Pulsation properties of ultra-massive DA white dwarf stars with ONe cores

Ultra-massive hydrogen-rich white dwarfs stars are expected to harbour oxygen/neon cores resulting from the progenitor evolution through the super asymptotic giant branch phase. Crystallization process resulting from Coulomb interactions is expected to occur, leading to the formation of a highly crystallized core. Pulsating ultra-massive white dwarfs offer an unique opportunity to infer the occurrence of crystallization in white dwarfs interiors as well as physical processes related with dense plasmas. We study the pulsation properties of ultra-massive hydrogen-rich white dwarf stars with oxygen/neon cores. We employ a new set of ultra-massive white dwarf evolutionary sequences of models with stellar masses in the range $1.10 \leq M_{\star}/M_{\sun} \leq 1.29$ computed taking into account the complete evolution of the progenitor stars and the white dwarf stage. During the white dwarf cooling phase, we consider element diffusion. When crystallization sets on in our models, we take into account latent heat release and also the expected changes in the core chemical composition due to phase separation according to a phase diagram suitable for oxygen and neon plasmas. We compute nonradial pulsation $g$ modes of our sequences of models at the ZZ Ceti phase by taking into account the presence of a solid core. We explore the impact of crystallization on their pulsation properties, in particular the structure of the period spectrum and the distribution of the period spacings. We find that the chemical rehomogeneization due to phase separation during crystallization leaves clear imprints in the pulsation spectrum, particularly strong features in the diagrams of period spacing versus periods. We also find that it is not possible, in principle, to discern whether a white dwarf has a nucleus made of carbon and oxygen or a nucleus of oxygen and neon by simply studying the spacing between periods.