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Ultra-massive hydrogen-rich (DA) white dwarfs (WD) are expected to have asubstantial portion of their cores in a crystalline state at the effectivetemperatures characterizing the ZZ Ceti instability strip, as a result ofCoulomb interactions. Asteroseismological analyses of these WDs can providevaluable information related to the crystallization process, the core chemicalcomposition and the evolutionary origin of these stars. We present a thoroughasteroseismological analysis of the ultra-massive ZZ Ceti star BPM~37093, whichexhibits a rich period spectrum, on the basis of a complete set of fullyevolutionary models that represent ultra-massive oxygen/neon(ONe)-core DA WDstars harbouring a range of hydrogen (H) envelope thicknesses. We also carryout preliminary asteroseismological inferences on two other ultra-massive ZZCeti stars that exhibit fewer periods, GD~518, and SDSS~J0840+5222. We found amean period spacing of $\Delta \Pi \sim 17$ s in the data of BPM~37093,associated to $\ell= 2$ modes. We found asteroseismological models for thethree objects under analysis, two of them (BPM~37093 and GD~518) characterizedby canonical (thick) H envelopes, and the third one (SDSS~J0840+5222) with athinner H envelope. We also derive asteroseismological distances which aresomewhat different to the astrometric measurements of {\it Gaia} for thesestars. Asteroseismological analyses like the one presented in this paper couldlead to a more complete knowledge of the processes occurring duringcrystallization inside WDs. Also, they could make it possible to deduce thecore chemical composition of ultra-massive WDs, and in this way, to infer theirevolutionary origin, i.e., if the star has a ONe core and then is the result ofsingle-star evolution, or if it harbour a carbon/oxygen (CO) core and is theproduct of a merger of the two components of a binary system.

Asteroseismological analysis of the ultra-massive ZZ Ceti stars BPM~37093, GD~518, and SDSS~J0840+5222