| Abstract
| - Aims. The determination of the location of the theoretical ZZ Ceti instability strip in the log g − Teff diagram has remained a challenge over the years due to the lack of a suitable treatment for convection in these stars. For the first time, a full nonadiabatic approach including time-dependent convection is applied to ZZ Ceti pulsators, and we provide the appropriate details related to the inner workings of the driving mechanism. Methods. We used the nonadiabatic pulsation code MAD with a representative evolutionary sequence of a 0.6 M⊙ DA white dwarf. This sequence is made of state-of-the-art models that include a detailed modeling of the feedback of convection on the atmospheric structure. The assumed convective efficiency in these models is the so-called ML2/ α = 1.0 version. We also carried out, for comparison purposes, nonadiabatic computations within the frozen convection approximation, as well as calculations based on models with standard grey atmospheres. Results. We find that pulsational driving in ZZ Ceti stars is concentrated at the base of the superficial H convection zone, but at depths, near the blue edge of the instability strip, somewhat larger than those obtained with the frozen convection approach. Despite the fact that this approach is formally invalid in such stars, particularly near the blue edge of the instability strip, the predicted boundaries are not dramatically different in both cases. The revised blue edge for a 0.6 M⊙ model is found to be around Teff = 11 970 K, some 240 K hotter than the value predicted within the frozen convection approximation, in rather good agreement with the empirical value. On the other hand, our predicted red edge temperature for the same stellar mass is only about 5600 K (80 K hotter than with the frozen convection approach), much lower than the observed value. Conclusions. We correctly understand the development of pulsational instabilities of a white dwarf as it cools at the blue edge of the ZZ Ceti instability strip. Our current implementation of time-dependent convection however still lacks important ingredients to fully account for the observed red edge of the strip. We will explore a number of possibilities in the future papers of this series.
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