Classical Cepheid pulsation models. I. Physical structure

The pulsation properties and modal stability of Cepheid models are investig ated in both linear and nonlinear regimes. The linear survey is based on no nadiabatic, radiative models, whereas the nonlinear one relies on full-ampl itude models that include a nonlocal and time-dependent treatment of stella r convection. To account for Cepheid pulsation characteristics over a subst antial portion of the region in which they are expected to be pulsationally unstable, a wide range of stellar masses (5 less than or equal to M/M-circ le dot less than or equal to 11) and effective temperatures (4000 less than or equal to T-e less than or equal to 7000 K) was adopted. The luminosity of each model was fixed according to the mass-luminosity (ML) relations pre dicted by evolutionary models that either neglect or take into account a mi ld convective core overshooting. Moreover, in order to estimate the effects of the helium and metal content on the limiting amplitude behavior of both Magellanic Clouds and Galactic Cepheids we adopted three different chemica l compositions, namely, Y = 0.25, Z = 0.004; Y = 0.25, Z = 0.008; and Y = 0 .28, Z = 0.02. For each set of input parameters we investigated the modal s tability of both fundamental and first-overtone modes. The results of recent linear investigations are confirmed by our finding th at linear observables such as periods and blue edges of the instability str ip are only marginally affected by the chemical composition and that either an increase in metallicity or an increase in both the helium and metal con tent causes a mild shift of these edges toward lower effective temperatures . The approach to the nonlinear limit cycle stability, the physical structure , and the mechanisms that govern the pulsation instability are described in detail. The main results of this analysis are as follows: (1) At fixed che mical composition the width of the instability strip changes going from low - to high-mass Cepheids. (2) At fixed mass and luminosity an increase in me tallicity shifts the instability strip toward lower effective temperatures. A thorough analysis of the total nonlinear work inside the instability str ip points out that this effect is due to a decrease in the pulsation destab ilization caused by the H ionization region. Therefore, the current theoret ical scenario suggests that, at fixed period, metal-poor pulsators are brig hter than metal-rich pulsators. (3) The dynamical structure of full-amplitu de, first-overtone models supports the evidence that their nonlinear limit cycle behavior has been properly identified. The variations over a full pulsation cycle of the convective structure of f undamental and first-overtone pulsators located close to the blue and the r ed edges of the instability strip are discussed by taking into account the changes of the convective quantities across the convectively unstable regio n. As expected, we find that the main effect of convection on the limit cyc le behavior is either to reduce the local radiative driving of the destabil izing regions, thus reducing the final amplitudes, or to damp the oscillati ons toward lower effective temperatures. We also find that the limiting amp litude behavior of high-mass, high-amplitude fundamental pulsators, and in particular the appearance of secondary features along their light and veloc ity curves, is tightly connected with the convection/pulsation interaction. By comparing the convective velocity perturbations close to the surface lay ers with the turbulent velocities obtained by spectroscopic measurements we find that toward lower effective temperatures both the absolute values of the convective velocity and its variation over the cycle agree reasonably w ell with observational data. However, the time behavior of the convective v elocity in blue models and the strong decrease of this velocity predicted a t low optical depths out of the maximum compression phases are presently no t confirmed by observations. Both theoretical and observational shortcoming s that could explain such a discrepancy are briefly discussed. The comparison between the linear periods currently adopted in the literatu re and the nonlinear periods obtained in this investigation shows a very go od agreement in the mass range from 5 to 9 M-circle dot, whereas at 11 M-ci rcle dot we find that linear, nonadiabatic, convective periods are systemat ically shorter than the nonlinear ones. Finally, the drawbacks of adopting linear observables for constraining the actual properties of Cepheids are d iscussed.