2007ApJ...660..723B

The mere location of a beat Cepheid model in a period ratio versus period diagram (Petersen diagram) puts very tight constraints on its metallicity Z. The beat Cepheid Petersen diagrams are revisited with linear nonadiabatic turbulent convective models, and their accuracy as a probe for stellar metallicity is evaluated. They are shown to be largely independent of the helium content Y, and they are also only weakly dependent on the mass-luminosity relation that is used in their construction. However, they are found to show sensitivity to the relative abundances of the elements that are lumped into the metallicity parameter Z. Rotation is estimated to have but a small effect on the ``pulsation metallicities.'' A composite Petersen diagram is presented that allows one to read off upper and lower limits on the metallicity Z from the measured period P₀ and period ratio P₁₀.