days conformed to with any exactitude. As in the case of Mira, prediction has to be qualified with a large allowance for unexplained disturbance.

FIG. 32.—Light-Curve of U Orionis (Porro).
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At high maxima χ Cygni radiates about 6500 times more powerfully than at low minima. The star, that is to say, has a range of fully nine and a half magnitudes, from the fourth to near the fourteenth. But in some of its cycles it fails to ascend beyond 6·5 magnitude; for it resembles the other stars of this class in having no fixed measure of change.[679] Its period is now 406 days; it has lengthened, on an average, by a quarter of an hour at each recurrence since Kirch, in July 1686, missed from its wonted place the star located by Bayer _in collo Cygni_;[680] nor is there yet any sure sign of a compensatory reversal. The nature of the secular perturbation thus betrayed can scarcely be imagined. Argelander noticed besides deviations from the mean period up to forty days, and sought, with imperfect success, to analyse and regularise the inequalities upon which they depended.[681] The increase of light in this variable occupies 171 days, or considerably less than half the period. Its most brilliant phases are brief, while fainter maxima are sometimes prolonged for a couple of months. In 1847 the star remained visible to the naked eye during 97 days, although the usual time of “lucidity” is, by Argelander’s estimate, only 52 days.[682] The scarlet blaze of its light is often very striking.

R Hydræ is an accelerating variable. In 1708 the interval from one maximum to the next was 500 days; it had shortened to 437 in 1870, and to 425 in 1891. The highest maxima are of 3·5 magnitude, the lowest more than six times less bright. The minima, on the other hand, occur with fair uniformity at 9·7 magnitude. Strongly red in all its phases, R Hydræ displays a gorgeous colonnaded spectrum lit up with bright hydrogen lines.

The variability of L_{2} Puppis was discovered by Gould at Cordoba in 1872. The range in magnitude—3·5 to 6·3—is moderate, the period—137 days—comparatively short. Wide departures from it, however, are not infrequent, and it is almost equally divided between the ebb and the flow of luminosity.[683] The colour of this star suggests a conflagration, and its spectrum resembles and is no less effective than that of Mira.[684] An exceptionally large proper motion, for a member of its class, has been determined for it by Professor Porter of Cincinnati.

An analogous object is met with in W Puppis. Here the rise occupies 62 days, the decline only 58, the visual limits of variation being the eighth and eleventh,[685] the photographic, the ninth and twelfth magnitudes. The discrepancy is naturally accounted for by the non-actinic quality of light conspicuously red to the eye. The detection of bright hydrogen lines in a third-type spectrum gave Mrs. Fleming in 1895[686] the clue to the character of this star. The fluctuations inferred to take place from that unfailing symptom were looked for and quickly found. The light-curve of W Puppis is very regular, and takes a much sharper bend at minimum than at maximum.

In S Ursæ Majoris we meet a much older acquaintance. Its periodicity, discovered by Pogson in 1853, was established by a record of its magnitude made by Lalande in 1790. It is of a highly perturbed nature. The maximum brightness varies between 6·7 and 8·2 magnitude; the minima are uncertain to the extent of perhaps three magnitudes, some unusually faint at 13·3 magnitude having been watched by Baxendell. The actual length of the cycle is about 226 days; it is modified by a recurring inequality with a range of nearly eight days, but much more extensively by irregular deviations. These seem to be connected with two curious inflections of the light-curve. About six weeks before maximum the rise is arrested, sometimes for a few days, sometimes for as many weeks. A corresponding stay in the decrease of light usually precedes each minimum.[687] Upon the duration of these halts evidently depends the retarded or hurried accomplishment of the phases. Noteworthy besides is the occasional equalisation of the times occupied in waxing and waning. This is apparently a consequence of the partial abolition in certain cycles of the pause before minimum. That of 1875 was distinguished by a steady maximum lasting from 23rd February to 13th April, and followed by a decrease quicker than the preceding increase.[688] Similarly, the late Sir Cuthbert Peek’s diagram for 1894 (copied in Fig. 33) shows a flat maximum antecedent to a precipitate decline. Again, four years later, the light during two months scarcely varied from the eighth magnitude;[689] and it may be remarked that, as in the sun, long maxima are low maxima. The mean light-curve of S Ursæ, from observations made at Harvard College, 1889–99, is depicted in Fig. 34. Only the general course of change can be followed by its means; the effects of temporary obstructions or disturbances are necessarily eliminated.

