Fig. 130.—The light curve of Algol.
The arrows shown in [Fig. 130] are a feature not usually found with light curves, but in this case each one represents a spectroscopic determination of the motion of Algol in the line of sight. These observations extended over a period of more than two years, but they are plotted in the figure with reference to the number of hours each one preceded or followed a minimum of the star's light, and each arrow shows not only the direction of the star's motion along the line of sight, the arrows pointing down denoting approach of the star toward the earth, but also its velocity, each square of the ruling corresponding to 10 kilometers (6.2 miles per second). The differences of velocity shown by adjacent arrows come mainly from errors of observation and furnish some idea of how consistent among themselves such observations are, but there can be no doubt that before minimum the star is moving away from the earth, and after minimum is approaching it. It is evident from these observations that in Algol we have to do with a spectroscopic binary, one of whose components is a dark star which, once in each revolution, partially eclipses the bright star and produces thus the variations in its light. By combining the spectroscopic observations with the variations in the star's light, Vogel finds that the bright star, Algol, itself has a diameter somewhat greater than that of the sun, but is of low density, so that its mass is less than half that of the sun, while the dark star is a very little smaller than the sun and has about a quarter of its mass. The distance between the two stars, dark and bright, is 3,200,000 miles. [Fig. 129], which is drawn to scale, shows the relative positions and sizes of these stars as well as the orbits in which they move.
The mere fact already noted that close binary systems exist in considerable numbers is sufficient to make it probable that a certain proportion of these stars would have their orbit planes turned so nearly edgewise toward the earth as to produce eclipses, and corresponding to this probability there are already known no less than 15 stars of the Algol type of eclipse variables, and only a beginning has been made in the search for them.
Fig. 131.—The light curve of β Lyræ.
206. Variables of the β Lyræ type.—In addition to these there is a certain further number of binary variables in which both components are bright and where the variation of brightness follows a very different course. Capella would be such a variable if its orbit plane were directed exactly toward the earth, and the fact that its light is not variable shows conclusively that such is not the position of the orbit. [Fig. 131] represents the light curve of one of the best-known variable systems of this second type, that of β Lyræ, whose period is 12 days 21.8 hours, and the student should read from the curve the magnitude of the star for different times during this interval. According to Myers, this light curve and the spectroscopic observations of the star point to the existence of a binary star of very remarkable character, such as is shown, together with its orbit and a scale of miles, in [Fig. 132]. Note the tide which each of these stars raises in the other, thus changing their shapes from spheres into ellipsoids. The astonishing dimensions of these stars are in part compensated by their very low density, which is less than that of air, so that their masses are respectively only 10 times and 21 times that of the sun! But these dimensions and masses perhaps require confirmation, since they depend upon spectroscopic observations of doubtful interpretation. In [Fig. 132] what relative positions must the stars occupy in their orbit in order that their combined light should give β Lyræ its maximum brightness? What position will furnish a minimum brightness?
