Double Stars

The two dog-stars, Sirius and Procyon, are double stars of ex ceptional historic interest. Being conspicuous stars they were well observed a hundred years ago and used as fundamental refer ence stars for determining time, etc. It was found that they were moving irregularly—not with uniform proper motion like other stars. It was evident that each was being disturbed by the gravitation of a massive body in its neighbourhood, although the companions were invisible. The theory was given by Bessel in 1844, and orbits were computed from the observations, the periods of revolution being 5o and 39 years respectively. The disturbing stars, whose existence was thus convincingly demonstrated, have since been seen. The companion of Sirius was observed by Alvan Clarke in 1862, and is a comparatively easy object for modern telescopes; the companion of Procyon. which is more difficult, was observed by Schaeberle in 1896. They are faint stars, re spectively 1 o and 13 magnitudes fainter than their primaries. Nevertheless, they must be massive bodies to exert so large a pull on their brilliant neighbours.

Masses of Stars.

The orbital motion of double stars conforms to the law of gravitation. It gives evidence that gravitation is universal in the stellar system. The study of binary systems per forms a unique service in the general advance of our knowledge of the stars since it is through it that we arrive at knowledge of the masses of the stars. By the law of gravitation the extent to which a body disturbs the motion of other bodies is proportional to its mass. It is when we find bodies in close proximity that we obtain a chance to observe the disturbance, and so obtain a measure of the mass. It is good fortune for the astronomer that the course of evolution has been such as to provide pairs of stars close enough together; otherwise we should probably still be in total ignorance as to the masses of stars, except in so far as the sun's known mass might be assumed to be typical.

If are the masses of the two components, a the mean distance between them (strictly the semi-axis major of their relative orbit), and P the period of revolution, Kepler's laws give where k is a universal constant. Let us measure the mass in terms of the sun's mass as unit, the period in years, and a in astronomi cal units, i.e., in terms of the earth's distance from the sun. Apply ing the equation to the earth's motion round the sun (the earth's mass being negligible ) we see that for these units k Now apply the equation to Sirius. The mean distance of the two components is 7.55 seconds of arc. To convert this into linear measure we must know the parallax of Sirius, 0.37 second. This

means that one astronomical unit seen at the distance of Sirius would appear to extend 0.37 second; hence 7.55 seconds corre sponds to 20.4 astronomical units, determining a. The period P is 49 years. Hence We learn, therefore, that the combined mass of the two com ponents is three and one-half times that of the sun. If it is preferred to express the mass in tons, this can be done since the sun's mass is 1,980,000,000,000,000,000,000,000,000 tons.

To find the masses of the two stars separately we must deter mine their absolute orbits about their common centre of gravity instead of the relative orbit considered above. This means meas uring the motions of the components with respect to surrounding stars instead of with respect to one another. It is found that the bright star has the greater share of the mass, nearly in the ratio 3 :1.

From the visual double stars, together with the spectroscopic binaries (described below), an idea of the masses of stars in general has been obtained. Comparatively few determinations reach high accuracy, because a rather accurate parallax is re quired which is not generally forthcoming. The first thing that strikes us is the wonderful uniformity of mass. By far the majority of the determinations give between one-third and three times the sun's mass, which seems a very small range when com pared with the great differences of luminosity. Another result brought out is the close relation of mass to luminosity, the brighter stars being the more massive. It is probable that (exclud ing a peculiar class of stars known as white dwarfs) the luminosity depends almost entirely on the mass; it makes little difference whether the star is in a dense or in a diffuse state. The theory of this relation will be explained later. Having checked it by the masses determined for double stars, we can use it to find the masses of other stars whose absolute brightness is known.

We naturally select the most conspicuous stars for special investigation, and as a result we tend to pick out exceptionally high masses. Among the spectroscopic binaries some very high masses have been found, which, however, are believed to be exceptional. For one binary of Type 0 discovered by J. S. Plaskett the components have masses greater than 87 and 73 in terms of the sun. (Only a lower limit can be stated.) Another 0 type binary has masses 36 and 34. The eclipsing variable V Puppis has two components each of mass 19.2. There is at present no evidence of any stellar masses below one-sixth of the sun's mass.