Deep red, and often hazy when faint, this star has been seen nearly white at maximum—a not uncommon kind of colour-fluctuation. It gives a poorly-developed spectrum of the third type.

T Ursæ Majoris has a total range of nearly six magnitudes, and a period of 302 days; but its variations make no approach to uniformity. The maximum brightness is largely uncertain; the minima are sometimes, though rarely, as low as 13·5 magnitude. The luminous tide flows, at certain epochs, with extreme rapidity. Between 5th January and 22nd February 1901, for instance, the star increased from 12·4 to 7·7 magnitude. In forty-six days it acquired a seventy-six-fold brilliancy, and the augmentation was accompanied by a blanching of its rays. Of their dull ruddy hue scarcely a tinge survived at full light. Fig. 35 reproduces the mean curve drawn at Harvard, which is, of course, much more symmetrical than any of the individual curves serving as its basis. The maxima and the minima appear from it to be about equally sharp.

FIG. 33.—Light-Curve of S Ursæ Majoris in 1894 (Peek).
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The curve of T Cassiopeiæ, on the other hand, cannot be smoothed into shapeliness. It is represented in Fig. 36. The secondary maximum occasioning the hump on the upward branch is never absent, and protracts the cycle to 445 days, considerably more than half of which (240 days) are occupied by the abnormally impeded phase of increase. The period is affected by a compensatory inequality.

FIG. 34.—Mean Light-Curve of S Ursæ Majoris (Pickering).
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FIG. 35.—Mean Light-Curve of T Ursæ Majoris (Pickering).
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FIG. 36.—Mean Light-Curve of T Cassiopeiæ (Pickering).
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The variability of R Leonis was detected by Koch in 1782; yet six score years of scrutiny have only sufficed to render more manifest the almost hopeless intricacy of the laws to which it is subject. Since 1890 the maxima have been persistently accelerated, computations, founded on a nominal period of 312 days, being left in the lurch in November 1896 by forty-three days. That there is a large periodic inequality admits of no doubt; “but the observations of the last few years,” Dr. Chandler remarked in 1896, “show that it is complicated with other unknown terms,” the neglect of which, pending the development of their nature, seemed to him safer than the attempt to use them for purposes of prediction in ignorance of their value. That is to say, the phases can be registered as they occur, but defy accurate anticipation. The glowing colour and brilliant spectrum of the star make it an object of singular beauty and interest. Its total range is from 5·2 to 10 magnitude, but the oscillations are often of less amplitude.

The variability of V Delphini was discovered by Mrs. Fleming in 1891 by the shining of bright hydrogen lines amid the flutings of its spectrum.[690] It is of enormous extent. Between maximum and minimum-light there is a difference of close upon ten magnitudes. Observed as of 7·5 magnitude on 1st October 1899 with the forty-inch Yerkes refractor, the star had on the ensuing 20th July sunk to invisibility, and must therefore have been below the seventeenth magnitude.[691] The period is 540 days.

A strange anomaly in the light-change of R Lyncis was placed on record at Sir Cuthbert Peek’s observatory in 1898.[692] From a smouldering minimum the star had risen by 2nd March to 10·6 magnitude; when, suddenly reversing its course, it dropped in eighteen days to the thirteenth magnitude, but finally resumed the interrupted process of brightening, and mounted at the customary rate to a maximum of 7·5 magnitude on 11th August. Such apparent caprices constitute indeed a baffling enigma, but should, for that reason, be the more steadily kept in view in dealing with the general question of stellar variability. The high and low phases of R Lyncis are alike definitely marked. The period assigned to them is 380 days.

The variation of R Cygni exceeds eight magnitudes. In rising from one extreme to the opposite it gains a 2500-fold increase of light. The maxima, however, as usual in this class of variables, are very unequal, some being seven times more brilliant than others. Mr. Espin believed in 1888 that a regular alternation of high and low phases might be counted upon;[693] but their subsequent disordered succession belied the inference. The star is among those in which dimness is occasionally attended by a curious diffuseness of aspect. Thus in February and March 1894, having previously sunk out of sight with a 6⅓-inch refractor, it came again into view, at the Rousdon Observatory, in the shape of a small bluish nebula, resembling a faint comet.[694] This object, which had contracted on 24th March into a needle-point of light of the twelfth magnitude, resumed its nebular appearance in February 1895 and March 1896. The mean period of R Cygni is 426 days; but the interval between the maxima of November 1890 and February 1892 amounted to 457.[695] No more than 150 days are, as a rule, spent in the rise.

