STARS VARIABLE IN LONG PERIODS.
[Illustration:
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.
[Illustration:
FIG. 32.—Light-Curve of U Orionis (Porro).
]
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.
[Illustration:
FIG. 33.—Light-Curve of S Ursæ Majoris in 1894 (Peek).
]
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.
[Illustration:
FIG. 34.—Mean Light-Curve of S Ursæ Majoris (Pickering).
]
[Illustration:
FIG. 35.—Mean Light-Curve of T Ursæ Majoris (Pickering).
]
[Illustration:
FIG. 36.—Mean Light-Curve of T Cassiopeiæ (Pickering).
]
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.
[Illustration:
FIG. 37.—Light-Curve of T Andromedæ (Pickering).
]
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]
[Illustration:
FIG. 38.—Mean Light-Curve of S Cephei (Pickering).
]
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.