A simple model for Cepheid variability.

A simple, mathematically tractable one-zone model of Cepheid variability is constructed from the well known nonadiabatic equations governing the process. The central feature of this model is that the equation of motion is discontinuous; e. g. the equation of the compression phase differs from that of the expansion phase. (The existence of this discontinuity was deduced from astronomical observations on -Cephei.) The difference between the compression and expansion phases is not qualitative but merely quantitative and, mathematically speaking, it may be arbitrarily small; nevertheless, it harbors the mathematical mechanism for the limit cycle. Necessary conditions for the existence of the limit cycle are derived, and the entire theory is applied to (5-Cephei. The predicted motion of the model preserves qualitatively and quantitatively that observed on 8 -Cephei. Key words: Cepheids - limit cycles