The Cepheid mode problem

The modal behavior of RR Lyrae stars and low mass Cepheids has been investigated using a nonlinear relaxation technique and stability analysis. The advantages of this type of numerical approach in investigations of preferred mode of pulsation are discussed. The results obtained for both classes of variable stars are quite similar: first harmonic pulsation toward the blue, fundamental pulsation toward the red, and mixed-mode behavior at the extreme red edge of the instability strip. In addition, stars near the center of the strip can pulsate in either the fundamental or the first harmonic mode. Possible implications for observational results, including the Oosterhoff dichotomy of globular clusters and the beat Cepheids, are discussed.