Variable Stars

We may hope ultimately to learn much as to the physical state of the stars from these two effects; but, unfortunately, they are only just within our range of detection, and it is difficult to obtain accurate measurements of their amount. Meanwhile, an examination of the light-curve during the eclipses teaches us much about the dimensions of the system. The method of analys ing the light-curves was developed by H. N. Russell and H. Shapley; for an example of the results obtainable see ALGOL. As a rule the fainter component is found to have the larger diameter although it has the smaller mass; i.e., the companion is one of the giant diffuse stars of fairly low density and surface tempera ture. The eclipses are usually partial, but are in a few stars total or annular. The number of eclipsing variables known at present is about 200.

Cepheid Variables.

Like the preceding class the Cepheid variables have short periods seldom exceeding 20 days, but the cause of the variation is entirely different. A very significant fact is that the colour of the light (or the spectrum) is different at maximum and minimum light, showing that the star undergoes an actual physical change. The surface temperature is much higher at maximum than at minimum, and, in fact, the changes of brightness may be ascribed to the changes of temperature. It is probable that the Cepheid variable is a pulsating star—a globe which swells and contracts with a regular period. Leaving aside the question as to how the star comes to be in this oscillating state, the pulsation theory agrees with the main phenomena. The alternate compression and rarefaction naturally produces the changes of temperature; moreover, the approach and recession, as the part of the surface presented towards us heaves up and down, is observed and measured spectroscopically. The most striking confirmation is the agreement of the theoretical period of such a pulsation with the observed period. The natural free period of a pulsation of a spherical mass of gas should vary approxi mately as the inverse square root of the density, and the observa tions show that the Cepheids closely follow this law; moreover, the absolute value of the period can be calculated (with a small margin of uncertainty due to our ignorance of the chemical con stitution of the star's interior) and the observed period is found to agree. On the other hand, no satisfactory theoretical explana tion has . yet been given of the phase-relation between the velocity-curve and light-curve. The mathematical theory of a

pulsating star seems to show that maximum brightness must occur at the moment of greatest compression, whereas in all the more typical Cepheids it is found to occur a quarter-period later.

The study of Cepheid variables is likely to lead to results of the greatest importance, since they give the opportunity of observ ing stellar matter in motion, thereby extending the information obtainable from the ordinary static stars. They are important also for another reason. Practically all our knowledge of the distances and dimensions of the more remote objects of the sidereal universes has grown up from a study of Cepheids. In 1912 it was noted by Miss Leavitt that, when the periods and apparent magnitudes of the variables in the Lesser Magellanic Cloud were plotted as abscissae and ordinates, the points lay on a smooth curve. Since the stars in the Cloud must all be at approximately the same distance from us, this indicates that the absolute brightness is a definite function of the period. H. Shap ley subsequently found the same uniformity in a number of globular clusters. The same period-magnitude curve is repeated in each cluster, except that the curve is displaced as a whole towards fainter or brighter (apparent) magnitude, according as the cluster is remote or near. It follows that Cepheids of the same period have the same absolute luminosity, and presumably are alike in all respects. The absolute brightness being identical, the apparent brightness indicates the distance; e.g., if the apparent magnitude of the Cepheids of 5-day period in a particular globular cluster is 13 we know at once that the cluster is roo times as distant as a Cepheid of apparent magnitude 3; if the 5-day Cepheids observed in a spiral nebula have apparent magnitude 18, the nebula is ten times more remote than the cluster. Thus the general structure of the universe can be plotted out to scale. The scale is made absolute by a study of the brighter and nearer Cepheids which are not beyond the range of ordinary methods of distance determination. The only caution required in using these variables as standard lights for gauging distance is that we must have evidence that their light has not been dimmed by passing through absorbing matter. This point has been carefully studied, and it is believed that (except in particular localities) inter stellar space is practically transparent ; but the evidence is, per haps, not beyond reproach.