Three-mode resonances in double-mode cepheids

The three-wave resonances are studied for models with helium enriched inhomogeneous outer layers. The resonance among the fundamental mode, the first overtone, and the third overtone is studied for several models with Ysub(S) = 0.5 and Zsub(S)/Xsub(S) = 0.02/0.70. The model having the evolutionary mass cannot give both the observed period ratio and a sufficiently strong resonance. Masses less than the evolutionary mass or with more enriched helium abundance for the outermost layers are needed to explain the observation. (author)