We present evidence that PG1159 stars could harbour He–rich envelopes substantially thinner than those predicted by current evolutionary models with current estimates of mass loss, which may be attributable to an extensive mass–loss episode during the born–again AGB phase. Specifically, we show that the models with thin He–rich envelopes predict remarkably large magnitudes of the rates of period change of the trapped and untrapped modes observed in the pulsating star PG 1159035. This is a consequence of the much shorter evolutionary timescale of the models with thin He–rich envelopes during the low–gravity PG1159 regime. Our findings are particularly interesting in view of the suggestion of an evolutionary link between the helium–deficient PG1159 star H1504+65 and the recently discovered white dwarfs with almost pure carbon atmospheres.

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