GIANT STARS
Our ancestral sun, as pictured by Laplace, originally extended
in a state of luminous vapor beyond the boundaries of the solar
system. Rotating upon its axis, it slowly contracted through loss
of heat by radiation, leaving behind it portions of its mass, which
condensed to form the planets. Still gaseous, though now denser than
water, it continues to pour out the heat on which our existence
depends, as it shrinks imperceptibly toward its ultimate condition
of a cold and darkened globe.
Laplace's hypothesis has been subjected in recent years to much
criticism, and there is good reason to doubt whether his description
of the mode of evolution of our solar system is correct in every
particular. All critics agree, however, that the sun was once enormously
larger than it now is, and that the planets originally formed part
of its distended mass.
Even in its present diminished state, the sun is huge beyond easy
conception. Our own earth, though so minute a fragment of the primeval
sun, is nevertheless so large that some parts of its surface have
not yet been explored. Seen beside the sun, by an observer on one
of the planets, the earth would appear as an insignificant speck,
which could be swallowed with ease by the whirling vortex of a
sun-spot. If the sun were hollow, with the earth at its centre,
the moon, though 240,000 miles from us, would have room and to
spare in which to describe its orbit, for the sun is 865,000 miles
in diameter, so that its volume is more than a million times that
of the earth.
[Illustration: Fig. 19. Gaseous prominence at the sun's limb, 140,000
miles high (Ellerman).
Photographed with the spectroheliograph, using the light emitted
by glowing calcium vapor. The comparative size of the earth is
indicated by the white circle.]
But what of the stars, proved by the spectroscope to be self-luminous,
intensely hot, and formed of the same chemical elements that constitute
the sun and the earth? Are they comparable in size with the sun? Do
they occur in all stages of development, from infancy to old age?
And if such stages can be detected, do they afford indications
of the gradual diminution in volume which Laplace imagined the
sun to experience?
[Illustration: Fig. 20. The sun, 865,000 miles in diameter, from
a direct photograph showing many sun-spots (Whitney)
The small black disk in the centre represents the comparative size
of the earth, while the circle surrounding it corresponds in diameter
to the orbit of the moon.]
STAR IMAGES
Prior to the application of the powerful new engine of research
described in this article we have had no means of measuring the
diameters of the stars. We have measured their distances and their
motions, determined their chemical composition, and obtained undeniable
evidence of progressive development, but even in the most powerful
telescopes their images are so minute that they appear as points
rather than as disks. In fact, the larger the telescope and the
more perfect the atmospheric conditions at the observer's command,
the smaller do these images appear. On the photographic plate, it is
true, the stars are recorded as measurable disks, but these are due
to the spreading of the light from their bright point-like images,
and their diameters increase as the exposure time is prolonged.
From the images of the brighter stars rays of light project in
straight lines, but these also are instrumental phenomena, due
to diffraction of light by the steel bars that support the small
mirror in the tube of reflecting telescopes. In a word, the stars
are so remote that the largest and most perfect telescopes show
them only as extremely minute needle-points of light, without any
trace of their true disks.
[Illustration: Fig. 21. Great sun-spot group, August 8, 1917 (Whitney).
The disk in the corner represents the comparative size of the earth.]
How, then, may we hope to measure their diameters? By using, as
the man of science must so often do, indirect means when the direct
attack fails. Most of the remarkable progress of astronomy during
the last quarter-century has resulted from the application of new and
ingenious devices borrowed from the physicist. These have multiplied
to such a degree that some of our observatories are literally physical
laboratories, in which the sun and stars are examined by powerful
spectroscopes and other optical instruments that have recently advanced
our knowledge of physics by leaps and bounds. In the present case
we are indebted for our star-measuring device to the distinguished
physicist Professor Albert A. Michelson, who has contributed a long
array of novel apparatus and methods to physics and astronomy.
