On the second-overtone stability among Small Magellanic Cloud Cepheids

We present a new set of Cepheid, full amplitude, non-linear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical of Cepheids in the Small Magellanic Cloud (SMC) and for stellar masses ranging from 3.25 to 4 M_⊙. Predicted φ ₂₁ Fourier parameters agree, within current uncertainties, with empirical data for pure first- and second-overtone variables as well as for first-/second-overtone (FO/SO) double-mode Cepheids collected by Udalski et al. in the SMC. On the other hand, predicted I -band amplitudes are systematically larger than the observed ones in the short-period range, but attain values that are closer to the empirical ones for log  P _SO≥−0.12 and log  P _FO≥0.1 . We also find, in agreement with empirical evidence, that the region within which both second and first overtones attain a stable limit cycle widens when moving towards lower luminosities. Moreover, predicted P _SO/ P _FO and P _FO/ P _F period ratios agree quite well with empirical period ratios for FO/SO and fundamental/FO double-mode SMC Cepheids.
Interestingly enough, current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators. In fact, we find that the fit of the predicted period–luminosity–colour ( V , V – I ) relation to empirical SMC data supplies a distance modulus ( DM ) of 19.11±0.08 mag . The same outcome applies to pure FO Cepheids and FO components in FO/SO Cepheids, and indeed we find DM =19.16±0.19 mag . Current distance estimates do not account for, within current uncertainties on photometry and reddening, the so-called short distance scale.