Second overtone pulsators among delta Scuti stars

We investigate the modal stability of stellar models at masses and luminosity levels corresponding to post-main-sequence luminous delta Scuti pulsators. The envelope models have been computed at fixed mass value (M/M. = 2.0), luminosity level [log (L/L.) = 1.7], and chemical composition (Y = 0.28, Z = 0.02). According to a nonlinear approach to radial oscillations, the present investigation for the first time predicts the occurrence of stable second overtone pulsators. More generally, we found that when moving inside the instability strip from lower to higher effective temperatures, the models show a stable limit cycle in three different pulsation modes: fundamental and first and second overtones. The shapes of both light and velocity curves are presented and discussed, providing a useful tool for the identification of second overtone pulsators among the known groups of radially pulsating stars. Comparison with observations shows that our nonlinear, nonlocal, and time-dependent convective models provide light curves in agreement with observed values, suggesting that second overtone pulsators have already been observed, though misclassified as fundamental pulsators. In a limited region of the instability strip we also found some models presenting mixed-mode features, i.e., radial pulsators that show a stable limit cycle in more than one pulsational mode. The period ratios of mixed-mode pulsators obtained by perturbing the first and the second overtone radial eigenfunctions are in agreement with observed values. This result is a crucial point for understanding the pulsation properties of delta Scuti stars, since it provides sound evidence that these variables during their evolution off the main sequence are pure or mixed-mode radial pulsators. Finally, the physical structure and the dynamical properties of second overtone pulsators are discussed in detail. The role played by the nodal lines in the destabilization of second overtone pulsators is also pointed out.