_U_ Pegasi is a star which proved as perplexing as Tau Cygni. It was
first supposed to be of the Algol type, with a period of about two
days. Then it was found that a number of minima occurred during this
period, and that the actual interval between them was only a few hours.
The great difficulty in the case arises from the minuteness of the
variation, which is but little more than half a magnitude between the
extremes. The observations of Wendell, at the Harvard Observatory, with
the polarizing photometer, enabled Pickering to reach a conclusion
which, though it may still be open to some doubt, seems to be the most
likely yet attainable. The star is of the Beta Lyræ type; its complete
period is 8 hours 59 minutes 41 seconds, or 19 seconds less than nine
hours; during this period it passes through two equal maxima, each of
magnitude 9.3, and two unequal minima 9.76 and 9.9, alternately.
[Illustration: FIG. 3. LIGHT CURVE OF U PEGASI, OF THE BETA LYRÆ TYPE,
FROM OBSERVATIONS BY WENDELL AT THE HARVARD OBSERVATORY. MAGNITUDE AT
MAXIMUM, 9.32; AT PRINCIPAL MINIMUM, 9.90; AT SECONDARY MINIMUM, 9.76.
PERIOD, 9 HOURS.]
The difference of these minima, 0m. 14, is less than the errors which
really ordinarily affect measures of a star’s magnitude with the best
photometers. Some skepticism has, therefore, been felt as to the
reality of the difference which, if it does not exist, would reduce the
periodic time below four and one-half hours, the shortest yet known.
But Pickering maintains that, in observations of this kind upon a
single star, the precision is such that the reality of the difference,
small though it be, is beyond reasonable doubt.
Taking Pickering’s law of change as a basis, Myers has represented
the light-curve of _U_ Pegasi on a theory similar to that which he
constructed for Beta Lyræ. His conclusion is that, in the present case,
the two bodies which form the visible star are in actual contact. A
remarkable historic feature of the case is that Poincaré has recently
investigated, by purely mathematical methods, the possible forms of
revolving fluid masses in a condition of equilibrium, bringing out a
number of such forms previously unknown. One of these, which he calls
the apiodal form, consists of two bodies joined into one, and it is
this which Myers finds for _U_ Pegasi.
Quite similar to these two cases is that of Zeta Herculis. This star,
ordinarily of the seventh magnitude, was found, at Potsdam, in 1894,
to diminish by about one magnitude. Repeated observations elsewhere
indicate a period of very nearly four days. Actually it is now found
to be only ten minutes less than four days. The result was that during
any one season of observation the minima occur at nearly the same hour
every night or day. To an observer situated in such longitude that they
occur during the day, they would, of course, be invisible.
Continued observations then showed a secondary minimum, occurring
about half-way between the principal minima hitherto observed. It
was then found that these secondary minima really occur between one
and two hours earlier than the mid-moment, so that the one interval
would be between forty-six and forty-seven hours and the other between
forty-nine and fifty. The time which it takes the star to lose its
light and regain it again is about ten hours. More recent observations,
however, do not show this inequality, so that there is probably a rapid
motion of the pericenter of the orbit.
It will be seen that this star combines the Algol and Beta Lyræ types.
It is an Algol star in that its light remains constant between the
eclipses. It is of the Beta Lyræ type in the alternate minima being
unequal.
From a careful study, Seliger and Hartwig derived the following
particulars respecting this system:
Diameter of principal star, 15,000,000 kilometers.
Diameter of smaller star, 12,000,000 kilometers.
Mass of the larger star, 172 times sun’s mass.
Mass of the smaller star, 94 times sun’s mass.
Distance of centers, 45,000,000 kilometers.
Time of revolution, 3d. 23h. 49m. 32.7s.
It must be added that the data for these extraordinary numbers are
rather slender and partly hypothetical.
Beta Lyræ is always of the same brightness at the same hour of its
period, and Algol has always the same magnitude at minimum. It is true
that the length of the period varies slowly in the case of these stars.
But this may arise from the action of other invisible bodies revolving
around the visible stars. This general uniformity is in accord with the
theory which attributes the apparent variations to the various aspects
in which we see one and the same system of revolving stars.
Another variable star showing some unique features is Eta Aquilæ. What
gives it special interest is that spectroscopic observations of its
radial motion show it to have a dark body revolving round it in a very
eccentric orbit, and in the same time as the period of variation. It
might therefore be supposed that we have here a star of the Algol or
Beta Lyræ type. But such is not the case. There is nothing in the law
of variation to suggest an eclipsing of the bright star, nor does it
seem that the variations can readily be represented by the varying
aspects of any revolving system.
The orbit of this star has been exhaustively investigated by Wright
from Campbell’s observations of the radial motion. The laws of change
in the system are shown by the curves below, which are reproduced, in
great part, from Wright’s paper in the ‘Astrophysical Journal.’
[Illustration: FIG. 4. LIGHT-CURVE AND RADIAL VELOCITY OF ETA AQUILÆ.]
The lower curve is the light-curve of the star during a period of 7.167
days. Starting from a maximum of 3.5 mag., it sinks, in the course of 5
days, to a minimum of 4.7m. It was found by Schwab that the diminution
is not progressive, but that a secondary maximum of 3.8m. is reached
at the end of the second day. After reaching the principal minimum it
rises rapidly to the principal maximum in 2¼ days.
The upper curve shows the radial velocity of the star during the
period of variation. It will be seen that the epoch of greatest
negative velocity, which referred to the center of mass of the system,
is 16.2 km. per second, occurs at the time of maximum brightness. The
greatest positive velocity, 23.9 km., occurs during the sixth day of
the period just after the time of minimum brightness.
Finally, the moments of inferior and superior conjunction of the dark
body with the bright one are neither of them an epoch of minimum
brightness, which takes place half-way between the two.
The most plausible conclusion we can draw is that the light of the star
is affected by the action of the dark body during its revolution. But
how the change may be produced we cannot yet say.