FIG. 37.—Light-Curve of T Andromedæ (Pickering).
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The unique form of light-curve represented in Fig. 37 is assigned by Professor Pickering to T Andromedæ. Derived from photographic data, it awaits visual confirmation, yet can scarcely be widely erroneous.[696] The uniform progression it depicts need not, indeed, be accepted as a rigid reality; it must be encroached upon by sundry kinds of disturbance, and the maxima, however brief, cannot be instantaneous; at every full tide there is an interval of “slack water.” Nevertheless, if even the mean curve prove to be linear, the circumstance will be of great interest, and the star, meanwhile, merits close attention. Owing to its redness the photographic curve is transposed downward on the scale to the extent of one and a half magnitudes,[697] so that the variable shows four times brighter to the eye than to the sensitive plate. Hence changes of colour, should they at any time supervene, would necessarily produce large distortions in the automatically registered course of light-fluctuation. The systematic comparison of visual and photographic determinations of magnitude might, indeed, be used as an effectual means of testing the permanence in hue of long-period variables. While it remained constant, the curves of light-change, obtained retinally and chemically, should flow parallel to one another; they would merge together if the star blanched, and diverge still farther if it reddened. The variability of T Andromedæ was discovered by Dr. Anderson of Edinburgh in 1893. The period seems to have suddenly shortened from 281 to 265 days in 1895.

Variables of the fourth spectral type are mostly crimson-tinted, and have protracted periods. Indeed, these two characteristics show some kind of mutual dependence,[698] Chandler’s rule, “the redder the star the longer the period,” being, on the whole, conformed to. Apposite examples are furnished by S Cephei, U and V Cygni. The period of S Cephei averages 484 days, but is subject to an alternate lengthening and shortening.[699] More than half of it, or about 257 days, is occupied in the ascent from minimum to maximum, and this exceptional arrangement is consistently maintained. The light-curve is highly irregular. Smoothed out by striking a decennial balance, it took the form shown in Fig. 38 from the Harvard College representation. But its dissymmetry is greatly modified from that of the tracing given by the observations of any single period. Usually there is a rather swift increase and decrease, followed by intervals of approximate constancy, at maximum, of about a hundred, at minimum, of fifty days.[700] Not unfrequently, however, the curve has a sharp apex, and its downward flow is interrupted by a secondary rise. Such “stand-stills” (as Mr. Maxwell Reed calls them) are a familiar feature of long-period variability. Seventh-magnitude brightness is never fully attained by S Cephei, and it occasionally drops below the thirteenth magnitude. Like many very red stars, it has accesses of bad definition. They occur, very remarkably, not at low light, but near maxima, when “a ruddy haze” seems to envelop a definite disc.[701]

FIG. 38.—Mean Light-Curve of S Cephei (Pickering).
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In 463 days, almost equally divided between the gain and the loss of brightness, U Cygni varies from 7·0 to 11·6 magnitude; yet with no approach to regularity. The maxima are sometimes fainter than the eighth magnitude; the minima fluctuate, it is thought cyclically,[702] from 9·4 to 11·6 magnitude. The periodicity, too, is complicated by an outstanding disturbance.

The period of V Cygni is 418 days, and the rise, which occupies 220 days, is disproportionately slow. Lindemann registered a steady decline in the maximum-brightness of the star, from 6·8 magnitude in 1882 to 8·4 in 1891;[703] in some cycles it does not exceed 9·5 magnitude; while the minima occur, with tolerable uniformity, at the low level of 13·5 magnitude. The maxima are succeeded, at intervals of two months, by subordinate phases of recovery. The colour of V Cygni is especially intense. The carmine of its beams corresponds to a powerful stoppage of the complementary blue and violet radiations, by which a splendid preponderance is secured to the red end of the spectrum. No bright lines have been certainly recognised in the dispersed light of either U or Y Cygni; they are, as we have seen, prominent in U Hydræ, a fourth-type variable of no settled periodicity.

