8.1: Introduction

That some stars vary in brightness has been known from time immemorial. That this variation is the result of intrinsic changes in the star itself has been known for less than 100 years and the causes of those variations have been understood for less than 30 years. It is not a simple matter to distinguish the light variations resulting from eclipses by a companion from those caused by physical changes in the star itself. However, for the cepheid variables (named for the prototype example δ Cepheii), the treatment of the light variations as if they resulted from eclipses by a companion leads to some absurd results. If this were the case, the orbit of the companion would have to be highly elliptical with the semimajor axes pointed toward the earth. This somewhat Ptolemaic view suggests that the binary hypothesis is incorrect but is far from conclusive. Further analysis shows that the sum of the radii for the two hypothetical stars would exceed their separation. Such a situation is even less likely. However, the coup degrace is administered to the binary hypothesis when one considers the radial velocity curve produced by the star throughout a period of light variation. Here one finds that maximum radial velocity occurs near minimum light, which is nearly the reverse of that required by the binary hypothesis. Thus, one is left with almost no other option than to conclude that this class of stars is intrinsically varying.

While a number of other types of stars were seen to exhibit similar behavior, considerable interest was generated by the Cepheid variables themselves when it was found that a relationship exists between the period of variability and the absolute luminosity at maximum brightness. This period-luminosity relationship was found to hold true, in one form or another, for the intrinsic variables. While it is true that the RR Lyrae stars have basically the same absolute magnitude regardless of their period, this can be viewed as a period luminosity relation since the very determination of the RR Lyrae nature of a star establishes its luminosity. Thus, variable stars could be used as "standard candles" for the purposes of distance determination. Although it is not necessary to understand the physical processes giving rise to the variation of light in these stars to use them to determine distances to associated objects, the lack of such understanding may result in large errors of interpretation. Such was the case with the Cepheid variables, and the result was an error in the distances to galaxies of about a factor of 2. Although this error was uncovered before the nature of stellar pulsation was understood, there can be little doubt that such an understanding would have signaled the danger much earlier and possibly prevented much confusion.

The detailed nature of the origin of pulsation for the intrinsic variables was not understood until the computational power existed for the accurate construction of model stars. Then, for the two most important classes of intrinsic variables, it was found that the mechanism producing the light variations resulted from oscillations in the ionization equilibrium in the outer layers of the star and had nothing to do with oscillations in the energy generation process itself. However, in order to construct these models, it is necessary to have some idea about the nature of the stars themselves. Here their variations provide the clues required. From the stability of the periods of these pulsating stars, it is clear that the oscillations are resonant oscillations, and their periods will tell us much about the stars involved. We have already established the conceptual foundation for this determination in the Virial theorem.