SIMBAD references

HR 7308 is the classical Cepheid with the shortest known period. The oscillation occurs in the second (or a higher) radial overtone and the amplitude of the oscillation varies almost periodically with a modulation period of about 800 oscillation periods. A beating between two closely spaced oscillation modes as an explanation for the variable amplitude has been ruled out on the basis of a theory linear in the amplitudes of the modes. We reconsider the beating hypothesis in a nonlinear framework. It is shown that a resonance between a radial mode that is linearly unstable and a low-degree, low-order p-mode that is linearly stable can produce periodic amplitude variations of the radial mode such as observed on HR 7308. The resonance can also lead to situations for which the periodic oscillation of the amplitude of the radial mode is damped. A possible connection with the Blazhko effect in RR Lyrae stars is discussed.