From the close uniformity of stellar masses it follows that the stars of gigantic volume like Betelgeuse must be of extremely low density. Assuming that the mass of Betelgeuse is something less than 10o times the sun's mass, in order to fill a volume so million times greater than the sun, the density must be less than that of air.
Spectroscopic Binaries.—When a source of light is approach ing us, the lines in its spectrum appear displaced towards the violet end; when receding, the displacement is towards the red end. By means of this "Doppler effect" (see LIGHT) the velocity of a star in the line of sight can be measured. In examining the stars with a spectroscope we sometimes turn the instrument on to what is telescopically a single point of light, but is actually a double star with components too close to be separated. Since the two components have different velocities towards or away from us their spectra will not be exactly superposed and every spectra line will appear double. The first example of this was found by E. C. Pickering in 1889. This was the star Mizar already mentioned as the first visual double star to be discovered. The two components seen in the telescope take at least 3,00o years to perform their revolution ; but the doubling of the spectral lines of the brighter component shows that it is itself a double star with a revolution period of 104 days. If a star showing a doubled spectrum is watched for some time it is seen that the doubled lines close up and then cross one another. This is in accordance with the theory of orbital motion, for the two corn ponents must approach us and recede from us alternately in the course of a revolution.
It is only when the two components are of nearly equal bright ness that this doubling of the spectral lines can be observed. A difference of about two magnitudes is sufficient to render the fainter spectrum invisible. In the majority of spectroscopic binaries only the brighter spectrum is observed, and the binary character is inferred from the periodic approach and recession of the source emitting it. The argument is that the changing dis placement of the spectral lines shows that the source of light is describing an orbit ; there must be some mass for it to revolve around ; and therefore a fainter component must exist although invisible. Rather more than a thousand spectroscopic binaries have been discovered, and definite orbits have been computed for about 25o of these. The spectroscope can only measure velocity in the line of sight, and many binaries must escape de tection through having their orbits nearly perpendicular to the line of sight.
Spectroscopic binaries afford valuable additional information as to the masses of stars, but of a statistical rather than of an indi vidual kind. When one component only is observed, all that can be deduced is a rather complicated function of the masses and the unknown inclination of the orbit; but when both spectra are observed, a minimum mass of each component can be found.
This minimum mass has to be multiplied by i (i=inclina tion of orbit plane to the sky plane) which is unknown unless the star can also be observed visually or is an eclipsing variable, but in researches on the average mass of any class of stars a suitable mean value of this factor may be used.
In rare cases the same system may be observed as a visual and a spectroscopic binary; but in general only the close pairs with periods less than a year are detected spectroscopically, and wide pairs with periods of many years or centuries are detected visually. Many intermediate pairs must escape both methods of discovery. The first star to be observed by both methods was a Centauri. The results have a special interest because they afford a deter mination of the star's distance entirely independent of the ordi nary method of parallax measurement. The visual observations determine the angular size of the orbit ; the spectroscopic obser vations determine the same quantity in kilometres; so that we have only to compute the distance at which the given length subtends the given angle. The result for a Centauri satisfactorily checked the ordinary trigonometric determination of its dis tance.
Multiple systems containing more than two components are not uncommon. We have already noticed the system of Mizar. The star Castor is an easy visual double, both components of which are spectroscopic binaries. These systems all appear to be built by successive subdivisions of one mass into two, and it is clear that after such a fission a long period of evolution and condensation must elapse before either of the resulting masses is ready to divide again. An important question is whether the widely-separated pairs were originally formed with their present separation or whether the distance has increased in the course of time. It is difficult to resist the impression that the components gradually recede from one another, especially as the statistics show markedly that the stars supposed to be oldest in evolution form the widest pairs. Two causes are acting which will tend to increase the initial separation to some extent, viz., the mutual tidal forces and the loss of mass of the stars by radiation ; but neither can produce a large effect. The cumulative effect of per turbations by casual approaches of other stars would in the long run, drive the components further apart ; this process, however, is too slow to produce much effect, even in the long periods of stellar evolution. The general problem of the formation of double stars is discussed in the article COSMOGONY.