A Text-Book of Astronomy

by George C. Comstock

Fig. 129.—Illustrating the motion of a spectroscopic binary.

203. Spectroscopic binaries.—In the year 1890 Professor Pickering, of the Harvard Observatory, announced the discovery of a new class of double stars, invisible as such in even the most powerful telescope, and producing no perturbations such as have been considered above, but showing in their spectrum that two or more bodies must be present in the source of light which to the eye is indistinguishable from a single star. In [Fig. 129] we suppose A and B to be the two components of a double star, each moving in its own orbit about their common center of gravity, C, whose distance from the earth is several million times greater than the distance between the stars themselves. Under such circumstances no telescope could distinguish between the two stars, which would appear fused into one; but the smaller the orbit the more rapid would be their motion in it, and if this orbit were turned edgewise toward the earth, as is supposed in the figure, whenever the stars were in the relative position there shown, A would be rapidly approaching the earth by reason of its orbital motion, while B would move away from it, so that in accordance with the Doppler principle the lines composing their respective spectra would be shifted in opposite directions, thus producing a doubling of the lines, each single line breaking up into two, like the double-sodium line D, only not spaced so far apart. When the stars have moved a quarter way round their orbit to the points A', B', their velocities are turned at right angles to the line of sight and the spectrum returns to the normal type with single lines, only to break up again when after another quarter revolution their velocities are again parallel with the line of sight. The interval of time between consecutive doublings of the lines in the spectrum thus furnishes half the time of a revolution in the orbit. The distance between the components of a double line shows by means of the Doppler principle how fast the stars are traveling, and this in connection with the periodic times fixes the size of the orbit, provided we assume that it is turned exactly edgewise to the earth. This assumption may not be quite true, but even though the orbit should deviate considerably from this position, it will still present the phenomenon of the double lines whose displacement will now show something less than the true velocities of the stars in their orbits, since the spectroscope measures only that component of the whole velocity which is directed toward the earth, and it is important to note that the real orbits and masses of these spectroscopic binaries, as they are called, will usually be somewhat larger than those indicated by the spectroscope, since it is only in exceptional cases that the orbit will be turned exactly edgewise to us.

The bright star Capella is an excellent illustration of these spectroscopic binaries. At intervals of a little less than a month the lines of its spectrum are alternately single and double, their maximum separation corresponding to a velocity in the line of sight amounting to 37 miles per second. Each component of a doubled line appears to be shifted an equal amount from the position occupied by the line when it is single, thus indicating equal velocities and equal masses for the two component stars whose periodic time in their orbit is 104 days. From this periodic time, together with the velocity of the star's motion, let the student show that the diameter of the orbit—i. e., the distance of the stars from each other—is approximately 53,000,000 miles, and that their combined mass is a little less than that of α Centauri, provided that their orbit plane is turned exactly edgewise toward the earth.

There are at the present time (1901) 34 spectroscopic binaries known, including among them such stars as Polaris, Capella, Algol, Spica, β Aurigæ, ζ Ursæ Majoris, etc., and their number is rapidly increasing, about one star out of every seven whose motion in the line of sight is determined proving to be a binary or, as in the case of Polaris, possibly triple. On account of smaller distance apart their periodic times are much shorter than those of the ordinary double stars, and range from a few days up to several months—more than two years in the case of η Pegasi, which has the longest known period of any star of this class.

Spectroscopic binaries agree with ordinary double stars in having masses rather greater than that of the sun, but there is as yet no assured case of a mass ten times as great as that of the sun.

204. Variable stars.—Attention has already been drawn ([§ 23]) to the fact that some stars shine with a changing brightness—e. g., Algol, the most famous of these variable stars, at its maximum of brightness furnishes three times as much light as when at its minimum, and other variable stars show an even greater range. The star ο Ceti has been named Mira (Latin, the wonderful), from its extraordinary range of brightness, more than six-hundred-fold. For the greater part of the time this star is invisible to the naked eye, but during some three months in every year it brightens up sufficiently to be seen, rising quite rapidly to its maximum brilliancy, which is sometimes that of a second-magnitude star, but more frequently only third or even fourth magnitude, and, after shining for a few weeks with nearly maximum brilliancy, falling off to become invisible for a time and then return to its maximum brightness after an interval of eleven months from the preceding maximum. In 1901 it should reach its greatest brilliancy about midsummer, and a month earlier than this for each succeeding year. Find it by means of the star map, and by comparing its brightness from night to night with neighboring stars of about the same magnitude see how it changes with respect to them.

The interval of time from maximum to maximum of brightness—331.6 days for Mira—is called the star's period, and within its period a star regularly variable runs through all its changes of brilliancy, much as the weather runs through its cycle of changes in the period of a year. But, as there are wet years and dry ones, hot years and cold, so also with variable stars, many of them show differences more or less pronounced between different periods, and one such difference has already been noted in the case of Mira; its maximum brilliancy is different in different years. So, too, the length of the period fluctuates in many cases, as does every other circumstance connected with it, and predictions of what such a variable star will do are notoriously unreliable.

205. The Algol variables.—On the other hand, some variable stars present an almost perfect regularity, repeating their changes time after time with a precision like that of clockwork. Algol is one type of these regular variables, having a period of 68.8154 hours, during six sevenths of which time it shines with unchanging luster as a star of the 2.3 magnitude, but during the remaining 9 hours of each period it runs down to the 3.5 magnitude, and comes back again, as is shown by a curve in [Fig. 130]. The horizontal scale here represents hours, reckoned from the time of the star's minimum brightness, and the vertical scale shows stellar magnitudes. Such a diagram is called the star's light curve, and we may read from it that at any time between 5h. and 32h. after the time of minimum the star's magnitude is 2.32; at 2h. after a minimum the magnitude is 2.88, etc. What is the magnitude an hour and a half before the time of minimum? What is the magnitude 43 days after a minimum?