The thermally pulsing phase on the asymptotic giant branch (TP-AGB) is the last nuclear burning phase experienced by most of low and intermediate mass stars. During this phase, the outer chemical stratification above the C/O core of the emerging white dwarf is built up. The chemical structure resulting from progenitor evolution strongly impacts the whole pulsation spectrum exhibited by ZZ Ceti stars, which are pulsating C/O core white dwarfs located on an narrow instability strip at T eff sim 12000 K. Several physical processes occurring during progenitor evolution strongly affect the chemical structure of these stars, being those found during the TP-AGB phase ones of the most relevant for the pulsational properties of ZZ Ceti stars. We present a study of the impact of the chemical structure built up during the TP-AGB evolution on the stellar parameters inferred from asteroseismological fits of ZZ Ceti stars. Our analysis is based on a set of carbon-oxygen core white dwarf models with masses from 0.534 to 0.6463M_{odot} derived from full evolutionary computations from the ZAMS to the ZZ Ceti domain. We compute evolutionary sequences that experience different number of thermal pulses. We find that the occurrence or not of thermal pulses during AGB evolution implies an average deviation in the astero- seimological effective temperature of ZZ Ceti stars of at most 8% and of the order of < 5% in the stellar mass. For the mass of the hydrogen envelope, however, we find deviations up to 2 orders of magnitude in the case of cool ZZ Ceti stars. For hot and intermediate temperature ZZ Ceti stars shows no differences in the hydrogen envelope mass in most cases. Our results show that, in general, the impact of the occurrence or not of thermal pulses in the progenitor stars is not negligible and must be taken into account in asteroseismological studies of ZZ Ceti stars.
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