  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.
