With the advent of new radiative opacities, the gross discrepancies in period ratio between observed stars and theoretical models have been eliminated in both the “beat” and “bump” Cepheid regimes (Moskalik, et al. 1992; Kanbur & Simon 1994). This paves the way for detailed modeling of the beat and bump stars.

We begin here by summarizing one such effort, the full description of which is given by Simon & Kanbur (1994). In this study, the slope of the evolutionary luminosity-mass relation is taken to be dlogL/dlogM = 4.0 (Stothers and Chin 1991) and the intercept determined by forcing models which follow this slope to also conform with the bump Cepheid resonance condition P2/P0 = 0.50 at P0 = 10d (Simon & Schmidt 1976; Buchler =et al. 1990). We then model separately each of the dozen known galactic beat Cepheids, subject to the just mentioned evolutionary constraint imposed by the 10-day resonance. We find masses and luminosities, ranging from M = 4Mʘ, log L = 3.0 at P0 = 3d to M = 6Mʘ, log L = 3.5 at P0 = 1Od. Furthermore, a range of metallicity, 0.01<Z<0.02, is required among the beat stars, whose period ratios, P1/P0,are predicted to decrease as the metallicity rises. This trend has been observed (Andrievsky et al. 1993). However, “standard” evolutionary tracks for Z = 0.02 [e.g., the Geneva calculations (Schaller, et al. 1992) or the Padua calculations (Bressan, et al. 1993)] cannot produce Cepheids with parameters as given above - first because the models are somewhat underluminous at given mass, and second because the calculated blue loops do not reach the instability strip for M = 7Mʘ. On the other hand, the models described by El Eid (1994) do penetrate the strip at masses as low as 4 or 5 Mʘ, but display a luminosity-to-mass ratio considerably too small to satisfy the resonance condition for bump Cepheids. Possible resolutions to these problems include a deep Fe convection zone whose effect would be to lower the period ratios (Cox 1993), and/or an opacity increase near 1 × 106K, which could extend the blue loops (Stothers & Chin 1994). Each of these schemes require more research.