On the second overtone stability among SMC Cepheids

We present a new set of Cepheid, full amplitude, nonlinear, convective models which are pulsationally unstable in the second overtone (SO). Hydrodynamical models were constructed by adopting a chemical composition typical for Cepheids in the Small Magellanic Cloud (SMC) and stellar masses ranging from 3.25 to 4 solar masses. Predicted phi{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. (1999a,b) in the SMC. On the other hand, predicted I band amplitudes are systematically larger than the observed ones in the short period range. 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 toward 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 F/FO double-mode SMC Cepheids. Finnaly, current models support the evidence that pure SO Cepheids and SO components in FO/SO Cepheids are good distance indicators.