THE INTERFEROMETER
The instrument in question, known as the interferometer, had previously
yielded a remarkable series of results when applied in its various
forms to the solution of fundamental problems. To mention only a
few of those that have helped to establish Michelson's fame, we may
recall that our exact knowledge of the length of the international
metre at Sevres, the world's standard of measurement, was obtained
by him with an interferometer in terms of the invariable length of
light-waves. A different form of interferometer has more recently
enabled him to measure the minute tides within the solid body of the
earth--not the great tides of the ocean, but the slight deformations
of the earth's body, which is as rigid as steel, that are caused by
the varying attractions of the sun and moon. Finally, to mention
only one more case, it was the Michelson-Morley experiment, made
years ago with still another form of interferometer, that yielded
the basic idea from which the theory of relativity was developed
by Lorentz and Einstein.
[Illustration: Fig. 22. Photograph of the hydrogen atmosphere of
the sun (Ellerman).
Made with the spectroheliograph, showing the immense vortices,
or whirling storms like tornadoes, that centre in sun-spots. The
comparative size of the earth is shown by the white circle traced
on the largest sun-spot.]
The history of the method of measuring star diameters is a very
curious one, showing how the most promising opportunities for scientific
progress may lie unused for decades. The fundamental principle
of the device was first suggested by the great French physicist
Fizeau in 1868. In 1874 the theory was developed by the French
astronomer Stéphan, who observed interference fringes given by a
large number of stars, and rightly concluded that their angular
diameters must be much smaller than 0.158 of a second of arc, the
smallest measurable with his instrument. In 1890 Michelson, unaware
of the earlier work, published in the _Philosophical Magazine_ a
complete description of an interferometer capable of determining
with surprising accuracy the distance between the components of
double stars so close together that no telescope can separate them.
He also showed how the same principle could be applied to the
measurement of star diameters if a sufficiently large interferometer
could be built for this purpose, and developed the theory much
more completely than Stéphan had done. A year later he measured
the diameters of Jupiter's satellites by this means at the Lick
Observatory. But nearly thirty years elapsed before the next step
was taken. Two causes have doubtless contributed to this delay. Both
theory and experiment have demonstrated the extreme sensitiveness
of the "interference fringes," on the observation of which the
method depends, and it was generally supposed by astronomers that
disturbances in the earth's atmosphere would prevent them from
being clearly seen with large telescopes. Furthermore, a very large
interferometer, too large to be carried by any existing telescope,
was required for the star-diameter work, though close double stars
could have been easily studied by this device with several of the
large telescopes of the early nineties. But whatever the reasons,
a powerful method of research lay unused.
The approaching completion of the 100-inch telescope of the Mount
Wilson Observatory led me to suggest to Professor Michelson, before
the United States entered the war, that the method be thoroughly
tested under the favorable atmospheric conditions of Southern
California. He was at that time at work on a special form of
interferometer, designed to determine whether atmospheric disturbances
could be disregarded in planning large-scale experiments. But the
war intervened, and all of our efforts were concentrated for two
years on the solution of war problems.[*] In 1919, as soon as the
100-inch telescope had been completed and tested, the work was
resumed on Mount Wilson.
[Footnote *: Professor Michelson's most important contribution during
the war period was a new and very efficient form of range-finder,
adopted for use by the U. S. Navy.]
A LABORATORY EXPERIMENT
The principle of the method can be most readily seen by the aid
of an experiment which any one can easily perform for himself with
simple apparatus. Make a narrow slit, a few thousandths of an inch
in width, in a sheet of black paper, and support it vertically
before a brilliant source of light. Observe this from a distance of
40 or 50 feet with a small telescope magnifying about 30 diameters.
The object-glass of the telescope should be covered with an opaque
cap, pierced by two circular holes about one-eighth of an inch in
diameter and half an inch apart. The holes should be on opposite
sides of the centre of the object-glass and equidistant from it,
and the line joining the holes should be horizontal. When this
cap is removed the slit appears as a narrow vertical band with
much fainter bands on both sides of it. With the cap in place, the
central bright band appears to be ruled with narrow vertical lines
or fringes produced by the "interference"[*] of the two pencils of
light coming through different parts of the object-glass from the
distant slit. Cover one of the holes, and the fringes instantly
disappear. Their production requires the joint effect of the two
light-pencils.
