It is a curious fact that the ancient astronomers, notwithstanding
the care with which they observed the heavens, never noticed that
any of the stars changed in brightness. The earliest record of such
an observation dates from 1596, when the periodical disappearance of
Omicron Ceti was noticed. After this, nearly two centuries elapsed
before another case of variability in a star was recorded. During the
first half of the nineteenth century Argelander so systematized the
study of variable stars as to make it a new branch of astronomy. In
recent years it has become of capital interest and importance through
the application of the spectroscope.
Students who are interested in the subject will find the most complete
information attainable in the catalogues of variable stars, published
from time to time by Chandler in the ‘Astronomical Journal.’ His third
catalogue, which appeared in 1896, comprises more than 300 stars whose
variability has been well established, while there is always a long
list of ‘suspected variables’--whose cases are still to be tried. The
number to be included in the established list is continually increasing
at such a rate that it is impossible to state it with any approximation
to exactness. The possibility of such a statement has been yet
further curtailed by the recent discovery at the Harvard Observatory
that certain clusters of stars contain an extraordinary proportion
of variables. Altogether at the time of the latest publication, 509
such stars were found in twenty-three clusters. The total number of
these objects in clusters, therefore, exceeds the number known in the
rest of the sky. They will be described more fully in a subsequent
chapter. For the present we are obliged to leave this rich field out
of consideration and confine our study to the isolated variable stars
which are found in every region of the heavens.
Variable stars are of several classes, which, however, run into each
other by gradations so slight that a sharp separation cannot always be
made between them. Yet there are distinguishing features, each of which
marks so considerable a number of these stars as to show some radical
difference in the causes on which the variations depend.
We have first to distinguish the two great classes of irregular and
periodic stars. The irregular ones increase and diminish in so fitful a
way that no law of their change can be laid down. To this class belong
the so-called ‘new stars’, which, at various periods in history, have
blazed out in the heavens, and then in a few weeks or months have
again faded away. It is a remarkable fact that no star of the latter
class has ever been known to blaze out more than once. This fact
distinguishes new stars from other irregularly variable ones.
Periodic stars are those which go through a regular cycle of changes in
a definite interval of time, so that, after a certain number of days,
sometimes of hours, the star returns to the same brightness. But even
in the case of periodic stars, it is found that the period is more
or less variable, and, in special cases, the amount of the variation
is such that it cannot always be said whether we should call a star
periodic or irregular.
The periodic stars show wide differences, both in the length of the
period and in the character of the changes they undergo. In most cases
they rapidly increase in brightness during a few days or weeks, and
then slowly fade away, to go through the same changes again at the end
of the period. In other cases they blaze up or fade out, from time
to time, like the revolving light of a lighthouse. Some stars are
distinguished more especially by their maximum, or period of greatest
brightness, while others are more sharply marked by minima, or periods
of least brightness. In some cases there are two unequal minima in the
course of a period.
Chandler’s third catalogue of variable stars gives the periods of
280 of these objects, which seem to have been fairly well made out.
A classification of these periods, as to their length, will be
interesting. There are, of periods:
Less than 50 days 63 Stars.
Between 50 and 100 days 6 ”
” 100 ” 150 ” 9 ”
” 150 ” 200 ” 18 ”
” 200 ” 250 ” 29 ”
” 250 ” 300 ” 40 ”
” 300 ” 350 ” 44 ”
” 350 ” 400 ” 44 ”
” 400 ” 450 ” 18 ”
” 450 ” 500 ” 6 ”
” 500 ” 550 ” 1 ”
” 550 ” 600 ” 1 ”
” 600 ” 650 ” 1 ”
It will be seen from this that, leaving out the cases of very short
period, the greater number of the periods fall between 300 and 400
days. From this value the number falls off in both directions. Only
three periods exceed 500 days, and of these the longest is 610 days. We
infer from this that there is something in the constitution of these
stars, or in the causes on which their variation depends, which limits
the period. This limitation establishes a well-marked distinction
between the periodic stars and the irregular variables to be hereafter
described.
Returning to the upper end of the scale, the contrast between the great
number of stars less than fifty days, and the small number between
fifty and one hundred, seems to show that we have here a sharp line
of distinction between stars of long and those of short period. But,
when we examine the matter in detail, the statistics of the periods
do not enable us to draw any such line. About eight periods are less
than one day, and the number of this class known to us is continually
increasing. About forty are between one and ten days, and from this
point upwards they are scattered with a fair approach to equality
up to a period of one hundred days. There is, however, a possible
distinction, which we shall develop presently.
[Illustration: FIG. 1. THE LAW OF CHANGE IN A VARIABLE STAR.]