A fundamental distinction is apparent between the two chief kinds of stellar variability. Stars with “short” periods are—in a few cases demonstrably, in the rest presumably—close pairs, their mode of circulation prescribing, in some unknown way, their laws of light-change. The strict accuracy of its fulfilment hence results as if by mechanical constraint. Mira-variables, on the contrary, give no signs of duplicity; and the marked irregularity of their phases affirms their origin through a complex interaction of physical disturbances. That these are internal and constitutional, there is the best reason to believe. Spectroscopic symptoms are fairly decisive on the point. They have as yet, however, been very partially observed. A bare gleaning of facts has been gathered, and we want a full harvest as a foundation for safe inferences. A spectroscopic study throughout their cycles of variable carbon-stars would, for instance, be most valuable. The behaviour of the bright lines shown by them might even prove crucial, first, as regards the position in their atmospheres of the emitting strata, next, as to the seat of the recurring commotions. The spectra of U and V Cygni and of R Leporis may be cited as among those claiming systematic and prolonged observation.

The reality of the diffuse aspect intermittently presented by certain variables could readily be tested by examining them at such times with a reflector. Refractors, owing to their imperfect colour-correction, often produce abnormal images of objects peculiarly tinted. Nevertheless, if this were the true and only explanation of the effects in question, we should expect to find them develop under uniform conditions, and they appear instead incalculably, and as if by caprice. An instructive example is furnished by V Cygni. On 19th July 1882, six weeks after a maximum, Lindemann[704] saw the variable at Pulkowa as an indistinct coppery disc. But at the same interval, _before_ the high maximum of 31st August 1882, it showed not a trace of nebulosity, although intensely red. On 8th October 1883 it appeared almost blood-coloured and very diffuse, while nine days later its image was point-like, stellar, and precise. Analogous observations have been made by Mr. Grover, Sir Cuthbert Peek’s assistant, on R, S, and T Cassiopeiæ, R and S Ursæ Majoris, and several other objects of their class; and by Mr. Knott on U Geminorum, which, as a white star giving a continuous spectrum, ought to come regularly to focus. For not a few stars, such as R Coronæ and S Herculis, dim, bluish nebulosities are substituted at low minima; and not uncommonly, even on nights of excellent definition, variables in moderately high phases appear sharp, though very red, and as if projected on a background of glowing haze. Then again, they present a clearly outlined disc, or a “large, woolly, ill-defined image resembling a small but bright planetary nebula.”[705] Most of these diversities defy anticipation; they can be associated with no particular stages of variation, and some of the reddest stars, R Leonis and R Leporis among the number, appear to be exempt from them. Yet their literal interpretation as indicative of physical alterations in the bodies affected by them would lead to consequences of outrageous improbability. Provisionally, at any rate, the wiser course is to refer them to a combination of atmospheric and instrumental causes. With these, no doubt, a genuine change of luminous quality concurs, whereby semi-extinct stars, being thrown out of focus, assume a nebular disguise. It is noteworthy that the records of a series of observations on the minima of twenty-two long-period variables, executed with the Yerkes forty-inch refractor in 1900,[706] include no mention of unusual phenomena. Attention, however, seems to have been directed entirely to the determination of magnitudes, nor had any of the stars on the list (U Geminorum excepted) been previously remarked for optical peculiarities.

A clue to the labyrinth of stellar variations is likely to be afforded by the continued investigation of solar periodicity. Comparisons of the spot-curve with the light-curves of Mira, χ Cygni, T Ursæ, or almost any of their congeners, bring a conviction that the phenomena differ in degree rather than in kind. The plottings of solar and stellar disturbances show the same character of dissymmetry, and the same order of irregularity. In both classes of representation, high summits are usually sharp, low summits blunt. In both, the course of change is now halting, now hurried. Hesitations, subordinate ascents, and subordinate subsidences before completing the phase, are common features. There is, indeed, no mode of departure from uniformity traceable in the solar cycle that cannot be strictly paralleled in the caprices of stellar emission. The analogy has been rounded out by the discovery that the sun, at spot-maxima, is essentially a bright-line star. Its spectrum then shares, in a just perceptible degree, the blazing quality that distinguishes the spectra of Mira-variables. This is a further and an irrefragable proof of the correspondence of the epochs. Light-maxima in the stars match spot-maxima in the sun. In each case a development of internal energy gives rise to enhanced incandescence, accompanied, in the single specimen of a sub-variable star within reach of detailed observation, by rendings of the photospheric envelope, and outbursts of chromospheric flames. Looking a little closer, we can discern the probability that the cyclical variations of all these bodies depend essentially upon a rise and fall of activity in the vertical circulation by which radiation is maintained. The rate of conveyance of heated matter from within outward must be a determining factor of photospheric brilliancy, transcendent lustre implying unusual celerity of transport. This is the vital process of suns, the checking of which must immediately become sensible in their diminished output of light. Here, if anywhere, will be found the secret of stellar variability.