[Footnote *: For an explanation of the phenomena of interference,
see any encyclopæedia or book on physics.]
Now suppose the two holes over the object-glass to be in movable
plates, so that their distance apart can be varied. As they are
gradually separated the narrow vertical fringes become less and
less distinct, and finally vanish completely. Measure the distance
between the holes and divide this by the wavelength of light, which
we may call 1/50000 of an inch. The result is the angular width
of the distant slit. Knowing the distance of the slit, we can at
once calculate its linear width. If for the slit we substitute a
minute circular hole, the method of measurement remains the same,
but the angular diameter as calculated above must be multiplied
by 1.22.[*]
[Footnote *: More complete details may be found in Michelson's Lowell
Lectures on "Light-Waves and Their Uses," University of Chicago
Press, 1907.]
To measure the diameter of a star we proceed in a similar way,
but, as the angle it subtends is so small, we must use a very large
telescope, for the smaller the angle the farther apart must be the
two holes over the object-glass (or the mirror, in case a reflecting
telescope is employed). In fact, when the holes are moved apart to
the full aperture of the 100-inch Hooker telescope, the interference
fringes are still visible even with the star Betelgeuse, though its
angular diameter is perhaps as great as that of any other star.
Thus, we must build an attachment for the telescope, so arranged
as to permit us to move the openings still farther apart.
[Illustration: Fig. 23. Diagram showing outline of the 100-inch
Hooker telescope, and path of the two pencils of light from a star
when under observation with the 20-foot Michelson interferometer.
A photograph of the interferometer is shown in Fig. 24.]
THE 20-FOOT INSTRUMENT
The 20-foot interferometer designed by Messrs. Michelson and Pease,
and constructed in the Mount Wilson Observatory instrument-shop,
is shown in the diagram (Fig. 23) and in a photograph of the upper
end of the skeleton tube of the telescope (Fig. 24). The light from
the star is received by two flat mirrors (Ml, M4) which project
beyond the tube and can be moved apart along the supporting arm.
These take the place of the two holes over the object-glass in
our experiment. From these mirrors the light is reflected to a
second pair of flat mirrors (M2, M3), which send it toward the
100-inch concave mirror (M5) at the bottom of the telescope tube.
After this the course of the light is exactly as it would be if
the mirrors M2, M3 were replaced by two holes over the 100-inch
mirror. It is reflected to the convex mirror (M6), then back in
a less rapidly convergent beam toward the large mirror. Before
reaching it the light is caught by the plane mirror (M7) and reflected
through an opening at the side of the telescope tube to the eye-piece
E. Here the fringes are observed with a magnification ranging from
1,500 to 3,000 diameters.
[Illustration: Fig. 24. Twenty-foot Michelson interferometer for
measuring star diameters, attached to upper end of the skeleton
tube of the 100-inch Hooker telescope.
The path of the two pencils of light from the star is shown in
Fig. 23. For a photograph of the entire telescope, see Fig. 4.]
In the practical application of this method to the measurement of
star diameters, the chief problem was whether the atmosphere would
be quiet enough to permit sharp interference fringes to be produced
with light-pencils more than 100 inches apart. After successful
preliminary tests with the 40-inch refracting telescope of the
Yerkes Observatory, Professor Michelson made the first attempt
to see the fringes with the 60-inch and 100-inch reflectors on
Mount Wilson in September, 1919. He was surprised and delighted to
find that the fringes were perfectly sharp and distinct with the
full aperture of both these instruments. Doctor Anderson, of the
observatory staff, then devised a special form of interferometer
for the measurement of close double stars, and applied it with
the 100-inch telescope to the measurement of the orbital motion
of the close components of Capella, with results of extraordinary
accuracy, far beyond anything attainable by previous methods. The
success of this work strongly encouraged the more ambitious project
of measuring the diameter of a star, and the 20-foot interferometer
was built for this purpose.
