Do the Magellanic Cepheids Pose a New Puzzle?

The observed Magellanic Cloud (MC) Cepheid data pose a new challenge to both stellar structure and stellar evolution. The Fourier analysis of the LMC and SMC data indicate that the 2 : 1 resonance (P2/P0 = 0.5) between the fundamental mode of pulsation and the second overtone occurs with a period P0 of ≈ 10 days, just as in our Galaxy. The implications of this resonance are difficult to reconcile with linear radiative Cepheid models computed for the low metallicity of the MC. They also require a large upward shift in the mass-luminosity relation (MLR), seemingly larger than is comfortable for evolutionary calculations. The disagreement worsens if we interpret the structure in the first overtone Fourier parameters near 3 days as the result of an alleged resonance with the fourth overtone. In contrast to earlier expectations, the beat Cepheid data with P1/P0 ≈ 0.7, as well as those with P2/P1 ≈ 0.8, impose weak constraints, at best, on the MLRs.