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.
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.