PRECISION ASTEROSEISMOLOGY OF PULSATING PG-1159 STARS

Observations of the pulsation spectrum of the hot white dwarf PG 1159-035 with the Whole Earth Telescope provide rich detail on the normal mode spectrum of nonradial g-modes in this star. We present a grid of evolutionary models appropriate for PG 1159 stars in an effort to model the details of their observed pulsation spectra. We can match the observed pulsation frequencies to remarkable precision using models derived from standard post-asymptotic giant branch (AGB) stellar models. A grid of post-AGB models with systematically varied stellar mass, effective temperature, surface helium layer thickness, and helium abundance is used to explore how the pulsation properties depend on these quantities. The models show that the mean spacing between consecutive overtone g-mode periods is a direct probe of the total stellar mass. Regular departures from uniform period spacing result from resonant mode trapping by the sharp composition gradient at the base of the He-rich surface layer. The depth of the He/C + O composition transition region governs the periods of maximum departure from uniform spacing while the steepness of the composition gradient affects the amount of departure. While most modes show periods that increase with time, some trapped modes show periods that decrease with time because trapped modes are much more sensitive to the contraction of the outer nondegenerate layers than nontrapped modes. Comparison with the observed periods in PG 1159-035 yields a best fit with a mass of 0.59 +/- 0.01 M., an effective temperature of almost-equal-to 136,000 K, and a He-rich layer of approximately 0.004M* with Y(surf) almost-equal-to 0.27. This fit is in very good agreement with prior pulsational and spectroscopic studies of this star. The mode nearest 516 s is almost a trapped mode in the best-fit model. We therefore interpret the observed negative value of the period derivative as resulting from mode trapping. The 539 s mode in PG 1159-035 is a trapped mode in our models and shows a negative dP/dt, so we suggest that observational determination of dP/dt for this mode will show a larger negative value than seen in the 516 s mode. We discuss the applications of our model grid to other pulsating PG 1159 stars, and implications of our results for PG 1159 on models of white dwarf formation and chemical evolution.