The New Heavens

by George Ellery Hale

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."

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.