Low-mass, helium-enriched PG1159 stars: a possible evolutionary origin and the implications for their pulsational stability properties

Aims. We examine a recently–proposed evolutionary scenario that could explain the existence of the low–mass, helium– enriched PG1159 stars. We focus in particular on the study of the pulsational stability properties of the evolutionary models predicted by such scenario. Methods. We assess the overstability of pulsation g−modes of stellar models as evolution proceeds along the PG1159 domain. Stellar models are extracted from the full evolution of a 1-M⊙ model star that experiences its first thermal pulse as a late thermal pulse (LTP) after leaving the AGB. The evolutionary stages corresponding to the born–again episode and the subsequent helium sub-flashes are taken into account in detail. Results. Under reasonable mass–loss rate assumptions, the evolutionary scenario reproduces the high helium abundances observed in some PG1159 stars. We find that, despite the high helium abundance in the driving layers, there exists a narrow region in the log Teff−log g diagram for which the helium–enriched PG1159 sequence exhibits unstable pulsation modes with periods in the range 500 to 1600 s. In particular, the nonpulsating helium–enriched PG1159 star, MCT 0130−1937, is located outside the theoretical instability domain. Our results suggest that MCT 0130−1937 is a real non-pulsating star and that the lack of pulsations should not be attributed to unfavorable geometry. Conclusions. Our study hints at a consistent picture between the evolutionary scenario that could explain the existence of helium–enriched PG1159 stars and the nonvariable nature of MCT 0130−1937. We also present theoretical support for the unusually high helium abundance observed in the nonpulsating PG1159 star HS 1517+7403. We suggest that HS 1517+7403 could be a transition object linking the low–mass helium–rich O(He) stars with the helium–enriched PG1159 stars via the evolutionary connection K1−27 → HS 1517+7403 → MCT 0130−1937.