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Ultra-massive white dwarfs are relevant for their role as type Ia Supernovaprogenitors, the occurrence of physical processes in the asymptoticgiant-branch phase, the existence of high-field magnetic white dwarfs, and theoccurrence of double white dwarf mergers. Some hydrogen-rich ultra-massivewhite dwarfs are pulsating stars, and as such, they offer the possibility ofstudying their interiors through asteroseismology. On the other hand, pulsatinghelium-rich ultra-massive white dwarfs could be even more attractive objectsfor asteroseismology if they were found, as they should be hotter and lesscrystallized than pulsating hydrogen-rich white dwarfs, something that wouldpave the way for probing their deep interiors. We explore the pulsationalproperties of ultra-massive helium-rich white dwarfs with carbon-oxygen andoxygen-neon cores resulting from single stellar evolution. Our goal is toprovide a theoretical basis that could eventually help to discern the corecomposition of ultra-massive white dwarfs and the scenario of their formationthrough asteroseismology, anticipating the possible future detection ofpulsations in this type of stars. We find that, given that the white dwarfmodels coming from the three scenarios considered are characterized by distinctcore chemical profiles, their pulsation properties are also different, thusleading to distinctive signatures in the period-spacing and mode-trappingproperties. Our results indicate that, in case of an eventual detection ofpulsating ultra-massive helium-rich white dwarfs, it would be possible toderive valuable information encrypted in the core of these stars in connectionwith the origin of such exotic objects. The detection of pulsations in thesestars has many chances to be achieved soon through observations collected withongoing space missions.

The pulsational properties of ultra-massive DB white dwarfs with carbon-oxygen cores coming from single-star evolution