Limit-cycle behavior in one-zone convective models

We present the results of a detailed set of one-zone models that account for the coupling between pulsation and convection following the original prescriptions of Stellingwerf (1986). Motivated by the arbitrary nature of the input parameters adopted in this theoretical framework, we computed several sequences of models that cover a substantial fraction of the parameter space and a longer integration time. We also included a turbulent pressure term and found that this physical mechanism plays a crucial role in the pulsation characteristics of the models by removing the sharp discontinuities along the light and the velocity curves showed by models that do not account for turbulent pressure. Finally, we investigated the vibrational and the pulsational stability of completely convective models. We consider as the most important finding of the present work the identification of a well-defined region in the parameter space where they approach limit-cycle stability. Several numerical experiments performed by adopting different values of the adiabatic exponent and of the shell thickness indicate that the coupling between pulsation and convection is the key driving mechanism for LPVs, a finding supported by recent theoretical predictions.