Ultra-massive white dwarfs are powerful tools to study various physical processes in the Asymptotic Giant Branch (AGB), type Ia supernova explosions and the theory of crystallization through white dwarf asteroseismology. Despite the interest in these white dwarfs, there are few evolutionary studies in the literature devoted to them. Here, we present new ultra-massive white dwarf evolutionary sequences that constitute an improvement over previous ones. In these new sequences, we take into account for the first time the process of phase separation expected during the crystallization stage of these white dwarfs, by relying on the most up-to-date phase diagram of dense oxygen/neon mixtures. Realistic chemical profiles resulting from the full computation of progenitor evolution during the semidegenerate carbon burning along the super-AGB phase are also considered in our sequences. Outer boundary conditions for our evolving models are provided by detailed non-gray white dwarf model atmospheres for hydrogen and helium composition. We assessed the impact of all these improvements on the evolutionary properties of ultra-massive white dwarfs, providing up-dated evolutionary sequences for these stars. We conclude that crystallization is expected to affect the majority of the massive white dwarfs observed with effective temperatures below $40,000, rm K$. Moreover, the calculation of the phase separation process induced by crystallization is necessary to accurately determine the cooling age and the mass-radius relation of massive white dwarfs. We also provide colors in the GAIA photometric bands for our H-rich white dwarf evolutionary sequences on the basis of new models atmospheres. Finally, these new white dwarf sequences provide a new theoretical frame to perform asteroseismological studies on the recently detected ultra-massive pulsating white dwarfs.
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