New evolutionary models for massive ZZ Ceti stars. II. The effects of crystallization on their pulsational properties

We present in this work new pulsational calculations for improved carbon-oxygen DA white dwarf models suitable for the study of massive ZZ Ceti stars. The background models employed in this study, presented in detail in a recent paper by Althaus et al. (2003), are the result of the complete evolution of massive white dwarf progenitors from the zero-age main sequence through the Asymptotic Giant Branch (AGB) and mass loss phases to the white dwarf regime. Abundance changes are accounted for by means of a full coupling between nuclear evolution and time-dependent mixing due to convection, salt fingers, and diffusive overshoot. In addition, time-dependent element diffusion for multicomponent gases has been considered during the white dwarf evolution. Crystallization and chemical rehomogenization due to phase separation upon crystallization in the core of our models have been fully considered. The effects of crystallization on the period spectrum of these massive white dwarf models are assessed by means of a detailed pulsational analysis. We find that the theoretical pulsation spectrum is strongly modified when crystallization is considered, in particular concerning the mode trapping properties of the equilibrium models. We also discuss at some length the implications of our study for BPM 37093, the most massive ZZ Ceti star presently known. We find that if BPM 37093 has a stellar mass of $\approx 1.00$ \msun its observed spectrum could bear the signature of overshoot episodes during the helium core burning.