The law of change in a variable star is represented to the eye by a
curve in the following way. We draw a straight horizontal line _A X_ to
represent the time. A series of equidistant points, _a_, _b_, _c_, _d_,
etc., on this will represent moments of time. One of the spaces, _a_,
_b_, _c_, etc., may represent an hour, a day, or a month, according
to the rapidity of change. We take _a_ to represent the initial
moment, and erect an ordinate _aa’_, of such length as to represent
the brightness of the star on some convenient scale at this moment. At
the second moment, _b_, which may be an hour or a day later, we erect
another ordinate _bb’_, representing the brightness at this moment. We
continue this process as long as may be required. Then we draw a curve,
represented by the dotted line, through the ends of all the ordinates.
In the case of a periodic star it is only necessary to draw the curve
through a single period, since its continuation will be a repetition of
its form for any one period.
We readily see that if a star does not vary, all the ordinates will
be of equal length, and the curve will be a horizontal straight line.
Moreover, the curve will take this form through any portion of time
during which the light of the star is constant.
There are three of the periodic stars plainly visible to the naked eye
at maximum, of which the variations are so wide that they may easily
be noticed by any one who looks for them at the right times, and knows
how to find the stars. These stars are:
Omicron Ceti, called also _Mira Ceti_.
Beta Persei, or Algol.
Beta Lyræ.
It happens that each of these stars exemplifies a certain type or law
of variations.
_Omicron Ceti._ On August 13, 1596, David Fabricius noticed a star in
the constellation Cetus, which was not found in any catalogue. Bayer,
in his ‘Uranometria’, of which the first edition was published in 1601,
marked the star Omicron, but said nothing about the fact that it was
visible only at certain times. Fabricius observed the star from time to
time, until 1609, but he does not appear to have fully and accurately
recognized its periodicity. But so extraordinary an object could
not fail to command the attention of astronomers, and the fact was
soon established that the star appeared at intervals of about eleven
months, gradually fading out of sight after a few weeks of visibility.
Observations of more or less accuracy having been made for more than
two centuries, the following facts respecting it have been brought to
light:
Its variations are somewhat irregular. Sometimes, when at its
brightest, it rises nearly or quite to the second magnitude. This
was the case in October, 1898, when it was about as bright as Alpha
Ceti. At other times its maximum brightness scarcely exceeds the fifth
magnitude. No law has yet been discovered by which it can be predicted
whether it shall attain one degree of brightness or another at maximum.
Its minima are also variable. Sometimes it sinks only to the eighth
magnitude; at other times to the ninth or lower. In either case it is
invisible to the naked eye.
As with other stars of this kind, it brightens up more rapidly
than it fades away. It takes a few weeks from the time it becomes
visible to reach its greatest brightness, whatever that may be. It
generally retains this brightness for two or three weeks, then fades
away, gradually at first, afterward more rapidly. The whole time of
visibility will, therefore, be two or three months. Of course, it can
be seen with a telescope at any time.
The period also is variable in a somewhat irregular way. If we
calculate when the star ought to be at its greatest brightness on the
supposition that the intervals between the maxima ought to be equal,
we shall find that sometimes the maximum will be thirty or forty days
early, and at other times thirty or forty days late. These early or
late maxima follow each other year after year, with a certain amount of
regularity as regards the progression, though no definable law can be
laid down to govern them. Thus, during the period from 1782 to 1800 it
was from thirteen to twenty-four days late. In 1812 it was thirty-nine
days late. From 1845 to 1856 it was on the average about a month too
early. Several recent maxima, notably those from 1895 to 1898, again
occurred late. Formulæ have been constructed to show these changes, but
there is no certainty that they express the actual law of the case.
Indeed, the probability seems to be that there is no invariable law
that we can discover to govern it.
Argelander fixed the length of the period at 331.9 days. More recently,
Chandler fixed it at 331.6 days. It would seem, therefore, to have
been somewhat shorter in recent times. It was at its maximum toward
the end of October, 1898. We may, therefore, expect that future maxima
will occur in July, 1901; June, 1902; May, 1903; April, 1904, and so
on, about a month earlier each year. During the few years following
1903 the maxima will probably not be visible, owing to the star being
near conjunction with the sun at the times of their occurrence. The
most plausible view seems to be that changes of a periodic character,
involving the eruption of heated matter from the interior, of the body
to its surface, followed by the cooling of this matter by radiation,
are going on in the star.
The star _Algol_, or _Beta Persei_, as it is commonly called in
astronomical language, may, in northern latitudes, be seen on almost
any night of the year. In the early summer we should probably see it
only after midnight, in the northeast. In late winter it would be seen
in the northwest. From August until January one can find it at some
time in the evening by becoming acquainted with the constellations.
