Abstract
The present letter is aimed at exploring the influence of overshooting during the central helium burning in pre-white dwarf progenitors on the pulsational properties of PG 1159 stars. To this end we follow the complete evolution an intermediate-mass white dwarf progenitor from the zero age main sequence through the thermally pulsing and born-again phases to the domain of the PG 1159 stars. Our results suggest that the presence of mode-trapping features in the period spacings of these hot pulsating stars could result from structure in the carbon-oxygen core. We find in particular that in order to get enough core structure consistent with observational demands, the occurrence of overshoot episodes during the central helium burning is needed. This conclusion is valid for thick helium envelopes like those predicted by our detailed evolutionary calculations. If the envelope thickness were substantially smaller, then the occurrence of core overshooting would be more difficult to disentangle from the effects related to the envelope transition zones.
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