A Theoretical Analysis of Pulsation Driving in PG 1159 Stars

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Abstract

Our understanding of stars of the PG 1159 spectral type is not yet satisfactory, in spite of the recent success of asteroseismology. Kawaler and coworkers match the observed pulsation frequencies of PG 1159-035 and PG 2131+066 quite well with evolutionary models, but they fail to identify the mechanism exciting their pulsations. Stanghellini, Cox, & Starrfield show that the classical Κ, γ mechanism acting in the C/O partial ionization zone can excite certain g-modes but requires compositions that seem unrealistic. Here we study the impact of the new OPAL opacities on the conditions required to drive the modes observed in the PG 1159 spectral class stars. To this end, we present the nonadiabatic pulsation results of a parametric survey of quasi-evolutionary models of PG 1159 pre-white dwarfs. We examine the effect of varying the chemical composition of the driving region, the stellar radius, and stellar mass on the location of the instability strip and the maximum unstable period. Changes in the oxygen mass fraction of the driving region and the stellar radius have a strong effect on the predicted spectrum of unstable modes. We do not find unstable modes with periods longer than 150 s unless the driving region, located near 10-9 M_*, has at least 50% oxygen. The maximum unstable period increases by factors of 2-3 when we increase the radius of our models by 40%-50%. Decreasing the stellar mass also increases the radius, and the maximum unstable period increases from ∼300-400 s at 0.65 M_sun to ∼800 s at 0.50 M_sun for models with 50:50 C/O cores. Based on these results, we suggest that no pulsating PG 1159 star has a driving region with photospheric abundances; rather they are probably oxygen-rich. In addition, we believe PG 1159-035 and PG 1707+427 probably have larger radii than the seismological models of Kawaler & Bradley predict, because our evolutionary models with pure oxygen cores fail to predict unstable modes with periods up to the ∼1000 s we observe. Models with larger radii also have rates of period change closer to that observed for the 516 5 mode of PG 1159-035. In contrast, our present 50:50 C/O evolutionary models are able to duplicate the observed maximum unstable periods of the two coolest pulsating PG 1159 stars, PG 2131+066 and PG 0122+200. This suggests that the last two stars have radii close to that predicted by our models, and that their driving regions are less oxygen-rich than in the hotter pulsating PG 1159 stars.

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