HOW BIG ARE STARS?

Auckland Star, Volume LXII, Issue 38, 14 February 1931, Page 7 (Supplement)

HOW BIG ARE STARS?

MEASURING METHODS.

LUMINOSITY AND BULK.

SOME GIANT DIAMETERS.

(By REGULUS, in "Melbourne Age.")

If the distance or a spherical object, and also the angle the object subtends at the eye are known, then the size- of the object can be found. To come down to actual figures, the diameter of the sphere is equal to the distance of the sphere multiplied by the angle it subtends, measured in seconds of arc, and divided by 206,265. For example, the angle of the moon subtends at its average distance is by measurement 1865.16 seconds of arc, and from other observations the average distance has been determined as 238,900 miles. The diameter of the moon will be the. product of these two numbers divided by 206,265. The value thus found is 2160 miles. I Again, the angle subtended by the sun at its average distance is 1919.26 seconds, while the average distance of the sun is 92,900,000 miles. The diameter of the sun will be> the product of these divided by 206,265. Working this out, the result is 864,000 miles. This method can be applied to the sun and moon, and also t'o all the major planets, for in each case the object will show a disc in the telescope, and the angular diameter of this disc can be measured. The distance from the earth at the moment of observation can also be determined, and thus the diameter in miles can be found. But when we look at a star in. the telescope no disc can be seen; the angular diameter of the star is. so small that no matter what magnification is used there is never any visible disc to measure, and consequently a direct determination of the angual diameter is impossible. If it is desired to find out how big the stars are, other methods will have to be resorted to. First Method. If the mass and density of the star are known, the volume can be found, and then finding the diameter is only a matter of arithmetic. In non-technical language, it is evident that if we know how many tons there are in the star, and also how many tons per cubic mile, division will give how many cubic miles there are in' the volume of the star. Knowing the volume in cubic miles, a little arithmetic gives the diameter in miles. Knowledge of the density of stars can only be obtained in special cases, namely, for double stars such as the famous star Algol, where one component passing in front of or behind the other produces or suffers eclipse, total or partial. Assuming the mass of each component equal to that of the sun, approximate values of the density and the dimensions of the system can be found, the general result being that the density of these stars may vary from three times to one-millionth that of the sun. In special cases where the spectra of the components can both be measured, the actual diameter of the stars can be determined. Thus one component of the star Beta Lyrae has a diameter 40 times that, of the sun, while each component of the star W Ursae Majoris has a diameter eight-tenths that of the sun. The probable conclusion that can be drawn from the knowledge we have. of. the masses and densities of binary systems is that the diameter of some stars is as small as half, while the diameter of others may <he 100 times that of the sun. Second Method. The second method of determining the diameter of the star proceeds on quite different lines. Suppose the total amount of light that a star gives out can be determined, and also the amount it gives out per square mile of surface, then by division the number of square miles in the Burface can be found. The diameter follows as a mere matter of arithmetic. Taking the second of these first, the temperature of the outer layer of the star can be found from the spectrum of the star, and the amount of light radiated per square mile depends in a known way on this temperature. Now for the total amount of light given out by the star—its luminosity. If the apparent brightness is known and also the distance, the luminosity is readily calculated. Thus Alpha Centauri appears one fifty-nine thousand millionth as bright as the sun, Multiply this by the square of the distance, which is 270,000 times the distance of the sun, and its luminosity is found to be 1.2 times that of the sun. As another example, we may take the comparison of Sirius. Its luminosity is one-three hundred and sixtieth that of the sun, while the amount of light emitted per square mile is two and a half times as great as for the sun. Combining these two, its surface is only one-nine hundredth and its diameter is one-thirtieth that of the sun, or 29,000 miles. Third Method. The third method depends on the determination of the angular diameter and the distance. We saw that for the sun, moon and the major planets the angular diameter is actually measured, but for the stars there is 110 prospect of the disc being seen to enable a measurement to be made. But use can be made of the interference of - light to determine the angular diameter. If the star were actually a point of light, then by a suitable arrangement of mirrors the image of the star would be seen to be crossed by a series of dark bands. If the star is not a point, then the dark bands from different parts of the surface are relatively displaced, and in a definite position of tho mirrors—the separation of the mirrors depending on the angular diameter of the star—the dark bands will entirely disappear. Several measures of the distance of Alpha Orionis have been made, but there is considerable percentage uncertainty. Taking the distance to be such that the radius of the earth's orbit subtends an angle of .020 seconds of arc at the star, the diameter of Alpha Orionis comes out as 210,000,000 miles. Similarly, other stellar diameters have been determined —Antares 400,000,000 miles; Aldebaran, 270,000,000 miles; Arcturus, 21,000,000 miles. A larger apparatus permitting a mirror separation of 50 feet has just been completed at Mount Wilson, and with this it will be possible to arrive at the diameter of some fifty stars. Summary. Thus some of the stars have diameters as great as 400,000,000 miles, more than 400 times that of the sun; while on the other hand, the companion of Sirius has a diameter of only 29,000 miles. Comparing these extremes, there is the remarkable range in diameter of 12,000 to 1, while the ratio of the volumes is some two million million to one. Representing the dwarf star by a steel ball one-tenth of an inch in diameter, the giant star would be represented by a large dome no less than 100 feet across.