The Theory of Cepheid Variability

Abstract

It is now just 50 years since Eddington's first paper on Cepheid pulsation (1). He recognized immediately the central problem of the maintenance of pulsation and proceeded to develop (2) the linear theory leading to the period-density relation. He continued to devote considerable attention (3) to understanding the physical mechanisms responsible for exciting pulsation and recognized all of the essential aspects of that problem.

His point of view on pulsation was expressed in Stars and Atoms: 'to be able to see the machinery of a star throbbing with activity is most instructive for the development of our knowledge'. This view constitutes the theme of the work I will discuss here on the application of non-linear methods to the Cepheid variables.

The discussion will be divided into three main parts, of which the first will be devoted to the methods of investigation. The second part will be aimed at understanding the physical causes of pulsation and the mechanism of amplitude limitation. The third part will discuss the various results of pulsation calculations. The objective of this part will be to find ways by which all the significant physical parameters (mass M, mean effective temperature T_e05, mean luminosity L₀₅, and helium mass fraction Y) that control pulsation can be deduced from observation of the variable star.

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