  Asteroseismology of white dwarf (WD) stars is a powerful tool that allows to
reveal the hidden chemical structure of WD and infer details about their
evolution by comparing the observed periods with those obtained from stellar
models. A recent asteroseismological study has reproduced the period spectrum
of the helium rich pulsating WD KIC 08626021 with an unprecedented precision.
The chemical structure derived from that analysis is notably different from
that expected for a WD according to currently accepted formation channels, thus
posing a challenge to the theory of stellar evolution. We explore the relevant
micro- and macro-physics processes acting during the formation and evolution of
KIC 08626021 that could lead to a chemical structure similar to that found
through asteroseismology. We quantify to which extent is necessary to modify
the physical processes that shapes the chemical structure, in order to
reproduce the most important features of the asteroseismic model. We model the
previous evolution of KIC 08626021 by exploring specific changes in the
12C+alpha reaction rate, screening processes, microscopic diffusion, as well as
convective boundary mixing during core-He burning. We find that, in order to
reproduce the core chemical profile derived for KIC 0862602, the 12C+alpha
nuclear reaction rate has to be increased by a factor of $\sim$ 10 during the
helium-core burning, and reduced by a factor of $\sim$ 1000 during the
following helium-shell burning, as compared with the standard predictions for
this rate. In addition, the main chemical structures derived for KIC 0862602
cannot be reconciled with our present knowledge of white dwarf formation. We
find that within our current understanding of white dwarf formation and
evolution, it is difficult to reproduce the most important
asteroseismologically-derived features of the chemical structure of KIC
08626021.