It is nearly of the second magnitude. One might look at it a score
of times without seeing that it varied in brilliancy. But at certain
stated intervals, somewhat less than three days, it fades away to
nearly the fourth magnitude for a few hours, and then slowly recovers
its light. This fact was first discovered by Goodrick in 1783, since
which time the variations have been carefully followed. The law of
variation thus defined is expressed by a curve of the following form:
[Illustration: FIG. 2. LAW OF VARIATION OF A STAR OF THE ALGOL TYPE.]
The idea that what we see in the star is a partial eclipse caused by
a dark body revolving round it, was naturally suggested even to the
earliest observers. But it was impossible to test this theory until
recent times. Careful observation showed changes in the period between
the eclipses, which, although not conclusive against the theory, might
have seemed to make it somewhat unlikely. The application of the
spectroscope to the determination of radial motions, enabled Vogel, of
Potsdam, in 1889, to set the question at rest. His method of reasoning
and proceeding was this:
If the fading out which we see is really due to an eclipse by a dark
body, that body must be nearly or quite as large as the star itself,
else it could not cut off so much of its light. In this case, it is
probably nearly as massive as the star itself, and therefore would
affect the motion of the star. Both bodies would, in fact, revolve
around their common center of gravity. Therefore, when after the dark
body has passed in front of the star, it has made one-fourth of a
revolution, which would require about seventeen hours, the star would
be moving towards us. Again, seventeen hours before the eclipse, it
ought to be moving away from us.
The measurement of six photographs of the spectrum, of which four
were taken before the eclipses and two afterward, gives the following
results:
Before eclipses: Velocity _from_ the sun equals 39 km. per second.
After eclipses: Velocity _toward_ the sun equals 47 km. per second.
These results show that the hypothesis in question is a true one, and
afforded the first conclusive evidence of a dark body revolving around
a distant star. A study of the law of diminution and recovery of the
light during the eclipse, combined with the preceding motions, enabled
Vogel to make an approximate estimate of the size of the orbit and of
the two bodies. The star itself is somewhat more than a million of
miles in diameter; the dark companion a little less. The latter is
about the size of our sun. Their distance apart is somewhat more than
three millions of miles; the respective masses are about one-half and
one-fourth that of the sun. These results, though numerically rather
uncertain, are probably near enough to the truth to show us what an
interesting system we here have to deal with. We can say with entire
certainty that the size and mass of the dark body exceed those of any
planet of our system, even Jupiter, several hundred fold.
The period of the star is also subject to variations of a somewhat
singular character. These have been attributed by Chandler to a motion
of the whole system around a third body, itself invisible. This theory
is, however, still to be proved. Quite likely the planet which causes
the eclipse is not the only one which revolves around this star. The
latter may be the center of a system like our solar system, and the
other planets may, by their action, cause changes in the motion of
the body that produces the eclipses. The most singular feature of the
change is that it seems to have taken place quite rapidly, about 1840.
The motion was nearly uniform up to near this date; then it changed,
and again remained nearly uniform until 1890. Since then no available
observations have been published.
It is found that several other stars vary in the same way as Algol;
that is to say, they are invariable in brightness during the greater
part of the time, but fade away for a few days at regular intervals.
This is a kind of variation which it is most difficult to discover,
because it will be overlooked unless the observer happens to notice the
star during the time when an eclipse is in progress, and is thoroughly
aware of its previous brightness. One might observe a star of this
kind very accurately a score of times, without hitting upon a moment
when the partial eclipse was in progress. On the principle that like
effects are due to like causes, we are justified in concluding that in
the cases of all stars of this type, the eclipses are caused by the
revolution of a dark body, now called ‘Algol variables,’ round the
principal star.
A feature of all the Algol variables is the shortness of the periods.
The longest period is less than five days, while three are less than
one day. This is a result that we might expect from the nature of the
case. The nearer a dark planet is to the star, the more likely it
will be to hide its light from an observer at a great distance. If,
for example, the planet Jupiter were nearly as large as the sun, the
chances would be hundreds to one against the plane of the orbit being
so nearly in the line of a distant observer that the latter would ever
see an eclipse of the sun by the planet. But if the planet were close
to the sun, the chances might increase to one in ten, and yet farther
to almost any extent, according to the nearness of the two bodies.
Still, we cannot set any definite limit to the period of stars of this
type; all we can say is that, as the period we seek for increases, the
number of stars varying in that period must diminish. This follows not
only from the reason just given, but from the fact that the longer the
interval that separates the partial eclipses of a star of the Algol
type, the less likely they are to be detected.