The effects of a 2:1 resonance in nonlinear radial stellar pulsations

A single set of amplitude equations is derived which applies to and describes the finite-amplitude behavior of a resonant (2 omegaalpha about equal to omegabeta) pulsator, both in and out of resonance. A detailed analysis of these equations and a discussion of their relevance for stellar pulsators are presented. Given the simplicity of the formalism, its ability to describe the systematics of the observed behavior of the (singly periodic) Cepheid and RR Lyrae stars is remarkable. The formalism, in accordance with the observation of the classical Cepheids, shows a very sharp break (bifurcation) in the vicinity of the resonance. Little doubt is left that the 'bump' behavior has its origin in the 2:1 resonance between the fundamental and the second radial overtone.