The difficult and delicate problem of adjusting the mirrors of
this instrument with the necessary extreme accuracy was solved by
Professor Michelson during his visit to Mount Wilson in the summer
of 1920, and with the assistance of Mr. Pease, of the observatory
staff, interference fringes were observed in the case of certain
stars when the mirrors were as much as 18 feet apart. All was thus
in readiness for a decisive test as soon as a suitable star presented
itself.
THE GIANT BETELGEUSE
Russell, Shapley, and Eddington had pointed out Betelgeuse (Arabic
for "the giant's shoulder"), the bright red star in the constellation
of Orion (Fig. 25), as the most favorable of all stars for measurement,
and the last-named had given its angular diameter as 0.051 of a
second of arc. This deduction from theory appeared in his recent
presidential address before the British Association for the Advancement
of Science, in which Professor Eddington remarked: "Probably the
greatest need of stellar astronomy at the present day, in order
to make sure that our theoretical deductions are starting on the
right lines, is some means of measuring the apparent angular diameter
of stars." He then referred to the work already in progress on
Mount Wilson, but anticipated "that atmospheric disturbance will
ultimately set the limit to what can be accomplished."
[Illustration: Fig. 25. The giant Betelgeuse (within the circle),
familiar as the conspicuous red star in the right shoulder of Orion
(Hubble).
Measures with the interferometer show its angular diameter to be
0.047 of a second of arc, corresponding to a linear diameter of
215,000,000 miles, if the best available determination of its distance
can be relied upon. This determination shows Betelgeuse to be 160
light-years from the earth. Light travels at the rate of 186,000
miles per second, and yet spends 160 years on its journey to us
from this star.]
On December 13, 1920, Mr. Pease successfully measured the diameter
of Betelgeuse with the 20-foot interferometer. As the outer mirrors
were separated the interference fringes gradually became less distinct,
as theory requires, and as Doctor Merrill had previously seen when
observing Betelgeuse with the interferometer used for Capella. At
a separation of 10 feet the fringes disappeared completely, giving
the data required for calculating the diameter of the star. To
test the perfection of the adjustment, the telescope was turned to
other stars, of smaller angular diameter, which showed the fringes
with perfect clearness. Turning back to Betelgeuse, they were seen
beyond doubt to be absent. Assuming the mean wave-length of the
light of this star to be 5750/10000000 of a millimetre, its angular
diameter comes out 0.047 of a second of arc, thus falling between
the values--0.051 and 0.031 of a second--predicted by Eddington and
Russell from slightly different assumptions. Subsequent corrections
and repeated measurement will change Mr. Pease's result somewhat,
but it is almost certainly within 10 or 15 per cent of the truth.
We may therefore conclude that the angular diameter of Betelgeuse
is very nearly the same as that of a ball one inch in diameter,
seen at a distance of seventy miles.
[Illustration: Fig. 26. Arcturus (within the white circle), known
to the Arabs as the "Lance Bearer," and to the Chinese as the "Great
Horn" or the "Palace of the Emperors" (Hubble).
Its angular diameter, measured at Mount Wilson by Pease with the
20-foot Michelson interferometer on April 15, 1921, is 0.022 of a
second, in close agreement with Russell's predicted value of 0.019
of a second. The mean parallax of Arcturus, based upon several
determinations, is 0.095 of a second, corresponding to a distance of
34 light-years. The linear diameter, computed from Pease's measure
and this value of the distance is about 21 million miles.]
But this represents only the angle subtended by the star's disk.
To learn its linear diameter, we must know its distance. Four
determinations of the parallax, which determines the distance,
have been made. Elkin, with the Yale heliometer, obtained 0.032
of a second of arc. Schlesinger, from photographs taken with the
30-inch Allegheny refractor, derived 0.016. Adams, by his spectroscopic
method applied with the 60-inch Mount Wilson reflector, obtained
0.012. Lee's recent value, secured photographically with the 40-inch
Yerkes refractor, is 0.022. The heliometer parallax is doubtless
less reliable than the photographic ones, and Doctor Adams states
that the spectral type and luminosity of Betelgeuse make his value
less certain than in the case of most other stars. If we take a
(weighted) mean value of 0.020 of a second, we shall probably not
be far from the truth. This parallax represents the angle subtended
by the radius of the earth's orbit (93,000,000 miles) at the distance
of Betelgeuse. By comparing it with 0.047, the angular diameter of
the star, we see that the linear diameter is about two and one-third
times as great as the distance from the earth to the sun, or
approximately 215,000,000 miles. Thus, if this measure of its distance
is not considerably in error, Betelgeuse would nearly fill the
orbit of Mars. All methods of determining the distances of the
stars are subject to uncertainty, however, and subsequent measures
may reduce this figure very appreciably. But there can be no doubt
that the diameter of Betelgeuse exceeds 100,000,000 miles, and
it is probably much greater.
