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 (P 2 /P 0 5 0.5) between the fundamental mode of pulsation and the second overtone occurs with a period P 0 of 210 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 P 1 /P 0 2 0.7, as well as those with P 2 /P 1 2 0.8, impose weak constraints, at best, on the MLRs. Subject headings: Cepheids—Magellanic Clouds— stars: oscillations One of the exciting by-products of the search for dark matter has been the collection of a large number of good quality data on tens of thousands of stars in the Magellanic Clouds (MCs). In particular, hundreds of Cepheids have been observed and Fourier analyzed in the last year (Beaulieu 1995; Beaulieu et al. 1995, 1996; Alcock et al. 1995; Welch et al. 1995). These efforts greatly increase the number and especially the diversity of known Cepheids. Indeed, it has been known for some time that the Magellanic Clouds, LMC and SMC, are observed to have metallicities Z 2 0.01 and 0.005, respectively (Luck & Lambert 1992), and are thus metal poor compared with the Galaxy, for which X 2 0.70, Z 2 0.02. Both MCs are expected to have a slightly larger hydrogen content. Observations indicate that the Galaxy as well as the MCs have a substantial dispersion in composition, although the latter seems to be somewhat smaller in the SMC. The time seems ripe to examine whether observations, stellar pulsation, and stellar evolution can provide a self-consistent picture of the Cepheids. It is now well known that the so-called Hertzsprung progression of the bump in the Cepheid light curves is related to a resonance (P20 [ P 2 /P 0 5 0.5) between the self-excited fundamental mode of pulsation and the second overtone. In addition to such asteroseismological constraints, which are based on observed periods and inferred resonances, there also exist similar constraints based on observed period ratios, as in the case of beat Cepheids. The pulsation calculations have to be consistent with these observed constraints, on the one hand, and with the mass-luminosity relations (MLRs) that arise from stellar evolutionary tracks, on the other. Moskalik, Buchler, & Marom (1992, hereafter MBM; see also Kanbur & Simon 1993) performed a survey of pulsation models with the new Livermore opacities (Iglesias, Rogers, & Wilson 1992) and found that stellar pulsation calculations, stellar evolution calculations, and observations of Galactic Cepheids are basically in agreement. In retrospect, these studies were very limited in their stellar parameter ranges because, at the time, nobody expected the LMC and SMC Cepheids to be so different from their Galactic siblings. In this Letter we examine the constraints that the new MC observations impose on Cepheid models. Our hydrostatic models and their linear stability analyses are computed with a relatively coarse 200 point mesh. We have checked that this mesh gives a reasonable resolution for the eigenvectors and for the work integrands (except in the vicinity of the sharp partial hydrogen ionization front). Models have been computed for the compositions X 5 0.70 and 0.80, each with Z 5 0.004, 0.01, 0.02, and 0.03 for which OPAL (Iglesias et al. 1992) and Alexander & Ferguson (1994) opacities are available. Convection has been ignored. The constraints that we have to deal with here all involve finding, by iteration, the M and L that are compatible with a given period, period ratio, and composition. The effective temperature, of course, also enters the picture. In order to accommodate the finite width of the instability strip, we need to allow for a range of T eff, which we define in terms of the distance DT from the linear blue edges (for the corresponding M and L). In order to reduce the model dependence of our results, we deliberately refrain from using T eff directly (its definition is somewhat sensitive to the treatment of radiative transport in the surface layer). Furthermore, its observational uncertainty is large. Let us first examine the constraints imposed by the 2;1 ‘‘bump’’ resonance (P 20 5 0.5) near P 0 5 10 days. We are faced with several problems when we try to quantify the constraints. First, the instability strip has a finite width, and the pulsators that are in exact resonance are therefore spread over a range in T eff, and thus also in P 0 . In the Galaxy, this 1 [email protected]. THE ASTROPHYSICAL JOURNAL, 462 :L83–L86, 1996 May 10 q 1996. The American Astronomical Society. All rights reserved. Printed in U.S.A.