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 Stephan, 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 Stephan 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 encyclopaeedia 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).