On the second-overtone stability among Small Magellanic Cloud Cepheids

We present a new set of Cepheid, full amplitude, non-linear, convective mod els which are pulsationally unstable in the second overtone (SO). Hydrodyna mical models were constructed by adopting a chemical composition typical of Cepheids in the Small Magellanic Cloud (SMC) and for stellar masses rangin g from 3.25 to 4 M-circle dot. Predicted phi (21) Fourier parameters agree, within current uncertainties, with empirical data for pure first- and seco nd-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, pr edicted I-band amplitudes are systematically larger than the observed ones in the short-period range, but attain values that are closer to the empiric al ones for log P-SO greater than or equal to -0.12 and log P-FO greater th an or equal to 0.1. We also find, in agreement with empirical evidence, tha t the region within which both second and first overtones attain a stable l imit cycle widens when moving towards lower luminosities. Moreover, predict ed P-SO/P-FO and P-FO/P-F period ratios agree quite well with empirical per iod ratios for FO/SO and fundamental/FO double-mode SMC Cepheids. Interestingly enough, current models support the evidence that pure SO Ceph eids and SO components in FO/SO Cepheids are good distance indicators. In f act, 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 component s in FO/SO Cepheids, and indeed we find DM = 19.16 +/- 0.19 mag. Current di stance estimates do not account for, within current uncertainties on photom etry and reddening, the so-called short distance scale.