Classical Cepheid Pulsation Models. I. Physical Structure

The pulsation properties and modal stability of Cepheid models are investigated in both linear and nonlinear regimes. The linear survey is based on nonadiabatic, radiative models, whereas the nonlinear one relies on full-amplitude models that include a nonlocal and time-dependent treatment of stellar convection. To account for Cepheid pulsation characteristics over a substantial portion of the region in which they are expected to be pulsationally unstable, a wide range of stellar masses (5<=M/M_solar<=11) and effective temperatures (4000<=T_e<=7000 K) was adopted. The luminosity of each model was fixed according to the mass-luminosity (ML) relations predicted by evolutionary models that either neglect or take into account a mild 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 chemical 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 stability of both fundamental and first-overtone modes.

The results of recent linear investigations are confirmed by our finding that linear observables such as periods and blue edges of the instability strip are only marginally affected by the chemical composition and that either an increase in metallicity or an increase in both the helium and metal content 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 chemical composition the width of the instability strip changes going from low- to high-mass Cepheids. (2) At fixed mass and luminosity an increase in metallicity shifts the instability strip toward lower effective temperatures. A thorough analysis of the total nonlinear work inside the instability strip points out that this effect is due to a decrease in the pulsation destabilization caused by the H ionization region. Therefore, the current theoretical scenario suggests that, at fixed period, metal-poor pulsators are brighter than metal-rich pulsators. (3) The dynamical structure of full-amplitude, 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 fundamental and first-overtone pulsators located close to the blue and the red edges of the instability strip are discussed by taking into account the changes of the convective quantities across the convectively unstable region. As expected, we find that the main effect of convection on the limit cycle behavior is either to reduce the local radiative driving of the destabilizing regions, thus reducing the final amplitudes, or to damp the oscillations toward lower effective temperatures. We also find that the limiting amplitude behavior of high-mass, high-amplitude fundamental pulsators, and in particular the appearance of secondary features along their light and velocity curves, is tightly connected with the convection/pulsation interaction.

By comparing the convective velocity perturbations close to the surface layers 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 well with observational data. However, the time behavior of the convective velocity in blue models and the strong decrease of this velocity predicted at low optical depths out of the maximum compression phases are presently not confirmed by observations. Both theoretical and observational shortcomings that could explain such a discrepancy are briefly discussed.

The comparison between the linear periods currently adopted in the literature and the nonlinear periods obtained in this investigation shows a very good agreement in the mass range from 5 to 9 M_solar, whereas at 11 M_solar we find that linear, nonadiabatic, convective periods are systematically shorter than the nonlinear ones. Finally, the drawbacks of adopting linear observables for constraining the actual properties of Cepheids are discussed.