The extremely small angle subtended by this enormous disk is explained
by the great distance of the star, which is about 160 light-years.
That is to say, light travelling at the rate of 186,000 miles per
second spends 160 years in crossing the space that lies between
us and Betelgeuse, whose tremendous proportions therefore seem
so minute even in the most powerful telescopes.
STELLAR EVOLUTION
This actual measure of the diameter of Betelgeuse supplies a new
and striking test of Russell's and Hertzsprung's theory of dwarf
and giant stars. Just before the war Russell showed that our old
methods of classifying the stars according to their spectra must
be radically changed. Stars in an early stage of their life history
may be regarded as diffuse gaseous masses, enormously larger than
our sun, and at a much lower temperature. Their density must be
very low, and their state that of a perfect gas. These are the
"giants." In the slow process of time they contract through constant
loss of heat by radiation. But, despite this loss, the heat produced
by contraction and from other sources (see p. 82) causes their
temperature to rise, while their color changes from red to bluish
white. The process of shrinkage and rise of temperature goes on so
long as they remain in the state of a perfect gas. But as soon as
contraction has increased the density of the gas beyond a certain
point the cycle reverses and the temperature begins to fall. The
bluish-white light of the star turns yellowish, and we enter the
dwarf stage, of which our own sun is a representative. The density
increases, surpassing that of water in the case of the sun, and
going far beyond this point in later stages. In the lapse of millions
of years a reddish hue appears, finally turning to deep red. The
falling temperature permits the chemical elements, existing in a
gaseous state in the outer atmosphere of the star, to unite into
compounds, which are rendered conspicuous by their characteristic
bands in the spectrum. Finally comes extinction of light, as the
star approaches its ultimate state of a cold and solid globe.
[Illustration: Fig. 27. The giant star Antares (within the white
circle), notable for its red color in the constellation Scorpio,
and named by the Greeks "A Rival of Mars" (Hubble).
The distance of Antares, though not very accurately known, is probably
not far from 350 light-years. Its angular diameter of 0.040 of a
second would thus correspond to a linear diameter of about 400
million miles.]
We may thus form a new picture of the two branches of the temperature
curve, long since suggested by Lockyer, on very different grounds, as
the outline of stellar life. On the ascending side are the giants,
of vast dimensions and more diffuse than the air we breathe. There
are good reasons for believing that the mass of Betelgeuse cannot
be more than ten times that of the sun, while its volume is at
least a million times as great and may exceed eight million times
the sun's volume. Therefore, its average density must be like that
of an attenuated gas in an electric vacuum tube. Three-quarters
of the naked-eye stars are in the giant stage, which comprises
such familiar objects as Betelgeuse, Antares, and Aldebaran, but
most of them are much denser than these greatly inflated bodies.
The pinnacle is reached in the intensely hot white stars of the
helium class, in whose spectra the lines of this gas are very
conspicuous. The density of these stars is perhaps one-tenth that
of the sun. Sirius, also very hot, is nearly twice as dense. Then
comes the cooling stage, characterized, as already remarked, by
increasing density, and also by increasing chemical complexity
resulting from falling temperature. This life cycle is probably
not followed by all stars, but it may hold true for millions of
them.
