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.
[Illustration:
FIG. 25.—Curves representing the Variations (A) in Light, (B) in
Radial Velocity of ζ Geminorum (Campbell).
]
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.
[Illustration:
FIG. 26.—Orbit of ζ Geminorum (Campbell).
]
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.
[Illustration:
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.
[Illustration:
FIG. 28.—Light-Curves of Cluster-Variables (Bailey).
]
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.