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.”
[Illustration:
FIG. 22.—Light-Curve of η Aquilæ (Schur).
]
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.
[Illustration:
FIG. 23.—Orbit of η Aquilæ (Wright).
]
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.
[Illustration:
FIG. 24.—Light-Curve of S Sagittæ (Yendell).
]
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.