The existence of giant and dwarf stars has been fully proved by
the remarkable work of Adams and his associates on Mount Wilson,
where his method of determining a star's distance and intrinsic
luminosity by spectroscopic observations has already been applied
to 2,000 stars. Discussion of the results leads at once to the
recognition of the two great classes of giants and dwarfs. Now
comes the work of Michelson and Pease to cap the climax, giving us
the actual diameter of a typical giant star, in close agreement with
predictions based upon theory. From this diameter we may conclude that
the density of Betelgeuse is extremely low, in harmony with Russell's
theory, which is further supported by spectroscopic analysis of
the star's light, revealing evidence of the comparatively low
temperature called for by the theory at this early stage of stellar
existence.
TWO OTHER GIANTS
The diameter of Arcturus was successfully measured by Mr. Pease
at Mount Wilson on April 15. As the mirrors of the interferometer
were moved apart, the fringes gradually decreased in visibility
until they finally disappeared at a mirror separation of 19.6 feet.
Adopting a mean wave-length of 5600/10000000 of a millimetre for
the light of Arcturus, this gives a value of 0.022 of a second of
arc for the angular diameter of the star. If we use a mean value
of 0.095 of a second for the parallax, the corresponding linear
diameter comes out 21,000,000 miles. The angular diameter, as in
the case of Betelgeuse, is in remarkably close agreement with the
diameter predicted from theory. Antares, the third star measured
by Mr. Pease, is the largest of all. If it is actually a member of
the Scorpius-Centaurus group, as we have strong reason to believe,
it is fully 350 light-years from the earth, and its diameter is
about 400,000,000 miles.
[Illustration: Fig. 28. Diameters of the Sun, Arcturus, Betelgeuse,
and Antares compared with the orbit of Mars.
Sun, diameter, 865,000 miles.
Arcturus, diameter, 21,000,000 miles.
Betelgeuse, diameter, 215,000,000 miles.
Antares, diameter, 400,000,000 miles.]
It now remains to make further measures of Betelgeuse, especially
because its marked changes in brightness suggest possible variations
in diameter. We must also apply the interferometer method to stars
of the various spectral types, in order to afford a sure basis for
future studies of stellar evolution. Unfortunately, only a few
giant stars are certain to fall within the range of our present
instrument. An interferometer of 70-feet aperture would be needed
to measure Sirius accurately, and one of twice this size to deal
with less brilliant white stars. A 100-foot instrument, if feasible
to build, would permit objects representing most of the chief stages
of stellar development to be measured, thus contributing in the
highest degree to the progress of our knowledge of the life history
of the stars. Fortunately, though the mechanical difficulties are
great, the optical problem is insignificant, and the cost of the
entire apparatus, though necessarily high, would be only a small
fraction of that of a telescope of corresponding aperture, if such
could be built. A 100-foot interferometer might be designed in
many different forms, and one of these may ultimately be found
to be within the range of possibility. Meanwhile the 20-foot
interferometer has been improved so materially that it now promises
to yield approximate measures of stars at first supposed to be
beyond its capacity.
[Illustration: Fig. 29. Aldebaran, the "leader" (of the Pleiades),
was also known to the Arabs as "The Eye of the Bull," "The Heart
of the Bull," and "The Great Camel" (Hubble).
Like Betelgeuse and Antares, it is notable for its red color, which
accounts for the fact that its image on this photograph is hardly
more conspicuous than the images of stars which are actually much
fainter but contain a larger proportion of blue light, to which
the photographic plates here employed are more sensitive than to
red or yellow. Aldebaran is about 50 light-years from the earth.
Interferometer measures, now in progress on Mount Wilson, indicate
that its angular diameter is about 0.020 of a second.]
While the theory of dwarf and giant stars and the measurements just
described afford no direct evidence bearing on Laplace's explanation
of the formation of planets, they show that stars exist which are
comparable in diameter with our solar system, and suggest that the
sun must have shrunk from vast dimensions. The mode of formation
of systems like our own, and of other systems numerously illustrated
in the heavens, is one of the most fascinating problems of astronomy.
Much light has been thrown on it by recent investigations, rendered
possible by the development of new and powerful instruments and by
advances in physics of the most fundamental character. All the
evidence confirms the existence of dwarf and giant stars, but much
work must be done before the entire course of stellar evolution
can be explained.