CHAPTER VIII 
VARIABLE STARS 
Cepheid Variables 
123. Although variable stars of the Cepheid type show a periodic 
change of radial velocity it is improbable that they are binary systems. 
The theory which now seems most plausible attributes their variation to 
the pulsation of a single star; and accordingly the varying radial velocity 
measures the approach and recession of the surface presented towards 
the observer as the star swells and contracts. If this explanation is correct 
we have an opportunity of extending the study of the internal state of a 
star from static to disturbed conditions. 
The leading facts about these variables ascertained by observational 
study are as follows— 
About 170 galactic Cepheids are known with periods ranging from a 
few hours to about 50 days; so-called “orbits” have been determined for 
20 of these from measurements of radial velocity. In addition large 
numbers of Cepheids have been found in some globular clusters; among 
these periods less than 12 hours are especially prevalent. Cepheids have 
also been found in the Andromeda nebula. 
Relatively few periods are between 0-7 and 3 days, so that the Cepheids 
may be subdivided into two groups with periods above and below this gap. 
The light-range rarely exceeds l m -2 visual; the photographic range is 
greater than the visual. The spectral type changes during the period, 
corresponding to a higher temperature at maximum than at minimum. 
The light-curve and the velocity-curve are closely similar*; the 
correspondence is the more marked because both curves are usually un- 
symmetrical. The light-variation is marked by a rapid rise to maximum 
and a comparatively slow decline often arrested by a definite hump in 
the downward course of the curvef. This asymmetry is reproduced in 
the velocity-curve; if interpreted as orbital motion it indicates that the 
orbit is eccentric with periastron at the point farthest from the observer. 
There are occasional exceptions to this rule. 
The relation of phase between light and velocity is very definite, 
maximum light occurring simultaneously with—or perhaps slightly before 
* When plotted according to the usual conventions the one is a mirror image of 
the other. 
f A progressive relation between the period and the form of the light-curve has 
been found by E. Hertzsprung. For periods 2-3 days and again for periods 10-12 
days the curve is fairly symmetrical {Bull. Astr. Inst. Netherlands, No. 96).